KINETICS OF CARBON NANOTUBE GROWTH WITH ...zz418br0139/deep...nanotubes (SWNTs), (2) Electric eld...

KINETICS OF CARBON NANOTUBE GROWTH WITH APPLICATIONS IN

HYDROGEN STORAGE

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Ranadeep Bhowmick

June 2010

This dissertation is online at: http://purl.stanford.edu/zz418br0139

© 2010 by Ranadeep Bhowmick. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

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http://purl.stanford.edu/zz418br0139

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Bruce Clemens, Primary Adviser


Brett Cruden, Co-Adviser


Mark Brongersma

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

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Abstract

Carbon nanotubes (CNTs) have unique transport and elastic properties due to their high aspect

ratios. Hence there is considerable interest in using these tubes as field emitter cathodes, composite

materials with enhanced electrical and mechanical properties, electronic components and recently

for hydrogen storage applications taking advantage of the high specific surface areas. In this thesis

three different aspects of carbon nanotubes were studied: (1) Controlled growth of single walled

nanotubes (SWNTs), (2) Electric field directed Chemical Vapor Deposition (CVD) of multi walled

(MWNTs) and (3) Spillover Mechanism of hydrogen storage in Pt-SWNT composites.

The kinetics of carbon nanotube growth was studied in the context of the CVD process. A

generic model for growth of 1-d nano structures via the Vapor-Liquid-Solid (VLS) mechanism is ap-

plied to the nanotube growth. This model considers the energetics of individual mass transfer steps

through each phase and at the phase interfaces. The flux is then written in terms of the change in

chemical potential. Laser interferometry was applied in a cold-wall thermal CVD reactor to measure

the growth of the MWNT films in-situ. Temperature dependent studies in the steady-state regime

were used to obtain activation energies which are consistent with the interfacial transport step.

Consideration of the catalyst activation/de-activation process in the non-steady regimes requires

the rate limiting step to be in the vapor-liquid transition. Application of an electric field during

the MWNT growth was found to enhance both the growth rate and alignment of the MWNTs.

Temperature dependent studies in the presence and absence of the electric field show that there are

actually two activated processes involved, with rate-limiting step being independent of applied field

at high temperature. At higher temperatures, the rate-limiting step is the carbon dissolution into

the catalyst particle, while at lower temperatures it is the carbon dissociation at the catalyst-vapor

interface that limits the growth. Application of an electric field enhances the decomposition of the

C precursor in the vapor phase, thus circumventing this low temperature activation barrier. The

enhanced alignment of the MWNTs with the electric field is explained by tensile stretching over-

coming the defect-induced kinking of the MWNTs. Calculations show that this benefit is obtained

at a minimum field level, with no benefit arising from further increase in field strength.

The catalyst particle size is one of the key parameters that determine the morphology of the 1D

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carbon nanostructures in both processes studied. The thermodynamics of the nano-particle forma-

tion and carbon dissolution are studied and applied to these processes. While the diameter serves

to template the CNT diameter, the Gibbs Thompson effect predicts a size dependent suppression of

melting point which determines the nature of CNT formed. In the CVD process, higher pressures

were found to form larger particle sizes which led to nanofiber growth. At these diameters, the melt-

ing point suppression puts the Fe-C particle in a dual solid-liquid phase. Carbon flux accumulates

in the dual phase during growth until the dual phase becomes energetically unfavorable. At this

point, the particle reverts to a single solid phase regime by discarding excess carbon, resulting in

a discontinuous graphitic structure characteristic of Carbon nanofibers. For smaller particles, the

phase is entirely liquid and leads to steady state carbon flux and CNT growth. Controlling the iron

bearing precursor concentration of the solution fed into the floating catalyst reactor was found to

control particle size, and hence SWNT diameter, within this regime. For similar catalyst particle

size distributions, increasing the temperature increased the range of SWNT diameters and chiralities

obtained. The thermodynamic energy barrier for SWNT formation at the different diameters was

calculated and shown to be consistent with the observed variation.

Finally, the mechanism of hydrogen uptake in transition metal-doped SWNT was studied. Molec-

ular hydrogen, dissociated by metal catalyst nanoparticles, diffuses to the nanotube surface forming

stronger bonds. In-situ 4-probe conductivity tests were performed on mats of Pt doped SWNT dur-

ing hydrogen uptake. On hydrogen charging the resistivity of the Pt doped SWNT mat increased.

This is due to the formation of C-H bonds, which breaks the symmetry of the CNT electronic struc-

ture resulting in formation of localized defects, thereby increasing the resistivity. Initial studies of

the temporal dependence of hydrogen uptake suggest a diffusion-limited process. XPS was employed

to measure the extent of sp3 C-H bonding.

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Acknowledgments

The 3,160th and final ”Calvin and Hobbes” strip ran on Sunday, 31st December, 1995. It depicted

Calvin and Hobbes outside in freshly-fallen snow, reveling in the wonder and excitement of the

winter scene. ”It’s a magical world, Hobbes, ol’ buddy... Let’s go exploring!” wrote Bill Watterson.

I arrived at Stanford almost six years back bearing a similar sentiment. The journey since has

continued to be exciting; not only because of the knowledge I gained but more importantly because

of all the extraordinary people with whom i came to share the ride.

My thesis work depended a lot on valuable contributions from many people. I would first like

to thank my thesis advisors, Prof. Bruce Clemens and Dr. Brett Cruden. I am deeply indebted

for their guidance, knowledge and experience. They gave me enough freedom to take the project

in whichever direction I wanted, while guiding me back to the right path when I strayed from the

problem in hand. Prof. Clemens has a natural affinity for identifying the fundamentals of a problem

and coming up with simple mathematical models to describe it. Talking with him always gave me

new insights and he also encouraged me to think outside the box. Dr. Cruden’s door was always open

(at least to the time he moved to a separate building) and I could approach him with the smallest

of problems. His help and constant support, particularly during the initial years, was invaluable. I

am indebted to him for a lot of the experimental and theoretical work that went into this thesis.

Thanks Bruce and Brett.

I would also like to thank Professors Tom Jaramillo, Paul McIntyre and Marc Brongersma for

their time and for serving on my thesis committee. I know Profs have very busy schedules but I

would like to thank them for taking time off to help me in making my thesis so much more cohesive.

A special mention should be made to Stephanie Sorensen, Fi Verplanke and Christina Konjevich

for helping me on all the administrative issues, particularly in making me turn in the right forms at

the right time, an area I am prone to procrastination.

I received much help for the different characterization techniques used for this work. I would

like to thank Ann Marshall, Bob Jones and Chuck Hitzman for training and help with the TEM ,

SEM, and AES respectively. I would like to thank Prof. Anders Nilsson and his group at SLAC,

particularly Srivats, Daniel and Hiro for their help with the XPS studies. I would like to thank Dr.

Cattien Nguyen for letting me use his instruments and the ”dirty” clean room at NASA, Ames. I

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would like to thank Dr. Alan Cassell and Lance Delzeit for their advice at the beginning of my stint

at NASA Ames. A special thanks to John Roth for his Igor codes to interpret the Interferometry

scan data.

I spent little time at my home office, 210 McCullough. But, will always cherish the stimulating

discussions I had with the Clemen’s gang specially Cara, Steve, and Randy. I would like to thank

Yong, Gloria, and Aditi for their help during the qualifiers. Thanks to Vardaan, Melody, and Chia

for their help with all things lab related. Also mention has to be made of the study group Randy,

Angie, Tania, Joav, Owen,Yen Chen, Kemal, Jason, and Nathan who made it possible to stay afloat

through the 20 odd course requirements for MatSci.

Over and onto NASA; I would like to express my gratitude to all of Brett’s crew mostly from the

past: Sarah, DJ, Alex, Quoc, Dmitry, Terry, and Hiro. A special thanks to Jay, for all his help in

the lab and for being a good sounding board for all my ideas. Even if one tenth of our ideas worked

we would have been ”rich and famous” by now. Thanks to Cattien’s group: Setha, Jeremy, Bryan,

Jovi, Darrell for sharing instruments, and for lunches and coffee breaks in the afternoon. These guys

made life at NASA fun.

I had some memorable times during my stay at Stanford thanks to the ”Bong group” Abhirup,

Pijush, Avishekda, Somdattadi, Samantak, Avisek and many others. They made the transition from

India to USA easy and were my cultural and culinary link to India.

Thanks to my aunt and cousin for always being there. Thanks to my parents and my sister

for their ever-embracing support of my desired studies. Last, but certainly not the least, thanks

to Denise for bearing with me during a busy final year. I wish I knew you earlier. Thank you

everybody.

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Contents

Abstract iv

Acknowledgments vi

1 Introduction 1

1.1 The number ’4’ and the number ’6’ . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Hybridization and relevant C isomers . . . . . . . . . . . . . . . . . . . . . . 2

1.2 sp2 derived C configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 3D Graphite and 2D Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 0D Fullerene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 1D Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Electronic Structure of SWNTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.1 Electronic structure of graphene . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3.2 Energy Dispersion for SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.3 Band gaps, Kataura Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Synthesis of Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4.1 Physical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.2 Chemical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Overview of Hydrogen Storage Technologies . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.1 Hydrogen storage in SWNTs involving a chemical bond . . . . . . . . . . . . 18

1.6 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Experimental Methods 21

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Reactor Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 CVD reactor for MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Vertical flow reactor for SWNT growth . . . . . . . . . . . . . . . . . . . . . 23

2.3 Deposition Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.1 Sputter Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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2.3.2 Quartz Crystal Microbalance (QCM) . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 In-situ diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.1 Laser Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4.2 Residual Gas Analyzer (RGA) . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4.3 4 Probe Resistivity studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 Ex-situ Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.5.1 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5.2 UV-Vis-NIR absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 41

2.5.3 X-ray Photoelectron spectroscopy (XPS) . . . . . . . . . . . . . . . . . . . . . 43

2.5.4 Auger Electron Spectroscopy (AES) . . . . . . . . . . . . . . . . . . . . . . . 44

2.5.5 Electron Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.5.6 Thermogravimetric Analyzer (TGA) . . . . . . . . . . . . . . . . . . . . . . . 46

3 Kinetics of MWNT Growth 47

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2 Catalyst for growth of MWNT films . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1 Importance of the Al buffer layer . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3 MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4 Kinetic Model for MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.1 Mass Transport processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.2 Steady State growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4.3 Thermodynamic Driving force for MWNT growth . . . . . . . . . . . . . . . 57

3.4.4 Rate Limiting Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.5 Catalyst Activation and Poisoning . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5 Results and Validation of the Kinetic Model . . . . . . . . . . . . . . . . . . . . . . . 61

3.5.1 Temperature dependent MWNT growth at P=265 Torr . . . . . . . . . . . . 62

3.5.2 Pressure dependent growth runs at T = 750oC . . . . . . . . . . . . . . . . . 67

3.5.3 Temperature dependent MWNT growth at P=760 Torr . . . . . . . . . . . . 71

3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4 Growth Transition from CNT to CNF 75

4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.3 Experimental details and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.3.1 Growth of MWNT/CNFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.3.2 Characterization of catalyst particle size . . . . . . . . . . . . . . . . . . . . . 80

4.3.3 TEM characterization of growths as a function of particle size . . . . . . . . . 87

4.4 Brief literature review on CNFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

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4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.5.1 Thermodynamic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5 Electric field assisted MWNT growth 98

5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.3 Experimental Technique: Catalyst preparation by Block Co-polymer Micelle Templates100

5.3.1 Characterization of the catalyst particles . . . . . . . . . . . . . . . . . . . . 101

5.3.2 Control of catalyst size and separation using micelle templates . . . . . . . . 103

5.4 Experimental technique: MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.5.1 Characterization of the MWNT forests from sputter deposited Fe films . . . . 106

5.5.2 Characterization of the MWNT grown from catalysts obtained from micelle

templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.6 Discussion: Tube Alignment and applied field . . . . . . . . . . . . . . . . . . . . . . 112

5.6.1 Alignment for isolated MWNT . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.6.2 Alignment of nanotubes in a dense MWNT array . . . . . . . . . . . . . . . . 116

5.7 Discussion: Growth kinetics and electric field . . . . . . . . . . . . . . . . . . . . . . 119

5.7.1 Further investigations of growth: time resolved reflectivity studies . . . . . . 120

5.7.2 RGA Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.7.3 Analysis of the kinetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6 Diameter control of SWNTs 130

6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.3 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.4.1 Dependence on the reaction time . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.4.2 Effects of Ferrocene concentration . . . . . . . . . . . . . . . . . . . . . . . . 139

6.5 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

7 H2 Storage in Pt-SWNT composites 153

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.2 Prior studies on hydrogen storage in Pt-SWNT composites . . . . . . . . . . . . . . 154

7.3 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

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7.4 Conductivity Tests on Pt-SWNT composite samples during hydrogen charging . . . 157

7.4.1 In-situ 4 probe conductivity tests . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.5 XPS characterization of SWNT films . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

8 Conclusions and Future Work 169

8.1 MWNT growth model and in-situ tracking of tube height . . . . . . . . . . . . . . . 169

8.2 Catalyst size and nanotube morphology . . . . . . . . . . . . . . . . . . . . . . . . . 170

8.3 Electric-field assisted MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

8.4 Chirality, Diameter control of SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

8.5 Hydrogen Storage in Pt-doped SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . 171

A Tip Amplitude of MWNT 173

B Algorithm for analyzing interferometer scans 177

B.1 Savitzky-Golay filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

B.2 Fourier Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

C Quantifying alignment of Carbon Nanotubes 189

C.1 Orientation Analysis of nanotubes in MWNT forests . . . . . . . . . . . . . . . . . . 189

C.2 Orientation Analysis of isolated MWNTs . . . . . . . . . . . . . . . . . . . . . . . . 190

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List of Tables

1.1 Candidate materials for Hydrogen Storage . . . . . . . . . . . . . . . . . . . . 17

3.1 Activation energy values of rate limiting steps obtained from the literature 74

5.1 Cycle periods and steady state growth rates as a function of temperature

and bias magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.1 Hydrogen uptake with catalyst particle density. . . . . . . . . . . . . . . . . . 156

xii

List of Figures

1.1 The elements of Group 14 (IV A) of the periodic table. . . . . . . . . . . . . . . . . . 1

1.2 spn hybridization of the C atoms, and the corresponding orientation of the C-C bonds.

Also shown are the graphite and diamond crystalline structures. . . . . . . . . . . . 3

1.3 (a) Unit Cell of Graphite (b) Graphene unit cell (c) Brillouin zone of graphene is

represented by the shaded hexagon. The high symmetry points Γ, K,M are shown in

the schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Honeycomb lattice of a nanotube. Shown in the figure is the chiral vector, Ch,

that determines the orientation of the nanotube lattice. Also shown are the achiral

nanotubes, armchair and zig-zag. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Brillouin Zone of (4,2) chirality SWNT is represented by the line segment WW’, which

is parallel to K‖ . K‖ and K⊥ are reciprocal lattice vectors corresponding to T and

Ch respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Energy dispersion relation for graphene over the Brillouin zone. (b) is a contour

plot for the electronic band structure of graphene. Fig. (c) is a schematic of real and

reciprocal space for a chiral SWNT. Such diagrams help to illustrate the metallic/semi-

conducting nature of the SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.7 1D Energy dispersion relation for (9,0) SWNT. Fig. (a) is part of the unit cell and

Brillouin zone of a zigzag SWNT. X points for the zigzag nanotubes correspond to k =

±π/√

(3)ao. The corresponding 1D DOS for (9,0) SWNT per unit cell of a graphene

are also shown. The dotted line is the DOS corresponding to graphene . . . . . . . 10

1.8 (a) Scematic of DOS for semiconducting and metallic SWNT with the S11, S22,M11

transitions shown . Fig. (b) Kataura plot for graphing the optical transitions between

van Hove singularities as a function of SWNT diameter. . . . . . . . . . . . . . . . 12

1.9 Dissociation of molecular H2 over catalytic metal doped SWNT . . . . . . . . . . . 18

1.10 Atomic Hydrogen pump: Schematic of the sequential steps of an atomic hydrogen

pump: dissociation of molecular hydrogen, spillover, and surface diffusion on a nan-

otube surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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2.1 Schematic of the reactor used to grow MWNT with an applied DC bias . . . . . . . 22

2.2 Schematic of the top and bottom electrode/flange assembly . . . . . . . . . . . . . . 23

2.3 Uniformity of MWNT growth across the bottom electrode . . . . . . . . . . . . . . . 24

2.4 Vertical reactor setup for SWCNT growth. . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 The principle of interferometry. (a) Schematic of light reflection by a single, non-

absorbing layer bounded on either side by semi-infinite non-absorbing layers. The

incident laser beam reflects off the film surface and the substrate-film interface. The

reflected beams interfere as described in the text. (b) Fresnel coefficients for the two

interfaces considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.6 Schematic of the interferometer set-up, used as an in-situ diagnostic to determine the

height of the MWNT films. Fig. (a) plots the fringe thickness corresponding to the

maxima and the minima in the interferogram as a function of the incident angle. It

also plots the magnitude of beam attenuation corresponding to the fringe thickness.

(b) The reflected laser beam is made to focus on a photovoltaic cell by a concave

mirror. The intensity of the beam is tracked by measuring the photovoltaic current

using a pico-ammeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.7 Interferometer scans recorded in-situ during MWNT growth. The first three reflec-

tivity plots correspond to same growth conditions but different growth times. The

fourth reflectivity plot is from a higher pressure growth. The rectangles on the plots

show when the growth stopped. Also shown are SEM images of MWNT forests cor-

responding to three of the growth runs. . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.8 Algorithm for analyzing the interferometer scans. In Fig.(a) an attenuating back-

ground signal is obtained from the plot, by using the Savitzky-Golay smoothing func-

tion. (b) The background is subtracted from the normalized raw signal to obtain the

interfering signal. The amplitude of this signal decays with height of the MWNT.

The solid lines are Beer-Lamber law . MWNT heights and the growth rates obtained

from the interferometer scans are plotted in Fig. (c). . . . . . . . . . . . . . . . . . 32

2.9 (a) Schematic of a RGA . (b) Sample mass spectrum obtained for MWNT growth; T

= 750oC,gas pressure= 400 Torr, H2 : C2H4 flow rates = 150:250 sccm; imposed field

= .45V/µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.10 Schematic of the 4 probe setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.11 Raman spectrum obtained from a HiPCO sample, with 785 nm laser . . . . . . . . . 37

xiv

2.12 Comparison of the line-shape of the G-band for a metallic, semiconducting SWNT

and that of a MWNT. The Raman spectrum of the SWNTs were obtained from the

same sample, but with different laser energies (514 nm for the metallic and 785 for

the semiconducting). This shows the importance of using different wavelengths to

fully characterize a given sample. The MWNT spectrum was obtained with a 514 nm

laser. Also shown in the plots are the D-bands . . . . . . . . . . . . . . . . . . . . . 39

2.13 Assigning (n,m) to SWNTs from RBM signals. (b) Kataura plot, charting the exper-

imental optical transition as a function of SWNT diameter. (a) RBM signal obtained

from HiPCO nanotubes with 785 nm laser excitation. From a comparison of the res-

onant energy and the diameter of the tube (obtained from the RBM frequency) the

chirality of the SWNT can be determined. As an example, two of the RBMs observed

in the sample spectrum are assigned chiralities (9,4) and (10,5). These SWNTs belong

respectively to the chiral family, ”2n+m” , 22 and 25 respectively. . . . . . . . . . . 40

2.14 Absorption spectrum obtained for HiPCO SWNTs. Marked in the plot are absorption

lines corresponding to S11, S22 and M11 transitions . . . . . . . . . . . . . . . . . . 42

2.15 (a) Emission of a photoelectron.(b) A sample XPS spectrum . . . . . . . . . . . . . 43

2.16 (a) Schematic of the Auger process. (b) Auger spectrum of micelle patterned iron

catalyst particles on a Si substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.1 Characterization of the catalyst particles obtained by annealing sputtered Fe films

on a buffer layer of Al. (a) Cartoon of the process. (b) SEM image of the catalyst

particles after the annealing step. (c) Catalyst particle size distribution (d) Line scan

of the substrate using an Auger probe. . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 Comparison of MWNT growths with and without the Al buffer layer . . . . . . . . . 51

3.3 Auger depth profile of as-sputtered films with and without the Al buffer layer. The

nominal thickness of Fe directly deposited on the Si substrate was 13nm, while 5nm

of Fe was deposited on 10 nm Al, sputter deposited on Si . . . . . . . . . . . . . . . 52

3.4 Time resolved reflectivity plots off the catalyst substrate during the pre-MWNT

growth regime. Also plotted are the corresponding chamber temperatures. . . . . . . 53

3.5 (a) Schematic of the four mass transfer processes. Figure (b) is a schematic of the

chemical potential drop that results in the carbon flux from the vapor phase across the

vapor-liquid interface, through the liquid catalyst and finally across the liquid-solid

interface to form the MWNT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

xv

3.6 The rate limiting steps for the MWNT synthesis process. The driving force for the

MWNT growth approximately equals the chemical potential drop across the rate-

limiting step. Fig.(a) is a schematic of the chemical potential drop for interface-limited

growth, with the two limiting cases vapor-liquid interface and liquid-solid interface

shown. Fig.(b) is a schematic of the diffusion limited MWNT growth processes,

limited liquid and vapor phase diffusivities respectively. The dotted line is a schematic

of the chemical potential change for a growth condition where the rate limiting step

is a combination of the diffusive and interface transport processes. . . . . . . . . . . 59

3.7 Keeping count; (a) available attachment sites on the catalyst surface, (b)the number

of catalyst particles initiating MWNT growth in the time interval dt. The mean time

for catalyst activation is τn, while the mean time for catalyst poisoning is τp. No and

Ng are respectively the total number of particles and number of catalyst particles that

have resulted in MWNT growth at time ’t’ . . . . . . . . . . . . . . . . . . . . . . . 60

3.8 SEM images of the MWNT forests obtained after the completion of growth runs in

each of the above cases. These heights, marked by rectangles are plotted in Fig.3.9(c).

A tilted sample holder was used for the SEM imaging, with the angle of the tilt

being 45o. Thus to obtain the actual height of the CNTs corrections were made to

compensate for the tilt angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.9 Normalized interferometer scans for temperature dependent growth of MWNTs at

pressures of 265 Torr, Fig (a). The heights obtained from the interference fringes are

plotted in Fig (b), while Figure (c) plots the growth rates of the MWNTs. The solid

dark lines in (c) mark the linear regime for MWNT growth, corresponding to the

steady state growth conditions, described in the kinetic model. The corresponding

growth rates from Fig (c) are used in the article for analysis/validation of the growth

model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.10 Fig. (a) is an Arrhenius plot of the temperature dependent thermal CVD growth of

MWNT in the temperature range 700-800oC. The activation barrier obtained from the

linear fit is ∼190 kJ/mol. Fig. (b) is a plot of the experimental interferometer heights

and the corresponding theoretical fits of the growth model. The fitting parameters

being the experimental growth rates, and the mean lifetime for catalyst activation

and poisoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.11 Time evolution of pressure and reflectivity during the interrupted growth experiment. 66

xvi

3.12 Pressure dependent growth of MWNT at T=750oC. Fig. (a) plots normalized in-

tensity as obtained from the photovoltaic currents. Increasing pressure increases the

growth rate of the MWNT as is evident from (a) and plotted in (b). Fig. (b) also

shows that higher the pressure shorter is the time to reach steady state values. The

catalyst poisoning mean lifetime is also shorter at higher pressures. (c) SEM images

of the MWNT revealing their final heights at pressures of 151, 405 and 760 Torr

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.13 Fig. (a) plots the experimental growth rates ’o’ and the predicted growth rates (solid

line) for the pressure dependent growths. The growth rates were predicted by ex-

trapolating the average experimental growth rate at P=265 Torr after accounting

for the changes in pressure and gas composition. Increasing pressures decrease the

driving force for MWNT growth, but results in enhanced kinetics accounting for the

increased growth rates. Fig. (b) plots the experimental and theoretical fits for the

MWNT heights. With increase in pressure the height of the MWNT films first increase

and then decrease. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.14 Temperature dependent growth of MWNT at P=760 Torr. Fig. (a) plots normalized

intensity as obtained from the interferometer plots. Fig. (b) plots the experimental

and predicted growth rates. The growth rates were predicted again starting from

the T=750oC / P=265 Torr growth velocity, while accounting for temperature and

pressure changes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.1 Effect of pressure on the morphology of nanotubes. (a-b)Catalyst particles prepared

by annealing sputter deposited thin Fe films. (c) Particles prepared from block co-

polymer micelle templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 1D Carbon nanostructures. (a-b) carbon nanotubes. Schematic downloaded from

www.ibmc.u−strasbg.fr/ict/images/SWNT−MWNT.jpg (c) Examples of CNF mor-

phologies. Schematic from www.pyrografproducts.com/Merchant5/graphics/sfnt −orangecones.gif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.3 SEM images showing the dependence of the thickness of the sputtered Fe layer and

growth pressures on the nature of carbon morphologies obtained . . . . . . . . . . . 78

4.4 Heights of CNTs/CNFs plotted as a function of growth pressure . . . . . . . . . . . 79

4.5 Raman spectrum obtained using 514 nm excitation laser for nanostructures grown

from a 8nm sputtered Fe film as a function of pressure . . . . . . . . . . . . . . . . . 80

4.6 Evolution of particle sizes vs. catalyst thickness and annealing pressures . . . . . . . 81

4.7 Plot of particle sizes obtained from Fig.4.6 for the 2nm and 5nm sputtered Fe film

thickness. The particles were assumed to be circular for simplicity. The X-axis is the

calculated diameter corresponding to the particulate area. . . . . . . . . . . . . . . . 82

xvii

4.8 Auger depth profile for an annealed 2nm Fe/10nm Al/ Si substrate. (a) Depth profile

for an as deposited sample(5nm sputtered Fe). (b) cartoon of the annealing process

and SEM image of the catalyst particles formed after annealing. (c ,d) Profiles ob-

tained by sputtering on the substrate and a particle respectively. The same elemental

color codes and markers are used for all the depth profiles discussed in this chapter . 84

4.9 Auger depth profile for annealed 13nm Fe/10nm Al/ Si substrate as function of anneal-

ing pressure(a) Depth profile obtained from sputtering on the substrate. (b) Depth

profile from a particle. (c) Schematic of particle evolution with annealing pressure . 86

4.10 TEM characterization of 1D carbon structures as a function of particle size. (a)

CNTs formed from small catalyst particles, (b) Defective, kinky fibers formed from

large particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.11 TEM characterization of 1D carbon structures obtained from intermediate particle sizes 88

4.12 (a) In-situ TEM studies of nanofiber growth (1). (b) Atomic scale observation of the

formation of SWNTs (2). (c) Distribution of fiber diameter with temperature from

data reported by various groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.13 Plot of size dependent melting point of Fe. The dotted line marks the growth tem-

perature used for this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.14 (a) Relevant portion of the binary Fe-C phase diagram. (b) Schematic of the evolution

of the stacked-cup morphology of the CNFs . . . . . . . . . . . . . . . . . . . . . . . 93

4.15 Energetics of the CNF formation process. The black dashed line marks the volume

fraction that triggers the contraction of the catalyst leaving behind a graphitic ledge 95

5.1 Patterned carbon nanotube structures for enhanced field emission. Also plotted are

field emission currents from the two different cathode structure. Introducing an extra

edge in the donut structure leads to current enhancement . . . . . . . . . . . . . . . 99

5.2 Schematic of the different steps to synthesize Fe nanoparticles via a block copolymer

micellar route . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3 Size and density distribution of the Fe catalyst particles obtained from (a) block

copolymer templates and (b) from sputter depositing 2.5 nm thin Fe film. The Y-axis

for both the plots are percentage values . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.4 Fe mapping of the particles obtained from the micelle template.(a) SEM image and

(b)corresponding Fe map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.5 EM studies of MWNT yield from micellar nanoparticles. (c,d) Bright and dark field

TEM images of particles subsequent to MWNT growth . . . . . . . . . . . . . . . . 104

5.6 Controlling spatial density by controlling the size of the PS polymer . . . . . . . . . 105

5.7 Controlling particle size by controlling the metal loading ratio . . . . . . . . . . . . . 106

5.8 SEM images of MWNT films grown at 400 Torr as a function of bias . . . . . . . . . 106

5.9 SEM images of MWNT films grown at 760 Torr as a function of bias . . . . . . . . . 107

xviii

5.10 Height of the CNTs as a function of imposed electric field . . . . . . . . . . . . . . . 108

5.11 Characterization of the alignment of the e-field aligned MWNT forests. Fig. (a-c)

describes the methodology for quantifying the alignment of the forests. Fig. (a) is

the original SEM image of the forests ;(b) the edges has been blurred to remove the

edges from showing up when doing the 2D FFT of the images;(c) contour plot of the

FFT of (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.12 (a) High magnification SEM side-view images of MWNT films grown at different

biases. Fig.(b) plots the alignment and the height of the forests vs. the applied

biasing voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.13 SEM images of MWNT grown from micelle templates. MWNTs (a-d) are grown

under the influence of increasing electric fields. The magnitude of the bias is printed

on the respective images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.14 Alignment of MWNT for different biasing conditions. Figs (a-c) describe the align-

ment algorithm. Fig (b) defines the edges from the original SEM image (a). Straight

segments are fitted to the edges so obtained, and the angles made by these segments

are measured with respect to the horizontal plane. Fig (d) is a bar chart that com-

pares the fraction of lengths oriented with in an angular range for different applied

electric fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.15 Schematic of a MWNT oriented at an angle θ to an applied electric field (a). Fig (b)

is a schematic of two different vibrating growth models; case (I) where the CNTs are

not touching and case (II) where the tip of the CNTs might interact. . . . . . . . . . 113

5.16 Plots the lower order vibrating amplitudes of the tube tip as a function of the applied

field and the tube height. The , ∆ correspond to the first and second order ampli-

tudes. The area between the dashed line corresponds to the distribution of half the

inter tube separation, D; amplitudes greater than these values will result in case (ii)

growth mode. (1V/µm = 106V/m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.17 (a) Schematic of a forest of MWNT, simulated as a bundle of springs. Parameters of

the spring, coil radius = D, pitch = λ. Fig (b) plots the alignment of MWNT in the

forests, measured by the angle 〈ϕ〉(see text for details), as a function of the applied

field. The markers are angles obtained from the FFT of SEM images of the MWNT

forests, while the dotted lines are theoretical fits, simulating the forests as springs

with constant Ks. Fig. (c) is a plot of MWNT heights while the dashed lines are

simulated plots of MWNT height if they were only being stretched by electrostatic

forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

xix

5.18 (a) Time resolved reflectivity plots for the temperature dependent growth runs. The

solid lines are interferometer scans for zero bias growth, while the dashed lines are

the corresponding scans for a negative bias of 0.3V/µm. In between the two sets

is the interferogram for a bias of 0.22V/µm and growth temperature of 750oC. The

plots are offset for clarity, with scans obtained from the same bias magnitude grouped

together. Fig. (b) plots the experimental heights obtained from the interferometer

scans and their theoretical fits. Fig. (c) is a plot of the relative change in density of the

MWNT film with change in bias and temperature. The reference density corresponds

to MWNT films grown at T=700oC with zero bias . . . . . . . . . . . . . . . . . . . 121

5.19 Characterization of the reactor gases: (a)RGA results; Bar chart showing the change

in mole fraction of the relevant gaseous compounds between the start and the end

of the MWNT growth runs. The change in species density are normalized by the

residual fractions in the RGA before the admission of the reacting gases into the mass

analyzer at the onset of growth. Fig. (b) plots the change in reactor pressure for the

different growth runs, while keeping the in and outflow of gases constant. . . . . . . 125

5.20 Arrhenius plots of normalized steady state growth rates plotted as a function of the

inverse of temperature. Three sets of data are presented; MWNT growth under no

bias at lower (265 Torr.) and higher pressures(760 Torr.) in the absence of an electric

field and temperature dependent growth runs for an applied electric field of 0.3 V/µm.

The activation energy calculated from the plots are printed on the figure . . . . . . . 126

5.21 Plot of energy of the carbon precursor and CHx (dissociation products of ethylene)

as a function of distance form the catalyst interface. The orange, red dotted lines

corresponds to the energetics for a zero bias growth. The blue line represents the

energetics of the vapor-catalyst mass transfer step for an electric field assisted growth 128

6.1 Tem images of SWCNT bundles grown at (a) 1000oC and (b) 1050oC with 0.25-wt%

ferrocene and 1000 sccm of H2 flow, S/Fe =0.2. . . . . . . . . . . . . . . . . . . . . 132

6.2 Raman of the SWNT samples collected from different parts of the furnace (a)RBM

modes (b)D and G bands (c) Normalized IRBM/IG (d) IG/ID ratio as a function of

the furnace position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.3 Kataura plot for the S22, M11 and S33 transitions. Also plotted in the Fig. is the

position of the 785 and 635 laser lines, and a 50 nm shift to account for the bundling

of SWNTs. The 2n+m family of the SWCNT are shown for the MOD1 and MOD2

S22 transitions (joined by black solid line) and for the M11 transitions (joined by green

dashed line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.4 UV-Vis-NIR of the samples collected from different parts of the furnace (b) S22 tran-

sitions after subtracting the background (c) Comparison of the absorbance % from

the spectra corresponding to the peaks obtained from Fig. (b) . . . . . . . . . . . . 136

xx

6.5 TGA of the samples from different parts of the furnace . . . . . . . . . . . . . . . . . 138

6.6 Raman of the SWCNT samples as a function of ferrocene concentration. (a) RBM

modes with 785 nm laser, 635 nm laser (inset). (b) D and G bands from 785 nm laser.

(c) Normalized IRBM/IG (d) IG/ID ratio and the extent of G split as a function of

temperature. The labels for Fig. (a) and (b) are the same. The label for Fig. (d) is

also true for Fig. (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

6.7 TEM images of the samples. Fig. (a) and (b) are TEM images from 1.0 wt% sample

while (c) is the image from SWCNTs formed with 0.25 wt% ferrocene. . . . . . . . . 141

6.8 SWCNT diameter and (b) Fe catalyst particle size distribution for sample prepared

with 0.25 and 1.0 wt% ferrocene respectively, obtained from the TEM images. . . . . 142

6.9 UV-Vis-NIR of the samples collected as a function of ferrocene concentration. (b)

S22 transitions after subtracting the background (c) Comparison of the absorbance %

from the spectra corresponding to the peaks obtained from Fig (b) . . . . . . . . . . 143

6.10 TGA of the samples prepared with different amount of ferrocene in the precursor

solution. For the fit data x is the wt% of ferrocene in the sample. . . . . . . . . . . 144

6.11 Raman of the SWNT samples synthesized at different temperatures. (a) RBM modes

with 785 nm laser and (b) 635 nm laser. (c) D and G bands from 785 nm laser. (d)

Normalized IRBM/IG as a function of temperature (e) Shows the variation of IG/ID

and the extent of G split with temperature. The color legend for Fig. (a) and (c) is

the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.12 UV-Vis-NIR of the samples collected as a function of SWNT growth temperature.

(inset, a)M11 and S33 transitions.(b) S22 transitions after subtracting the background.

The color legend for all the Figures is the same. . . . . . . . . . . . . . . . . . . . . 147

6.13 (a) SWCNT diameter and (b) Fe catalyst particle size distribution for SWCNTs,

obtained from TEM analysis, grown at 900oC and 1100oC. . . . . . . . . . . . . . . 148

6.14 Theoretical plot to show the temperature dependence for the critical radius for SWC-

NTs. The solid circles show the mean for the diameter distribution from TEM analysis

at 900 and 1000oC. The arrows mark the most abundant range for the SWNT from

absorption spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.15 Abundance maps for SWCNT grown at 900oC (a) and 1100oC (b). For comparison

the abundance map for HIPCO characterized using a similar procedure is shown. A

darker color implies a larger abundance of SWCNT, from absorbance studies. The

red dotted line shows the positions of the SWCNT diameter distributions obtained

from TEM study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

xxi

7.1 TEM morphologies of deposited Pt nanoparticles on SWNTs as a function of the

nominal thickness of the deposited films: (a) 0.2nm, (b) 0.5nm, (c) 1.0nm and (d)

3.0nm. (e) Room temperature isotherms for Sp-Pt SWCNT hybrids with different

nominal thickness of the sputtered catalyst. (f) Pt catalyst number density for Sp

Pt hybrids with 0.2 and 0.5 nm thick films. (Inset) Schematic of SWCNT bundle

decorated with Pt nanoparticles, for the density calculation. . . . . . . . . . . . . . 155

7.2 SEM images of SWNT films used for the conductivity and spectroscopy studies. (a,b)

Dense and sparse distribution of as grown SWNT films. (c) Spin cast HiPCO SWNT

films (d) Monolayer coverage of SWNT films prepared by LB technique (e) AFM

scan of the LB films. (f) Representative Raman spectrum obtained from the HiPCO

SWNT samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.3 Change in current passing through a Pt-doped SWNT film (nominal thickness =

0.5 nm) on repeated exposure to hydrogen. Also plotted is the change in hydrogen

pressure inside the chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.4 Resistance change as function of hydrogen charging for as-deposited and Pt sputtered

SWNT samples. Also shown is the change in resistance of the Pt-SWNT hybrid film

on exposure to air. For comparison, changes to a 0.6 nm thick sputtered Pt film on

quartz on exposure to hydrogen is also plotted. . . . . . . . . . . . . . . . . . . . . 160

7.5 Resistivity changes with hydrogen exposure for CNTs with different Pt loadings . . . 161

7.6 Hydrogen uptake efficiency for SWNT films with varying thickness. The Pt loading

was kept identical for all samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.7 Hydrogen uptake measured at different temperatures. The Pt loading and the film

thicknesses are the same for all the runs. . . . . . . . . . . . . . . . . . . . . . . . . . 164

7.8 XPS overview of the samples before and after hydrogenation. 0.6nm Pt+ LB SWNT

film composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

7.9 (a)XPS before and after hydrogenation of As-grown films. Fitted XPS peaks of as-

grown samples, before (b); and after Hydrogen exposure(c) . . . . . . . . . . . . . . 166

7.10 (a)XPS before and after hydrogenation of 0.6 nm Pt-LB film hybrids. Fitted XPS

peaks of as-grown samples, before (b); and after hydrogen charging(c) . . . . . . . . 167

A.1 Allowed frequencies for the lower order modes as a function of height and strength of

applied electric field during growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

xxii

Chapter 1

Introduction

1.1 The number ’4’ and the number ’6’

The elements with four valence electrons, group 14 of the periodic table, are special. Its the only

group containing solid elements at ambient conditions, which exhibit three distinct property domains

: ranging from non-metallic to metalloid to weakly metallic, Fig.1.1. Si, [Ne]3s23p2, the second most

abundant element in the earth’s crust is the backbone of the semiconductor industry with a band

gap of 1.12 eV at 300K. The next element in the group Ge,[Ar]3d104s24p2, is also a semiconductor

material with a band gap of 0.74 eV at 300K, used mostly in fiber-optic systems and infra-red

optics. Sn, with electronic configuration [Kr]4d105s25p2, is the first metal of the group. It is also

the element which has the largest number of stable isotopes, 10. The next element in the group is

the heavy metal, Pb,[Xe]4f145d106s26p2. This along with Bi, are the heaviest elements known that

have a stable nuclei. Even so, in a group having such unique elements as those mentioned above, C

is the enigma.

Gro

up

14

(IV

A)

[He]2s22p2

[Ne]3s23p2

[Ar]3d104s24p2

[Kr]4d105s25p2

[Xe]4f145d106s26p2

C

Si

Ge

Sn

Pb

14

6

32

50

82

Figure 1.1: The elements of Group 14 (IV A) of the periodic table.

1

CHAPTER 1. INTRODUCTION 2

The reason being the atomic number of C, 6. The atomic number 6 leads to an electronic

configuration of 1s22s22p2. The inner 1s2 orbital contains two strongly bound core electrons. The

four valence electrons in the 2nd orbital are relatively weakly bound and the energy difference between

the upper 2p energy levels and the lower 2s energy levels is small compared to C-C chemical bond

energies. Hence the electronic wavefunction for these four electrons can mix, changing the occupation

of the 2s and 2p atomic orbitals, to enhance the binding strength of C with the neighboring atoms.

This ability of C to exhibit spn hybridization sets it apart from the rest of the group 14 elements. C

exhibits all three possible hybridizations, sp, sp2 and sp3; while the other group 14 elements, e.g. Si,

Ge, exhibit primarily sp3 hybridization. (It is interesting to note that as a consequence , all elements

of this group assume a diamond cubic crystalline shape in their 3d state, stable or not. Diamond is

an insulator but depending on how tightly packed to the inner core the outer level electrons are, the

diamond cubic forms of the other elements in the group first transition to form semiconductors, Si

and Ge, and further down the group they are metallic.) The lack of sp and sp2 bond formation in

Si and Ge is possibly due to the prolate structure of the outermost p-orbitals. For C, the absence of

nearby oriented inner orbitals facilitates hybridization, and hence the importance of the number ’6’.

1.1.1 Hybridization and relevant C isomers

The spn hybridization of the C atoms is responsible for the dimensionality of the C - based solids. C

is the only element that has isomers across all dimensions, fullerenes (0-D) to diamond(3-D)(3). In

the following subsections the C solid phase structures vis-a-vis their spn hybridization are described.

In spn hybridization, (n+1) σ bonds are formed per carbon atom. These σ bonds form the skeleton

of the local structure for the n-dimensional morphology. In Fig.1.2 the sigma bonds are shown by

the lighter colored lobes, while the darker lobes represent the relatively weaker π bonds.

sp hybrids

In this, the 2s orbital mixes with only one of the three p-orbitals resulting in the formation of two

sp hybrid orbitals, and two unchanged p orbitals. The subsequent bond formation involves sp-sp

overlap between adjacent C atoms forming σ bonds and two additional π bonds formed by p-p

overlap. The two σ bonds can make only a one-dimensional chain structure, [−C ≡ C−]n. The 3D

structure formed by gathering these chains, carbyne, is formed at high temperatures and pressures.

sp3 hybrids

The 2s orbital mix with three 2p orbitals to form four sp3 orbitals. The four resulting σ bonds

define a regular tetrahedron that results in the formation of a 3-D diamond structure (Fig.1.2). As a

result diamond is an isotropic, cubic, high band-gap (5.3 eV) insulator. The strong σ bonds make it


s orbital

p orbital

2 sp orbital

3 sp2 orbital

4 sp3 orbital

Linear

Planar

Tetrahedral

graphite

diamond

Figure 1.2: spn hybridization of the C atoms, and the corresponding orientation of the C-C bonds.Also shown are the graphite and diamond crystalline structures.

one of the most thermally conductive and highest melting point solids known. Along with graphite,

diamond is the main allotropic form of C.

sp2 hybrids

In sp2 hybridization the 2s orbital mixes with two of the three available 2p orbitals, forming three

sp2 orbitals with one p-orbital remaining unchanged. All σ bonds formed with adjacent C atoms are

in the same plane, while the π orbital for each C atom exists perpendicular to this plane, resulting in

the formation of a planar 2-D structure. Graphite is formed by ABAB stacking of these 2D planes.

Under ambient conditions, and in bulk form the graphite phase with strong in-plane trigonal bonding

is the stable phase. It is interesting to note that sp2 hybridization which forms a planar structure

also forms a planar local structure in the closed polyhedra ( 0-D ) of the fullerene family and in the

cylindrical morphology (1-D) of carbon nanotubes (CNTs).

Amorphous C, the other ubiquitous form of C, refers to a highly disorganized network of C atoms

that have no long range ordering. The C atoms have predominantly sp2 bonding, with about ∼ 10%

sp3 bonds and almost no sp bonding(3). Hence they exhibit some short range order, though the

nature of this order varies significantly from one growth condition to another. For characterizing

the short range order of amorphous C two parameters are the most important. First is the ratio


of sp3/sp2 bonding, and second the hydrogen content (H impurities are present to passivate the

dangling bonds present in the disordered structure).

1.2 sp2 derived C configurations

1.2.1 3D Graphite and 2D Graphene

As mentioned before, graphite is a 3D layered hexagonal lattice of C atoms (Fig.1.3). A single layer

of graphite forms the 2D material graphene. The in-plane nearest neighbor distance aC−C of 1.421A

in graphite results in an in-plane lattice constant, ao = |~a1| = |~a2| = 2.46A. The z-axis lattice

constant of 6.70A results in an interplanar distance of 3.35A. Hence the interaction between two

adjacent layers is small compared to the intra-layer interactions. Thus the electronic structure of

2D graphene acts as a good first approximation for 3D graphite.

In Fig.1.3, the unit cell and the corresponding Brillouin zone of graphene is shown; ~a1,~a2 are

unit vectors in real space, and ~b1,~b2 are the reciprocal lattice vectors.

~a1 = (

√3

2ao,

ao2

), ~a2 = (

√3

2ao,−

ao2

)

~b1 = (2π√3ao

,2π

ao), ~b1 = (

2π√3ao

,−2π

ao)

The reciprocal space lattice constant has the magnitude |~b1| = |~b1| = 4π/√

3ao. The first Brillouin

zone is obtained by constructing the Wigner-Seitz unit cell of the graphene reciprocal lattice. It is

shown in the figure by a shaded hexagon. Three high symmetry points of the Brillouin zone; center,

corner and center of the edge are defined by Γ, K and M respectively. The significance of these

points will be discussed in a later section dealing with the electronic structure of graphene.

1.2.2 0D Fullerene

The 60 C atoms in C60 are located at the vertices of a truncated icosahedron(3). This molecule

is often thought of as a ”rolled up” graphene sheet. This is because, (1) the aC−C distance in

C60 is almost identical to that of graphene (2) each C atom is trigonally bonded to three other C

atoms in a sp2 derived bonding configuration and (3) most of the faces on the truncated icosahedron

are hexagons ( 20 hexagons and 12 pentagons). It is energetically unfavorable for two pentagons

to be adjacent to each other, as this will lead to higher local curvature and larger strain. Hence

in general the pentagons are surrounded by hexagons. This tendency of the pentagons not to be

adjacent to one another is called the ”isolated pentagon rule”. The smallest molecule to satisfy

the rule is C60, where each pentagon is surrounded by 5 hexagons, and each hexagon by 3 other

hexagons and 3 pentagons. Because of the closed shell characteristic of C60 and other fullerenes,

the nominal sp2 bonding between C atoms occur on a curved surface, in contrast to the trigonal


M

graphite graphene

Unit Cell

Brillouin Zone

(a) (b)

(c)

a1

a2

b1

b2

x

y

kx

kyK

Figure 1.3: (a) Unit Cell of Graphite (b) Graphene unit cell (c) Brillouin zone of graphene isrepresented by the shaded hexagon. The high symmetry points Γ, K,M are shown in the schematic.

bonds of graphene that are truly planar. This curvature of the bonds leads to some admixture of

sp3 bonding, characteristic of tetrahedrally bonded diamond. The extent of the sp3 bonding and

hence the strain in the fullerenes decrease with increasing size of the molecule.

1.2.3 1D Carbon Nanotubes

Carbon nanotubes are essentially members of the extended fullerene family. Structurally they can

be described as concentric tubes formed by rolling graphene sheets into cylinders. Depending on the

number of conformal tubes, the carbon nanotubes are classified as single-walled carbon nanotube

(SWNT), double-walled carbon nanotube (DWNT),CNTs having more than two concentric cylinders

are generally termed multi-walled carbon nanotube (MWNT). Neglecting the hemispherical ends,

the nanotubes are generally considered to be 1D owing to the large aspect ratio of the cylinders

(∼ 104− 106). It has to be mentioned here that other forms of 1D carbon isomers exist, but instead

of having a tubular structure they typically have a stacked cone or bamboo like structure (i.e. the

interior of the 1D morphology is not hollow). These are known as carbon nanofibers; Chapter 4 will

deal with these nanostructures in more details. Also, formation mechanism of carbon nanofibers in

preference to nanotubes will be discussed.


a1

a2

Tube axis

armchair (n,n)

zigzag (n,0)

chiral (n,m)

Ch= na1+ ma2

0

T

Figure 1.4: Honeycomb lattice of a nanotube. Shown in the figure is the chiral vector, Ch, thatdetermines the orientation of the nanotube lattice. Also shown are the achiral nanotubes, armchairand zig-zag.

The orientation of the hexagonal ring in the lattice relative to the nanotube axis has impor-

tant bearing on the carbon nanotube structure and its transport properties, Fig.1.4. The primary

morphological classification of SWNT is achiral (symmorphic, mirror image identical to the original

morphology) and chiral (non-symmorphic). The two possible cases for achiral tubes are armchair

and zigzag, as shown in the figure. These SWNTs are named after the shape of the edge of the

cross-sectional ring of the carbon nanotubes. The chiral nanotubes have a spiral symmetry whose

mirror image cannot be superimposed on the original. In MWNT the interaction between the tubes

are relatively weak. Hence the lattice structure of the different layers are generally incommensurate

with each other, resulting in the turbostratic structure.

Unit Cell of SWNT

The unit cell for SWNT is given by the rectangle generated by the chiral vector, Ch and the

translational vector, T , as shown by the shaded rectangle on the unrolled honeycomb lattice of the

carbon nanotube in Fig.1.4. The chiral vector which is perpendicular to the nanotube axis defines

the morphology and the properties of the SWNT. It can be expressed by real space vectors of the

hexagonal lattice as:

Ch = n~a1 +m~a2; (n,m are integers, 0 ≤ |m| ≤ n)


The diameter of the SWNT is given by the relation, dt = L/π, where ’L’ is the circumferential length

of the tube.

L = |Ch| =√

Ch ·Ch = ao√n2 +m2 + nm (1.1)

It has to be noted here, that in a reciprocal manner the diameter of the SWNT will control the chiral

vector and hence the property of the CNTs. Advantage of this is taken while synthesizing SWNT

with controlled parameters in chapter 6. The chiral angle, θ,(0 ≤ θ ≤ 30o) is defined between the

vectors Ch and ~a1

θ = cos−1 =Ch · a1

|Ch||a1|=

2n + m

2√

n2 + m2 + nm

In particular the armchair and zigzag SWNT have θ equal to 30o and 00 respectively.

The translation vector T is parallel to the nanotube axis and is normal to Ch in the unrolled

honeycomb lattice, Fig.1.4. It can be expressed in terms of the basis vectors ~a1 and ~a2 as T =

t1 ~a1 + t2 ~a2. Thus the nanotube unit cell is formed by a cylinder of diameter, |Ch|/π, and height

T . Next knowing the area of the nanotube unit cell, the number of hexagons N per unit cell can be

obtained.

N =|Ch × T || ~a1 × ~a2|

(1.2)

Each hexagon, has 2 C atoms. Therefore there are 2N C atoms (or 2pz orbitals) in each cell of the

carbon nanotube.

Brillouin Zone of SWNT

Formulations for the reciprocal lattice vectors K‖ along the nanotube axis and K⊥ in the circum-

ferential direction are obtained from the relation

Ch.K⊥ = 2π, Ch.K‖ = 0

T .K⊥ = 0, T .K‖ = 2π

Solving which we get the relations;

K‖ =1

N(−t2~b1 + t1~b2), K⊥ =

1

N(m~b1 − n~b2)

In the direction of the tube axis, K‖ corresponds to the translational period |T |, its length being

|K‖| = 2/|T |. As the nanotubes are considered to be infinitely long, the wave vector along K‖

is continuous. The first Brillouin zone in this direction is the interval (−1/|T |, 1/|T |], as shown

by WW’ in Fig.1.5. Since SWNTs are 1D materials, only K‖ is a reciprocal lattice vector. K⊥

gives discrete k values in the direction of the chiral vector. The wave vector K⊥ is quantized and

has dimensions of K⊥ = 2/dt. It is easily noticed that N K⊥ = (−t2~b1 + t1~b2) corresponds to a

reciprocal lattice vector of 2D graphene sheet, and hence any two vectors differing by NK⊥ should


Ch = 4a1+2a2

a1

a2

M

KW

W’K K

ll l l

b2

b1

Brillouin Zone of (4,2) SWNT

Figure 1.5: Brillouin Zone of (4,2) chirality SWNT is represented by the line segment WW’, which isparallel to K‖ . K‖ and K⊥ are reciprocal lattice vectors corresponding to T and Ch respectively.

be equivalent. It can also be shown that t1 and t2 do not have a common divisor and hence the

N wave vectors µK⊥ ( µ = 1, . . . , N − 1) are discrete. The first Brillouin zone of SWNT therefore

consists of N lines parallel to the nanotube axis separated by |K⊥| = 2/dt and k ∈ (−π/|T |, π/|T |]as shown in Fig.1.5.

1.3 Electronic Structure of SWNTs

The electronic structure of SWNTs are derivative of that of graphene. As mentioned in the last

sub-section the Brillouin zone of SWNT consists of wave vectors parallel to the nanotube axis.

The energy bands will then consist of 1D energy dispersion relationships which are in essence cross

sections of the dispersion for graphene.

1.3.1 Electronic structure of graphene

The three σ bonds of graphene are planar, while the unchanged 2p orbital that is perpendicular

to the plane forms the π covalent bond. These π electrons are the valence electrons and hence are

most relevant for calculating the electronic structure, transport and other solid state properties for

graphene based materials. In general a tight binding calculation for the π electrons is sufficient to

describe the electronic band structure.


Fig.1.6(a) is a schematic of the energy dispersion for graphene through out its Brillouin zone.

The upper half of the curves describe the anti-bonding π∗ energy bands, while the lower half is

the bonding π energy bands. The upper antibonding and the lower bonding bands are degenerate

at K, the high symmetry corner point for the graphene Brillouin zone. The Fermi energy passes

through the K points. Since there are two π electrons per unit cell of graphene, they occupy the

lower bonding band. Hence graphene is a semi metal. The existence of a zero band gap at the K

points gives rise to the quantum effects in the electronic structure of CNTs. As shown in Fig.1.6(a)

the energy difference between the bonding and the antibonding bands is maximum at Γ, the center

of the Brillouin zone.

MM

(a) (b)

Ch a1

a2

M

KW

W’

K

Kll

l l

b1

VO

real space

reciprocal space

b2

(c)

Figure 1.6: Energy dispersion relation for graphene over the Brillouin zone. (b) is a contour plot forthe electronic band structure of graphene. Fig. (c) is a schematic of real and reciprocal space for achiral SWNT. Such diagrams help to illustrate the metallic/semi-conducting nature of the SWNT


1.3.2 Energy Dispersion for SWNT

For a SWNT, which has 2N C atoms per unit cell, the 1D dispersion relations are given by the

expression(4):

Eq(k) = Eq(kK‖

|K‖|+ qK⊥), (q = 0, 1, . . . , N − 1; and− π

|T |< k <

π

|T |) (1.3)

The N pairs of energy dispersion curves given by eqn. (1.3) correspond to cross sections of the

energy dispersion curves of graphene where cuts were made by the lines[k

K‖|K‖|

+ qK⊥

]. Fig.1.7

shows the 1D dispersion energy plots for a high symmetry zigzag SWNT. If for a (n,m) SWNT one

of the cutting lines passes through the corner point, K, of the graphene Brillouin zone, where the

bonding π and antibonding π∗ bands are degenerate, then the 1D energy bands have a zero energy

gap and the (n,m) SWNT is metallic at room temperature. But if the cutting line does not pass

through a K point, the corresponding SWNT will be semiconducting. The (n,m) SWNT is metallic

Figure 1.7: 1D Energy dispersion relation for (9,0) SWNT. Fig. (a) is part of the unit cell andBrillouin zone of a zigzag SWNT. X points for the zigzag nanotubes correspond to k = ±π/

√(3)ao.

The corresponding 1D DOS for (9,0) SWNT per unit cell of a graphene are also shown. The dottedline is the DOS corresponding to graphene

if | ~V K| is an integral multiple of |K⊥|, Fig. 1.6(c).

V K = ΓKcosθ =|b1|2

cos(π

6)cosθ


On substituting the expressions for the cosine of the chiral angle, cosθ, and the diameter dt of the

(n,m) SWNT we get the relation:

V K =2n+m

3

2

dt∵ |K⊥| = 2/dt

V K =2n+m

3|K⊥| (1.4)

Hence the condition for metallic nanotubes is that (2n+m) or equivalently (n-m) is a multiple of 3.

By this token for a completely random distribution of SWNT one third of the CNTs are metallic,

the rest semi-conducting.

Density of States for SWNT

Fig.1.7 plots the 1D density of states for a zigzag SWNT. The DOS of nanotubes have a high

energy dependance, but the DOS near the Fermi energy level is of most importance. The DOS for a

metallic SWNT is non zero at E=0, while it is zero for semiconducting SWNTs. The most prominent

feature for the DOS is the presence of singularities (van Hove peaks) corresponding to extrema in

the Eq(k) relations, characteristic of 1D nanomaterials. Van Hove singularities result in remarkable

optical properties of SWNTs. Optical transitions occur between (v1 − c1, v2 − c2) etc states of

the semiconducting and metallic SWNTs as shown in Fig. 1.8, and are labeled as S11, S22,M11 . . .

transitions. The energies between the singularities depend on the nanotube structure, and hence are

used for fingerprinting SWNTs in spectroscopic studies.

1.3.3 Band gaps, Kataura Plots

The simple tight binding model predicts that the energy band gap for the semiconducting nanotubes

varies inversely with the diameter of the tube, and are independent of the chiral angle of the SWNTs.

Eg,11 =2γoaC−C

dtEg,22 =

4γoaC−Cdt

(1.5)

where γo is the interaction energy between the neighboring C atoms. Deviations from the linear rela-

tion predicted by eqn. 1.5 are expected because of the trigonal equi-energy contours in the graphene

Brillouin zone (Fig.1.6) rather than circular contours around K assumed for simpler calculations.

It is also observed that chirality also plays a significant role in determining the transition energies

since it determines the angle of the cutting lines with respect to the trigonally distorted contours

(5; 6).These effects are more pronounced for smaller diameter SWNTs. Such effects shift transition

frequencies, corresponding to the energy gap, from linear relations in directions related to the values

of (n-m) mod 3, and the direction of shift reverses between the first and second van Hove branches.

Calculations taking into consideration all these have been performed but are complex in nature.


Hence to provide a ready reference for these optical transitions an experimental graph named the

”Kataura plot” is generally used that relates the band gap energies (generally in units of frequency,

as it is used mostly for spectrographic analysis) with that of diameter. Fig.1.8 is a Kataura plot

derived from the experimental work and theoretical chirality assignment done by the Strano at al.

(7). Kataura plots will be revisited while discussing Raman spectroscopy for SWNT in the next

chapter.

v1

v1v2

c1

c1c2

Figure 1.8: (a) Scematic of DOS for semiconducting and metallic SWNT with the S11, S22,M11

transitions shown . Fig. (b) Kataura plot for graphing the optical transitions between van Hovesingularities as a function of SWNT diameter.

A brief note about the electronic property of MWNT. In general the MWNT have a much larger

diameter(∼ 5 − 50nm) compared to the SWNT, where the diameters are typically less than 2nm.

As predicted by eqn. 1.5, in general the bandgap varies inversely with the diameter. Hence for all

practical purposes MWNT are metallic in nature.

1.4 Synthesis of Carbon Nanotubes

In this section the different methods for carbon nanotube growth are briefly explained. Extensive

research effort over the last two decades have led to discovery of a wide variety of techniques,

catalyst combinations, growth conditions etc for synthesis of CNTs. The synthesis techniques can

be divided into two broad categories: physical methods, which rely on the high energies to release

the C atoms from their precursors, such as arc discharge, laser vaporization and flame synthesis.


Chemical methods, which catalytically decompose the carbon precursors to release the C atoms, is

the other category and has become the method of choice for most researchers.

1.4.1 Physical methods

Arc Discharge

In arc discharge method, C atoms are evaporated by plasma of an inert gas (He, Ar) at low pressures

ignited by passing high currents between two carbon rods placed end to end. Arc discharge has

been developed into an excellent technique for producing both high quality MWNTs and SWNTs.

MWNTs can be obtained by controlling the growth conditions such as the pressure of the inert gas in

the discharge chamber and the arcing current (8). For the growth of SWNT a metal catalyst is needed

in the arc discharge system. Bethune et al. (9) used a carbon anode containing a small percentage

of Co catalyst to generate decent amounts of SWNTs in the soot material. The disadvantage of this

technique is that it produces a mixture of components and hence requires purification of CNTs from

soot and other impurities.

Laser ablation

Synthesis of CNTs by laser vaporization was first demonstrated by Guo et al. (10). In this method a

pulsed or a continuous laser is used to vaporize a graphite target in a reactor filled with an inert gas

and maintained at high temperatures. The vapor so formed forms a very hot plume that expands

and hence cools rapidly. As the vaporized species cool, small C atoms and other molecules condense

to form clusters. From these initial clusters tubular molecules grow into CNTs. The condensates

obtained by laser ablation are contaminated with CNTs and other forms of carbon nanoparticles.

MWNTs are generally formed if pure graphite electrodes are used. Synthesis of SWNT have been

reported on introduction of small amounts of Co,Ni, Fe etc to the graphite electrodes.

Flame Synthesis

This method is based on the synthesis of SWNTs in a controlled flame environment, that produces

the temperature to form C atoms from inexpensive hydrocarbon precursors (11). Small aerosol

metal catalyst islands are also formed in the process, and the CNTs grow from these islands to form

predominantly SWNTs by a mechanism similar to the arc discharge and laser ablation methods.

1.4.2 Chemical methods

Chemical methods can be further classified into the substrate based chemical vapor deposition (CVD)

method and the floating catalyst, aerosol method.


Chemical Vapor Deposition

CVD of CNTs is essentially a 2 step process, catalyst preparation generally by heating carbide

forming transition metal thin films. This is followed by heating the reactor to the high growth

temperature at which point a carbon precursor generally a hydrocarbon is flowed into the reaction

chamber. The hydrocarbon dissociates by pyrolysis and in most cases the catalyst particles aid

the dissociative process. Subsequently it is generally accepted that the C atoms so formed undergo

dissolution and saturation in the catalyst nanoparticle. The precipitation of the C atoms from

the saturated particle leads to the formation of carbon nanotubes. The process described above is

called the thermal CVD process (12). Over time different methods for CNT synthesis with CVD

have been developed. One of the most common variations is the plasma enhanced CVD (PECVD)

method where a glow discharge is generated in the reactor chamber(13; 14). The plasma aids in

dissociating the precursor molecules. By carefully selecting the growth conditions the synthesized

product formed can range from SWNT, for a far field plasma , to MWNT and carbon nanofibers. In

another variation of the CVD process, a continuous wave CO2 laser was used to pyrolyse sensitized

gas mixtures of metalo-orgacene and a hydrocarbons(15).

In Chapter 3, the kinetics of carbon nanotube growth is studied in the context of the CVD process.

A generic model for growth of 1-d nanostructures via the Vapor-Liquid-Solid (VLS) mechanism is

applied to the nanotube growth. Laser interferometry is applied in a cold-wall thermal CVD reactor

to measure the growth of the MWNT films in-situ. The combination of experimental studies and

theoretical modeling is done to better understand the rate limiting step of the MWNT growth

process and to provide a road map for similar studies for different growth conditions.

Controlled Nanotube growth

The popularity of the CVD method over the physical methods is attributed to aligned and

ordered nanotube structures that can be grown on surfaces with control impossible to achieve by

arc discharge or laser ablation techniques.

One field of CNT synthesis that has gained much prominence in recent years is directed growth of

CNTs. This is due to the increased research for using of CNTs as transistors, interconnects, sensors,

field emission cathodes etc. For example long arrays of well aligned CNTs was achieved by orienting

the substrates with respect to the gas flow directions (16). Various groups have also demonstrated

directional growth of high- density single-walled carbon nanotubes on a- and r-plane sapphire sub-

strates over large areas (17; 18). It is believed that strong nanotube/substrate interaction plays an

important role in attaining the observed nanotube orientation.

External electric field has been applied during growth to orient CNTs. Advantage is take of the

anisotropy of the CNTs, the polarizability in the axial direction of the tubes being greater than in

the radial direction (19).The most popular technique to date being plasma enhanced chemical vapor

deposition (PECVD) (20; 21; 22; 13). In PECVD, a high bias voltage is applied for generating a


glow discharge. In this case the potential does not vary linearly between the electrodes, but rather

is constant except in the sheath region near the cathode where it decreases approximately linearly

(23). The height of the CNTs is smaller than the characteristic Debye length of the plasma, and

hence the CNTs are oriented by the high plasma sheath electric fields. However, complimentary

studies show that along with the electric fields generated in the sheath region other mechanisms like

crowding effect of the high density films, non-uniform stresses across the catalyst particle surface etc

(22) helped in aligning the CNTs. High rates of flame synthesis of aligned MWNTs using a DC field

in flames have also been reported (24).Hongjie Dais group successfully demonstrated electric field

directed growth of single-walled carbon nanotube (SWNT) by thermal chemical vapor deposition

process (CVD) (25; 26). They were able to horizontally align SWNTs suspended over trenches

and also directly on substrates by suitable choice of electrode materials, directed electric fields of

optimal strengths, and suitable surface treatments. Further studies have been made to characterize

and model horizontally directed SWNT growth with a local field (27; 28). Interactions primarily

with the substrate were considered and two growth modes, surface and free growing, were proposed.

Avigal et al. were the first to study aligned growth of MWNT under a DC electric field applied

perpendicular to the substrate (29). They observed that aligned growth of MWNT was possible

only under a positive sample bias. A negative bias resulted in random growth while in the absence

of an applied electric field there was no growth.

In Chapter 5, we report the results of applying an electric field for producing vertically aligned

MWNT films and individual MWNTs. The electric field applied here is perpendicular to the sub-

strate. We address there the two most important issues believed to control the alignment of the

CNTs, spatial density of the MWNT and the magnitude of the applied bias. Also studied was the

effect of the applied field on the growth kinetics of the MWNT films.

Floating Catalyst / Vapor Phase Growth method

In the floating catalyst method, catalyst particles are suspended in a flow of a carbon containing gas,

both being continuously fed into the reactor. This presents a viable way for continuous production

of SWCNTs and avoids catalyst-poisoning issues. Sen et al. (30) were the first to use pyrolysis of

metallocenes such as ferrocene, cobaltocene and nickelocene to produce the transition metal catalyst

particles. An Ar-H2 atmosphere was used for the pyrolysis of metallocene/benzene mixtures to give

high yields of carbon nanotubes and metal-filled onion-like structures. Cheng et al. (31) improved

upon the floating catalyst method, used previously for the production of carbon nanofibers, to pro-

duce SWNTs, with a diameter distribution of 1.69 ± 0.34 nm. Ferrocene was used as the catalyst and

carbon was provided by the decomposition of benzene at temperatures of 1100− 1200oC. Hydrogen

was used as the carrier gas; while a sulfur-containing additive, thiophene, was used to enhance the

growth of the SWNTS. Ci et al. (32) synthesized SWNTs without an amorphous carbon coating by

thermally decomposing acetylene in the temperature range of 750 − 1200oC using Fe(CO)5 as the


Fe catalyst precursor. In all these above cases, Fe-precursors were pyrolized in a separate furnace

before being introduced to the reactor where the SWNTs were synthesized. Nasibulin et al. (33)

developed a true aerosol method for the growth of SWNT, where the two steps of formation of the

SWNT and their sampling were done directly from the gaseous phase rather than collecting SWNTs

from the cooler parts of the furnace as in the previous studies. Catalyst particles were formed by

a hot wire generator and introduced directly into the reactor. Disproportionation of CO provided

the carbon atoms while the reaction took place in a H2/N2 ambient. The SWNT produced were

collected using an electrostatic precipitator. Smalley and co-workers developed the so-called HiPCO

procedure, which has become the benchmark for bulk SWNT production. In this method (34), the

Fe catalyst for the SWNT growth was obtained by thermal decomposition of Fe(CO)5 in a heated

flow of carbon monoxide at high temperatures and pressures.

Alcohol precursors have more recently been introduced instead of traditional hydrocarbon sources.

These resulted in a better yield of the SWNT presumably because of the role of the decomposed

OH radicals. The reaction of OH radical with solid carbon reduces the formation of soot and hence

restricts the generation of amorphous carbon in the SWNT product (35). Zhu et al. (36), were

the first to report the direct synthesis of long strands of ordered single-walled carbon nanotubes

with a floating catalyst method in a vertical furnace. n-Hexane with ferrocene and thiophene was

introduced into the reactor after heating the reactor to the pyrolysis temperature. SWNTs formed

in abundance during this continuous process, and SWNT production of ∼ 0.5g/h were reported. Li

et al. (37) developed a technique to spin continuous fibers and ribbons of carbon nanotubes, spun

directly from the synthesis zone of a vertical flow reactor. They used ethanol and ferrocene as the

carbon and catalyst precursor, respectively, H2 as the carrier gas and thiophene as a yield promoter.

In Chapter 6 synthesis of SWNTs using a variation of Li’s method will be described. A detailed

investigation of the reaction parameter space of the vertical furnace for SWCNT production was

performed as a function of temperature, carrier gas flow rate and the precursor solution flow rate.

1.5 Overview of Hydrogen Storage Technologies

Concern over dwindling oil reserves and the environmental impact of greenhouse gas emissions have

motivated intense research and development of alternative fuels in the past few decades. Among

possible candidates, hydrogen is a promising fuel resource since it is the lightest and most abundant

element in the universe. It is nontoxic and highly volatile. The delivered energy per mass of hydrogen

is very high compared to other conventional fuel materials. When hydrogen is combusted with air,

carbon dioxide is not produced by the reaction.

But, there are many challenges to be overcome to establish a viable hydrogen economy. These

include production cost, safety, efficient storage, public acceptance, and competition with other tech-

nologies. Among these challenges, efficient hydrogen storage seems to be the key technical problem.


Table 1.1: Candidate materials for Hydrogen Storage

Examples Nature Desorption Kinetics Pros Consof H bond Temp

Metal MgH2 Chemical Too Slow High Irrev.Hydrides Mg2NiH4 high capacityChemical NaAlH4 Chemical High Medium Very high Regene-.Hydrides Mg(BH4)2 capacity rationCarbon CNT Physical Too Fast Rev Lowbased AC∗ Low Capacity

Carbon CNT Chemical Low Slow Less Lowbased AC∗ Energy Capacity

(doped)Metal MOF ! Physical Too Fast Large Low

organic low surface capacityhybrids area

An ideal technique for hydrogen storage should meet three important criteria; high storage den-

sity on both gravimetric and volumetric base, safety, and ease of use (fast uptake/release kinetics

and reasonable thermodynamics). This is most easily realized in solid state storage methods. Cur-

rently promising candidate storage materials are considered to be metal hydrides, chemical hydrides,

carbon-based materials, and organic/inorganic hybrid materials. General features of these materials

and their hydrogen storage properties are summarized in Table (1.1)(AC∗:activated Carbon; MOF !

: Metal-Organic framework).

Metal hydrides (MHx) typically accommodate hydrogen atoms in octahedral or tetrahedral in-

terstitial sites in the host metal lattice structure. Due to the incorporation of hydrogen in lattice,

the metal structure experiences a volume expansion during the hydrogen absorption process. The

hydride formed is stable and requires an appreciable amount of energy to release the hydrogen from

these materials (38). Chemical hydrides are chemical compounds formed between Li, Mg, B, Al, N

and hydrogen; usually as metal-borohydrides or amides. Theoretically, very high gravimetric density

can be achieved since light elements are used. But, the irreversibility of hydrogen regeneration from

these materials needs to be improved for their viable use.Hydrogen storage techniques in carbon

based materials and metal-organic hybrids basically depend on the physical adsorption of hydrogen

at cryogenic temperatures. Large surface areas can capture the hydrogen at the low temperatures.

Due to the weak interaction of hydrogen with those materials, it is challenging to achieve high stor-

age densities under ambient conditions. A more detailed discussion of hydrogen storage in carbon

nanotubes that involves chemical bonding is described in the following section.


Pote

ntia

l Ene

rgy

“2H+M”

“H2+ M”

Edissc

without Pt (activated dissc.)

with Pt (spontaneous diisc.)

distance from SWNT surface

activation

barrier Ea

bulkinterfacegas

Figure 1.9: Dissociation of molecular H2 over catalytic metal doped SWNT

1.5.1 Hydrogen storage in SWNTs involving a chemical bond

A more viable option for ambient condition hydrogen storage in SWNTs is via the formation of

hydrogen chemical bonds with SWNT. This route showed initial promise, with initial investigations

showing a hydrogen uptake capacity of 5-10 wt% (39). However, in contrast, recent papers tend

to report storage capacities in pure carbon-based materials at ambient temperature of far less than

1wt% (40). Today it is widely agreed that the combination of pure carbon nanotubes and molecular

hydrogen is capable of storing only a very small amount of hydrogen under ambient conditions.

Fig(1.9), a schematic of the Lennard-Jones potential for molecular H2 and two H atoms as a function

of distance from the SWNT interface, explains the limited bond forming capability of pristine SWNT.

The flat minima in the H2 + M curve corresponds to the physisorbed H2. The deep minima in the

2H+M curve corresponds to chemisorbed H. When the two plots intersect above the zero energy

line (corresponding to the potential energy of H2 far form the surface), the chemisorption requires

an activation energy. This is the scenario for the pristine SWNT.

But pristine SWNT has been known to form bonds with an atomic hydrogen source, which can

significantly increase the amount of stored hydrogen (41; 42; 43). With this in mind an alternate

technique for hydrogen storage in CNTs was developed. The hydrogen molecule can be spontaneously

dissociated at the surface of catalyst metals such as Pd, Pt, Ni, Ru, and Rh. A schematic of the

dissociation path is drawn in Fig(1.9) where the Lennard-Jones potential plots for molecular and

atomic hydrogen intersect below the zero energy line. The dissociated hydrogen atoms can then

spill onto the underlying carbon nanotube structure by spillover mechanism. The hydrogen atoms


H2

H

Pt

dissociation spillover diffusion

sample chamber

Figure 1.10: Atomic Hydrogen pump: Schematic of the sequential steps of an atomic hydrogenpump: dissociation of molecular hydrogen, spillover, and surface diffusion on a nanotube surface.

can then find favorable sites on the nanotube surface through surface diffusion ultimately forming

bonds. This is graphically represented in Fig(1.10). Thus, stable C-H bond can be created even

though a conventional molecular hydrogen storage is used.

”Spillover” mechanism has been exploited by several groups for enhanced hydrogen uptake in

SWNTs and other carbon based materials such as MWNTs, Carbon nanofibers, activated carbon

etc (40; 44; 45; 46; 47). Despite this there is a healthy amount of speculation about the validity

of the spillover mechanism. Also further investigations need to be done to improve the low uptake

capacity and slow kinetics. This was the motivation for in-situ 4-probe conductivity tests during

hydrogen uptake reported in Chapter 7.

1.6 Dissertation Overview

Chapter 2 describes in some detail the experimental set-ups (reactors for CNT growth), and char-

acterization techniques used in the remainder of the thesis. Chapter 3 discusses the growth kinetics

of thermal CVD grown MWNTs. Chapter 4 describes the evolution of catalyst particle size as a

function of sputtered film thickness and annealing pressures. Size determines the phase of particles

during nanotube growth, which is shown to have implications in determining the nanotube morphol-

ogy. Chapter 5 studies the effects of an imposed electric field in altering the orientation and growth

kinetics of MWNTs. Chapter 6 reports a detailed parametric analysis of chirality families and diam-

eter distributions in SWNT production by the floating catalyst method. Chapter 7 presents the work


on Pt-doped SWNTs. Change in resistivity of the composite mats and spectroscopic determination

of the nature and extent of C-H bonds on hydrogen charging are reported.

Chapter 2

Experimental Methods

2.1 Introduction

In this chapter reactors used for CNT growth, catalyst deposition tools, in-situ characterization tools

for monitoring growth and finally different techniques used to characterize CNT and CNT composites

are introduced. A short write-up is written about each technique followed by the rationale in using

it. Wherever appropriate, details of sample preparation, experimental procedure and analysis steps

are described.

2.2 Reactor Configurations

2.2.1 CVD reactor for MWNT growth

Fig.2.1 is a schematic of the cold-wall CVD reactor used for this study. A linear translation stage

controls the distance between the two stainless steel electrodes. The grounded lower electrode serves

as a hot plate for CNT growth, embedded with a Joule heater and thermocouple, controlled by a

temperature controller (Fuji). The top electrode is maintained at a positive or negative DC bias with

respect to the grounded substrate. Pressure inside the chamber is monitored with a transducer and is

controlled by a manual valve. The precursor gases are flown into the reactor chamber from the sides.

The relative flow rates for the C precursor, ethylene, and the carrier gas, hydrogen, were controlled

by mass flow controllers (MKS Type 247). A Residual Gas Analyzer is connected downstream of

the reactor to determine the reacting gas composition. The other important accessory for the CVD

reactor is the interferometer setup used to monitor the MWNT heights in-situ.

Fig.2.2(a) shows the top electrode/reactor assembly. There are two conflat flange (NW80) ports

in the top flange. One is for the linear motion feedthrough (MDC) that controls the separation

between the top and bottom electrodes. Total linear travel is 2 inches with a least count of 0.001

21

CHAPTER 2. EXPERIMENTAL METHODS 22

motion controller

electrical feed through

to RGA

to vacuum

pump

substrate

heating stage

thermocoupletemperature

controller

MFC

+ / -

H2

C2H

4

Figure 2.1: Schematic of the reactor used to grow MWNT with an applied DC bias

inch. The other port is for an electrical feedthrough. This is used to maintain the top electrode at

a positive or negative bias with respect to the bottom electrode assembly which is grounded. The

power supply used for the electric field assisted growth studies is a Matsusada AU15R2 (voltage range

= 15kV, current = 2mA). The top electrode is electrically isolated from the rest of the chamber.

Schematic of the bottom electrode assembly is shown in Fig.2.2(b). The bottom electrode doubles

up as the hot plate for the thermal CVD reactor. The resistive heating element is NiCr (80:20) which

seats flush on grooves cut into a ceramic (Zirconia phosphate) block. A thermocouple located close

to the center of the bottom electrode is used to measure the substrate temperature. This feedback is

used to set the desired growth temperature and control temperature ramp rates. Electrical insulation

is maintained through teflon spacers.

The hot plate is approximately 2.4 inches in diameter. Jay Longson studied the uniformity

of the MWNT growth across the hot plate area. For this MWNT growths were done on 1cm2

substrates placed along the diameter of the bottom electrode, both parallel and normal to the gas

flow direction. The MWNT heights were measured using the SEM, and the normalized heights

plotted in Fig.2.3. It is observed from the plots that MWNT growth rates are faster towards the

center of the plate than towards the edges. This can be attributed to non-uniform heating of the


bottom electrode

thermocouple

heatingelement

reactorchamber

teflon

teflon

ceramic stagefor the heating element

top electrode

mot

ion

trans

lato

r

Cu

clam

pC

u cl

amp

ceramic rod

iso flange NW80

toelectrical feed through

(a) (b)

Figure 2.2: Schematic of the top and bottom electrode/flange assembly

substrates due to greater heat loss at the edges of the hot plate. The MWNT growth rates further

dip down towards the electrode edge closest to the entry port for the cold precursor gases into the

chamber. Comparatively uniform growth were obtained in an approximate 20mm2 area near the

center of the hot plate. All the growth results reported in this work is from MWNT growths from

substrates placed within this area.

2.2.2 Vertical flow reactor for SWNT growth

Fig. 2.4 is a schematic showing the details of the vertical flow reactor used for bulk SWNT growth.

The reactor is a 3-inch diameter 5 feet long quartz tube. It is placed in a three-zone vertical tube

furnace (Lindgerg Blue). The temperature of each of these zones can be independently controlled.

The temperature of the vertical flow reactor was maintained between 900 and 1100oC. The furnace

output runs through ∼4 feet unheated tubing to an exhaust hood, and hence the entire SWNT

production takes place at near atmospheric pressure. The exhaust runs through a bubbler filled

with water, this strips the exhaust gas off any residual carbon content. Precursor solution is made

of ethanol, the chosen carbon source, in which ferrocene is dissolved. Hydrogen is used as the carrier

gas. The precursor solution was pumped into the carrier gas using a peristaltic pump (VWR, flow

rates 0.03-2 ml/min). The precursor solution was vaporized at temperatures of 150 to 200 oC in

the delivery tube; the gaseous products were carried directly to the bottom of the furnace through

a nozzle. The temperature of the vertical flow reactor was maintained between 900 and 1100oC.

Ar was used for ramping up the reactor temperature to the desired value, and also for cooling


Figure 2.3: Uniformity of MWNT growth across the bottom electrode

the reactor after the growth run. The flow rates were controlled by mass flow controllers (MKS

247). The gaseous mixture is expected to be pyrolized in the first zone/bottom of the furnace with

nucleation and growth of the SWNTs in the other zones. The grown nanotubes were transported

out of the reaction zone by the flowing gases and were collected on the cooler parts of the furnace in

the form of very light, diaphanous membrane. These thin films could be easily peeled off from the

reactor walls using tweezers.

2.3 Deposition Tools

2.3.1 Sputter Deposition

Sputtering is one of the most widely-used fabrication methods for metal thin film deposition. Two

different sputtering systems were used for this work. Catalyst thin films for MWNT growth were

sputter deposited using a IBS/e system from South Bay Technologies. Substrates for MWNT growth

were prepared by sputter depositing requisite thicknesses of Fe films on top of a 10 nm Al buffer layer

on C-type Si. Most of the Pt-SWNT composites used for hydrogen storage studies were prepared

by sputter depositing Pt using the ”Kobe” chamber in the Geballe Advanced Materials lab.

For deposition of Pt on nanotube sample, the SWNTs is first dispersed in isopropyl alcohol by

ultrasound-sonication. The SWNT-alcohol solution is then spin coated on a glass substrate. The

alcohol residue is removed by outgassing at ∼ 250oC in an evacuated chamber prior to subsequent

metal deposition. The sample is loaded into the load-lock, and then is translated into the main

chamber. The load-lock is pumped out by a turbo molecular pump that is backed by a mechanical

rotary pump. The deposition chamber is pumped out by a cryogenic pump which traps molecules


Ar / airH

2 carrier gas

to exhaust

bubbler

vert

ical fu

rnace

precursor

solutionMFC

MFC

top flange

peristaltic

pump

bottom

flange

heating

tape

quartz

tube

inlet

tube

(1)

(2)

(3)

Figure 2.4: Vertical reactor setup for SWCNT growth.

in a sorption matrix at cryogenic temperature which is cooled by the vaporization of compressed

He gas. The metal target is negatively biased at several hundred volts against nearby surrounding

chamber which is grounded. Once the working gas is ionized, they are accelerated toward the target

with high kinetic energy. The metal atoms can then be sputtered off through momentum transfer

and deposited onto a substrate. In our sputtering system, Ar is used at pressure range between 1.5

to 5 mTorr. The deposition rate is monitored by a quartz crystal microbalance. (The deposition

rate at the substrate position is calibrated by measuring the actual thickness of the deposited film.

By comparing the thickness measured by the rate monitor and the actual film thickness, a geometric

factor(referred as to tooling factor) can be calculated.The deposited sample thickness is measured

by a low-angle symmetric Xray diffraction technique.) The thickness of the sputter deposited film

on SWNT mats is referred to as the nominal thickness (thickness of the deposited film assuming it

to be on an ideally flat surface).

2.3.2 Quartz Crystal Microbalance (QCM)

QCM is a technique often used to detect small changes in mass. This technique operates by measuring

the resonant frequency of a single quartz crystal. The resonance of the crystal varies as the mass on


the crystal varies. Thus, it can be used to detect very small quantities of mass change, and hence

deposition on an atomic scale. The change in resonant frequency is related to film thickness by the

following equation:

Tf =NqρqπρfZf

tan−1

[Z tan

(π(fo − f)

fo

)](2.1)

where Tf is the film thickness, ρq and ρf are the quartz crystal and film densities, f is the measured

frequency,fo is the frequency of the crystal with the film on it, and Z is a material property known

as the Z-factor. The Z-factor is given by the relation:

Z =

√ρqUqρfUf

(2.2)

where U is the shear modulus of the films. The QCM is used inside the sputterer to measure the

thickness of the thin film deposited. For MWNT catalysts a 2.5 nm Fe thin film is deposited on a

10 nm buffer layer of Al, which in turn was deposited on (110) Si wafer. For hydrogen storage in

SWNT films, Pt is sputter deposited on a thin mat of SWNT prior deposited on a suitable substrate.

For this Pt of nominal thickness in the range of 0.1nm to 1.5 nm was used. All these thicknesses

are measured using a QCM. For the Pt doped SWNT samples, tooling factors of the samples were

performed prior to the actual deposition in order to determine the sputter rates.

2.4 In-situ diagnostics

2.4.1 Laser Interferometry

Laser interferometry is a technique used to monitor changes in thickness for a thin film, and is based

on the interference of light reflected off a thin film.

The reflectance from an interface is defined as the ratio of reflected to incident energies. For

reflection from a transparent medium,

R =E2or

E2oi

= r2 =(ni cos θo − no cos θ1)2

(ni cos θo + no cos θ1)2

where r denotes the reflection amplitude coefficient or the fresnel coefficient, no and ni being the

refractive index of the ambient and the transparent medium respectively. The incident beam and the

refracted beam makes an angle θo and θ1 respectively with the surface normal. The corresponding

expression for an absorbing medium is obtained by replacing n with n+ ik, where k the imaginary

part of the refractive index is related to the absorption coefficient of the medium.

Reflection of light by a single film

To derive the expression for reflection from a single film, we consider the simplest case of a

single non-absorbing layer bounded on either side by semi-infinite non-absorbing layers, Fig. 2.5.


substrate (2)

film (1)

air (0)

01

2d

incident reflected

o

1 1

r1 , t1’

t1 , r1’

r2 , t2’

t2 , r2’

r1 t1r2t1’

t1r2r1’t1

t1r2 t1r22r1’

t1r22r1’t1’

t1r22r1’2

t1r23r1’2

t1r23r1’2t1’

(a) (b)

Figure 2.5: The principle of interferometry. (a) Schematic of light reflection by a single, non-absorbing layer bounded on either side by semi-infinite non-absorbing layers. The incident laserbeam reflects off the film surface and the substrate-film interface. The reflected beams interfere asdescribed in the text. (b) Fresnel coefficients for the two interfaces considered.

The notation for the amplitude coefficients are such that, the fraction of the amplitude of a wave

reflected when entering a film is r and while leaving r′. The subscript denotes the medium in which it

is reflected. A similar notation is used for the amplitude-transmission coefficients, t (Fig. 2.5(b). The

incident beam will generate a large number of multiply internally reflected rays. Each of the reflected

rays bears a fixed phase relation to all other rays. The phase difference arise from the optical path

length and from phase shifts occurring at various reflections. But the waves are mutually coherent

and if brought to focus at a point will interfere.

Apart from the first all the waves undergo an odd number of reflections within the film. As

shown in Fig. 2.5(a) the amplitudes of the reflected waves are respectively r1, t1r2t′1, t1r2

2r′1t′1 ,

t1r23r′1

2t′1 . . . Hence the total reflected amplitude at the focal point will be:

reff = r1 + t1r2t′1 exp(−2iδo) + t1r2

2r′1t′1 exp(−4iδo) + . . . (2.3)

where δo is the phase difference between adjacent reflected waves due to the optical path length

difference corresponding to a film thickness of d.

δo =2π

λn1d cos θ1 (2.4)

For a non-absorbing medium it can be shown from the conservation of energy that t1t′1 = 1 − r2

1.


Because of a 180o phase shift r = −r′, so that on summation eqn.(2.3) becomes:

reff =r1 + r2 exp(−2iδo)

1 + r1r2 exp(−2iδo)(2.5)

The corresponding reflectance is given by R = reff · r∗eff :

R =r21 + 2r1r2 cos(2δo) + r2

2

1 + 2r1r2 cos(2δo) + r21r

22

(2.6)

The above relation describes the oscillatory nature of the reflected intensity of the interfering beams

with a change in the thin film thickness, having a maximum of Rmax =( r1+r21+r1r2

)2

and a minimum of

Rmin =( r1−r21−r1r2 )2. The phase change resulting in this peak to trough transition is 2δo = π and from

eqn(2.4) the corresponding change in film thickness is given by:

∆dC =λ

4n1 cos(θ1)(2.7)

cos(θ1) =

√1−

[sin(θo)

n1

]2

(2.8)

where λ is the wavelength of the incident laser beam. This thickness, ∆dC , will be referred to as the

fringe thickness. Thus eqns. (5) and (2.8) can be used to estimate the thickness of a film from the

interferometer signal. By counting the number of peaks and troughs in the interferometer signal the

MWNT height and hence the growth rates can be estimated after calibrating the fringe thickness

corresponding to a given growth condition.

Interferometer set-up

Fig. 2.6 is a schematic of the interferometer setup. Side viewports allow the entry and exit of a laser

beam (630 - 680 nm), emitted from a DC power supply stabilized diode, into the chamber. The

separation between the two electrodes constrains the incident angle of the beam. The maximum

separation in between the electrodes is limited because: (i) strength of the applied electric field

decreases for an applied potential with increasing distance between plates and (ii) the top electrode

reflects heat thus helping in pyrolysis of the precursor gases. Hence, larger the separation between

plates higher is the heat loss and smaller the growth rates. For all the interferometer scans used

in the present study the distance between the electrodes were maintained at 10 mm. Given this

separation between the electrodes and their relative position with respect to the view ports a di-

rect reflection from the MWNT surface could be obtained only for almost grazing incidence. But,

beam incident at large angles to the normal (Fig.2.6(b)) limits the MWNT height resolution. The

MWNT forest height corresponding to adjacent peak and valleys in the interference pattern is given

by the eqn.2.8.The relation predicts that with increasing angle the fringe height increases, hence


500

400

300

200

cyc

le th

ickn

ess

(nm

)

806040200

angle (degrees)

0.8

0.7

0.6

0.5

I/Io

500400300200

cycle thickness (nm)

(a)

630 nm 680 nm

Laser Diode stabilized by DCpower supply

view

port

concavemirror

PVcell

pico-ammeter

Si substrate

catalystlayer

o

1

Figure 2.6: Schematic of the interferometer set-up, used as an in-situ diagnostic to determine theheight of the MWNT films. Fig. (a) plots the fringe thickness corresponding to the maxima andthe minima in the interferogram as a function of the incident angle. It also plots the magnitude ofbeam attenuation corresponding to the fringe thickness. (b) The reflected laser beam is made tofocus on a photovoltaic cell by a concave mirror. The intensity of the beam is tracked by measuringthe photovoltaic current using a pico-ammeter.


decreasing the resolution, Fig.2.6(a). Also for higher angles of incidence the beam that reflects off

the MWNT-substrate interface travels a larger distance through the MWNT forest, for the same

height of MWNT. This will result in attenuation of this beam, Fig.2.6(a), resulting in lesser number

of interference fringes, thereby restricting the maximum height that can be monitored by this tech-

nique. To overcome this difficulty the beam was made to reflect multiple times off the Si substrate

and the polished top stainless steel electrode. The beam reflects off the MWNT forest only once, as

shown in the schematic. This way the beam incident angle was reduced, increasing the measured

height resolution. The exit beam is made to reflect off a concave mirror onto a photo-voltaic cell

placed at the focal point of the mirror. The intensity of the beam reflected from the MWNT surface

is monitored by tracking the photo-induced current from the cell using a pico-ammeter (Keithley

487), in 100 µsec time intervals.

Plots in Fig. 2.7 are examples of the interferometry scans recorded during MWNT Growth. The

plots have two distinct features, attenuation of the reflected intensity accompanied by an oscillatory

character. The oscillations called the Fabry Perot fringes occur due to the interference of two beams,

as has been described in the previous section. The first beam is reflected off the top of the MWNT

film, while the second beam is reflected from the MWNT-substrate interface. The amplitude of the

fringes decay rapidly as the second beam is being absorbed during its path through the MWNT

films. The overall decay of the total reflected signal is a function of the extinction coefficient of the

MWNT films grown.

Figure 2.7: Interferometer scans recorded in-situ during MWNT growth. The first three reflectivityplots correspond to same growth conditions but different growth times. The fourth reflectivity plotis from a higher pressure growth. The rectangles on the plots show when the growth stopped. Alsoshown are SEM images of MWNT forests corresponding to three of the growth runs.


Reproducibility of growth and diagnostic technique

To estimate the reproducibility of growth and the reliability of the interferometer technique in mea-

suring film heights, MWNT growths were done for different time durations. The growth of the

MWNT films were halted and the chamber rapidly evacuated after the appearance of different num-

ber of fringes in successive experiments. The corresponding heights of the MWNT were determined

from SEM images. The first three scans in Fig. 2.7 were all done under the same conditions,

T=250oC, P = 265 Torr for the same mass flow rates of hydrogen and ethylene. The same ap-

proximate temporal position of the interference fringes attests to the reproducibility of the method.

The SEM heights for the growths terminated after 1 and 3 cycles are 440 and 2.6 µm respec-

tively, setting the cycle thickness to be approximately 425 nm. The fourth scan shown in Fig.2.7

was performed for same temperature and flow rates but at higher pressure of P = 400 Torr. The

growth was stopped after the appearance of 5 approximate fringes, the corresponding SEM height

measured at 4.0 µm, setting the approximate fringe thickness to 400 nm. The difference in fringe

thickness could be attributed to a change in the refractive index value for the MWNT film, possible

due to differences in the densities of the MWNT films grown at different conditions . Indeed the

cycle thickness has been found to vary by as much as ±50nm from the 425 nm value for the 750oC

growth. Therefore an universal fringe thickness cannot be attributed for all the growth runs.

Calibration and Analysis method of the Interferometer scans

Fig. 2.8 details the algorithm for analyzing the interferograms. The obtained raw interferometer scan

data is normalized by the photovoltaic current at the onset of growth. Due to decay in intensity

of the interfering beams, determining the exact position of the peaks and valleys of the scan is a

problem. To get around this problem, a procedure was developed to fit the scan with a background,

Fig. 2.8(a). This was done using a Savitzky-Golay filter. The filter does a kth order local polynomial

regression on a series of at-least ’k+1’ values to determine the smoothed value at each point. This

is widely used in analytical chemistry studies (48). The analysis range is determined by the range

where the peaks and valleys due to the interference were observed. The number of points used

for the Savitzky Golay smoothing depended upon the frequency of the interfering signal. The net

interfering signal is obtained after subtracting the fitted background from the original scan data,

and is plotted in Fig (b). The position of the peaks and valleys are obtained and knowing the

average fringe thickness for the growth, the corresponding heights and hence the growth rates of

the MWNTs were determined. This is plotted in Fig.2.8(c). As mentioned in the last section an

universal fringe thickness cannot be used for all conditions; hence the fringe thickness has to be

calibrated for each of the growth conditions studied. This is done by setting up growth parameters

such that the interference fringes were visible to the end of the growth run. In such a case the

fringe thickness was estimated by dividing the final SEM heights of the CNTs with the number of

observed cycles (i.e. assuming same approximate cycle heights for the entire run). The final height


1.0

0.8

0.6

0.4

0.2 N

orm

aliz

ed In

tens

ity

700600500400300200100 time(secs)

-60x10-3

-40

-20

0

20

40

60

net

Sig

nal

700600500400300200100

25

20

15

10 Gro

wth

rate

(nm

/sec

)

12x103

8

4

0

Height of M

WN

T (nm)

Growth started Growth stopped

Height of MWNT from SEM

normalized raw intensity fitted background net Signal Height of MWNT growth rates

Figure 2.8: Algorithm for analyzing the interferometer scans. In Fig.(a) an attenuating backgroundsignal is obtained from the plot, by using the Savitzky-Golay smoothing function. (b) The back-ground is subtracted from the normalized raw signal to obtain the interfering signal. The amplitudeof this signal decays with height of the MWNT. The solid lines are Beer-Lamber law . MWNTheights and the growth rates obtained from the interferometer scans are plotted in Fig. (c).

of the MWNT film, determined from SEM analysis, is also plotted in Fig.2.8. The Igor macro which

performs this entire analysis starting from the raw scan data can be found in Appendix B.

The interferometer scans can also be used to quantify the density of the MWNT films that can

be used as a metric for nanotube yield. As seen in Fig.(b) the amplitude of the net interfering signal

decays with time, due to absorption of the part of the incident beam passing through the growing

MWNT film. This beam is in the same phase at points that correspond to the peaks and valleys of

the net interfering signal. Knowing the height corresponding to these points in the interferometer

scans, the decaying intensity data can be fitted by the Lambert-Beer law: IIo = exp(−αl), where α is

the absorption coefficient and l the distance travelled by the beam through the MWNT film. This

fit is shown by solid lines in Fig.2.8(b). The absorption coefficient so obtained is dependent among


other factors the density of the MWNT forest. The method for extracting the density information

from the absorption coefficient will be discussed in Chapter 5.

A caveat about using the interferometer technique for determining growth rates and carbon nan-

otube heights. This technique works well for heights below 10 µm. Beyond this height range for

most cases the interference fringes cannot be detected, and hence height/growth information lost.

Thus the time resolved reflectivity method could not be used to study the decay in growth rates due

to catalyst poisoning for most growth conditions. Hence the primary focus of this study is in the

steady state growth regime, or the linear part of the sigmoidal shape of the MWNT growth plot.

Complimented by other microscopic characterization tools, e.g. time lapse photography, the inter-

ference method can be a very important tool in determining the complete kinetics of nanomaterial

growth(49).

2.4.2 Residual Gas Analyzer (RGA)

Figure 2.9: (a) Schematic of a RGA . (b) Sample mass spectrum obtained for MWNT growth; T =750oC,gas pressure= 400 Torr, H2 : C2H4 flow rates = 150:250 sccm; imposed field = .45V/µm

Residual Gas Analyzer (MKS Spectra products, microvision plus) was attached downstream of

the system to obtain mass spectra of the effluent gas. This was done to investigate the composition


of the reacting gas for different growth conditions, particularly as a function of the bias magnitude

of the applied electric field. Fig.2.9(a) is a schematic of the essential parts of the RGA. Electrons

emitted from hot filaments are used to ionize atoms and molecules. Ions with a specific mass-to-

charge ratio are then filtered by applying a combination of DC and RF voltages to each of the

quadra-pole. The mass filtered ions are then collected by the Faraday cup. A sample mass spectra

collected is shown in Fig2.9(b). For neutral species measurements, the acquired mass spectra must

be de-convoluted, as the resulting intensities, i, from the RGA are products of the original species’

cracking patterns (50). For a system of n species and m spectra, the following matrix must be solved

to estimate the neutral species density,D.

[im,1] = [am,n][Dn,1] (2.9)

where ai,n represents the cracking patterns for the nth species. The cracking patters are obtained

from the NIST chemistry web-book (51) and from in-house databases obtained from prior RGA

studies of nanotube and nanofiber growth conditions (50; 52). Results obtained in this way can be

compared relatively for a single species at varying conditions.

2.4.3 4 Probe Resistivity studies

v

to vacuum pump

view port

-+

CNT films

on quartz

- I + I

H2 inlet

xyz motion

control

ah

AB

(a) (b)

Figure 2.10: Schematic of the 4 probe setup

The presence of H induces a substantial component of sp3 bonding in SWNTs and as a result

the π and π∗ components to the electronic structure vanish. Hence the resistivity of the films should

change as a function of hydrogen charging time. Therefore in-situ 4-probe resistivity tests were

performed on mats of doped SWNT during hydrogen uptake. The four point probe is a versatile

technique to investigate electrical properties of materials, mostly resistivity of semiconducting thin

films. A 4 probe test is needed because it eliminates the contact resistance between the probes

and the material, and hence any change in resistance of the sample is solely due to the change in


resistivity of the material. Typically 4-probe resistivity measurement involves setting four, equally-

spaced point contacts down on the surface of a ”large” conductor, as shown in the Fig.2.10(b). Let a

be the probe spacing and h be the sample thickness. We assume that the sample is infinite (i.e., its

horizontal dimensions are much larger than the probe spacing). A current I is passed through the

sample via the outer two probes, and the voltage drop is measured between the inner two probes.

The high impedance of the voltmeter minimizes the current flow through the portion of the circuit

consisting of the voltmeter. Since, there is no potential drop across the contact resistance associated

with the inner probes, only the resistance associated with the material between the inner probes is

measured. For an infinitely thin specimen( h << a) like in our case of thin SWNT mats, the sample

resistivity in terms of I and ∆V , measured between the inner probes, is given by the relation:

ρ =π

ln 2h

(∆V

I

)For the two-dimensional case, the quantity ρ/h (which has units of Ohms) is called the two- dimen-

sional resistivity, sheet resistance, or resistance-per-square. In many thin film applications, one does

not know the film thickness or resistivity, only the sheet resistance.

Fig.2.10(a) is a schematic of the 4-probe set-up used for this study. The chamber can be evacuated

using a turbo pump backed by a roughing pump. All the four probes have xyz motion controls, and

an optical microscope connected to a CCD camera is used to ensure electrical contact with the

material. The only disadvantage is that the view port is not rated for positive pressures and hence

hydrogen pressure above an atmosphere cannot be used. To increase the signal to noise ratio the

4 probes are connected to an Agilent 4156B Semiconductor Parameter Analyzer via biaxial and

triaxial cables. Ports on the side can be used for gas flow into the chamber and also for electrical

feed throughs. An embedded heating element is used for temperature dependent hydrogen charging

experiments.

2.5 Ex-situ Diagnostics

Spectroscopic studies

Spectroscopy is the study of interaction of electro-magnetic waves with matter. The matter can

be atoms, molecules, atomic or molecular ions, or solids. The interaction of radiation with matter

can cause redirection of the radiation and/or transitions between the energy levels of the atoms or

molecules. There are basically 3 branches of spectroscopy:

Absorption: A transition from a lower level to a higher level with transfer of energy from the

radiation field to an absorber, atom, molecule, or solid.

Emission: A transition from a higher level to a lower level with transfer of energy from the

emitter to the radiation field. If no radiation is emitted, the transition from higher to lower energy


levels is called non radiative decay.

Scattering: Redirection of light due to its interaction with matter. Scattering might or might

not occur with a transfer of energy, i.e., the scattered radiation might or might not have a slightly

different wavelength compared to the light incident on the sample.

In this work four different spectroscopic techniques were used: Raman spectroscopy , UV-Vis-

NIR spectroscopy, X-Ray Absorption spectroscopy and Auger Electron Spectroscopy. Raman and

absorption spectroscopy characterizations complimented each other as these techniques were used

to study respectively the vibration and electronic transitions of SWNT, giving information about

SWNT diameter and chirality. Surface compositional analysis were done using X-ray and Auger

electron spectroscopy. The former was used to study the extent of sp3 bond formation in nanotubes,

while the later was chosen because of its high spatial resolution to obtain compositional maps of

catalyst nanoparticles.

2.5.1 Raman spectroscopy

Raman spectroscopy is used to study vibrational, rotational, and other low-frequency modes in a

system. It relies on inelastic scattering, or Raman scattering, of monochromatic light, usually from

a laser in the visible, near infrared, or near ultraviolet range. The laser light interacts with phonons

or other excitations in the system, resulting in the energy of the laser photons being shifted up

(Anti-Stokes) or down (Stokes). The shift in energy gives information about the phonon modes in

the system. Typically, a sample is illuminated with a laser beam. Light from the illuminated spot

is collected with a lens and sent through a monochromator. Wavelengths close to the laser line,

due to elastic Rayleigh scattering, are filtered out while the rest of the collected light is dispersed

onto a detector. A Renishaw NIR 780TF spectrometer with three lasers, Ar ion (514nm), HeNe(633

nm) and NIR (785nm) was used for this study, and only the Stokes signal was recorded. Raman

spectrum was obtained in the reflection mode, most often from CNTs dispersed onto a Si wafer.

RayleighScattering

StokesRamanScattering

Anti- StokesRamanScattering

virtualenergy states

vibrationalenergy states


Raman spectroscopy has proved to be a very powerful tool for characterizing nanotubes, SWNTs

in particular(53). The unique optical and spectroscopic properties observed in SWNTs are largely

due to the presence of van Hove singularities (vHSs) in the nanotube electronic and phonon DOS.

Whenever the energy of incident photons matches a vHS in the DOS of the valence and conduction

bands (subject to selection rules for optical transitions), one expects to find resonant enhancement.

There are two resonant conditions for optical transitions: (1) incidence resonance (resonance with

the incident light) EL = ∆E and (2) scattered resonance (resonance with the scattered photon)EL =

∆E + ~ω, where EL is the incident energy of the laser light, ∆E energy separation between two

electronic states and ω the frequency of the scattered phonon. The resonantly enhanced Raman

scattering intensity allows one to obtain detailed information about the vibrational properties of

nanotubes, even at the isolated individual SWNT level. Fig.2.11 is a representative Raman spectrum

of a SWNT. The most important features, namely the G-band, the D-band and the radial breathing

modes are tagged in the plot. Following subsections describes in some detail how these features can be

used to extensively characterize SWNT samples, revealing information about diameter distribution,

optical transition energies, chirality, metallic or semiconducting nature of the SWNTs, quality/purity

of the SWNTs etc.

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

inte

nsity

300250200150

wavenumber (cm-1)

1.0

0.8

0.6

0.4

0.2

0.0160014001200

RBMs

D-band

G-Band

Figure 2.11: Raman spectrum obtained from a HiPCO sample, with 785 nm laser

The G-band

The G band arises due to a first-order (implying that the lattice relaxes by emitting one phonon)

1-phonon emission Raman scattering event. The G-band involves an optical phonon mode between

the two dissimilar carbon atoms A and B in the graphite unit cell. In contrast to the graphite

Raman G band, which exhibits one single Lorentzian peak at 1582 cm−1 related to the tangential

mode vibrations of the C atoms, the SWNT G-band is composed of several peaks due to the phonon

wave vector confinement along the SWNT circumferential direction and due to symmetry-breaking


effects associated with SWNT curvature. The G-band frequency and lineshape can be used for (1)

diameter characterization, (2) to distinguish between metallic and semiconducting SWNTs, through

strong differences in their Raman lineshapes (53).

Fig2.12 indicates that the G-band feature for SWNTs consists of two main components, one

at 1590 cm−1 (G+) and the other peaked at about 1570cm−1 (G-). The G+ feature is associated

with carbon atom vibrations along the nanotube axis (Longitudinal Optical phonon mode) and its

frequency ωG+ is sensitive to charge transfer from dopant additions to SWNTs (up-shifts in ωG+ for

acceptors, and downshifts for donors ). The G- feature, in contrast, is associated with vibrations of

carbon atoms along the circumferential direction of the SWNT (Transverse Optical phonon), and

its line-shape is highly sensitive to whether the SWNT is metallic (BreitWignerFano line-shape) or

semiconducting (Lorentzian line-shape), as shown in Fig2.12. The BWF signal appears only when

the electronic density of states at the Fermi energy has a finite value. Thus we observe a BWF

line-shape only in metallic SWNTs, but not in semiconducting SWNTs or in graphite.

The frequency ωG+ is essentially independent of dt or chiral angle θ, while ωG− is dependent on

dt and whether the SWNT is metallic or semiconducting, but not on chiral angle θ:

ωG− = 1591− C/d2t (2.10)

where C for semiconducting and metallic SWNTs have values of 47.7 cm−1nm2 and 79.5cm−1nm2

respectively. Such diameter-dependent measurements can be used to corroborate (n, m) assignments

carried out on the basis of the RBM feature (as will be shown in Chapter 6). From the diameter

dependence for the G band modes shown in eqn.(2.10), it is clear that the G band for large diameter

carbon nanotubes is similar to the one peak G-band observed in graphite. This is actually the case

for the G band for large diameter MWNTs, where a single peak at 1582 cm−1 is observed,Fig2.12 ,

just like in graphite.

The D-band

Defect induced D mode in graphite/CNTs is assigned to a double-resonance Raman effect in sp2

carbon (54). Double resonance is similar to resonant Raman,but here in addition to the incoming or

outgoing resonances the elementary excitation makes a real transition. Double resonances are much

stronger than single resonances. The intensity of the D band is known to be inversely related to

crystallite size, and disappears for perfect crystals. Although, the contribution of defects in the tube

walls to the D band is still not completely understood, the intensity ratio of the D-band vis-a-vis the

intensity of the G-band has been found to be a good metric in determining the quality/purity of the

SWNT. From Fig2.12 it can be seen that the D-band is much more intense for MWNT than SWNT

implying that MWNT structure is more defective. The D-band appears at 1350 cm−1, though its

position has a strong dependence on the excitation energy (note the difference in position of the D


1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Inte

nsity

160014001200

wavenumber (cm-1)

160014001200 160014001200

metallic SWNT semiconducting SWNT

MWNT

! !

!

!

G+G+

G-

G-

D D

D

G

Figure 2.12: Comparison of the line-shape of the G-band for a metallic, semiconducting SWNT andthat of a MWNT. The Raman spectrum of the SWNTs were obtained from the same sample, butwith different laser energies (514 nm for the metallic and 785 for the semiconducting). This showsthe importance of using different wavelengths to fully characterize a given sample. The MWNTspectrum was obtained with a 514 nm laser. Also shown in the plots are the D-bands

band for the SWNTs excited with different laser wavelengths in Fig2.12).

Radial Breathing Modes (RBMs) in SWNTs

For SWNTs along with the G-band, the lower frequency radial breathing mode (RBM) are usually

the strongest features in SWNT Raman spectra. Both are first-order Raman modes. The RBM

is a unique phonon mode, appearing only in carbon nanotubes and its observation in the Raman

spectrum provides direct evidence that a sample contains SWNTs. The RBM is a bond-stretching

out-of-plane phonon mode for which all the carbon atoms move coherently in the radial direction,

as if the tube were breathing. They occur with frequencies ωRBM between about 100-300 cm−1.

These RBM frequencies are used for characterizing the nanotube diameter distribution in the

sample by the use of the relation ωRBM = A/dt +B, where the parameters A and B are experimen-

tally determined (53). The dependence A/dt comes form the fact that the mass of all the C atoms

along the circumferential direction is proportional to the diameter. The parameter B accounts for

tube-tube and tube-substrate interactions. For typical SWNT bundles on native Si-oxide surface in

the diameter range 1 < dt < 2nm, A = 234cm−1nm and B = 10cm−1 has been found. For isolated

SWNTs on an oxidized Si substrate, A = 248 −1nm and B = 0. However, for dt < 1 nm, the simple

ωRBM = A/dt + B relation is not expected to hold exactly, due to nanotube lattice distortions

leading to a chirality dependence of ωRBM . For large diameter SWNTs (dt > 2 nm), the intensity

of the RBM feature is weak and is hardly observable.Therefore, from the ωRBM measurement of

a RBM, it is possible to obtain the corresponding dt value. The RBM spectra for SWNT bundles


contain an RBM contribution from different SWNTs in resonance with the excitation laser line. For

a diameter characterization of the sample, analysis of the resonance condition should also be per-

formed. A single Raman measurement gives an idea of the SWNTs that are in resonance with that

laser line, but does not give a complete characterization of the diameter distribution of the sample.

However, by taking Raman spectra using many laser lines, a good characterization of the diameter

distribution in the sample can be obtained. Since semiconducting and metallic SWNTs of similar

diameters do not occur at similar Eii values, ωRBM measurements using several laser energies can

be used to characterize the ratio of metallic to semiconducting SWNTs in a given sample.

Figure 2.13: Assigning (n,m) to SWNTs from RBM signals. (b) Kataura plot, charting the experi-mental optical transition as a function of SWNT diameter. (a) RBM signal obtained from HiPCOnanotubes with 785 nm laser excitation. From a comparison of the resonant energy and the diameterof the tube (obtained from the RBM frequency) the chirality of the SWNT can be determined. Asan example, two of the RBMs observed in the sample spectrum are assigned chiralities (9,4) and(10,5). These SWNTs belong respectively to the chiral family, ”2n+m” , 22 and 25 respectively.

Next, knowing the dt values obtained from the measurements of ωRBM , and Eii ∼ EL from the

resonance condition, the RBM features can be used for making (n,m) assignments for SWNTs by

utilizing the Kataura plot, described in Chapter 1. As mentioned before, Kataura plots are experi-

mental graphs of optical transition energies vs nanotube diameter and hence act as a map to identify


the chiralities of the SWNT in a given sample. Simplest theoretical tight-binding treatments predict

that the optical transition energies of semi-conducting and metallic nanotubes depend linearly on

the diameter according to the relations(5; 55):

S11 =2aC−Cγo

dt

S22 =4aC−Cγo

dt

M11 =6aC−Cγo

dt

Such simplistic theoretical calculations neglect interactions between distant neighbors, the diam-

eter and chirality dependence of the curvature effects on transition energies, the interaction between

the SWNTs and the surfactant/solution used to disperse/ debundle the SWNTs etc. The net result

being a considerable discrepancies between the theoretical predicted value and the experimental ob-

servations. Hence rigorous studies have been made to come up with empirical relations that account

for these deviations and provide a reasonable fit between experimentally determined transition en-

ergies and the RBM frequencies(generally expressed as wavenumbers)(56; 7; 57; 6). Fig2.13(b) is a

Kataura plot that charts the empirical transition energies obtained from the work of Jorio et al(6).

as a function of wavenumber (ωRBM = A/dt + B; A and B for our data set had the best fit for A

= 230.78 cm−1nm and B = 7.14 cm−1).

One other factor that has to be considered when determining the chirality is the effect of bundling

of SWNTs. For bundled SWNTs, the spectral features are red shifted by 50-70 nm with the mag-

nitude of the shift depending on the extent of bundling and inter-nanotube contact area(58). Also,

due to the broadening of the electronic transitions the individual RBM spectrum is less resolved.

One important note is that the bundling effect has almost no effect on the frequency of the phonon

modes. Therefore the dotted blue line, blue shifted from the original position of the NIR laser by

50 nm, with no change to the wavenumber axis, will be a more appropriate representation of the

effective laser energy for bundled SWNT. Similarly the red dotted line accounts for the shift for the

HeNe laser,Fig2.13(b).

Hence knowing the frequency of the phonon modes (and therefore the diameter of the SWNTs)

and the incident laser energies; (n,m) assignments can be made to the SWNTs present in a sample

after accounting for the red shift due to bundling,Fig2.13 .

2.5.2 UV-Vis-NIR absorption spectroscopy

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation,

as a function wavelength, due to its interaction with a sample. A material’s absorption spectrum

is the fraction of incident radiation absorbed by the material over a range of frequencies. The

transmitted energy can be used to calculate the absorption.The most common arrangement is to


direct a generated beam of radiation at a sample and detect the intensity of the radiation that

passes through it. Radiation is more likely to be absorbed at frequencies that match the energy

difference between two quantum mechanical states of the molecules, and hence are like fingerprints

for the molecule in consideration. Therefore absorption spectroscopy is employed as an analytical

chemistry tool to determine the presence of a particular substance in a sample. The absorption

frequencies also depend on the interactions between molecules in the sample, the crystal structure

and hence symmetry(in solids) and on several environmental factors (e.g., temperature, pressure,

electromagnetic field). Absorption spectroscopy can also be used to measure the concentration of

an analyte by measuring the absorbance at some wavelength and applying the Beer-Lambert Law.

Absorption spectroscopy is performed across the electromagnetic spectrum. The UV-Vis-NIR

spectral range for the Lambda 950 (Perkin Elmer) used is 190 to 3300 nm.The light source is a

deuterium discharge lamp for UV measurements and a tungsten-halogen lamp for visible and NIR

measurements. The instruments automatically swap lamps when scanning between the UV and

visible regions. The wavelengths of these continuous light sources are dispersed by a holographic

grating. UV-Vis-NIR spectrometers utilize a combination of a Photo multiplier tube and a Peltier-

cooled PbS IR detector. The light beam is redirected automatically to the appropriate detector

when scanning between the visible and NIR regions.

For absorption analysis, dimethyl- formamide (DMF) was chosen as the solvent of interest since

it does not have absorption peaks in the same region as the SWNTs. Samples were prepared by

dissolving 0.1 mg of the sample in 10 ml of DMF and sonication for 15 min.

Figure 2.14: Absorption spectrum obtained for HiPCO SWNTs. Marked in the plot are absorptionlines corresponding to S11, S22 and M11 transitions


2.5.3 X-ray Photoelectron spectroscopy (XPS)

XPS (or ESCA, Electron spectroscopy for chemical analysis) is very useful for determining the

elemental composition on the surface (depths of 1-10 nm) of all non-volatile materials. It is a

quantitative spectroscopic technique that measures the elemental composition, empirical formula,

chemical state and electronic state of the elements that exist within a material. When the energy is

transferred from an X-ray photon to a core-level electron of an atom, the electron can be emitted.

The kinetic energy and the number of ejected photoelectrons is measured. Knowing the wavelength

of the incident X-rays and the kinetic energy of the emitted photoelectron the binding energy can

be retrieved from the equation:

Ebinding = Ephoton − (EK.E. + φ)

φ being the workfunction that needs to be calibrated with a known standard. XPS measurement is

surface sensitive since only the atoms near the surface lose their electrons without energy loss. But,

it can be used to provide elemental composition as a function of depth by analyzing a sample while

removing surface layers by ion etching. It is sensitive to all elements except H . The experiments

were carried out at the elliptical undulator Beam line 13-2 in SSRL, in the UHV end station. The

detector used was Scienta R3000 which has a kinetic energy resolution of 200meV. XPS was used

to quantify the extent of hydrogen uptake in the Pt-SWNT composite samples. This was done by

looking for spectral changes of the C1s peak before and after hydrogenation. The photon energy

used to probe the C1s peak was 400eV, while the overview scan was done at 700eV photon energy.

Nanotube samples are usually prepared on silicon substrates to avoid electron charging problems.

Fig.2.15 shows a XPS spectrum obtained before and after sputter deposition of Pt on a SWNT film.

The Pt 4f peak is used for calibration of the workfunction.

Figure 2.15: (a) Emission of a photoelectron.(b) A sample XPS spectrum


2.5.4 Auger Electron Spectroscopy (AES)

Auger electron spectroscopy (AES) has emerged as one of the most widely used analytical techniques

for obtaining the chemical composition of solid surfaces. It uses a primary electron beam (energies

in the range of 2 keV to 50 keV) to probe the surface of a solid material. Secondary electrons that

are emitted as a result of the Auger process are analyzed and their kinetic energy is determined.

The identity and quantity of the elements are determined from the kinetic energy and intensity of

the Auger peaks. The basic advantages of this technique are its high sensitivity for chemical analysis

in the 5- to 50-A region near the surface, a rapid data acquisition speed, its ability to detect all

elements above helium, and its capability of high-spatial resolution. The high-spatial resolution is

achieved because the specimen is excited by an electron beam that can be focused into a fine probe.

The spectroscope used for the study is a PHI 700 Scanning Auger Nanoprobe that provides down to

6nm secondary electron image resolution and 8nm Auger resolution with high elemental sensitivity.

Figure 2.16: (a) Schematic of the Auger process. (b) Auger spectrum of micelle patterned ironcatalyst particles on a Si substrate

The Auger process can be understood by considering the ionization process of an isolated atom


under electron bombardment. The incident electron with sufficient primary energy, Ep, ionizes the

core level, such as a K level. The vacancy thus produced is immediately filled by another electron

from L1. This process is shown in Fig.2.16. The energy (EK − EL1) released from this transition

can be transferred to another electron, as in the L2 level. This electron is ejected from the atom as

an Auger electron. The Auger electron will have energy given by

E = EK − EL1− EL2

and the excitation process is denoted as a KL1L2 Auger transition. The essential parts of an AES

therefore are an electron gun, electron energy analyzer and an electron detector. A typical Auger

electron spectrometer collects the data in the N(E) versus E integral mode. The data are then

mathematically differentiated using computer software to yield E dN(E)dE versus E Auger spectra.

For this work AES was used to characterize the iron catalyst nano particles, prepared form sputter

deposited thin films and also from block co-polymer templates. Depth profiling of the sputtered

catalyst thin films before and after annealing at different conditions were used to investigate the

amount of mixing between layers which has important consequences in the evolution of the catalyst

particle sizes.

2.5.5 Electron Microscopy

Scanning electron microscopy (SEM) was extensively used to characterize the nanotubes.The instru-

ment is an FEI XL30 Sirion SEM with FEG source and EDX detector. In conjunction with Raman

spectroscopy it was used as an initial diagnostic tool to characterize the quality and morphology

of the CNTs grown. It was used to determine the final heights of the MWNT films grown, which

complimented the interferometry scans to give growth rates. Image analysis of cross-sectional SEM

images of MWNT films and individual CNTs were used to quantify the alignment of the CNTs with

and without an applied electric field. SEM was also used to characterize the size distribution and

particle separation of the catalyst particles used for MWNT growths. Finally SEM was also used to

characterize the different types of Pt-doped SWNT films used for hydrogen uptake studies.

Transmission electron microscopy (TEM) was used for visual characterization of various carbon

nanotubes, carbon nanofibers and CNT-metal composites. Philips CM 20 TEM and FEI Tecnai

G2 F20 X-TWIN were used, both of which operated at a 200 kV accelerating voltage. Typically

the nanotube samples were dispersed in ultrasound-sonicated isopropyl alcohol solution, and then

coated on lacey- carbon supported Cu TEM grids for observation. High resolution (HRTEM) images

are typically taken at a magnification between 100 and 300k for nanotubes and composite samples.

A bright field imaging mode is operated by taking the transmitted beam through the objective

aperture and is useful for these samples since high contrast between carbon nanotubes and metals


is observed at relatively low magnification. For diffraction experiments, conventional and micro-

diffraction techniques are utilized. Conventional diffraction mode illuminates the parallel electron

beam (defocused C2 lens for small beam divergence) on a sample while micro-diffraction uses a

highly focused incident beam (focused C2 lens with large C2 aperture). By focusing the electron

beam on a sample, diffraction information from a small area of interest (typically beam diameter is

10-12 nm) can be retrieved.

2.5.6 Thermogravimetric Analyzer (TGA)

TGA, as the name implies, is a characterization technique that determines the change in weight

in relation to change in temperature. The analyzer consists of a high precision balance with an

alumina pan loaded with the sample. The pan is placed in a small electrically heated oven with

a thermocouple to measure the temperature. In some cases, there is a sheath of inert gas, Ar in

general, to prevent undesired reactions like oxidation of the sample. Analysis is carried out by

ramping the temperature, while recording the corresponding change in weight. The instrument used

is a Pyris1 TGA (Perkin Elmer).

The impurity content in a carbon nanotube sample can be measured using a TGA. Impurity

content is generally of two types: catalyst metal nanoparticles and amorphous carbon/soot that is

formed along with the nanotubes. The nanotube samples were loaded in ambient air. Since the

measurements are performed in a gas ambient, buoyancy effects become critical. To counter this,

sample weights taken for the measurements is 2-5 mg that is sufficient to obtain an accuracy of

around 0.5%. The typical operating temperatures range from 50 - 1000oC, with a ramp rate of

10oC/min for all the experiments. By subtracting the residual mass from the initial mass the metal

content of the samples can be calculated. The catalyst used for SWNT/MWNT growth for all the

studies were Fe nanoparticles. Fe oxidizes in the temperature range 200-400oC, hence the residue

after the TGA scan is Fe2O3. This has to be kept in mind while doing the relevant calculations.

Chapter 3

Kinetics of Multi-walled Carbon

Nanotube growth

3.1 Introduction

In this chapter we report the kinetics of carbon nanotube growth studied in the context of the

CVD process. A generic model for growth of 1-D nanostructures via the Vapor-Liquid-Solid (VLS)

mechanism is developed. Growth rates of MWNTs are determined using a time-resolved reflectivity

technique and are interpreted vis a vis the proposed model.

Growth of 1D nanomaterials via the CVD route has been well established. Initially it was in the

form of whiskers and platelets both inorganic (59; 60) and organic (carbon filaments) (61; 62; 63).

This field received further interest with the advent of carbon nanotubes and inorganic nanowires.

The VLS process, first proposed by Wagner et.al (59), is conventionally assumed to be the most

important growth mode for nanowires. In this model material from the vapor is incorporated

into a growing 1D structure via a liquid catalyst. Seminal work has been done to establish the

fundamental aspects of this mechanism (60) and to understand variations to this basic mechanism

(64). The carbon nanotube/nanofiber community in general also proscribe to the VLS mechanism

(63). Changes to this model have been suggested for growth conditions where the catalyst is in a

solid state at lower growth temperatures and/or larger catalyst particle dimensions (62). While there

has been general agreement about the approximate growth mechanism, the rate limiting step that

controls the growth rate of the CNT has been found to vary widely. Surface diffusion (65) and bulk

diffusion (61; 62; 66; 67) of carbon, the chemistry at the vapor-catalyst interface (68; 69; 70), the

diffusion of carbon on the nanotube surface(71), thermal decomposition of the gaseous precursors

(72), or a combination of two or more of these processes (71; 73) have been identified as the rate

limiting step. This is mostly because of the very wide range of parameter space studied: growth

47

CHAPTER 3. KINETICS OF MWNT GROWTH 48

conditions, catalyst combinations, choice of carbon precursors etc. Various mechanisms have been

proposed, mostly related to possible reaction steps at the catalyst interface, in an attempt to describe

the different morphologies of the CNTs and also to establish the occurrence of one rate limiting step

over another. This has led to the absence of a generic model to quantify the nanotube growth as one

particular mechanism for a given condition does not necessarily extrapolate to some other growth

condition. The basic idea behind the development of the model was the realization that the carbon

flux from the vapor to the CNT is driven by the favorable energetics of the entire process, a drop in

chemical potential of carbon. Hence instead of delving into the specifics of each mass transfer step,

the steady state carbon flux is described in terms of the chemical potential change for each step.

Equally interesting are the various methods that have been used to experimentally study the

kinetics of the CNT growth process. The absence of a robust characterization technique has also

contributed to the lack of understanding of growth mechanism. SEM observation of CNT heights

at different growth intervals (66), growth mark method (68) by interrupting the growth at different

time intervals are some of the post-situ techniques. These suffer from the disadvantage of inter-

rupted growth, reproducibility of the exact same growth conditions and finally, the number of data

points and hence the height resolution achievable. In-situ diagnostics employed include controlled

environment electron microscopy (67; 1) and field-emission microscopy (74; 75) during CNT growth.

These techniques are limited by the very low pressures involved. In situ time-lapse photography (49)

has been used, but suffers from height resolution problems particularly during the initial stages of

growth. Puretzky et al. (76) developed time resolved reflectivity (interferometry) as a tool to mon-

itor the MWNT height. This is a simple but at the same time very powerful technique, particularly

at smaller length scales, to monitor MWNT growth and has been adopted as the diagnostic of choice

for this study. The details of the thermal CVD reactor for MWNT growth and the interferometer

set-up have been described in detail in Chapter 2.

The layout of this chapter is such that details of preparation and characterization of the catalysts

used for growing MWNT films is described first. Next the kinetic model for MWNT growth is

described and in the final section experimental results are analyzed/compared in context of the

growth model.

3.2 Catalyst for growth of MWNT films

Catalysts for the growth of dense MWNT films were prepared by sputter depositing Fe film of the

required thickness on top of a 10 nm Al buffer layer on C-type Si. For all the growths in this

chapter the thickness of the sputtered Fe film is 2.5 nm. Next the deposited films were annealed

in an hydrogen atmosphere for 10 minutes. On annealing the Fe thin film balls up and results in

the formation of catalyst nanoparticles. Hydrogen ambient reduces the Fe-oxides formed during

transfer of the substrates from the sputterer to the growth reactor. The temperature is maintained


approximately at 550oC for the duration of the anneal. The hydrogen annealing pressure along with

the thickness of the sputtered Fe film are important in controlling the catalyst particle size. These

dependencies will be discussed in detail in Chapter 4.

Fig.3.1(b) is a representative SEM image of the catalyst particles obtained from annealing the

sputtered thin films. Particle density and size distribution analyses were done using Image J(77)

. Fig 3.1(c) is a histogram of particle sizes. The mean diameter of particles formed from the

continuous Fe film is 6.5 nm.The particle density was obtained by measuring the distance between

centers of two adjacent particles; the mean separation was estimated to be 25.2 nm. The chemical

composition of the catalyst particles obtained from annealing the sputtered films was studied using

Auger spectroscopy. Survey scans show the presence of oxygen, carbon, iron and aluminum. Carbon

is mostly from contamination of the substrate and the spectrometer chamber.

Fe

Al

Si

Fe-Al

Fe

6055504540

wt%

0.50.40.30.20.10.0 distance(µm)

6055504540

wt%

6055504540

wt%

6055504540

wt%

linescan 1

linescan 2

linescan 3

linescan 4

Al Fe

14

12

10

8

6

4

2

0

per

cent

age

20181614121086420

particle size (nm)

(a)

(b)

(c)

(d)

1 2

34

200 nm

Figure 3.1: Characterization of the catalyst particles obtained by annealing sputtered Fe films ona buffer layer of Al. (a) Cartoon of the process. (b) SEM image of the catalyst particles after theannealing step. (c) Catalyst particle size distribution (d) Line scan of the substrate using an Augerprobe.

Oxygen is possibly from oxides formed by iron and aluminum. The relative abundances of the Fe

(654eV) versus Fe (705eV) in the survey scans indicates formation of Fe-oxide (formed possibly post


annealing during sample transfer). Iron oxides do not catalyze carbon nanotube growth, hence care

was taken not to expose the catalyst particles after the annealing step. Compositional analysis of the

particles as opposed to the substrate reveal a larger oxygen content in the substrate implying most

of the oxygen comes from the Al. Fig 3.1(d) are line-scans obtained using the Auger probe. They

expectedly reveal an abundance of iron in the catalyst particle and that of Al in the substrate. The

presence of a significant amount of Al in the particles are probably due to significant background

noise arising from resolution limits of the Auger probe.

3.2.1 Importance of the Al buffer layer

The importance of the Al layer for MWNT growths can be observed in Fig.3.2. Figs (a,b) are

SEM images of sparse MWNT growth obtained from catalyst layers without Al (5 nm of Fe on

Si). Growth temperatures were 750oC and 800oC respectively. On introduction of the buffer Al

layer (2.5 nm Fe on 10 nm Al on Si) there was a dramatic increase in MWNT yield. Except from

the catalyst layers, the growth conditions were the same. It has been reported that a buffer layer

between the catalyst and substrate considerably affects the CNT growth. The buffer layer may act

as a diffusion barrier between Si and catalyst metal to prevent forming metal silicide deteriorating

catalytic activity (78; 79). Al or Al oxide is generally used as a buffer layer for the growth of SWNTs.

Delzeit at al.(80) and Zhang et al.(81) reported that Al film enhanced the formation of CNTs. Al

oxide was reported to be more efficient sub-layer for CNT growth than Al. It was proposed that Al

oxide formed during the heating prior to the CNT growth acted as a diffusion barrier preventing the

mixing of the catalyst with Si.

Auger depth profiles of as-sputtered substrates with and without the Al buffer layer is shown

in Fig.3.3. The sputter deposited Fe layers for the two cases have different thicknesses, and hence

the differences in time to etch away the Fe layer. The elemental atom fraction obtained from the

depth profile matches the composition of the different metal layers deposited. There is very little

intermixing between the layers, which is expected because the substrates were not annealed. The

interesting part is the variation of the atomic percentages of oxygen in the as-deposited layers. For

Fe sputtered directly on Si, oxygen can be seen at the Fe/Si interface due to the presence of a native

oxide layer on Si (which was not removed prior to deposition). Some amount of oxygen was present

on the Fe surface as this layer was exposed to air during transfer of the substrates. The absence

of oxygen in the bulk Fe evidences that the oxygen uptake was not during the sputter deposition

process. Interestingly this surface oxide is absent for the Fe/Al/Si substrate. The oxide layer might

have been etched away during the steps prior to Auger depth profiling. The oxygen concentration

varies with the Al composition, implying the presence of an Al-oxide. The reported at% of O is more

than that of Al only at the Al/Si interface, which as mentioned before, has to do with the native

Si-oxide. The Al-oxide formed during the sputter deposition process owing to the large affinity of Al

for oxygen. This Al-oxide layer sandwiched between the Fe and Si is responsible for the increased


(a)

(b)

(c)

(d)

500 nm

500 nm

500 nm

2 m T = 750oC

T = 750oC

T = 750oC

T = 800oC

Figure 3.2: Comparison of MWNT growths with and without the Al buffer layer

MWNT yield.

In-stiu reflectivity monitoring of substrate during the pre-MWNT growth step

The goal of the pretreatment procedure is to convert a catalyst film to nanoparticles for carbon

nanotube growth. Fig.3.4 shows the time evolution of the substrate temperature (hollow circles) and

the reflected light intensity (solid lines) during pretreatment step. For this study, the temperature

was ramped in a hydrogen ambient (P=100 Torr, flow rate =100 sccm), the annealing temperature

was 550oC and a hold time 10 minutes. Subsequent to the annealing step, the temperature was

ramped to 750oC, the set MWNT growth temperature. The reflectivity of two surfaces are shown

here, 10 nm Al/Si and 2.5nm Fe/ 10 nm Al/Si. The reflectivity of a bare Si film does not change

much in the temperature range studied, so all changes in the reflectivity plot should be due to the

deposited films. For Al/Si the reflectivity of the substrate remains approximately the same to 640oC,

subsequent to which there is a drastic reduction in reflectivity. This is due to the melting of the

residual Al in the film (Al, melting point = 660oC). In contrast, for the Fe/Al/Si the reflectivity

of the film starts dropping at 200oC, with a sharp drop in reflectivity around 550oC. This sharp

drop is probably due to surface roughening, coincident with the formation of catalyst particles. On

increasing the temperature, after the annealing step, the reflectivity starts increasing. It reaches a

plateau on holding the substrate temperature at the set MWNT growth temperature,corresponding

to ∼ 95% of the initial intensity. The interferometer scans for the MWNT growth were obtained


Fe

Si

Fe

Al

Si

100

80

60

40

20

0

at%

86420 sputter time (secs)


13nm Fe/ Si

5nm Fe/10nm Al/Si

C O Al Si Fe

Figure 3.3: Auger depth profile of as-sputtered films with and without the Al buffer layer. Thenominal thickness of Fe directly deposited on the Si substrate was 13nm, while 5nm of Fe wasdeposited on 10 nm Al, sputter deposited on Si

only after the reflectivity attained a steady value.

3.3 MWNT growth

Subsequent to the annealing step, the temperature is ramped up to the desired growth temperature.

After letting the temperature stabilize, the precursor gases, a mixture of ethylene and hydrogen,

were flown into the reactor at predetermined rates, and the interferograms recorded. Typical MWNT

growth durations were 10 minutes. The parameter space for MWNT growth is broad, an example of

catalyst composition was cited above. In the next chapter we report the dependencies of particle size

(determined by catalyst film thicknesses and annealing pressures) in determining the morphology

of the 1-D carbon nano structures. In this chapter we report the effects of temperature, pressure

and precursor chemical composition on MWNT growth rates and how well they can be predicted by

using the model developed. The MWNTs grown were characterized by SEM, TEM and Raman spec-

troscopy. Details of growth conditions will be described when discussing the results of a particular

set of experiments.


Figure 3.4: Time resolved reflectivity plots off the catalyst substrate during the pre-MWNT growthregime. Also plotted are the corresponding chamber temperatures.

3.4 Kinetic Model for MWNT growth

A simple kinetic model has been developed to quantify the synthesis of 1D nanomaterials (82).

The model developed here relies on that work. For this work we assume that the Fe catalyst

nanoparticle is in a liquid state under the MWNT growth conditions. This is a valid assumption

given the catalyst particle size and the corresponding suppression of the Fe-C eutectic temperature,

from Gibbs-Thompson effect. In general, these calculations are done taking into consideration only

the vapor-catalyst interfacial energy. The presence of a second interface between the catalyst and

the substrate is expected to further suppress the melting point, since the interfacial energy of a liquid

catalyst-solid substrate is lower. For the given size of catalyst particles, the vapor liquid solid (VLS)

process, discussed here, is the dominant mechanism for most 1-D materials. Carbon is obtained by

the thermal decomposition of ethylene. The Fe particles get saturated with carbon by reaction with

the vapor phase, and on supersaturation the extra carbon precipitates in the form of CNTs.

3.4.1 Mass Transport processes

Akin to (60) we consider four mass transport processes,Fig.3.5(a). First, the vapor phase transport

of molecules to the catalyst surface. Next is the vapor-liquid catalyst interaction, decomposition

reaction of gaseous molecules at the catalyst surface followed by transport of the carbon atoms

across the vapor-liquid interface. The next process is the liquid phase transport of C atoms across

the liquid catalyst nanoparticle. The final step is the incorporation of the C atoms into the growing


MWNT across the catalyst-tube interface. Such mass transfer steps have been considered for almost

all models describing 1D nanomaterial growth process. The novelty of this model over previous

models is instead of looking into the mechanism of each transfer process we consider the energetics

involved. Each step requires a thermodynamic diving force, in the form of a gradient in chemical

potential along a phase or a drop in the chemical potential across an interface (Fig.3.5 b). The mass

flux in each of the transfer processes is described in terms of these chemical potential changes. A

steady state is assumed, i.e. there is no accumulation of C atoms in any of the steps. This implies

the flux in each step is the same and the overall flux is determined by the slowest mass transfer step,

the ”rate limiting step”.

Figure 3.5: (a) Schematic of the four mass transfer processes. Figure (b) is a schematic of thechemical potential drop that results in the carbon flux from the vapor phase across the vapor-liquidinterface, through the liquid catalyst and finally across the liquid-solid interface to form the MWNT.

Diffusive Transport

Vapor Phase Transport

The first step is the vapor phase diffusion of the C containing precursor molecules to the catalyst

surface. The steady state condition in spherical co-ordinates is given by the relation:

∂2CVc

∂r2+

2

r

∂CVc

∂r= 0


where, CVc (r) is the concentration of the C-containing gas in the vapor phase. The boundary

conditions for the above equation are CVc (rp) = CV Lc ;CVc (∞) = CV∞c , where CV∞c and CVL

c are the

concentrations of the gas in the bulk and at the vapor-catalyst interface respectively. On solving,

the variation in C concentration as a function of distance from the catalyst particle (radius = rp) is

obtained:

CVc (r) = CV∞

c − [CV∞c − CVL

c ]rp

r(3.1)

The diffusive flux in the vapor phase is given by the relation

|JV| = Dv∂CV

c

∂r‖r=rp (3.2)

On substituting (3.1) above, and converting the concentration of the gas at the bulk and the interface

to their corresponding chemical potentials, µV∞c and µVL

c the vapor phase flux can be calculated.

JV =DvCV∞

c

RT[µV∞

c − µVLc

rNT] (3.3)

The catalyst particle size controls the outer diameter of the MWNT (83), and for simplicity it is

assumed, here, that the radius of the MWNT, rNT , is same as that of the catalyst particle, rp.

Liquid phase Diffusion

Diffusive flux of C through the liquid catalyst particle was similarly obtained. For simplicity,

the catalyst particle was assigned a cylindrical shape. Because of this simplification 1D diffusion of

carbon species through the catalyst can be assumed. For a steady state 1D transport,

JL = DLCLV

c − CLSc

rNT(3.4)

where CLVc and CLS

c are respectively the C concentrations at the liquid catalyst-vapor and catalyst-

MWNT interfaces. The relation, µ = µo+RT ln(γx) is used to relate the liquid state flux in eqn.( 3.4)

to a chemical potential change.

JL =DLCL

c

RT[µLS

c − µLVc

rNT] (3.5)

Interfacial Transport

Transport across the Vapor-Liquid Catalyst interface

The composition at the vapor-liquid interface is different from the equilibrium composition. The

corresponding drop in chemical potential is the driving force for transport of carbon across the

interface. The net flux across the interface, hence will depend on the magnitude of deviation of the

interface composition from the equilibrium. This simplistic model is valid only for small magnitude

of driving forces. The flux across the interface will also depend upon the net interface attachment


rate,RN,L, and the number of available sites on the liquid catalyst surface,σL.

JVL = RN,LσL(t) =kVL

RT[µVL

c − µLVc ] (3.6)

The first order reaction actually includes three processes, the attachment of the molecule to the

liquid surface, molecular dissociation and or reaction at the catalyst interface and finally the carbon

incorporation into the liquid surface. The reaction constant, kVL, is given by the relation:

kVL = σL(t)ν exp(−4G∗,VL

kBT) (3.7)

Here 4G∗,V Land ν are respectively the effective activation energy for all the vapor-liquid transfer

processes and the frequency of successful collisions of the gas molecules with the catalyst surface.

The number of available sites on the liquid catalyst particle has a temporal dependence as will be

shown in a later section dealing with catalyst activation and poisoning.

Transport across Liquid-Solid interface

Similar to the transport across the vapor-liquid interface, the driving force across the liquid

catalyst-solid CNT interface is driven by the drop in chemical potential of carbon from the liquid

catalyst to the solid nanotube.

JLS = RN,SσS =kLS

RT[µLS

c − µSc ]

kLS = σSν∗ exp(−4G∗,LS

kBT)

The stable carbon phase, under the growth conditions is graphite. But the carbon is precipitating

out in the form of nanotubes. Hence it is necessary to find the chemical potential of carbon in the

MWNTs. This can be done by adding to the chemical potential of graphite the energy required to

bend the planes into CNTs (63). The total elastic energy stored per unit length in a MWNT, of

inner radius rin and outer radius rNT , formed by bending of graphite planes is given by:

Ebend =πEa2

o

12ln(

rNT

rin) (3.8)

where E is the Young’s modulus of MWNT and ao the inter-planar spacing in graphite. Also

from Gibbs Thompson effect, for a given MWNT-vapor interfacial energy, γSV, the curvature of the

MWNTs results in a chemical potential increment by

4µ =γsv

CSc (rNT − rin)

(3.9)

where CSc is the concentration of C in the MWNT. Accounting for (3.8) and (3.9) the flux across


the liquid-solid interface is given by the relationship:

JLS =kLS

RT[µLS

c − [µSc,graphite +

1

CSc

(Ea2

o

12(r2NT − r2

in)ln(

rNT

rin) +

γsv

rNT − rin)]] (3.10)

3.4.2 Steady State growth rate

As mentioned before a steady state condition is assumed. Hence solving for the four flux equations

and eliminating the intermediate chemical potentials,the carbon flux from the vapor to the nanotube

is determined to be:

JVS =[µV∞

c − [µSc,graph + 1

CSc(

Ea2o

12(r2NT−r2in)ln( rNT

rin) + γsv

rNT−rin)]]

RT[ 1kVL

+ 1kLS

+ rNT

DvCV∞c

+ rNT

DLCLc

](3.11)

The corresponding steady state growth rate for the MWNT can be obtained by dividing the carbon

flux with the concentration of carbon in the MWNT.

vss =JVS

CSc

(3.12)

3.4.3 Thermodynamic Driving force for MWNT growth

The driving force for growth of the MWNT, is given by the relation ∆µ = µV∞c − (µS

c,graph +1

CSc(

Ea2o

12(r2NT−r2in)ln( rNT

rin))), as obtained from eqn.(3.11). Therefore to estimate the driving force for

growth of the nanotube the chemical potential for C in the precursor gas (ethylene was used for this

study) has to be determined. A way of doing so is to assume that gaseous C atom is in equilibrium

with ethylene vapor and then estimate the corresponding chemical potential of C. This can be

calculated from the following set of chemical reactions:

(1) C2H4(g)↔ 2C(s) + 2H2(g); ∆G1 = ∆Go1 + RT ln[

(aSC)2(pH2

)2

pC2H4

]

(2) 2C(s)↔ 2C(g); ∆G2 = ∆Go2 + RT ln[

p2C

(aSC)2

]

(3) C2H4(g)↔ 2C(g) + 2H2(g); ∆G3 = ∆Go3 + RT ln[

(pC)2(pH2)2

pC2H4

] (3.13)

The chemical potential of C in the vapor phase, in equilibrium with ethylene, is given by the relation:

µV∞C = µoV

C + RT ln(pC), where µoVC is the chemical potential of pure C vapor at 1 atmosphere, and

pC is the effective partial pressure of C corresponding to the chemical potential µV∞c . To calculate

this pressure we assume that the reaction (3) is in chemical equilibrium. Hence ∆G3 = 0, and we


get from eqn.(3.13),the partial pressure of C in the vapor phase:

p2C = [

pC2H4

(pH2)2

] exp

(−∆Go

3

RT

)It is also known that ∆Go

3 = ∆Go1 + ∆Go

2 = ∆Go1 + 2(µoV

c − µoSC ) and the stable solid C phase is

graphite, and hence

µV∞c − µo,S

c,graph = −1

2∆Go

1 +RT

2ln[

pC2H4

(pH2)2]

Replacing the partial pressures of ethylene and hydrogen by their molar fractions and the absolute

pressure,P, the total thermodynamic driving force for the MWNT formation , ∆µ = µV∞c −µS

c,MWNT,

equals

∆µ = −1

2∆Go

1 +RT

2ln[

xC2H4

(xH2)2]− lnP − 1

CSc

[Ea2

o

12(r2NT − r2

in)ln(

rNT

rin)

](3.14)

This driving force drives all the kinetic processes, vapor phase diffusion, vapor-liquid transport,

liquid phase diffusion and the final transport across the liquid-solid interface to form the MWNTs.

Eqn.(3.14) also reveals the parameters that can be used to control this driving force. The main

contenders are temperature, absolute pressure, the composition of the gas phase which in turn is

determined by the flow rates and also the radius of the catalyst particle since studies have shown a

relation between radius of MWNTs and catalyst particle sizes. Formation of MWNT also creates a

vapor-MWNT interface. Hence the energy to form this interface, eqn.(3.9), has to be subtracted from

the total thermodynamic driving force to get the net driving force for the reaction. A thermodynamic

length scale thus can be defined which formulates the balance between driving force and interfacial

energy cost.

rTh =γsv

CSc ∆µ(1− rin

rNT)

(3.15)

The magnitude of this length scale vis-a -vis the radius of the tube determines whether conditions

are favorable for MWNT growth. If the two length scales are the same, the net C flux from vapor

to MWNT is zero. If the radius of the tube is greater than rTh then the nanotube grows, while if

its smaller then the interface cost for growing the CNTs is too high and the MWNTs will not form.

3.4.4 Rate Limiting Steps

The steady state assumption of the kinetic MWNT growth model implies constant flux across the

four mass transfer steps. Hence the flux of the MWNT growth process will be controlled by the

slowest step or the rate limiting step. This rate limiting process can be either one or both of the

transport steps across the two interfaces, vapor-liquid and liquid-solid. On the other hand, diffusive

transport of the C atoms or the C bearing molecules across the vapor or/and liquid phases could

also control the growth rate of the MWNT. A kinetic length scale, rKin, can be defined as a balance

between the diffusive and interfacial kinetic processes;rKin = <DCc><k> . The effective diffusion term


vapor - liquid interface limited

liquid - solid interface limited

vapor

CNT/solid

liquid

(a)

µcVµcVL

µcLVµcLS

µcS

µcV

µcV

µcLV

µcLV

µcVL

µcVL

µcLS

µcS

µcSµcLS

limited vapor phase diffusion

limited liquid phase diffusion

vapor

CNT/solid

liquid

(b)µcV µcVL

µcLV µcLS µcS

µcV

µcV

µcVL

µcVL

µcLV

µcLV

µcS

µcS

µcLS

µcLS

Figure 3.6: The rate limiting steps for the MWNT synthesis process. The driving force for theMWNT growth approximately equals the chemical potential drop across the rate-limiting step.Fig.(a) is a schematic of the chemical potential drop for interface-limited growth, with the twolimiting cases vapor-liquid interface and liquid-solid interface shown. Fig.(b) is a schematic of thediffusion limited MWNT growth processes, limited liquid and vapor phase diffusivities respectively.The dotted line is a schematic of the chemical potential change for a growth condition where therate limiting step is a combination of the diffusive and interface transport processes.

,< DCc >, and the effective interface reaction term,< k >, being defined as

< DCc >= [1

DvCV∞c

+1

DvCLc

]−1

< k >= [1

kVL+

1

kLS]−1

The overall flux for the MWNT growth process, eqn.(3.11), then can be re-formulated in terms of

the rKin and rTh as

JVS = (∆µ

RT) < kCc > (

1− rTh

rNT

1 + rNT

rKin

) = (∆µ

RT) < DCc > (

1− rTh

rNT

rNT + rKin) (3.16)

If the growth process is interface limited, rKin >> rNT; opposite is the case for diffusion limited

growth. Schematic of the chemical potential distribution for all the four possible cases are shown

in Fig. 3.6. For diffusion limited growth (Fig. 3.6(b)) the driving force is used up to drive diffusion

across the relevant phase. For interface limited transport Fig. (a) the driving force for the growth

is used up mostly to account for the chemical potential drop across the corresponding interface. A

case in point is the transfer of C across the vapor-liquid interface. In this case the driving force is

used up to drive transport across the vapor-liquid interface. Hence the chemical potential of the

vapor-liquid interface will approximately be equal to the potential in the vapor phase, while the


potential of C at the liquid-vapor interface approximates that of the MWNT (lower left Fig. 3.6(a)).

3.4.5 Catalyst Activation and Poisoning

Figure 3.7: Keeping count; (a) available attachment sites on the catalyst surface, (b)the numberof catalyst particles initiating MWNT growth in the time interval dt. The mean time for catalystactivation is τn, while the mean time for catalyst poisoning is τp. No and Ng are respectively thetotal number of particles and number of catalyst particles that have resulted in MWNT growth attime ’t’

As mentioned while describing the interferometer set-up that the main focus of this article is in

modeling the steady state condition because of lack of experimental data on catalyst activation and

poisoning. But, for the sake of completeness in terms of a kinetic model formulating MWNT growth,

we include here the evolution of the average height of the MWNT films. The fitting parameters

for formulating the average length of the MWNT film are the steady state velocity, vss, that is

experimentally determinable, and the mean lifetimes of catalyst activation and poisoning. We assume

a mean lifetime for catalyst poisoning to be τp, where τp = τp,o exp(Ep/RT), Ep being the activation

energy for the poisoning process.

dσa = −σadt

τp(3.17)

∴ σa = σoexp[−t/τp] (3.18)

where σa is the number of available binding site on the catalyst particle at time ’t’, that initially


had σo binding sites. If all the catalyst particles were growing at the same time then, the average

catalyst activity will be the same as that of (3.18). But all catalyst particles are not activated at the

same time. Assuming mean lifetime for catalyst activation to be τn (again,τn = τn,o exp[En/RT], En

being the energy barrier for the catalyst activation process) the following relation is obtained.

dNg = [No −Ng]dt

τn(3.19)

where Ng is the number of catalyst particles growing CNTs at time t and No the total number

of catalyst particles. Solving for the above differential equation, knowing the boundary conditions

Ng(0) = 0,Ng(t) = Ng; results in

Ng(t) = No(1− exp[−t/τn])

The average number of binding sites available per catalyst then is given byNgσa

Nowhich equals

σL,avg(t) = σoexp[−t/τp](1− exp[−t/τn]) (3.20)

This value when substituted in eqn.(3.7) controls the flux of C atoms across the vapor-catalyst

interface, and hence is important in determining the growth rate of the MWNT. At intermediate

growth times τn < t < τp the MWNT growth rate is the steady state growth rate, while during

the incubation period it is influenced by the catalyst activation mechanism and at longer timescales

the rates are determined by the catalyst poisoning processes. As a first approximation the average

length increment of the MWNT forest in the time interval ’dt’ will be given by the relation

dLMWNT =vssσa,avg(t)dt

σo.

∴ LMWNT(t) =

∫ t

0

vssσa,avgdt

σo

= vssτp[1− exp[−t/τp] +τn

τn + τpexp[−t(

1

τn+

1

τp)]− 1] (3.21)

3.5 Results and Validation of the Kinetic Model

In this section interferometer scans obtained are presented and the data evaluated in terms of the

growth model developed in the previous section. Three sets of data will be discussed. The first

set is a temperature dependent growth of MWNT at intermediate pressures. For this set of data,

growth rates are determined, the corresponding activation energy and hence the rate limiting step

identified. The second set of data is from pressure dependent growth runs, and the final set of data

is again temperature dependent growth runs performed at atmospheric pressures. Results obtained


Figure 3.8: SEM images of the MWNT forests obtained after the completion of growth runs in eachof the above cases. These heights, marked by rectangles are plotted in Fig.3.9(c). A tilted sampleholder was used for the SEM imaging, with the angle of the tilt being 45o. Thus to obtain the actualheight of the CNTs corrections were made to compensate for the tilt angle.

from the first two data sets are then used along with the kinetic model to predict the results for the

third dataset, in an attempt to test the accuracy of the developed model.

3.5.1 Temperature dependent MWNT growth at P=265 Torr

For this set of experiments, the absolute pressure of the reactor chamber was maintained at 265

Torr. The growth temperature was increased in increments of 25oC from 700oC to 800oC. The mass

flow rates of hydrogen and ethylene were maintained at 110 sccm and 155 sccm respectively, during

the entire growth duration. Typical growth times are 600 seconds except for the 700oC sample, for

which the growth duration was 900 seconds. This was done to compensate for the low growth rates

observed at this temperature and obtain enough number of interfering fringes in the time resolved

reflectivity scans. The final heights of the MWNTs formed were measured using SEM and are shown

in Fig.3.8. Increasing growth temperatures result in the formation of straighter, taller and denser

MWNTs.

The corresponding interferograms are shown in Fig.3.9(a). At lower temperatures the curves

show pronounced oscillations in intensity. With increasing temperatures the oscillation frequency

of the reflectivity plots increase significantly, alluding to faster growth rates. At the same time the

amplitude of the oscillations decrease and the fringes become less discernible. The intensity of the

background signal also increases with temperature.

The background intensity is attributed to the laser beam reflected off the top of the CNT film,

while the oscillations are a result of the interference of this beam and the beam reflected off the


1.0

0.8

0.6

0.4

0.2

Nor

mal

ized

Inte

nsity

700600500400300200100 Time(secs)

Growth started

Growth stopped

(a) 700oC 725oC 750oC 775oC 800oC

30x103

25

20

15

10

5

0

Hei

ght o

f MW

NT

(nm

)

10008006004002000 Growth time(secs)

growth stopped

growth stoppedT=700 oC

(b) 700oC 725oC 750oC 775oC 800oC

70

60

50

40

30

20

10

0

Gro

wth

rate

s (n

m/s

ec)

6004002000 Growth time(secs)

(c)

700oC 725oC 750oC 775oC 800oC

Figure 3.9: Normalized interferometer scans for temperature dependent growth of MWNTs at pres-sures of 265 Torr, Fig (a). The heights obtained from the interference fringes are plotted in Fig(b), while Figure (c) plots the growth rates of the MWNTs. The solid dark lines in (c) mark thelinear regime for MWNT growth, corresponding to the steady state growth conditions, described inthe kinetic model. The corresponding growth rates from Fig (c) are used in the article for analy-sis/validation of the growth model.


interface between the MWNT and the substrate. Reflectance of a beam incident normal to the

surface is given by the relation:

R =(1− n)2 + k2

(1 + n)2 + k2= 1− 4n

(1 + n)2 + k2

where n,k are the real and imaginary parts of the refractive index of the reflecting surface. Increase

in density of the MWNT films, increases the n and k thereby increasing the reflectivity of the top

surface and hence the background intensity. At the same time density of the CNTs attenuates

the intensity of the beam reflected off the MWNT-substrate interface in accordance with the Beer-

Lambert law. These twin effects of increasing density of the MWNT films explain the decrease in

prominence of the interference fringes.

Fig. 3.9 (b) plots the MWNT heights obtained from the interference plots as a function of growth

time. As mentioned above, SEM images of the final heights were recorded from the same region of

the MWNT film that was probed by the laser beam for the interferometer curves. These heights

marked by rectangles are plotted in the figure also. Knowing the heights, the next step was to plot

the experimental growth rates, Fig. 3.9 (c). For the 700oC case, the maximum growth rate achieved

was 5.2 nm/sec obtained after approximately 350 seconds of growth. Increasing the temperature

to 725oC increases the growth rate to a maximum of 14 nm/sec achieved after a growth time of

approximate 280 seconds. Increasing temperatures further increased the growth rates, with growth

rates of 60nm/sec reported at 800oC, i.e. more than an order of magnitude increase from that

reported for 700oC. The observed growth rates in this study are relatively lower compared to those

reported in the literature. The reason for this is attributed to the cold-wall CVD reactor used

in contrast to those used in other studies. The other interesting feature observed was that with

increasing temperatures, the time required to reach steady state rates decreased. The linear, steady

state regime of the MWNT growth described by the model are marked by solid straight lines in

the in-situ MWNT height vs. growth time plot. The corresponding steady state growth rates from

Fig.(b) are used to determine the activation barrier for the rate limiting step.

The kinetic model developed in the last section describes four different mass transfer steps, each

characterized by either a diffusivity term or a rate constant. Both of these terms are generally as-

sociated with an Arrhenius type equation, described by a pre-factor, and an exponential term that

contains the activation energy for that process. Given the relatively small temperature range of the

current study, the activation barrier is approximately constant. Hence the motivation for the temper-

ature dependent experiments was to determine the activation barrier related to the MWNT growth

process and therefore identify the rate limiting step. The steady state growth rates determined

from the reflectivity plots are used for this purpose. The MWNT radius used for the calculations

has an outer radius of 5.8 nm. This is the same as the mean catalyst particle size, obtained under

the given growth conditions (84). The inner diameter of the MWNT was determined by solving


5.5

5.0

4.5

4.0

3.5

3.0

ln(vRT/∆µ)

1.02x10-31.000.980.960.94

1/T (K-1)

y = -23261x + 23.538linear fit

(a)

35x103

30

25

20

15

10

5

0

MW

NT

heig

ht (n

m)

10008006004002000 time(secs)

growth stoppedT = 700 oC

growth stopped(b) Experimental 700oC Experimental 725oC Experimental 750oC Experimental 775oC Experimental 800oC

fit 700oC fit 725oC fit 750oC fit 775oC fit 800oC

Figure 3.10: Fig. (a) is an Arrhenius plot of the temperature dependent thermal CVD growth ofMWNT in the temperature range 700-800oC. The activation barrier obtained from the linear fit is∼190 kJ/mol. Fig. (b) is a plot of the experimental interferometer heights and the correspondingtheoretical fits of the growth model. The fitting parameters being the experimental growth rates,and the mean lifetime for catalyst activation and poisoning.

for maxima condition of the change in chemical potential driving the formation of MWNT for a

given outer radius (63), which for an outer radius of 5.8 nm was 3.93 nm. The interfacial energy

γsv assumed is 0.077J/m2 (85) , and the Young’s modulus 1 TPa (86). The molar concentration

of C in the CNTs was obtained by the relation CMWNTc = Cgraphitec (1 − rin

2

rNT2 ), with Cgraphitec

assumed to be 1.8 × 105mole/m3 (87). The absolute pressure,P, for this set of experiments was

265 Torr and the molar fraction of the hydrogen and ethylene at the steady state growth condition

was approximated to be equal to their molar volume flow rate fractions. The remaining term to be

evaluated is the standard free energy of decomposition of ethylene at the growth temperature. This

can be obtained from the standard free energy of formation of ethylene from graphite and hydrogen

at the growth temperature. The thermochemistry data needed for this calculation, e.g. the standard

heats of formation of ethylene, and the constant pressure heat capacities, was obtained from the


NIST chemistry webbook (51). The experimental steady state growth rates were then normalized

by the calculated ′∆µ/RT′ from the model. Fig.3.10(a) is a logarithmic plot of these normalized

growth rates as a function of ’1/T’. The Arrhenius plot so obtained is approximately linear, giving

an activation barrier for the MWNT growth process of 192 kJ/mol under these conditions.

Table 1. contains a list of activation energy barriers reported in literature for the CNT growth

process. Diffusion limited processes have activation barriers typically in the range of 35 - 140 kJ/mol

and hence cannot be the rate limiting step. C diffusivity in liquid Fe is of the order of 10−5cm2/sec

, which leads to a growth rates in the order of mm/sec for T = 750oC , hence this cannot be the

rate limiting step. For catalyst in the solid state typical C diffusivities are 10−8cm2/sec giving

approximate growth rates of 100 µ/min , which is still much higher than the observed growth rates

here. Hence the MWNT growth process in this case has to be interface limited. The specifics of

which interface is limiting the growth is not uniquely identified, since the first order reaction rate

assumed for the C jump across the interfaces comprises of more than one reaction step. References in

Table 1 assign Ea values in the proximity range of 190 kJ/mol to the vapor-liquid interface processes.

Fig. 3.10(b) is a plot of the experimental heights determined from the interferometer studies

and the corresponding theoretical fits as predicted by (eqn.3.21) The fitting parameters being the

average experimental steady state growth rate and the mean life time for catalyst activation and

poisoning. The activation barriers obtained from an Arrhenius plot of the fitting parameters used

for the temperature dependent growth runs, τn and τp , were respectively 180 kJ/mol and 205

kJ/mol. The mean life time for the activation and poisoning for the T=750oC run used for fitting

the data is 2100 seconds and 115 seconds. The activation barriers obtained are remarkably close

to that reported in (76). They identify C dissolution(Ea = 210 kJ/mol) as the catalyst activation

step. The activation barriers for the poisoning of the catalyst particles by gas-phase decomposition

products(Ea = 260 kJ/mol) is also fairly close to that obtained from the catalyst poisoning mean

lifetime parameter values.

1.0

0.8

0.6

0.4

0.2

Inte

nsity

500400300200100Time(secs)

0.35

0.30

0.25

0.20

Intensity

1600140012001000Time(secs)

300

200

100

0 Pre

ssur

e(To

rr)

start growth

stop growth stop growth

restart growth

Figure 3.11: Time evolution of pressure and reflectivity during the interrupted growth experiment.


There is a finite time lag between the the onset of ethylene flow and the growth conditions

reaching a steady state in terms of pressure etc. set for a particular growth. This time lag and

not a catalyst activation could explain the incubation regime of CNT growth before the steady

state growth rates are achieved. To evaluate the validity of this hypothesis, an interrupted MWNT

growth experiment was performed, Fig.3.11. MWNT growth was stopped by evacuating the chamber

and cooling down the substrate. After waiting for 5 minutes the reactor temperature was ramped

back up to the 750oC, same as before interruption. On introduction of ethylene, growth resumed

instantaneously. This is in contrast to a time lag at the onset of growth (as observed in longer

time interval for the first interference fringe to appear). This proves that initial incubation period is

related to the mean life time of some activation process and is not due to growth conditions reaching

a steady state. Since the catalyst was already activated, on resumption of ethylene flow the MWNT

films started growing instantaneously.

(On a side note, while talking about numbers it has to be mentioned that the contribution of the

interfacial energy term to the net thermodynamic driving force is small. The ’rTh’ value calculated

for the given condition is only 0.04 nm, implying that under these conditions the MWNT will always

grow).

3.5.2 Pressure dependent growth runs at T = 750oC

Prior experiments have suggested the dependence of MWNT growth morphology and growth rates

on the absolute pressure. In separate studies, a transition from MWNT to carbon nanofibers has

been observed with increasing pressure (this is discussed in details in Chapter 4). This transition was

a function of the pressure and also of the catalyst particle size. The thermodynamic driving force for

the nanotubes described also suggests a pressure dependence. This set of experiments were therefore

designed to explore the pressure dependence of MWNT growth from catalyst particles obtained by

annealing 2.5nm Fe/10nm Al/ Si sample. For this set of experiments the growth temperature was

held at 750oC. The growth pressures used were 151 Torr, 265 Torr, 315 Torr, 405 Torr and 760 Torr.

The total gas flow during the experiment was maintained at 250 sccm, with the H2/(C2H4 + H2)

flow varied from 0.3, 0.4, 0.4, 0.5 and 0.6 respectively.

Fig.3.12(a) plots the normalized intensity curves recorded for the pressure dependent runs. The

frequency of oscillations increase with an increase in pressure. Unlike the temperature dependent

growths, the amplitude of oscillations and the background reflectivity are almost the same, implying

similar densities of the growing MWNT films. The signal attenuates much faster at higher pressures

and reaches the constant value faster. For the top four plots, interference fringes could be detected

untill the end of the 10 minute growth scan. In contrast for the P = 760 Torr run, the temporal

frequency first increases, reaches a constant value, then decreases and finally disappear. This implies

termination of growth for the high pressure condition. The growth rates obtained from the interfer-

ograms are plotted in Fig. (b). For the P=760 Torr case, the critical height was approximated by


Figure 3.12: Pressure dependent growth of MWNT at T=750oC. Fig. (a) plots normalized intensityas obtained from the photovoltaic currents. Increasing pressure increases the growth rate of theMWNT as is evident from (a) and plotted in (b). Fig. (b) also shows that higher the pressureshorter is the time to reach steady state values. The catalyst poisoning mean lifetime is also shorterat higher pressures. (c) SEM images of the MWNT revealing their final heights at pressures of 151,405 and 760 Torr respectively.

dividing the final SEM height of the CNTs by the number of fringes observed in the scan before the

fringes disappeared from the reflectivity plot. The average steady state growth rates increase from

an average of 20 nm/sec at P = 151 Torr to 35 nm/sec at P = 760 Torr. The growth rates reach

their steady state value faster with increasing pressure, 300 seconds for the P = 151 Torr growth as

opposed to 100 seconds for growth at atmospheric pressures. This implies a decrease in the mean

lifetime for catalyst activation. The P = 760 Torr growth also shows a decay in growth rates after

reaching a steady state. This possibly implies a decrease in mean lifetime of the catalyst poisoning

as a function of pressure. The final heights of the MWNT films grown were obtained from their

SEM images(e.g. Fig.3.12(c) ) and plotted along with the experimental heights from the reflectivity

curves in Fig.3.12(b). The SEM images show that the MWNT film height increases initially with


absolute pressure and then decreases, consistent with increased growth rate and poisoning at high

pressures.

The net driving force for the MWNT reaction actually decreases with increasing pressure,

eqn.(3.14), Fig.3.13(a). But the experimental results show an opposite trend, the steady state

growth rates increasing with pressure. To reconcile these two contrasting results, we note that the

pre-exponential factor for the rate constant for the vapor-liquid interface has an attempted frequency

term, ν. The collision frequency of gas molecules is given by the relation ν =< vavg > / < λmfp >,

where < vavg >= 8kBTπm

1/2is the average velocity of the gas molecules and < λmfp >= kBT√

2πd2P is

the mean free path for the gas molecules for an absolute pressure ,P. Taking into account that the

number of successful attempts should be proportional to the number of ethylene molecules colliding

with the catalyst, the attempt frequency should be of the form, ν = νoxC2H4P . Hence the steady

state growth rates for the conditions studied, that takes into account temperature, pressure and

compositional changes in the gas will be of the form :

vss ≈ (∆µ

RT)< k∗V L >

CScxC2H4

P (3.22)

Hence knowing the steady state growth rate for one condition, the growth rate for the other

conditions can be predicted. Taking the growth rate for P=265 Torr, T= 750oC case to be the

fitting parameter, the steady state growth rates for the remaining MWNT growth runs in the

pressure dependent set was predicted. This was done after accounting for the pressure induced

changes to the MWNT inner and outer radius. This theoretical fit is plotted as a solid line in

Fig.3.13(a). For comparison the experimental growth rates from the time resolved reflectivity plots

are also included. The remarkable proximity of the two plots attest to the validity of the growth

model. Hence with an increase of pressure the steady state growth rate increase but at a decreasing

rate.

Finally equation (3.21) was used to obtain theoretical fits for the height of the CNTs as deter-

mined from the interferograms and SEM imaging . The fitting parameters, similar to the temperature

dependent growth, being the experimental growth rates, and the catalyst activation and poisoning

mean lifetimes, τn and τp. τn values used for the fit ranged from a high of 270 seconds for the P =

151 Torr case, decreased to 50 sec for P = 405 Torr run, and bottomed out at 11 seconds for the P

= 760 Torr study. Similarly the mean lifetimes for the catalyst poisoning used for the fit decreased

from a high of 4500 seconds for the P = 151 Torr, to a low of 430 seconds for the P =760 Torr case.

From the temperature dependent growth studies we know both the catalyst activation and poison-

ing steps are related to the vapor-catalyst interface. Hence the corresponding rate constants for

activation and poisoning will have a similar dependence on pressure as that of the rate constant for

the mass transfer across the interface. Further studies are required to establish the functional form

of dependence of pressure on these mean lifetimes. Therefore to summarize, increasing pressures

increase the maximum attainable growth rates, but at the same time terminates growth faster, due


35

30

25

20

gro

wth

rate

s(nm

/sec

)

1.00.80.60.40.2 Pressure(atm)

68x103

64

60

56 ∆ µ

(J/m

ole)

0.40

0.35

0.30

0.25

0.20

0.15

xP (atm)

(a)

20x103

15

10

5

0

Hei

ght o

f tub

e (n

m)

10008006004002000 growth time (secs)

growth stopped

(b) Experimental 151 Torr Experimental 265 Torr Experimental 315 Torr Experimental 405 Torr Experimental 760 Torr

fit 151 Torr fit 265 Torr fit 315 Torr fit 405 Torr fit 760 Torr

Figure 3.13: Fig. (a) plots the experimental growth rates ’o’ and the predicted growth rates (solidline) for the pressure dependent growths. The growth rates were predicted by extrapolating theaverage experimental growth rate at P=265 Torr after accounting for the changes in pressure andgas composition. Increasing pressures decrease the driving force for MWNT growth, but results inenhanced kinetics accounting for the increased growth rates. Fig. (b) plots the experimental andtheoretical fits for the MWNT heights. With increase in pressure the height of the MWNT filmsfirst increase and then decrease.


to the simultaneous faster kinetics of catalyst poisoning. Hence with increasing pressures MWNT

heights first increase and then decrease beyond a threshold pressure.

While discussing the temperature dependent growth runs, mass transfer at the interface was

identified as the rate limiting step. But which of the two interfaces (vapor-catalyst or the catalyst-

CNT) that limits growth was not identified. From analysis of the catalyst deactivation it was

established that soot formation on the catalyst particles is the poisoning process. From the pressure

dependent studies, increase in collision frequency of the C precursor gas with the catalyst was found

to be responsible for the enhanced kinetics. Both of these processes are related to the vapor-liquid

interface and hence we can attribute the vapor-catalyst interface to be the rate limiting step for the

growth conditions studied.

3.5.3 Temperature dependent MWNT growth at P=760 Torr

The final set of experiments described here were performed at atmospheric pressures, the temperature

being varied from 700oC to 775oC in increments of 25oC, while the mass flow rates were kept constant

at 150 sccm for hydrogen and 100 sccm for ethylene. The corresponding time resolved reflectivity

plots are shown in Fig.3.14(a). Similar to the temperature dependent study at lower pressures, we

see that the temporal frequency of the fringes increase with temperature, but at the same time they

become less prominent. The scans are similar to the pressure dependent plots, in the sense that the

growth rates are higher, but also at the same time the height of the MWNT gets saturated much

faster, leading to the disappearance of fringes towards the end of the growth run.

Next the growth rates were predicted using eqn.(3.22) with the experimental steady state growth

rate for P = 265 Torr and T = 750oC condition as the fitting parameter. The pressure dependance

was mainly accounted for by the xC2H4P term in the expression, while the temperature dependence

was accounted for by the Arrhenius dependence of the interface transport constant, k, (activation

barrier = 192kJ/mole).The predicted growth rate also takes into account the changes in total driving

force, chemical composition of the gas, the absolute pressures, and the MWNT inner and outer radii.

It also discounts for the temperature change of the growth conditions, via the the activation energy

term, Ea, in the exponential part of the interferogram. This is plotted as the dark solid line in

Fig.3.14(b). The growth rates obtained experimentally are also plotted in the same figure. The

close proximity between the plots further reinforces the validity of the kinetic model developed, and

the identification of mass transport across the vapor-liquid interface as the rate limiting step.

It is to be noted that the activation energy of this growth set is similar to that for the temperature

dependent growth runs performed at 265 Torr, implying that both the growth conditions have the

same rate limiting step. If the rate limiting steps for these two sets of growths were different the

predicted and experimental steady state growth rates will not have matched.


1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Inte

nsity

600500400300200100 Time(secs)

(a) 700oC 725oC 750oC 775oC

140

120

100

80

60

40

20 Gro

wth

Rat

es (n

m/s

ec)

110010501000950 Temperature (K)

(b)

predicted growth rates experimental growth rates

Figure 3.14: Temperature dependent growth of MWNT at P=760 Torr. Fig. (a) plots normalizedintensity as obtained from the interferometer plots. Fig. (b) plots the experimental and predictedgrowth rates. The growth rates were predicted again starting from the T=750oC / P=265 Torrgrowth velocity, while accounting for temperature and pressure changes.


3.6 Conclusions

To conclude this chapter, a summary of the important points made are given below. An analysis

method was established based on the time resolved reflectivity plots and the SEM images of the

final heights of the MWNT films, to extract growth rate and hence height of the CNTs as a function

of time. The average density of the MWNT films can also be obtained. A kinetic model was

developed to quantify the steady state regime of 1D nanomaterial growth. Four mass transfer steps,

namely: the vapor phase diffusion of carbon containing molecules, their transport across the vapor

-liquid catalyst interface, diffusive flux through the liquid phase and the final transport across the

liquid catalyst-MWNT interface were identified. In contrast to earlier studies the model does not

delve into the specifics/mechanisms of each of the mass transfer steps. The novelty of this growth

model is that it considers the energetics of each transfer step instead, and equates the flux for each

step to a change in chemical potential along a phase or to a drop in chemical potential across an

interface. The average height of the MWNT film was formulated in terms of the experimental steady

state growth rate, and mean life times for catalyst activation and poisoning. The accuracy of this

model was then tested against growth data obtained. Temperature dependent studies established

the rate limiting step to be the vapor-liquid interface for the given growth conditions. Increasing the

absolute pressure decreased the thermodynamic driving force but increased the reaction rate kinetics

for MWNT growth, resulting in increased steady state growth rates. Simultaneously increase in

pressure enhanced the rate of catalyst poisoning thereby saturating the MWNT growth faster. This

leads to formation of shorter CNTs beyond a threshold pressure. Finally the kinetic model was used

to make a fairly accurate prediction for steady state growth rates for temperature dependent growth

of MWNT films at higher pressures. This attests to the validity of the growth model. This study

also helps establish the power of the interferometer as a tool to study the kinetics of nanomaterial

growth processes.


Tab

le3.

1:A

cti

vati

on

en

erg

yvalu

es

of

rate

lim

itin

gst

ep

sob

tain

ed

from

the

lite

ratu

re

Ea(k

J/m

ole)

Rate

lim

itin

gst

ep

T(K

)C

ata

lyst

Pre

cu

rsor

Morp

holo

gy

Refs

.

145

bu

lk/s

urf

ace

diff

usi

on

800-1

100

Ni

C2H

2fi

lam

ent

(61)

35su

rfac

ed

iffu

sion

425-8

05

Fe

C2H

2M

WN

T(6

5)

130

bu

lkd

iffu

sion

800-1

100

γF

eC

2H

2C

NF

(66)

43.9

-63

surf

ace

diff

usi

on

925

αF

eC

2H

2fi

lam

ent

(62)

94b

ulk

diff

usi

on

Fe 3

CC

2H

2C

NF

/C

NT

(68)

160

surf

ace

reac

tion

/dec

omp

osi

tion

of

C2H

4800-1

100

Fe

C2H

2C

NF

/C

NT

(68)

surf

ace

diff

usi

onof

Cov

erC

NT

+b

ulk

diff

usi

on

1050-1

100

CN

T(7

1)

67b

ulk

diff

usi

on

625-8

75

αF

eC

2H

2C

NF

(67)

142

bu

lkd

iffu

sion

625-8

75

γF

eC

2H

2C

NF

(67)

bu

lkd

iffu

sion

810-1

175

Fe/

Mo

C2H

2M

WN

T/S

WN

T(7

6)

79d

iffu

sion

atca

rbid

e/m

etal

inte

rface

900-1

000

Fe

C2H

2M

WN

T(8

8)

224

bu

lkd

iffu

sion

and

carb

on

solu

bil

ity

900

Fe

C2H

2(8

9)

180

Cd

isso

luti

on+

diff

usi

on

MW

NT

(73)

100

adso

rpti

onof

Cat

the

cata

lyst

surf

ace

900-1

100

Fe/

Al 2

O3

C2H

6M

WN

T(6

9)

145

HC

adso

rpti

on+

chem

ical

react

ion

900-1

100

Fe-

Co/A

l 2O

3C

2H

4M

WN

T(7

0)

100-

160

gas

ph

ase

dec

om

posi

tion

Co/M

o/M

gO

CH

4M

WN

T(7

2)

Chapter 4

Growth Transition from Carbon

Nanotubes to Carbon Nanofibers

4.1 Motivation

Chapter 3 dealt with MWNT growth from 2.5nm sputtered Fe film catalysts. All the growth runs

were done below or at atmospheric pressure. The next Chapter deals with the influence of an

applied field on MWNT growth kinetics. As explained in Chapter 5, it was necessary to grow CNTs

at pressures much higher than the ambient to apply large electric fields. Increasing pressure, though,

changed the structure of the MWNTs grown. The magnitude of the change varied changed with

the growth conditions. Fig.4.1 are SEM images attesting to the above statement. Fig(a) shows

the change in morphology for MWNTs grown from a 2.5 nm sputtered Fe film. At low pressures

the nanotubes formed are vertically aligned. Increasing the pressure resulted in the formation of

coiled CNTs, the extent of coiling being dependent on the growth pressure. The effect of increasing

the particle size was more drastic. Fig.4.1(b) shows the formation of carbon nanofibers, instead of

MWNTs, for growths from a 5nm sputtered Fe film at pressures of 1660 Torr. Similar observations

were made form MWNTs grown from catalysts prepared by block co-polymer micelle templates. The

formation of Fe catalysts from the micellar templates will be discussed in detail in the next chapter.

The pressure ranges that triggered the transition in the micellar particles was higher compared to

the 5nm sputtered Fe catalysts. The motivation then is to understand the cause behind the CNT to

CNF transition. This is important because CNFs have a different set of properties to that of CNTs

and hence are avoided for many applications.

75

CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 76

Figure 4.1: Effect of pressure on the morphology of nanotubes. (a-b)Catalyst particles preparedby annealing sputter deposited thin Fe films. (c) Particles prepared from block co-polymer micelletemplates

4.2 Introduction

There is some confusion regarding terminology for carbon nanotubes and carbon nanofibers. For

the purposes of this study CNTs are those structures that have a hollow core and straight side walls,

i.e. the basal graphite planes are parallel to the tube axis. Fig.4.2 (a-b) shows schematics and TEM

images for CNTs with single and multi walls. Apart form these, all carbon 1D structures that have

any graphitic ledges inside the core of the tubes will be referred to as CNFs. Fig.4.2 (c) are examples

of different CNF morphologies reported. They range from stacked cup to stacked cone structure,

and includes intermediate morphologies where the graphitic ledges are not so well defined.

The chapter is structured such that we discuss a systematic variation of MWNT growth condi-

tions, followed by rigorous SEM, Raman and TEM characterization of the structures obtained. This

is followed by investigations into the evolution of particle sizes as a function of the thickness of the

deposited Fe films and annealing pressure. In the last section we develop a thermodynamic model

to explain the formation of fibers as opposed to CNTs.


Figure 4.2: 1D Carbon nanostructures. (a-b) carbon nanotubes. Schematic downloaded fromwww.ibmc.u − strasbg.fr/ict/images/SWNT − MWNT.jpg (c) Examples of CNF morphologies.Schematic from www.pyrografproducts.com/Merchant5/graphics/sfnt− orangecones.gif

4.3 Experimental details and Results

4.3.1 Growth of MWNT/CNFs

From the initial observations, two parameter that were found to be of importance for the formation

of CNTs or CNFs were pressure and size of the catalyst particles. Hence we varied these two

parameters in a systematic manner to study their relative influences on the growth morphologies.

Four different catalyst substrates were prepared. The nominal thickness of the deposited Fe

layers were 2nm, 5nm, 8nm and 13nm respectively. All of these were deposited on a buffer Al layer

(10 nm thick), which was sputter deposited on Si. The substrates were cut into 1cm2 pieces and

transferred into the reactor chamber. All four substrates were grown from simultaneously to negate

any variations between different sets of growth. The reactor was evacuated and then the temperature

ramped up to 550oC under a hydrogen ambient (flow rate: 100 sccm and reactor pressure: 120 Torr).

The substrate was held at this temperature for 5 minutes. Following this the reactor temperature

was ramped up to the growth temperature of 750oC. The desired base pressure at the on-set of the

growth was achieved by manipulating the hydrogen flow rates and the valve positions. When the

temperature of the hot plate reached a steady value ethylene was flown into the chamber. The flow

rates of ethylene and hydrogen was maintained at 350 and 100 sccm respectively. The four different

growth pressures used for this study was 200, 760, 1120 and 1680 Torr. The growth duration for all

the runs was 10 minutes.

Fig.4.3 is a collage of SEM images of the MWNTs/CNFs obtained from the growth runs men-

tioned above. SEM images from growths on substrates with the same catalyst thickness are arranged


Figure 4.3: SEM images showing the dependence of the thickness of the sputtered Fe layer andgrowth pressures on the nature of carbon morphologies obtained

in a column, showing the dependence of growth pressure. Along the rows, the growth pressures are

the same, so the SEM images illustrate the influence of catalyst thickness on growth morphologies.

The final thickness of the films grown have a strong dependence on the growth conditions. This is

plotted in Fig.4.4. With an increase in pressure the height of the films decreased irrespective of the

nominal thickness of the deposited Fe layer. This decrease in thickness of the film has been explained

in the previous chapter. Increasing the pressure results in a higher growth rate, but at the same time

the rates of the competing process of catalyst poisoning also increases. This restricts the final height

of the films grown. The height of the films grown also have a strong dependence on the nominal Fe

thickness. As will be shown in a later section that the catalyst size is proportional to the catalyst

thickness. The diameter of the 1D structures in its turn is proportional to the particle size. The con-

centration of C in the CNTs can be obtained by the relation CMWNTc = Cgraphitec (1− rin

2

rNT2 ), showing

that the density of the MWNT is proportional to its diameter. Hence a simplistic explanation is

that with increasing particle size, for the same amount of C flux the height of the MWNT/CNFs

formed decreases (vss = Jvs/Cc).

More interesting, though, is the change in morphology of the CNTs. For the 2nm Fe catalyst

films MWNTs are obtained irrespective of the growth pressures. There is a significant change in

height of the film accompanied by formation of coiled CNTs, but the structures obtained are tubular.

This is evidenced by similar intensity ratios of the D-band and the G-band in the Raman spectrum,


30x103

25

20

15

10

5 Hei

ght

of C

NTs/

CNFs

(nm

)

1412108642

Thickness of Sputtered Fe (nm)

300 Torr 760 Torr 1220 Torr 1680 Torr

Figure 4.4: Heights of CNTs/CNFs plotted as a function of growth pressure

irrespective of the growth pressures. For thicker catalysts with an increase in pressure there is

a definite transition in morphology from CNTs to fibers. For example for the 8 nm thick films,

this transition takes place for growth pressures of 1120 Torr. Fig.4.5 plots the Raman spectrum

corresponding to the D and G-band positions for growths from the 8 nm sputtered film. The

intensity of the D band is inversely related to size of crystallites, and disappears for perfect tubular

structures. The intensity ratio of the D-band and the G- band has been found to be a good metric

in determining the quality of CNTs. Typically for MWNTs the intensity of the D-band is less than

that of the G-band, this is seen for plots for the 200 and 760 Torr growth. For higher pressures the

intensity of the D-band is greater than that of the G-band implying a presence of larger fraction

of defective structures in the sample studied. This agrees well with the SEM observations, where

we see an increasing fraction of CNFs in the sample for growths at absolute pressures of 1120 and

1680 Torr. The number fraction of fibers in the sample is even higher for growths from the 13nm

sputtered Fe film. For this thickness, the tube to fiber transition occurs at an even lower pressure

of 760 Torr. In spite of the transition from CNTs to CNFs, it has has to be noted that there is a

considerable faction of CNTs in the sample for the thicker films annealed at higher pressures.

The SEM images also show a transition from a root-growth (catalyst is rooted to the substrate)

to a tip-growth mode with increasing Fe film thickness and hence size of the catalyst particles. This

has been observed by other groups (90). The transition in growth mode was explained by interaction

between small carbon patches (poly-aromatic carbon or reticulated carbon chains) and the catalyst.

A strong interaction favors the formation of a graphene cap on the catalyst and leads to CNT growth

via the base-growth mode. On the contrary, a weak interaction induces a diffusion of the graphitic

section to the catalyst/substrate interface which drives the tip-growth mechanism.


1.0

0.8

0.6

0.4

0.2

0.0

norm

aliz

ed in

tens

ity

200018001600140012001000800600wavenumber(cm-1)


Figure 4.5: Raman spectrum obtained using 514 nm excitation laser for nanostructures grown froma 8nm sputtered Fe film as a function of pressure

4.3.2 Characterization of catalyst particle size

The last section studied the effect of pressure on growth. A major contributing factor if not the

most important one to the changes observed was the catalyst film thickness. This is because the

catalyst thickness influences the size of the catalyst particle. Therefore there is need to determine

the size of the catalyst particles used for the growth runs.

Like in the case for growth studies four identical substrates, with 2,5,8,13 nm of Fe sputtered on

a 10nm Al buffer layer sputter deposited on Si was used. These substrates went through the same

processing steps including the 5 minute annealing step. Following which the reactor temperature

and pressure was ramped to the same base values as used for the growth runs. On reaching a steady

750oC, the substrates were annealed at the same absolute pressure of 200, 760, 1120 and 1680 Torr

for 10 minutes (similar to the growth runs) using only hydrogen. This was done to investigate the

effect of the absolute pressure on the evolution of the catalyst particle sizes.

Fig.4.6 are representative images of the catalyst particles formed subsequent to the process

described above. The first thing to notice is the large difference in range of the catalyst particles

produced. On closer examination two general trends appear albeit one or two exceptions. First,

as expected the size of the catalyst particles increases with the thickness of the sputter deposited

Fe film, particularly for the higher annealing pressures. Secondly increasing the annealing pressure

resulted in formation of larger particle sizes. One exception being the 2nm sputtered Fe film. For the


Figure 4.6: Evolution of particle sizes vs. catalyst thickness and annealing pressures

2nm sputtered film, the mean particle size actually decreased on increasing the annealing pressure.

This can be seen from Fig.4.7 which plots the size distribution of the particles (percentage spatial

coverage of particles), obtained by Image J analysis of the SEM images of the particles from Fig.4.6.

The mean radius (approximating the particles to be circular in shape) of the particles for the 200

Torr anneal is 6.35 nm while for the 1680 Torr growth case the mean is 4.32 nm. This is probably due

to enhanced mixing between the Fe/Al layers at higher annealing pressures. For the 5nm sputtered

film, increasing annealing pressure resulted in an increase in the range of catalyst particle sizes, the

increase in range mostly due to the formation of larger particle sizes. The mean calculated particle

radius increased from a mean of 6.25 nm to 8.1 nm, on increasing the annealing pressure form 200 to

1680 Torr. Similar increase in particle sizes were observed for the thicker 8nm and 13 nm sputtered

films. Though, for the 13 nm sputtered films the largest particle size was obtained for annealing

pressure of 1120 Torr.

It has to be noted that the evolution of particle size on exposure to a combined flow of hydrogen

and ethylene might be different from that obtained when annealed under a hydrogen ambient. But

the above particle size trends should serve as a good indicator for actual values.


1086420

302520151050 particle size (nm)

15

10

5

0

% a

rea

cove

red

12

8

4

0

12

8

4

0

(a) 2nm Fe/ 10nm Al/ Si

16

12

8

4

03020100

particle size (nm)

8

6

4

2

0

6

4

2

0

% a

rea

cove

red

6

4

2

0


(b) 5nm Fe/ 10nm Al/ Si

Figure 4.7: Plot of particle sizes obtained from Fig.4.6 for the 2nm and 5nm sputtered Fe filmthickness. The particles were assumed to be circular for simplicity. The X-axis is the calculateddiameter corresponding to the particulate area.


Co-relation of the particle size and the MWNT/CNF growth runs

Nasibulin et al.(83) established a close relation between the catalyst particle size and the diameter

of the SWNTs grown. A rigorous statistical analysis of the particle sizes and diameter of the SWNT

obtained from the particles, established an approximate tube to particle radius ratio. Though,

strictly true for SWNTs, intuitively a similar co-relation between the diameter of the 1D carbon

structure and catalyst particle size should exist. A comparison of the SEM images of particle size

distributions, Fig.4.6, with that of SEM images for CNTs/CNFs, Fig.4.3, shows a close correspon-

dence between the two. Smaller particle sizes, obtained from the thin Fe catalyst films and even from

the thicker catalyst films at low annealing pressures, resulted in the formation of CNTs. For larger

particle sizes (8nm and 13nm sputtered films, annealing pressures 1120 and 1680 Torr) nanofibers

form. Intermediate particles result in a mixture of tube and fibrous growth. A significant amount

of small particles were obtained from annealing 8nm and 13nm sputtered films at high annealing

pressures. Correspondingly for these thick sputtered films and high growth pressures there is a con-

siderable fraction of MWNTs in the sample. These observations imply, catalyst particle size rather

than growth pressures is the contributing factor controlling the morphology of the 1D carbon nanos-

tructures. Pressure facilitates the process by influencing the size of the catalyst particles formed

during annealing and subsequent processing of the catalyst films.

Auger depth profiles of the annealed substrates

Annealing pressure influences the particle sizes formed. Auger depth profiling of the annealed sub-

strates were performed to investigate possible causes for this size dependence. Precise depth milling

through sputtering has made profiling an invaluable technique for chemical analysis of nanostruc-

tured materials and thin films. Depth profiles are shown as atomic concentration vs. sputtering

time. But, despite the advantages of high spatial resolution and precise chemical sensitivity at-

tributed to AES, quantification of AES data is difficult due to several limiting factors e.g. charging

of non-conducting samples. Still, the atomic concentration data is a good indication of the change

in chemical composition with depth. Typically the bombarding energies used for this study is 2kV

with a beam current of 1µA. This corresponds to a sputtering rate of 20nm/min for a Si standard.

Fig.4.8(c-d) are depth profiles of 2nm Fe/10 nm Al/ Si after annealing at 1120 Torr. As mentioned

before annealing results in the sputtered Fe thin film to ball up resulting in the formation of particles.

The high spatial resolution of the Auger probe allows the compositional analysis as a function of

depth from the particles so formed (d). Depth profile was also obtained from the substrate free of

particles (c). To compare depth profile obtained from an as-sputtered 5nm Fe film (discussed in the

last chapter) is also shown. In contrast to the as-sputtered film, the annealed film shows extensive

intermixing between the layers. The concentration plots show intermixing between Fe/Al layers

for profiles obtained both from the substrate and the particle. For the particle depth profile, Fe

signal intensity is more than the Al only at the interface implying as expected the particles formed


100

80

60

40

20

0

at%


5nm Fe/10nm Al/Si

C O Al Si Fe

(a) as sputtered

Fe

Al

Si

Fe-Al

Fe

80

60

40

20

0

at%


2nm Fe/10 nm Al /Si

(c) substrate

80

60

40

20

0

at%


C O Al Si Fe

(d) particle

Figure 4.8: Auger depth profile for an annealed 2nm Fe/10nm Al/ Si substrate. (a) Depth profile foran as deposited sample(5nm sputtered Fe). (b) cartoon of the annealing process and SEM image ofthe catalyst particles formed after annealing. (c ,d) Profiles obtained by sputtering on the substrateand a particle respectively. The same elemental color codes and markers are used for all the depthprofiles discussed in this chapter


are indeed Fe/Fe-oxide particles. The depth profiles described above is fairly representative of the

2nm Fe sputtered film irrespective of the annealing pressure. The only difference being enhanced

Fe/Al mixing between layers for signals obtained from the particles at higher annealing pressure. As

mentioned, while discussing the evolution of particle sizes for the 2nm sputtered film, this enhanced

mixing may account for the decrease in particle size with increase in annealing pressures.

Fig.4.9 are depth profiles obtained from post-annealed 13nm Fe/10nmAl/Si sputtered substrates.

The annealing pressures are tagged on to the corresponding depth profiles. The foremost observable

fact is the extensive intermixing between the layers. Extensive intermixing between Fe and Al have

been reported by other groups (91). This mixing also illustrates the need for the buffer layer to

be thicker compared to the catalyst layer. If the buffer layer is not thick enough Fe woul diffuse

through to the underlying Si, similar to this case. This is because Fe has an affinity for Si and

forms different complexes with it (92). For annealing at 200 Torr the depth profiles obtained from

the particle and substrate is the same, implying relatively limited mixing. The Fe concentration for

this case shows a double hump, Fe enrichment at the surface (which is expected) and also at the Si

interface. This looks like an impossible situation since it would imply Fe diffusing towards the Si

interface against a Fe concentration gradient. But it has been reported that Fe can precipitate at

the Si/Si-oxide interface (92) and is also known to form FeSix complexes with Si (e.g. FeSi, FeSi2)

at the Fe-Si interface (93). Thus the diffusion of Fe towards the Si interface is driven by a decrease

in chemical potential of Fe from elemental state to FeSix, and the increase in atomic concentration

reported is an artifact of the Fe-Si compound formed at the interface.

The extent of intermixing increases with annealing pressure. Another important trend observed

is with increasing annealing pressure, the Fe content for the substrate decreases while the iron

content for the particle is increasing. This implies there are two types of Fe diffusion taking place:

(i) Fe diffusing towards the Si layer as mentioned above and (ii) Lateral diffusion of Fe away from

the substrate towards already formed particles. The second effect is known as Ostwald ripening,

where the decrease in chemical potential (due to its inverse dependence on particle size) drives the

coarsening / agglomeration of smaller particles into a larger particle. This explains the formation

of larger particles with increasing annealing pressures (as was observed in Fig.4.6).

To conclude the increased intermixing between the different layers and enhanced Ostwald ripening

with increase in annealing pressure is responsible for the evolution of the observed particle size

distribution. The effect of pressure in facilitating intermixing or ripening is not clearly understood.

One possible explanation could be increasing chamber pressure increases the thermal contact between

the substrate and the hot plate, thereby increasing the effective temperature of the substrate which

drives the above mentioned processes.


10080604020

0

at%


10080604020

0100

80604020

0100

80604020

0

200 Torr

760 Torr

1120 Torr

1620 Torr

C O Al Si Fe

(a) substrate

100

80

60

40

20

0

121086420 sputter time(secs)

100

80

60

40

20

0 at%

100

80

60

40

20

0

100

80

60

40

20

0

200 Torr

760 Torr

1120 Torr

1620 Torr

(b) particle

Fe

Al

Si

FeSixFe-Al

Fe

Figure 4.9: Auger depth profile for annealed 13nm Fe/10nm Al/ Si substrate as function of annealingpressure(a) Depth profile obtained from sputtering on the substrate. (b) Depth profile from aparticle. (c) Schematic of particle evolution with annealing pressure


Figure 4.10: TEM characterization of 1D carbon structures as a function of particle size. (a) CNTsformed from small catalyst particles, (b) Defective, kinky fibers formed from large particles

4.3.3 TEM characterization of growths as a function of particle size

Small catalyst particle sizes resulted in the formation of smaller diameter MWNTs, Fig.4.10. The

MWNTs have only 2-3 side walls. There is some bending observed in the CNTs, but they have

straight side walls. On the other extreme the large catalyst particles (8nm sputtered Fe film, annealed

at 1680 Torr) results in formation of very defective, kinky, seemingly amorphous fibers of large

diameters. A closer look, though, reveals extensive graphitization of the thick side walls and the

presence of a very narrow hollow core. The graphitization pattern of the side walls followed the

shape of the catalyst particle.

Fig.4.11 are TEM images obtained from intermediate particle sizes formed from annealing a

8nm sputtered film at 1120 Torr. For the relatively smaller particles the 1D structures formed are

defective in that there are more kinks and bends compared to the CNTs reported in the previous

figure. Also graphitic ledges (marked by arrows) start to form across the tubes. These ledges are

not prominent as they are made of only a few graphitic planes. With increasing particle size the

stacked cup arrangement becomes prominent, as the number of graphitic planes bridging the hollow

core increases. The other notable feature is the very regular arrangement of the stacked cups in the

CNFs formed, indicative of a recurring origin.


Figure 4.11: TEM characterization of 1D carbon structures obtained from intermediate particle sizes

4.4 Brief literature review on CNFs

The methods for producing the carbon nanofibers have been developed and are in use since the early

1980s, due to the great effort carried out especially by Endo and co-workers (94) and Tibbetts et

al. (63). Most of carbon nanofibers are produced by catalytic CVD from a carbon feedstock (light

or aromatic hydrocarbons, CO) using an elemental transition metal (Fe, Ni, Co and Cu) as catalyst

(95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107). Plasma enhanced CVD (PECVD) is

another popular method of growing vertically aligned CNFs (13; 108; 109; 110; 111; 112). Fig.4.12

plots the diameter of CNFs obtained from the references mentioned above.

Two important observations can be made form the plot. For lower growth temperatures the

diameter of the nanofibers formed is small. Increasing temperature results in an increase in range of

fiber diameters. But, the diameter of the smallest fiber reported for a given temperature increases

almost linearly with increasing growth temperature (this is marked by the dashed red line in the

plot).

More recently,following the pathbreaking work by Helveg et al. (1), HRTEM has been employed


140

120

100

80

60

40

20

0

Nano

fiber

dia

met

er (

nm)

12001000800600400Temperature(oC)

(c)

Fe catalyst Ni catalyst PECVD

Figure 4.12: (a) In-situ TEM studies of nanofiber growth (1). (b) Atomic scale observation of theformation of SWNTs (2). (c) Distribution of fiber diameter with temperature from data reportedby various groups

to observe in-situ CNT/CNF growth in an atomic scale. This has resulted in fresh insight into the

mechanisms of 1D nanomaterial growth. Yoshida et al. (2) observed the nucleation and growth

process of carbon nanotubes (CNTs) from iron carbide (Fe3C) nanoparticles in CVD with C2H2

Fig.4.12(b). The size of the catalyst particle was 2nm and the growth temperature 600oC. After

the initial nucleation and incubation period the nanotube grows at a slow but constant growth

rate. The important thing to notice is that the catalyst particle does not change shape during

growth. Helveg et al. observed the formation of nanofibers Fig.4.12(a). Contrary to CNT growth,

the initial equilibrium shape of the catalyst particle transformed into a highly elongated shape. The

elongation of the Ni nanocrystal continues until it achieves an aspect ratio of up to, 4, before it

abruptly contracts to a spherical shape within less than, 0.5 sec, leaving behind a graphitic ledge.

The elongation/contraction scenario continues in a periodic manner as the nanofiber grows. Similar

observations were made by other researchers(113; 114).


4.5 Discussion

To summarize, particle size was found to be the most important contributing factor in determining

the morphology of the 1D nanostructure. For the growth conditions studied, particle sizes rp < 5

nm resulted in formation of MWNTs, and large particle sizes rp > 20 nm resulted in formation

of defective, kinky structures. Intermediate sizes resulted in the formation of carbon nanofibers,

with a very regular stacked-cup morphology. High pressures facilitated formation of nanofibers by

influencing the size of the catalyst particles formed. The other important factor that controls CNF

formation is the growth temperature. The smallest diameter CNF, reported at a particular growth

temperature, increased with increasing temperature. Also lowering the temperature resulted in a

decrease in diameter range of the fibers formed. HRTEM in-situ imaging of fiber growth reported

by other groups further revealed three important features: (i) the catalyst particle alter shape

(for CNT growth the catalyst particle retained their shape through out the growth process) (ii)

expansion/contraction of the particle is periodic resulting in the regular stacked morphology of the

CNFs and (iii) the time for contraction to the original size is almost an order of magnitude smaller

than the time taken for the particle to elongate.

Though oscillatory nature of the particle is considered to be integral to the formation of CNFs, to

date there is a lack of understanding of the origin/driving force for this oscillatory nature. We believe

the regular and abrupt nature of the contractions is due to a phase transition of the particle. The

most studied catalysts for CNT/CNF growth are the transition metals Fe, Co, Ni. It is important to

note that all three of them are carbide formers, have limited C solid solubility and forms an eutectic

at small weight percentages of C.

To reconcile the above observations we propose that the catalyst particles have to be in the

binary (liquid/solid) phase region to form CNFs, and the small particles resulting in CNT growth

is in the single liquid phase.

4.5.1 Thermodynamic Modeling

In this section we will describe the model in some detail and provide theoretical calculations in

support of the proposed model. First we will discuss the case for nanotube growth, followed by

carbon nanofiber growth.

Small single liquid phase catalyst particle

For the small particle sizes we have proposed that the particle is in a single liquid phase under

the MWNT growth conditions reported. CNT forms from these particles via a VLS mechanism

described in the last chapter. Four mass transfer steps: the vapor phase diffusion of carbon containing

molecules, their transport across the vapor -liquid catalyst interface, diffusive flux through the liquid

phase and the final transport across the liquid catalyst- MWNT interface were identified. CNT


growth was described as a steady state process, with no C accumulation inside the particle, the

slowest of the 4 mass transfer steps described being the rate limiting step.

1800

1600

1400

1200

1000

800

600

400

200

0

Mel

ting

Poin

t (K

)

0.1 1 10 100 1000Radius of Fe nanoparticle (nm)

Growth temperature (750 oC)

Figure 4.13: Plot of size dependent melting point of Fe. The dotted line marks the growth temper-ature used for this study.

The first question to be answered is the discrepancy in the growth temperature, 750oC and the

melting point (1536oC) or the eutectic temperature of 1175oC. This can be explained due to the

curvature dependance of chemical potential, Gibbs-Thompson effect.

For a solid particle of radius, rs, and a liquid particle of radius,rl the accompanying increment

in chemical potential is given by the relation:

µs = µs,∞ +2γsΩsrs

µl = µl,∞ +2γlΩsrl

where γ , Ω and µ∞ are interfacial energy, molar volume and the bulk chemical potential respectively.

At the melting point the chemical potential of the solid and liquid particles are equal. Hence from

the above two equations and the Turnbull approximation, ∆µ∞ =∆Hf∆TTMP

, we get the following

relation for size-dependent suppression of melting point:

T = TMP −2TMP

rs∆Hf

[γlΩl

(ρlρs

)1/3

− γsΩs

](4.1)

where ∆Hf = 13.80kJ/mole is the latent heat of fusion at TMP . The above equation also accounts

for mass conservation while transforming from the solid to the liquid state. The plot was obtained

by assigning the following parametric values: density of solid austenite is 7875 kg/m3, liquid iron


6980 kg/m3, molar volume of austenite = 7.117 cm3, the interfacial energies for austenite and liquid

iron being 2.55 and 1.92 J/m2 respectively. These values were obtained from the work of Sayama et

al.(115) on the eutectic growth of unidirectionally solidified iron-carbon alloy.

The size dependence of the suppression in melting point is plotted in Fig4.13. In effect with a

decrease in size of the particles (rp < 10nm) the entire phase diagram shifts downwards in tempera-

ture. From the plot we can see that a particle of approximate diameter 2nm will be in a liquid phase

at the growth conditions. This particle size is an underestimate because of the following reasons.

First, we considered pure Fe for the calculations, while in reality it is a Fe-C alloy which has a lower

liquidus temperature than the melting point of pure iron. Next the catalyst particle sizes are in

contact with a substrate, and in general the interfacial energy between two solid interfaces are larger

than between a solid-liquid interface. This will further bring down the liquidus temperature of the

catalyst particle. Thus in reality the largest particle size that will be in a liquid phase at the growth

temperatures is higher than that predicted by the above plot. These liquid phase catalyst particles

will form CNTs.

Intermediate catalyst particle sizes

For particles in this size range, the depression in liquidus temperature is not enough for it to be in

the liquid phase. But the downward shift in the phase diagram is enough for these particles to be

in the temperature range corresponding to a binary solid austenite-liquid Fe phase at the growth

temperatures, Fig.4.14. As observed from the in-situ TEM images CNF formation is a non-steady

state process.

Initially the catalyst is in the solid austenite phase. With the onset of growth, C starts accu-

mulating inside the particle. The C concentration goes up and eventually crosses the solidus line,

at that point the particle enters a two phase regime. Further increase in C concentration inside the

particle leads to an increase in volume fraction of the liquid phase. This results in an elongated

tail, encapsulated by the side walls, as seen in the TEM images. Fig.4.14(b) is a schematic of the

process. But, the formation of the liquid phase is accompanied by formation of different interfaces,

namely the solid-liquid interface inside the particle, the liquid-tube interface. With increase in the

carbon concentration inside the particle, the volume fraction of the liquid phase increases and along

with it the energy cost to pay for these extra interfaces (as shown in the ∆Gmix vs x schematic).

At some point this interfacial energy cost cannot be sustained. The particle wants to decrease its

energy content; the way to do so is to revert back to the original austenite solid solution phase. This

can be achieved only by casting away the excess carbon. The extruded C takes on the shape of the

contracting liquid phase giving the graphitic ledges, so formed, the stacked-cop morphology of the

CNFs. C diffusing through a liquid phase accounts for the much faster time scales for contraction of

the particle than for its elongation, which is accompanied by solid state diffusion. The entire process

described above keeps on repeating to form the regular ordered structure.


G

x

+L (vol. energy)

+L

liquid

LL

1150oCTe

mpe

ratu

re

graphene

+L +graphene

Figure 4.14: (a) Relevant portion of the binary Fe-C phase diagram. (b) Schematic of the evolutionof the stacked-cup morphology of the CNFs

Next we develop a thermodynamic model to predict the crossover point which initiates the phase

reversal. We consider a initial solid austenite particle of radius r. When the C wt% in the catalyst

particle crosses over the solidus line, a liquid phase starts forming as shown in the schematic on the

left of Fig.4.15, with the propagating solid-liquid circular interface at a distance z from the side of

the particle. If we assume same density for the solid and liquid phase; then the volume fraction of

the liquid phase formed, f , can be expressed as:

f =z2

4r2(3− z

r) (4.2)

But in reality, the density of the liquid iron phase is smaller, resulting in the formation of an


elongated tail as mentioned above. For simplicity we assume a cylindrical shape for the elongated

tail, the cylinder being encapsulated in a graphitic tubular structure, of outer diameter ro and inner

diameter ri. The length of the cylinder, l, being

l = fρsVs

πρlr2i

= kf (4.3)

Initially the particle was in the austenitic phase with volumetric free energy, Gs. On crossing

the liquidus line, the volumetric free energy of the binary phase particle can be expressed as:

GFeC = (1− f)Gs + fGl

= Gs + f [Gl −Gs]

where Gl is the volumetric free energy of the liquid phase. The change in volumetric free energy

accompanying the formation of the liquid phase is then given by:

∆G1 = f [Gl −Gs] (4.4)

Next we add the interfacial energy terms: the solid liquid interface that replaces the solid-vapor

interface and the new liquid-tube interface.

∆G2 = πr2i (γs,l + γl,v − γs,v) + 2πrikfγl,gr (4.5)

The first term of the above equation is negative, because the solid-vapor interfacial energy is larger

compared to the solid-liquid and liquid-vapor interfacial energy.

There is a simultaneous increase in the height of the graphitic tubular structure, and the accom-

panying decrease in chemical potential of C going from the vapor to the tubular structure provides

the driving force for the entire process.

∆G3 = −πr2okf(µVC − µNTC ) + 2πrokfγv,gr (4.6)

The total change in energy in going from the single phase austenitic particle to the binary phase

catalyst particle with the liquid phase encapsulated in a growing tubular shell is given by ∆Gtotal.

∆Gtotal = ∆G1 + ∆G2 + ∆G3 (4.7)

These energy changes are plotted in Fig.4.15. The plots correspond to a particle radius of 5 nm.

Given the particle size, the Gibbs Thompson relation is used to calculate the downshift of the phase

diagram and from there the weight fractions of C corresponding to the liquidus and the solidus lines.

Knowing these weight fractions, we substituted them into analytical expressions for volumetric free


-800x10-18

-600

-400

-200

0

200G

(J)

0.50.40.30.20.10.0 f

GIGIIGIIIGtotal

-vapor

-liquid

liquid-vapor

CNT-vapor

CNT-liquid

liquid

radius “r”

z

Figure 4.15: Energetics of the CNF formation process. The black dashed line marks the volumefraction that triggers the contraction of the catalyst leaving behind a graphitic ledge

energies from the work on thermodynamic analysis of Fe-C phase diagrams by Agren(116) to obtain

Gs and Gl. The outer radius of the tubular structure formed is assumed to be the same as the

particle size, which gives an inner radius of 3.5 nm from the work of Tibbetts (63). The formulation

for the change in chemical potential of C going from the vapor phase to the tubular structure was

dealt with in the previous chapter and is used here to estimate the driving force. The interfacial

energy values were again obtained from the work of Sayama et al.(115).

∆G2, that sums the interfacial energy contributions of the growing liquid phase, is the only

term that switches polarity as a function of the volume fraction of liquid phase formed. This is

because initially on formation of a binary phase, the solid-liquid interface replaces the higher energy

solid-vapor interface. But with increasing f the liquid-tube interfacial energy dominates and the

initial energy advantage is lost. Hence, ∆Gtotal, which corresponds to the energy change for the

elongated particle, eventually becomes energetically unfavorable compared to ∆G3, which in turn


is the energy change due to the formation of tubular section only. This will trigger the contraction

of the particle back to its original single phase state leaving behind the graphitic planes bridging

across the energetically stable tubular section.

Other factors that influence fiber formation

As was observed from literature review temperature plays an important part in controlling the

fiber diameter. For low growth temperatures only small particles can transform into a binary phase.

This puts an upper limit to the diameter range. On increasing the growth temperatures the diameter

range of particles forming CNTs will increase, but the smaller particles will be in a liquid state and

will form CNTs rather than fibers. This would set a lower limit for particle sizes forming fibers.

The principal effect of pressure is to facilitate the evolution of catalyst particle sizes. Increasing

pressure further aids fiber formation due to the dependence of chemical potential on pressure: δµδp |T =

Ω. The molar volume of liquid being larger than solid, higher pressures would result in an elevation

of melting point and hence responsible for the pressure dependent transition to fiber formation. But

since both solid and liquid are condensed phases the shift in melting point due to increasing pressures

would be minor. A more significant contribution is due to the pressure dependence of C flux across

the vapor-liquid interface as discussed in the last chapter. Carbon concentration inside the particle

will increase with increasing pressure, driving CNF formation due to formation of a mixed phase.

The ubiquitous use of PECVD for CNF growth has a similar origin. The plasma results in

decomposition of C precursor in the vapor phase itself, increasing the flux of C into the catalyst

particle which enhances C accumulation and hence fiber formation.

Large catalyst particles

For large catalyst particle sizes (rp > 15nm) the melting point suppression is negligible. Hence

the particles will be in a solid state at the growth conditions. Reshaping/restructuring of the

facets/planes of solid particles have been reported in contact with graphene (113; 2). This occurs to

minimize the interfacial energy of the graphene-solid interface. Subsequently, the side walls of the

tube replicate the facets of the solid catalyst particle. For example, catalysts exhibiting fcc facets

results in the formation of stacked-cone CNF morphology (117).

4.6 Conclusion

To summarize this chapter, it was established that catalyst particle size is one of the key parameters

that determine the morphology of the 1D carbon nanostructures. The inverse dependence of chemical

potential on size determines the nature of the particle under growth conditions. Smaller particle

exhibit a single liquid phase, conducive to the growth of CNTs. However, larger particles, are in a

dual solid-liquid phase during growth. The relative fraction of liquid phase increases with increasing

accumulation of carbon flux. Beyond a threshold carbon concentration, the dual phase becomes


energetically unfavorable, causing the particle to revert to a single solid phase regime by discarding

excess carbon. The resulting carbon layers replicate the morphology of the catalyst particle, leading

to the observed CNF structure. In the CVD process, higher pressures were found to form larger

particle sizes. AES depth profiles attributed this behavior to particle coarsening.

Chapter 5

Electric field directed Vertically

Aligned growth of Multiwalled

Carbon Nanotubes

5.1 Motivation

Carbon nanotube based field emission cathodes are sought for various applications such as microwave

amplifiers, x-ray tubes, Tetrahertz sources etc. Continuous or patterned CNT films are generally the

cathodes of choice. Continuous CNT film arrays have field enhancement β values typically between

1000 and 3000 . Patterning CNT films further improve the field emission characteristics and stable

current densities as high as 10 mA/cm2 for applied fields for 5-6 V/µm have been achieved (118).

The increased emission current is attributed to the electric field enhancement along the edge of the

patterned structures (known as the edge effect) due to a reduced field screening. Increasing the

edges of the pillars, by introducing new patterned film geometries, leads to a greater total current

from the cathode due to an increased number of emission sites(119), Fig.5.1.

Hence, the ideal field emission cathode would be an array of individual CNTs of optimal density

(to minimize the field screening effect). Similar cathode structures made of vertically aligned carbon

nanofiber arrays have been achieved. But the emission characteristics of CNFs are less than optimal

due to the their inherently disordered stacked structure and relatively larger diameters. Conse-

quently, CNF arrays tend to have β values lower than 1000 and experience structural degradation

at high emission currents. In contrast, both SWNTs and MWNTs have a smaller tip radius and a

ordered tubular structure yielding a higher field enhancement factor and greater mechanical stability

than CNFs(118). But, nanotubes tend not to grow vertically from a sparse catalyst distribution.

They grow vertically in dense films propped by the large van der Waals interaction between CNTs.

98

CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 99

-+

applied V

pillarsdonuts

I FE(A

mp

s)

Figure 5.1: Patterned carbon nanotube structures for enhanced field emission. Also plotted are fieldemission currents from the two different cathode structure. Introducing an extra edge in the donutstructure leads to current enhancement

One possible way to align individual CNTs would be application of a suitably directed electric field

during their growth.

5.2 Introduction

Electric field directed alignment of carbon nanotubes has been an active area of research since the

first study of carbon nanotube alignment and manipulation by electrostatic fields by Fishbine (120).

The basic mechanism takes advantage of the anisotropy of the CNTs, the polarizability along the

axial direction of the CNTs being greater than in the radial direction (19). The initial investigations

were restricted to orientation of CNTs dispersed in solutions by AC and DC electrophoresis (121;

122; 123; 124) . However these methods were not very successful due to the low solubility and

impurity of the CNTs and because of considerable viscous drag force involved.

Later investigations looked into aligning CNTs by incorporating an electric field during growth.

The most popular technique to date being plasma enhanced chemical vapor deposition (PECVD)

(20; 21; 22; 13; 24). In PECVD, a high bias voltage is applied for generating a glow discharge. In

this case the potential does not vary linearly between the electrodes, but rather is constant except

in the sheath region near the cathode where it decreases approximately linearly (23). The height

of the CNTs is smaller than the characteristic Debye length of the plasma, and hence the CNTs

are oriented by the high plasma sheath electric fields. However, complimentary studies show that


along with the electric fields generated in the sheath region other mechanisms like crowding effect

of the high density films, non-uniform stresses across the catalyst particle surface etc (22) helped in

aligning the CNTs. PECVD though, suffers from the disadvantage that it most often forms carbon

nanofibers rather than nanotubes, and nanotubes that do form are less oriented than the nanofibers.

Formation of CNTs or fibers is influenced by the growth conditions(13). High rates of flame synthesis

of aligned MWNTs using a DC field in flames have also been reported (24), though this technique

results in the formation of other carbon nanoforms depending upon the flame temperature and

concentration of chemical species.

Zhang et al. successfully demonstrated electric field directed growth of single-walled carbon

nanotube (SWNT) by thermal chemical vapor deposition process (CVD)(25; 26). They were able to

horizontally align SWNTs suspended over trenches and also directly on substrates by suitable choice

of electrode materials, directed electric fields of optimal strengths, and suitable surface treatments.

Further studies have been made to characterize and model horizontally directed SWNT growth with

a local field (27; 28). Interactions primarily with the substrate were considered and two growth

modes, surface and free growing, were proposed. Avigal et al. were the first to study aligned growth

of MWNT under a DC electric field applied perpendicular to the substrate (29). They observed that

aligned growth of MWNT was possible only under a positive sample bias. A negative bias resulted

in random growth while in the absence of an applied electric field there was no growth.

In this chapter, we use electric field directed growth for producing vertically aligned MWNT by

CVD. The electric field applied here is perpendicular to the substrate. The first part of the chapter

deals with the dependence of bias on the change in alignment of MWNTs. We address here the two

most important issues believed to control the alignment of the CNTs, spatial density of the MWNT

and the magnitude of the applied bias. To quantify the alignment of dense CNTs we develop a

novel technique, based on a two dimensional Fast Fourier Transform image analysis of Scanning

Electron Microscope images of nanotubes. A different technique based on the ability to detect

straight edges was developed to study the alignment of sparse MWNT grown from self-assembled

catalyst nanoparticles.

In the second part of the chapter we investigate the growth kinetics of field directed vertically

aligned MWNT. Interferograms recorded to monitor growth rates with and without bias were used

to determine activation barriers and corresponding rate limiting steps.

5.3 Experimental Technique: Catalyst preparation by Block

Co-polymer Micelle Templates

Two types of substrates are used to study the e-field effects on MWNT growth. Substrates for dense

MWNT growth were prepared by sputter depositing 2.5 nm of Fe on top of a 10 nm Al buffer layer

on C-type Si, as has been mentioned in the last two chapters. This technique has limited particle


Figure 5.2: Schematic of the different steps to synthesize Fe nanoparticles via a block copolymermicellar route

size control and results in formation of dense particle distributions. Hence to obtain a sparse but

uniform spatial distribution of catalyst nano particles we used a block co-polymer micelle template.

Block copolymers have been used extensively as self- assembled templates for the preparation of

periodic nanoparticle arrays. The choice of diblock copolymer determines the size of the nanoparti-

cles and more importantly determines the particle- particle spacing and therefore the spatial density

of catalyst particles. This approach has been applied successfully to form Au nanoparticle(125; 126).

Bennett et al.(127) and Liu et al.(128) used iron-loaded amphiphilic block copolymer polystyrene-

poly(acrylic acid) (PS-PAA) as templates to produce CNTs by thermal CVD.

The method of preparing the catalyst particles used is similar to that developed by Liu et al.(128).

For our experiments, PS-PAA di-block copolymer, with molecular weights of PS 42000= g/mol and

PAA =4300 g/mol, was dissolved in toluene with a concentration of 12 mg/mL and stirred for 4

hours. To convert all of the polymer material to the spherical micelle phase, the solution was heated

to 150oC for 20 minutes and then cooled to room temperature. FeCl3 was then added to the solution

with a 3:1 PAA monomer/ Fe mole ratio, as this reflects the charge ratio of the acrylic acid monomer

to the iron cation. The color of the micelle solution changed to dark yellow when the iron salts were

added. After adding the Fe salt the solution was stirred for 6 hours. Subsequent to this the solution

was diluted to 3.6 mg/ml. This was then spin-coated at 1500 rpm for 1 minute onto 10nm of

Al sputter deposited on Si(100). One drop was enough to form a monolayer coverage for a 1cm2

substrate. The micelle films were then heated in air to 400oC for 2 hours to remove the polymer,

leaving iron oxide particles on the Si substrate. Fig.5.2 is a schematic of the process described

above. For the right concentration and spin speeds a monolayer thick polymer can be deposited

which following calcination will result in the formation of self assembled uniform quasi-hexagonal

array of dots.

5.3.1 Characterization of the catalyst particles

The catalyst particle size and distribution controls the diameter and the density of the CNTs grown.

Fig.5.3 compares the catalyst particles obtained from the two different methods mentioned above.


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Figure 5.3: Size and density distribution of the Fe catalyst particles obtained from (a) block copoly-mer templates and (b) from sputter depositing 2.5 nm thin Fe film. The Y-axis for both the plotsare percentage values

Fig.5.3(a) shows the SEM image of the Fe particles formed by the micelle approach after thermally

removing the polymer. The particles so formed have a tighter size spread, and are arranged in a

quasi-hexagonal pattern. Fig. 5.3(b) is a representative image of the particles formed from the

continuous 2.5 nm Fe layer after annealing at 550oC. Fig.5.3(c) is a histogram of particle sizes.

The Fe particles obtained from the micelles have a narrow size distribution of 6.9± 0.8nm. Though

the mean diameter of particles formed from the continuous Fe film is similar, 6.5 nm, the spread

in the distribution is large. Fig.5.3(d) is a histogram of the particle density, obtained by measuring

the distance between centers of two adjacent particles. The sputter deposited films had a denser

particle distribution, with the mean separation between particles 25.2 nm. The particles formed

from the copolymer templates had a mean separation of 51.7 nm. Auger spectroscopy confirms

that the particles obtained by the micellar route is Fe-oxide. Fig.5.4 is an elemental map of a sparse

dispersion of micellar particles, attesting to the above fact. Also seen in the image is a large particle,

formed probably due to agglomeration of smaller particles.

For the catalyst particles obtained from the micelle templates the CNT yield is low, only about

20% of the catalysts grew CNTs, Fig. 5.5(a). Such behavior has been reported elsewhere (128).


Figure 5.4: Fe mapping of the particles obtained from the micelle template.(a) SEM image and(b)corresponding Fe map

One possible reason for the low yield could be micro-loading, where the chemical species present at

the surface are altered by catalytic surface reactions when the catalyst density is high. TEM of the

micellar particles was performed post MWNT growth. The motive was to look for distinguishing

features in particles that grew CNTs as opposed to those which did not catalyze MWNT growth.

For this, particles were deposited on an e-beam transparent Si-nitride TEM grid (50 nm thick).

TEM micrographs supported the observation that the MWNT yield of the particles were very low

Fig. 5.5(b). Due to the relatively thicker nitride membrane lattice images or proper CBED patterns

could not be obtained from the individual particles. Hence a crude dark field imaging method was

used to determine the crystallinity of the particles. To obtain a dark field image the metal strip

between the selected area diffraction apertures was used to block the transmitted image. Hence only

crystalline particles (diffracting in the right direction) can be observed as bright spots on the dark

field TEM images. Comparing the bright and dark field images from Fig. 5.5(d) we can see that

not all particles formed from the micelle template are crystalline. From Fig.(c) we observe that not

all crystalline particles resulted in formation of MWNTs. Only crystalline particles of intermediate

sizes resulted in MWNT growth. Thus, nanotube density obtained from the self-assembled particles

is sparse, and hence are relatively free of the steric crowding of neighboring CNTs. Therefore, we

were able to study the effect of electric field on arrays of isolated MWNT.

5.3.2 Control of catalyst size and separation using micelle templates

One of the advantages of the micellar route over the sputtered film method is the relatively stricter

and easier control of particle size and density. There are many simple strategies to control spatial

distribution. Increasing the concentration of the copolymer loaded in the toluene solution or by

decreasing the rpm during spin casting multilayers of polymer can be deposited which will increase

the density of the particles deposited.

A more controlled method of changing the spatial distribution is by choosing a block co-polymer


Figure 5.5: EM studies of MWNT yield from micellar nanoparticles. (c,d) Bright and dark fieldTEM images of particles subsequent to MWNT growth

with a different molecular weight PS polymer, Fig.5.6. This method is limited by the volume fraction

of PS:PAA, since only for a certain volume fraction spherical micelles form. Beyond this fraction

other forms of block copolymer templates form e.g lamellar, hexagonal arrangement of cylinders,

bi-continuous gyroids etc. Other methods of controlling density is adding PS polymer or blank

PS-PAA polymers to solution containing PS-PAA and Fe salt.

Increasing the size of PAA on the other hand can be used to increase the size of the catalyst

particle. This method is again limited by the relative volume fractions of PS and PAA. Another

method of controlling particle size is by changing the metal loading ratio. In Fig.5.7(a) FeCl3 was

added to the copolymer micellar solution at a loading ratio ∼ 0.3, leaving an excess carboxylic acid

groups. The Fe-oxide clusters, so formed, have a mean diameter of 3.61 nm. In Fig. (c) FeCl3

loading ratio is increased to ∼ 3. There is a significant excess of Fe compared to the carboxylic

groups, resulting in the formation of larger particles, mean diameter = 6.12 nm; almost doubling the

particle size by controlling the loading ratio. This method is limited by the saturation in the loading

capacity of the micelles, increasing the loading ratio beyond this limit will result in precipitation of

the excess Fe bearing salt from the micelle solution.


Figure 5.6: Controlling spatial density by controlling the size of the PS polymer

5.4 Experimental technique: MWNT growth

A brief recapitulation of the steps for growing MWNTs. The gap between the two electrodes is

maintained at 4 mm. Before growth the reactor was evacuated to a few mTorr pressure. The

substrate is annealed at 550oC for 5 minutes under hydrogen ambient. Following this step the

temperature is ramped to the growth temperature of 750oC. For CNTs grown from Fe nanoparticles

prepared by the micellar route, the annealing step is not performed. Ethylene and hydrogen flow

are maintained at 350 and 100 sccm respectively. Variations on the above operating conditions are

performed as described below. The most significant operating parameters for this study are the

chamber pressures and the magnitude of the biasing electric field. These two parameters are inter-

dependent. The breakdown voltage of the gas, between the parallel plates, determines the valid

ranges of these two parameters. The Paschen curve, which describes this behavior, shows that the

voltage necessary to arc across a fixed gap decreases with pressure to a minimum value, beyond which

it starts increasing with pressure. Similarly for decreasing gaps at fixed pressure (23). Maintaining

low gaseous pressure and small gap could be used to achieve high fields. Geometrical considerations

limit the minimum gap between the plates. Hence to achieve high fields it is either necessary to

drastically lower the pressure of the precursor gases or to operate at high-pressure regimes. Since

the precursor flux would be substantially diminished at low-pressure conditions, it is necessary to

operate at high pressure to apply high electric field. However, a pressure induced transition from

MWNT to carbon nanofibers limits maximum pressure in the reactor as discussed in the previous

chapter. The critical pressure that induces the change in morphology increases with a decreasing

catalyst particle size. At intermediate pressure regimes coiled MWNTs form, opposed to the straight

CNTs at lower pressures. Care has been taken to avoid the nanofiber formation pressure domain

for all the growth runs.

5.5 Results

The main motivation of this work was to study the effect of electric field on alignment of sparse

MWNT growth not hindered by steric effects suffered by dense MWNT forests. The initial field


0

5

10

15

20

25

1.5-

2

2-2.

5

2.5-

3

3.0-

3.5

3.5-

4.0

4.0-

4.5

4.5-

5.0

5.0-

5.5

5.5-

6.0

6.0-

6.5

6.5-

7.0

7.0-

7.5

7.5-

8.0

8.0-

8.5

perc

enta

ge

particle radius (nm)

PAA:FeCl3=1:3

PAA:FeCl3=3:1

Figure 5.7: Controlling particle size by controlling the metal loading ratio

assisted dense MWNT growths were dummy runs performed to get an idea of the parameter space.

But, interesting trends started to appear on application of bias even for the dense films, which called

for further investigation. In this section we report the height and alignment dependence of dense

MWNT films on the applied field followed by the alignment dependence for MWNTs grown form

block co-polymer micelle templates.

5.5.1 Characterization of the MWNT forests from sputter deposited Fe

films

Figure 5.8: SEM images of MWNT films grown at 400 Torr as a function of bias


SEM images of CNTs grown at a temperature of 750oC and a total pressure of 400 Torr are

shown in Fig.(5.8). The magnitude of the applied electric fields are zero, 0.75 and 1.0V/µm. In the

negative bias condition described here, the bottom electrode is grounded while the top is maintained

at negative potential with respect to the bottom. The SEM characterization of the CNTs reveal that

MWNTs grown with an applied bias resulted in cleaner, taller, straighter tubes Fig.(5.8). MWNT

were also grown under reverse bias (the top electrode is held at a positive potential in reference to

the grounded bottom electrode). Unlike (29)(where growth was reported only for the negative bias

condition) good growth was obtained for all these runs, with the MWNT morphology and height

showing similar trends.

However, for the 400 Torr growth, arcing was observed for higher applied fields. This has to

be avoided since various studies on plasma enhanced CVD growth of CNTs reveal that in the glow

discharge regime and higher current densities carbon nanofibers form in preference to CNTs (13; 22).

Hence following the Paschen curve, the reactor chamber pressure was maintained at 760 Torr to

access a larger range of biasing magnitude for manipulating the MWNT growth while remaining

within the dark discharge regime.

5 m

5 m

5 m

2 m

2 m

4 m

E = 0V/ m

E = +2V/ m

E = +6V/ m

E = -4V/ m

E = -6V/ m

E = -10V/ m

Figure 5.9: SEM images of MWNT films grown at 760 Torr as a function of bias


Fig. 5.9 shows SEM images of MWNT grown at a higher pressure of 760 Torr. The flow rates of

hydrogen and ethylene into the chamber were maintained at 350 sccm and 100 sccm respectively. To

systematically study the effect of increasing fields on the height and morphology of the CNTs, six

samples were grown with increasing biases from 0 to 1.0V/µm in increments of 0.2V/µm. Another set

of MWNTs were grown for the same conditions but with a reverse bias. However, arcing commenced

at lower fields (∼+0.8V/µm) relative to the negative bias case (∼ -1.4V/µm). Arcing for the reversed

bias conditions at lower fields than that of negative bias can be explained due to field emission and

thermionic emission from the growing carbon nanotubes (129). Electron emission from the MWNTs

can induce collision cascade ionization resulting in arcing between the plates. In the negative bias

growth, emitted electrons will be drawn back to the electrodes, reducing their interaction with the

gas. Fig.5.10 shows the increasing height of the CNTs with increasing bias. The height of the CNTs

increases with bias up to almost three times at 1.0V/µm compared to growth in the absence of a

field. Thus, with an applied electric field there is a definite enhancement in the growth rates.

14

12

10

8

6

4 Hei

ght

of t

he M

WNT

film

(µm

)

-1.0 -0.5 0.0 0.5

E-field magnitude (V/µm)

Figure 5.10: Height of the CNTs as a function of imposed electric field

Orientation analysis of nanotubes in MWNT forests

The extent of alignment of the CNTs is characterized by two-dimensional Fast Fourier Transform

(FFT) analysis of high magnification SEM images of the MWNT forests under different biasing

conditions. FFT has been used by Acharya et al. (130) to qualitatively describe the alignment of

electro-spun nanofibers. We have further developed the technique to include an orientation factor to

quantify the degree of alignment. The analysis procedure is shown schematically in Figs 5.11(a-c).

All image analysis was done using Matlab R2008a. To prevent edge effects in the FFT data, the edges

were blurred using a Gaussian low-pass filter as shown in Fig5.11(b). The FFT was then performed

on the edge-blurred images. Fig. 5.11(c) is a contour plot of the logarithm of magnitude of the

intensities, after the zero-frequency component of the Fourier transformed image has been shifted to


Figure 5.11: Characterization of the alignment of the e-field aligned MWNT forests. Fig. (a-c)describes the methodology for quantifying the alignment of the forests. Fig. (a) is the original SEMimage of the forests ;(b) the edges has been blurred to remove the edges from showing up whendoing the 2D FFT of the images;(c) contour plot of the FFT of (b).

the center of the spectrum. The intensities of this transformed image are used to quantify alignment.

For this we introduce the Hermans orientation factor, f . This quantity has been frequently used to

quantify orientation. For example, polymer scientists have used the Hermans orientation factor to

quantify in-plane orientations in semi-crystalline polymers (131). It is defined as:

f =3〈cos2 ϕ〉 − 1

2(5.1)

where

〈cos2 ϕ〉 =

∫I(ϕ) cos2 ϕ sinϕdϕ∫

I(ϕ) sinϕdϕ(5.2)

where I(ϕ) for this case is the absolute intensity of the FFT image at the azimuthal angle ϕ, defined

with respect to the ky = 0 line, as shown in Fig. 5.11(c). For perfectly straight nanotubes oriented

vertically with respect to the substrate, the FFT contour will be a straight line along ky = 0, hence

f = 1. For complete random orientation of the CNTs, the contour plot will be circular (instead of

elliptical as shown in Fig. 5.11(c)) and the correspondingly f= 0.

High magnification (50,000X) SEM images of the MWNT forests were taken for all the biasing

conditions as shown in Fig 5.12(a). It is important to recollect that pressure of the reactor has

important consequences on the morphology of the MWNT grown. As mentioned in the previous

chapter increasing pressure leads to the formation of coiled nanotubes, which can be evidenced from

comparing the SEM images Fig.5.12(a) with that of CNTs grown at lower pressures, Fig.5.8. At

least three images were taken for each sample to quantify the alignment of the base, middle and

the top regions of the forests. All SEM images were of the same magnification and size to avoid

introducing artifacts. Fig.5.12(b) plots the orientation factor vs. the magnitude of the applied bias.

Orientations factor for the base, middle and top of the forests for each biasing condition are reported.

The Herman orientation factor increased from an average of 0.16 for no bias to approximately 0.27

for the 1.0V/µm condition, showing a definite increase in alignment of the CNTs. For the same

sample, an increased alignment can be seen towards the top and middle of the forest as compared to


0.36

0.34

0.32

0.30

0.28

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

alig

nmen

t (H

erm

an p

aram

eter

)

-1.2 -0.8 -0.4 0.0 0.4 0.8 E-field magnitude(V/µm)

bottom alignment factor middle alignment factor top alignment factor

Figure 5.12: (a) High magnification SEM side-view images of MWNT films grown at different biases.Fig.(b) plots the alignment and the height of the forests vs. the applied biasing voltage

the portion of the MWNT forests near the substrate. This is true for almost all biasing conditions.

5.5.2 Characterization of the MWNT grown from catalysts obtained from

micelle templates

Next the effect of electric field on the growth of low density MWNTs was studied. Particles deposited

as a monolayer film show regular ordering but have a sparse coverage. These low-density particles

result in sparse non-uniform growth. Hence due to the absence of a crowding effect and with

no localized field to direct the growth of the CNTs, the MWNTs grown are randomly oriented,

Fig5.13(a). Figs 5.13(b-d) are representative images for MWNT growth under an increasing applied

bias, of the order of 1V/µm. All these growths were done under operating pressures of 1000 Torr.

This enabled us to achieve high electric fields of 1.2V/µm. Even with increasing bias, the SEM

images show the presence of nanotubes randomly oriented near the surface. This is particularly true

for regions where the density of MWNTs is high. In regions where the density of CNTs is sparse,

the MWNTs align along the direction of the applied bias, Fig. (b-d). Higher bias resulted in the

formation of taller and straighter CNTs. The number of CNTs aligning in the direction of the fields

also increased with increasing field.


Figure 5.13: SEM images of MWNT grown from micelle templates. MWNTs (a-d) are grown underthe influence of increasing electric fields. The magnitude of the bias is printed on the respectiveimages.

Orientation analysis of isolated MWNTs

The FFT based image analysis technique cannot quantify alignment of the isolated CNTs. For this,

an edge tracking method was developed based on the approach of Kovesi et al. (132). The basic

algorithm is described in Figs 5.14(a-c). The first step is to detect the edges of the CNTs. This is

done by looking for local maxima in the gradient of intensities of the SEM images of the isolated

nanotubes. The co-ordinates of the maxima positions are listed and linked together to obtain the

nanotube edges (Fig.5.14(b)). Straight segments are then fitted to each edge after defining minimum

length specifications (Fig.5.14(c)). Next, the angles made by the straight edges with respect to the

substrate are obtained. At least 25 CNTs were analyzed for each of the growth runs. Fig.5.14(d)

shows the alignment data in the form of a bar chart that plots fraction of tube lengths within a

certain angular range. The bar chart confirms the observations made from the SEM images. The

fraction of tube segments aligned along the direction of the field increases with bias, with fraction

of tube segments making an angle of 80− 90o to the substrate going up from 6% for no bias to more

than 20% for an applied bias of 1.2V/µm. The probability of a tube segment inclined more towards

the normal away from the base is near 30% for growth without a field. For growths under an applied

bias the probability of CNTs being inclined towards the direction of the applied field increases to

more than 60%. This probability appears independent of electric field magnitude above 0.65V/µm.


(a)

(b)

(c)

20

15

10

5

00-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90

angle (degrees)

20

15

10

5

0

20

15

10

5

0

per

cent

age

20

15

10

5

0

e-field = -1.20V/um e-field = -0.90V/um e-field = -0.65V/um no bias

Figure 5.14: Alignment of MWNT for different biasing conditions. Figs (a-c) describe the alignmentalgorithm. Fig (b) defines the edges from the original SEM image (a). Straight segments are fittedto the edges so obtained, and the angles made by these segments are measured with respect to thehorizontal plane. Fig (d) is a bar chart that compares the fraction of lengths oriented with in anangular range for different applied electric fields.

5.6 Discussion: Tube Alignment and applied field

Electrostatic alignment of CNT takes advantage of the unique 1D morphology of the CNTs. The

polarization coefficient along the axial direction of the tube is significantly larger than the radial

direction(19). The difference in polarizability, results in a net dipole moment that aligns the tube

in the direction of the field. However the nature and magnitude of the force may vary depending

on the nature of the CNTs (MWNT, metallic or semi-conducting SWNT), the spatial density and

the length of the CNTs. The discussion section is divided into two parts. First we consider the field

effects on the sparsely dispersed MWNT growing on isolated catalyst islands and then the dense

MWNT forests.


5.6.1 Alignment for isolated MWNT

Fig. 5.15(a) is a schematic of a MWNT oriented at an angle θ with respect to the field. The

dipole moment of a tube is ~p = αijLEj , where αij is the polarization tensor. For MWNTs the

axial polarizability tends to be a sum of the polarizabilities of all its constituent tubes, while the

transverse probability tends to that of the outermost tube of the MWNT (133). Hence, for all

subsequent calculations the effect of the transverse component will be neglected (i.e. αij ≈ α‖,

where α‖ is the polarizability along the tubular axis). Since, the dipole moment of the MWNT is

large, MWNTs are easier to align in the direction of the electric field. The magnitude of the torque

aligning the MWNT along the direction of the electric field is given by:

|τ | = 1

2α‖LE2 sin 2θ (5.3)

and the associated energy by:

|U| = 1

2α‖LE2 cos2 θ (5.4)

U is minimized for θ = 0, hence the torque tends to align the tube along the direction of the field.

D

L

x

y

u~L(1-‐u/2D)

(a) (b)

Figure 5.15: Schematic of a MWNT oriented at an angle θ to an applied electric field (a). Fig (b)is a schematic of two different vibrating growth models; case (I) where the CNTs are not touchingand case (II) where the tip of the CNTs might interact.

Similar to the approach of Lieber et al. (27) and Hongo et al. (28), two growth modes for the

vertical growth of MWNT are proposed, Fig 5.15(b), free growing and growing while in contact with

neighboring CNTs. For the vertical growth mode we neglect the interaction between the CNTs and

the surface. The nanotube grows vertically from the catalyst, with the tip of the CNTs vibrating


thermally with amplitude, u. In case of u <D/2 (Case I), where D is the separation between CNTs,

two neighboring tubes would never interact. This is true for short tube heights or for CNTs grown

from low-density catalyst particles. In case of u >D/2 (Case II), the CNTs have a finite chance of

touching the neighbors. This case corresponds to longer CNTs and for tubes grown from closely

spaced catalyst particles. When the two CNTs come in contact with each other, the probability of

short-range interaction forces (e.g. van der Waals, dipole-dipole interaction etc.) become significant

in controlling the orientation of the nanotubes.

To estimate the amplitude, the MWNTs are simulated as cantilever beams fixed at one end. In

the limit of small amplitude the motion of a vibrating rod under the influence of an electric field is

given by the equation (28):

ρAδ2y(x, t)

δ2t+ YI

δ4y(x, t)

δx4−α‖E

2

2

δ2y(x, t)

δx2= 0 (5.5)

The above differential equation balances the kinetic energy of the vibrating CNTs, and the elastic

energy due to bending and electrostatic forces due to the applied field on the polarizable CNTs. For

no bias growth the third term is zero. The vibration amplitude is controlled by the strain energy

to bend the tube. This amplitude for a tube of outer and inner radius, rNT and rin respectively is

given by (86)

u2E=0 =

0.424L3kBT

Y(r4NT − r4

in). (5.6)

Fig. 5.16 plots u as function of height of the tube (outer radius 5 nm, inner radius = 3.3 nm,

and Youngs modulus, Y = 1.0 TPa). Its also known from Fig.5.3, D/2 ∼ 25 nm. From the plot

we see that the vibration amplitude becomes greater than this value when the height of the tube is

3µm. For taller CNTs the growth crosses over to Case II mode, where the van der Waals interaction

becomes significant. The van der Waals interaction energy between two CNTs of radius R touching

is given by the relation (134)

EvdW ≈A√

R

24a3/2g

L(1− u

2D) (5.7)

where A is the Hamaker constant (for MWNT A ∼ 1eV), and ag is the gap between two graphene

sheets. The magnitude of this interaction energy is orders of magnitude higher even for short contact

lengths than the thermal energy at the growth temperature (∼0.086 eV). Hence, for taller CNTs

van der Waals causes stiction and prevents freestanding tube growth. The SEM image of growth

under no bias attests the above observation.

For biased growth, the solution of eqn. (5.5) is cumbersome. An analytical solution is not

possible. A numerical solution to the partial differential equation (5.5) was performed to obtain the

values for the allowed frequencies (please see the Appendix). The total elastic energy contained in


10-5

10-4

10-3

10-2

10-1

100

101

102

Am

plitu

de o

f the

tube

tip

(nm

)

108642 Height of the MWNT (!m)

E= 0V/m E= 10V/m E= 100V/m E= 1000V/m E= 10

4 V/m

E= 105 V/m

E= 106 V/m

Figure 5.16: Plots the lower order vibrating amplitudes of the tube tip as a function of the appliedfield and the tube height. The , ∆ correspond to the first and second order amplitudes. Thearea between the dashed line corresponds to the distribution of half the inter tube separation, D;amplitudes greater than these values will result in case (ii) growth mode. (1V/µm = 106V/m)

the vibration mode n is given by the relation :

Eelasticn = |YI

2

∫ L

0

(δ2yn

δx2)2dx|sin(ωt)=1 =

1

2celasticn u2

n (5.8)

where ω is the frequency of vibration, and cn, un are respectively the effective spring constant and

deflection of the nth vibrational mode.

Also the average energy of the nth mode is 〈En〉 = kT , half of which comes from the elastic

energy degree of freedom. Thus comparing equation (5.8) with kT we can obtain the amplitude for

each vibrational mode (28).

δn = (kBT

celasticn

)12 (5.9)


Knowing the allowed frequencies, the amplitude of each vibrational mode can be calculated. The

amplitudes for the lower order modes so obtained are plotted as a function of nanotube height

and applied field strength in Fig. 5.16. For no bias and low applied fields the amplitude of the

fundamental mode is greater than the higher order modes. But for large bias these amplitudes

are similar. The most important effect, though, is a decrease in the vibration amplitude of the

CNTs by a few orders of magnitude on application of an electric field. This is a consequence of the

large polarization tensor of the MWNT along the axial direction, of the order of 106A2 (135). The

amplitude of the tip is larger than D/2 only at very low applied fields of the order of ∼ 102V/m.

For the e-fields used in our study ∼ 106V/m and for tube heights typically obtained ( < 10µm) the

vibration amplitude is never greater than D/2. Hence the model suggests that the main impact of

the applied field is to keep growth in Case I regime. This is achieved at relatively small applied

fields. The above observations support the experimental results. Application of an electric field

enhances alignment, the presence of vertical CNTs, Fig 5.13(b-d), attests to that. But subsequent

increase in applied field from 0.65V/µm → 1.2V/µm does not result in any significant increase in

alignment.

We have neglected the contribution of the van der Waals interaction between the CNTs and the

substrate. This is a non-trivial interaction particularly during the initial stages of growth, when the

effect of the imposed electric field is limited as α‖ is length dependent. This attractive force with

the substrate will bend the CNTs, resulting in tube growths parallel to the substrate. In regions of

dense MWNT growth, this will increase inter tube interactions that would dictate alignment and

result in randomly oriented growth; as is seen from the SEM images. CNTs growing in a sparse

region free of these interactions in the early growth stages therefore should be perfectly oriented due

to the presence of the electric field. It has to be noted that even for these sparse CNTs, we dont

get straight tubes growing perpendicularly to the substrates. This is because defects in the tube

structure, introduced due to high-pressure growth conditions, result in the formation of kinks that

cannot be straightened by the imposed field.

For Case II growth with an imposed field, the dipole-dipole repulsive interaction between CNTs

would have to be considered. The maximum repulsive force between two dipoles separated by a

distance r is given by Edipole = p1p22πεεor3

(134). Due to the high value of the axial polarization and

the large applied fields, the dipole-dipole interaction would be the dominant short-range force. This

short range repulsive forces would further limit interaction between CNTs.

5.6.2 Alignment of nanotubes in a dense MWNT array

Calculations from the last section show that for field strengths used in this study the vibration

amplitudes of the MWNT tips are in the sub-Angstrom level. The spatial density of the catalyst

particles is not high enough to result in Case II growth even for the continuous Fe thin film substrates.

Thus the short-range forces are not significant and hence there should be limited or no interaction


between the CNTs. But the high magnification SEM images (Fig. 5.12(d-f)), even in the presence of

large electric field, show a coiled morphology. This is due to the presence of pressure-induced defects

to the MWNT structure that result in the formation of kinks. Thus, the MWNTs in the dense

forest can be simulated as a bunch of closely packed helical springs, as shown in Fig. 5.17(a). In

the absence of an electric field the main force acting on these CNTs is van der Waals that results in

the dense MWNT being aligned parallel to the growth direction. With the application of an electric

field, there is separation of charges along the length of the CNTs, resulting in significant repulsion

between tubes, which keeps them aligned. SEM images show straighter MWNTs with increasing

strength of applied fields, a fact also reflected by the FFT image analysis of the CNTs. The forces,

mentioned above, explain the general alignment of the MWNTs along the growth direction in the

presence and absence of an electric field but cannot explain formation of straighter CNTs with

increase in applied bias. Thus it calls for further investigation.

There is unbalanced stretching force acting on the CNTs in the direction of the applied field

(Fig 5.17(a)) that has not been considered. This tensile force may result in stretching of the spring

(the pitch changes, but the arc length of one coil remains the same) and hence may account for the

increased alignment by forming straighter CNTs. Thus its worthwhile to find the magnitude of the

forces involved. Parameters of the nano-coiled spring being considered are the coil radius, R, pitch

λ, and D, the spring diameter. It is also implicit in the model, that these parameters in the absence

of an applied field have average values characteristic of the growth conditions, e.g. temperature and

pressure. The spring constant K of the nanocoil is defined as the total applied force divided by the

total elongation. In terms of shear modulus of the material, G, and the geometry of the nanocoil,

K can be expressed as (136):

K =GR4

8D3NK =

Ks

N(5.10)

where Ks is the spring constant of a single turn of the MWNT coil and N, the total number of turns.

The value of Ks has been reported to vary between 10N/m to 1N/m (136; 137). The force needed

to stretch the coil by a distance x is then given by the equation:

Fspring = −Kx = −Ks∆λ (5.11)

where ∆λ is the elongation for a single coil, Fig.5.17(b). Next the magnitude of the electrostatic

force needs to be calculated. The charge on the nanocoil can be calculated by approximating it as

a cylindrical Gaussian surface. Hence

∵ εo

∮εE · dS = q ∴ qcoil ≈ πεεoDLE

The electrostatic force acting on the cylinder, in presence of an electric field of strength E, is given


by the relation:

Fe = −πεεoDLE2 (5.12)

Equating (5.11) and (5.12) the elongation per coil of the MWNT can be obtained.

∆λ(E) =πεεoDLE2

Ks(5.13)

D

~(D- D)

L

Fe(a)

0.40

0.35

0.30

0.25

0.20

0.15

alig

nmen

t (H

erm

an p

aram

eter

)

-1.2 -0.8 -0.4 0.0 0.4 0.8 E-field magnitude(V/µm)

(b) bottom alignment factor middle alignment factor top alignment factorcalculated parameter bottom Ks = 2.1 N/mcalculated parameter bottom Ks = 2.3 N/mcalculated parameter bottom Ks = 1.8 N/m

Figure 5.17: (a) Schematic of a forest of MWNT, simulated as a bundle of springs. Parameters of thespring, coil radius = D, pitch = λ. Fig (b) plots the alignment of MWNT in the forests, measuredby the angle 〈ϕ〉(see text for details), as a function of the applied field. The markers are anglesobtained from the FFT of SEM images of the MWNT forests, while the dotted lines are theoreticalfits, simulating the forests as springs with constant Ks. Fig. (c) is a plot of MWNT heights while thedashed lines are simulated plots of MWNT height if they were only being stretched by electrostaticforces.

Next step will be to check if this elongation per coil of the helical spring, can account for the

observed increase in alignment as a function of applied bias. To quantify the alignment of the CNTs

we used the Hermans orientation parameter. This parameter is basically the weighted average of the

square of cosine of the angle made with respect to the Kx axis of the transformed image; weighted

by the integrated intensity of the FFT-ed SEM image along that angle. The tangent of the average

of the angle so obtained is hence the ratio of the magnitudes of the resultant Ky and Kx vectors.

Ky and Kx are the axes of the transformed image along the x and y direction of the original SEM

images. Now a 2D image of the bundle of helical springs can be represented by a series of sinusoidal

curves, very similar to that shown in Fig 5.17(a). This in effect can be described by a cosine function

along the y direction, with amplitude 0.5D and wavelength λ, and a series of delta functions along

the x direction. Fourier transform of a cosine function results in an impulse function while a series


of delta functions transforms to a summation of exponential functions.

F〈D〉2

cos(2π

〈λ〉y) =

〈D〉4

(δ(Ky − 〈λ〉) + δ(Ky + 〈λ〉)) (5.14)

F∑

n

δ(x− n〈D〉) = (∑

n

exp(−i2πKxna)) (5.15)

where < D > and < λ > are respectively the average spring diameter and pitch for a particular

applied field. Hence, the expression for the average angle for the FFT image is given by the relation:

〈ϕ(E)〉 = tan−1[

C1〈λ(E)〉

C2〈D(E)〉

] (5.16)

= tan−1[C1

C2× 〈D(0)〉+ ∆D(E)

〈λ(0) + ∆λ(E)] (5.17)

For simplicity we assume that ∆D(E) ∼ −∆λ(E) , then the above equation takes the following form

〈ϕ(E)〉 = tan−1[tanϕ(0)1− ∆λ(E)

〈D(0)〉

1 + ∆λ(E)〈λ(0)〉

(5.18)

Substituting (5.13) in (5.18) we can calculate the dependence of ϕ(E) on the magnitude of the

applied field. Knowing ϕ(E) the Hermans orientation parameter f can be calculated from eqn.(1).

This is plotted in Fig. 5.17(b). The markers are angular data obtained from the FFT of the MWNT

images. The three dotted lines are theoretical fits for the Herman alignment parameter for the

bottom, middle and top portions of the MWNT. The spring constant is the fitting parameter, while

assigning ε = 1000 (138),< D > = 30 nm and L = 5.2µm as obtained from SEM images of the

MWNT forest grown in the absence of a local field. The theoretical fit predicts well the trends

observed from that of the experimental values. The relevant spring constants range from 1.8N/m

to 2.3 N/m, and these values fall within the range of spring constant values (1-10N/m) reported in

the literature. Therefore the increased degree of alignment can be attributed to the stretching of

the MWNT forests by the unbalanced out of plane electrostatic force acting on the CNTs.

It has to be noted that, stretching of the MWNT forests due to electrostatic forces does not

account for the increased height of the CNTs. It accounts only for an approximate height increase

of about 20% or about a tenth of the total height increase between E=0 to E=1V/µm condition.

5.7 Discussion: Growth kinetics and electric field

As discussed in the foregoing sections an applied electric field enhances the MWNT film heights

compared to that of a zero bias condition. This height enhancement could not be accounted for

by the formation of straighter CNTs obtained on application of a bias. Therefore we investigated


further the effect of electric field on MWNT film heights.

5.7.1 Further investigations of growth: time resolved reflectivity studies

Interferograms were recorded to track the height of the CNTs during growth in real time. In order to

accommodate the interferometer setup the minimum gap between the two electrodes was increased

to 10 mm. The view ports were not rated for positive pressures and hence the operating pressure

was restricted to 760 Torr. As a consequence, the magnitude of the maximum applied field without

electrically breaking down the precursor and carrier gases was limited to 0.3V/µm, about a third

of the maximum field used in 5.1. The flow rates of hydrogen and ethylene into the chamber were

maintained at 150 sccm and 100 sccm respectively. Lower flow rates were used here to reduce the

growth rate and improve the resolution of the interference fringes. Typical growth times are 10-15

minutes.

Fig.5.18(a) plots the interferometric signal recorded for nine different growth conditions. This

signal is indicative of the reflected intensity off the substrate. Attenuation of the reflected intensity

by absorption and scattering is accompanied by formation of fringes due to interference between the

beams reflected off the top of the MWNT surface and the catalyst substrate. At lower temperatures

the curves show pronounced oscillations in intensity. With increasing temperatures the oscillation

frequency increase significantly indicating faster growth rates. Fig.5.18(b)shows the experimental

heights as obtained from the interferometer scans and SEM imaging with the corresponding theoret-

ical fits, developed in Chapter 3. A closer look at the interferograms also reveal that the oscillation

time period decreases with increasing magnitude of the bias (See Table 5.1). These numbers also

show that the difference in cycle period between MWNT growth with and without a field decreases

with increasing growth temperature. At T = 775oC the cycle periods are approximately the same. In

other words, growth rates increased with an applied electric field, but the relative change decreased

with an increase in growth temperature.

Table 5.1: Cycle periods and steady state growth rates as a function of temperature andbias magnitude

Temp. electric field 1st period 2nd period growth rate(oC) (V/µm) (secs) (secs) (nm/sec)

700 0 153 162.2 7.80.3 120.7 115 11.8

725 0 67 65.8 18.80.3 59.8 60.1 22.4

750 0 33.5 31.5 34.50.22 32.8 28.2 35.80.3 29.1 26.8 39.4

775 0 21.28 17.7 610.3 21.7 18.0 60.7


1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Ref

lect

ivity

4003603202802402001601208040

Time (secs)

Gro

wth

sta

rted

(a) no bias (T=700

oC) no bias (T=725

oC) no bias (T=750

oC) no bias (T=775

oC) E = 0.3V/!m (T=700

oC) E = 0.3V/!m (T=725

oC) E = 0.3V/!m (T=750

oC) E = 0.3V/!m (T=775

oC) E = 0.22V/!m (T=750

oC)

28x103

26

24

22

20

18

16

14

12

10

8

6

4

2

0

MW

NT h

eigh

t (n

m)

10008006004002000 Time(secs)

SEM heights

SEM heights

(b) 775oC; E= 0V/µm 750oC; E= 0V/µm 725oC; E= 0V/µm 700oC; E= 0V/µm

775oC; E= 0.3 V/µm 750oC; E= 0.3 V/µm 725oC; E= 0.3 V/µm 700oC; E= 0.3 V/µm

1.4

1.3

1.2

1.1

1.0

ratio

MW

NT v

olum

e fr

actio

n

780760740720700

Temperature (oC)

(c)

E= 0V/µm E= 0.3V/µm

Figure 5.18: (a) Time resolved reflectivity plots for the temperature dependent growth runs. Thesolid lines are interferometer scans for zero bias growth, while the dashed lines are the correspondingscans for a negative bias of 0.3V/µm. In between the two sets is the interferogram for a bias of0.22V/µm and growth temperature of 750oC. The plots are offset for clarity, with scans obtainedfrom the same bias magnitude grouped together. Fig. (b) plots the experimental heights obtainedfrom the interferometer scans and their theoretical fits. Fig. (c) is a plot of the relative change indensity of the MWNT film with change in bias and temperature. The reference density correspondsto MWNT films grown at T=700oC with zero bias


The interferometer signals have two other distinguishing features. First, it can be seen that the

intensity of the background signal (non-oscillatory) increases with temperature. The background

intensity is attributed to the intensity of the laser beam reflected off the top of the CNT film in the

absence of interference effects. Reflectance of a beam incident normal to the surface is given by the

relation (139):

R = 1− 4n

(1 + n)2 + k2

where n, k are the real and imaginary parts of the refractive index of the reflecting surface. For an

effective medium material such as the MWNT forest, n and k, will increase with film density. This

indicates that the MWNT density is increased at higher temperature.

Secondly, the amplitude of the oscillations decrease, making the interference fringes less promi-

nent with an increase in temperature. A smaller decrease in oscillation amplitude is seen on applying

an electric field. Similar to the change in MWNT growth rates the relative change in amplitudes

with bias decrease with increasing temperature. This trend can be understood considering the origin

of the amplitude. The oscillations are a result of the interference of the beams reflected off the top

of the MWNT forest and the beam reflected off the nanotube-substrate interface. The intensity of

the second beam going through the MWNT forest will be attenuated following Beer Lambert law.

I

Io= exp(−αl) (5.19)

α = −1

I

dI

dx=

4πk

λo(5.20)

where α is the absorption coefficient, λo the wavelength of the incident beam and l the distance

travelled by the beam in the absorbing MWNT film. The absorption coefficient increases with

increasing density of the film, decreasing the beam intensity and hence the oscillation amplitude. At

the same time oscillation amplitude will reduce as l increases. These effects are separated by first

subtracting the attenuating background from the raw interferometer data (See Chapter 3 for details).

The MWNT film height, is determined from the interference signal facilitating the determination of

the absorption coefficient from eqns.(19 & 5.20).

The absorption coefficient can be alternatively defined as

α =4πσeff

εeff1/2c

(5.21)

where σeff is the effective conductivity, εeff the dielectric constant and c the speed of light in

vacuum (139). The effective dielectric constant and conductivity of the MWNT films can estimated

using formulae for a two component system, air and MWNT. Different formulations are available to

evaluate these properties, the simplest being the one due to Looyenga. This formulation has been

used by researchers to evaluate the density of nanotubes, optical properties of porous silicon etc.


(76; 140). The Looyenga formulation

ε1/3eff = ε

1/31 + f(ε

1/32 − ε1/31 )

σ1/3eff = σ

1/31 + f(σ

1/32 − σ1/3

1 )

where f is the volume fraction of the second phase, works well for systems away from the percolation

threshold (141). Applying the Looyenga formula to eqn.(5.21) and from the fact that the dielectric

coefficient and conductivity of the MWNT are orders of magnitude more than that of air, the effective

absorption coefficient of the MWNT films can be related to the volume fraction f and hence the

density of the films by the relation:

α ≈ 4πf3/2σMWNT

cε1/2MWNT

(5.22)

It is assumed that the intrinsic properties of the MWNTs do not change much with conditions.

Hence from eqn.(5.22) the absorption coefficients are proportional to f3/2, which is proportional to

the 3/2 power of spatial density. This is plotted in Fig.5.18(c). It is observed that the density of

the films increase with increasing temperature, as discussed based on the background intensity of

the scans. The density also increases with an imposed field for lower growth temperatures, while for

MWNT grown at 750oC and 775oC the densities are independent of the field.

5.7.2 RGA Analysis

As discussed in the previous sections increasing magnitude of the applied bias increases the height

and alignment of the MWNT films. The interferometer data supports this and also reveals that

the enhancement is temperature dependent. The height and density of the MWNTs increases on

application of an electric field, implying that the carbon yield in the MWNT forests is more. This

requires an increase in the carbon flux through the catalysts. Carbon flux can increase due to a

variety of reasons. For example, the increase in flux could be due to an increase in vapor phase

diffusive flux due to an increase in the chemical potential of the gases on application of an external

field. Alternatively, gas phase decomposition due to the applied field might add to the decomposition

reactions on the catalyst surface, increasing the net transport across the vapor phase-catalyst inter-

face. Either way this enhanced flux must be a consequence of imposing an external field. To verify

this, the reactor gas composition was monitored using the RGA. For neutral species measurements,

the acquired mass spectra must be de-convoluted, as the resulting intensities, i, from the RGA are

products of the original species’ cracking patterns (50). For a system of n species and m spectra,

the following matrix must be solved to estimate the neutral species density,D.

[im,1] = [am,n][Dn,1] (5.23)


where ai,n represents the cracking patterns for the nth species. The cracking patters are obtained

from the NIST chemistry web-book (51) and from in-house databases obtained from prior RGA

studies of nanotube and nanofiber growth conditions (50; 52). Results obtained in this way can

be compared relatively for a single species at varying conditions. Fig.5.19(a) shows the difference

between the density of species recorded after steady state condition was achieved and just before the

onset of growth. Five different conditions are shown,: without catalyst, growth in the absence of an

electric field, and growth with applied biases of 0.3V/µm, 0.4V/µm and 0.5V/µm. The pressure was

maintained at 400 Torr and temperature at 750oC. For the last case arcing was observed towards

the end of the growth run.

The chemical species tracked in Fig5.19(a) demonstrate the effect of field on the decomposition

of carbon precursor. The volume fraction of ethylene decreases by a small amount in the presence of

a catalyst and more significantly on application of a bias, suggesting that ethylene is decomposed on

the application of a field. Hydrogen does not show an appreciable change with the change of bias.

Concentration of the byproducts of ethylene decomposition show small but consistent increase on

application of an electric field, except for two of the higher molecular weight species. The amount

of carbon monoxide in chamber also increases particularly at a field strength of 0.5V/µm. This may

indicate an increase in carbon radicals which recombine with the residual oxygen in the RGA. The

net conclusion of the RGA data is therefore that the electric field assists in decomposition of the

carbon precursor.

The pressure change in the chamber maintained at constant pumping speeds during the growth

was monitored . For a constant inflow of gas, maintained by mass flow controllers, and an ap-

proximately constant pumping speed as determined by the valve conductance the change in reactor

pressure depends upon the number of moles of the gaseous species generated in the reactor. The

pressure change as a function of growth time is plotted in Fig.5.19(b) for the same MWNT growth

runs for which RGA analysis was performed. It is observed that with application of an electric field

there is a small but observable pressure increase. Similar small pressure increments were observed

for all growths on imposing an electric field. This suggests that electric field assisted breakdown of

the gaseous mixture results in the conversion of ethylene to its byproducts.

5.7.3 Analysis of the kinetic data

The current flowing between the two electrodes was measured to be non-zero but less than 1µA

implying that the field assisted MWNT growth conditions fall within the Townsend discharge regime.

The current density flowing in between the plates is given by the following expression (23):

I(z) = I(0) exp

(∫ z

0

αn(x′)dx′)

(5.24)


0.125

0.25

0.5

1

2

4

8

16

32

64

128

Cha

nge

in In

tens

ity

H2 C CH4 H2O C2 C2H2 C2H4 CO N2 O2 CO2

(a) no catalyst with catalyst 0.3V/µm 0.4V/µm 0.5V/µm (arcing)

120

100

80

60

40

20

0

cha

nge

in P

ress

ure

(Tor

r)

4003002001000 time(secs)

(b)

no catalyst with catalyst 0.3V/µm 0.4V/µm 0.5V/µm

Figure 5.19: Characterization of the reactor gases: (a)RGA results; Bar chart showing the changein mole fraction of the relevant gaseous compounds between the start and the end of the MWNTgrowth runs. The change in species density are normalized by the residual fractions in the RGAbefore the admission of the reacting gases into the mass analyzer at the onset of growth. Fig. (b)plots the change in reactor pressure for the different growth runs, while keeping the in and outflowof gases constant.

where I(0) is the current generated at the cathode, z is the separation in between the electrodes

and αn ,the first Townsend coefficient , is the inverse of an ”ionization” mean free path. Assuming

the discharge coefficient to be constant and for an electrode spacing d, the current density can be

written as I(d) = I(0) exp(αnd). The Townsend coefficient is a function of pressure and accelerating

field between the electrodes. Plugging in the typical form for αn the current density between the

parallel plates due to an applied field E can be expressed as:

I(d) = I(0) exp

(Apd exp

(−BpE

))(5.25)

where A,B are experimentally determined constants specific for a given gas and p is the cham-

ber pressure. Assuming that the density of dissociated products obtained from the field assisted


decomposition of ethylene, is determined from the current and hence charged species density, the

additional carbon flux may be written as :

Jef = KI(d) (5.26)

where K is a proportionality constant.

This hypothesis explains the field assisted height increase due to enhanced carbon flux through

the catalyst particle. But it fails to explain the observed height and growth rate dependencies on

temperature, and also the weakening impact of field at higher field magnitudes, Fig(5.10). These

trends may be explained by considering the overall kinetics of growth. Fig.(5.20) shows an Arrhenius

plot of steady state growth rates of MWNT with and without applied field, obtained from the analysis

of the interferometer data reported above. For reference, growth rates from another temperature

dependent study at growth pressures of 265 Torr is also shown(Chapter 3, Sec 5.1).

6.0

5.5

5.0

4.5

4.0

3.5

3.0

ln(v

RT/∆

µ)

1.04x10-31.021.000.980.960.94 1/T (K-1)

194 kJ/mole

189 kJ/mole

327 kJ/mole

198 kJ/mole

316 kJ/mole

P=265 Torr, no bias P=760 Torr, no bias P=760 Torr,E = 0.3V/µm

Figure 5.20: Arrhenius plots of normalized steady state growth rates plotted as a function of theinverse of temperature. Three sets of data are presented; MWNT growth under no bias at lower(265 Torr.) and higher pressures(760 Torr.) in the absence of an electric field and temperaturedependent growth runs for an applied electric field of 0.3 V/µm. The activation energy calculatedfrom the plots are printed on the figure

While a single activation energy could be extracted for the cases without field, the deviation

from such a fit at low temperature, and the similarity of the field enhanced case at high tempera-

ture, prompt us to consider a two activation energy model. The high temperature growth rates are


well fit by a straight line, giving an activation barrier of 198 kJ/mole, while the lower temperature

growths have an activation energy of ∼316 kJ/mole. Similar behavior was seen for the low pressure

growth runs, with an activation energy of 189 kJ/mole at high temperature and 327 kJ/mole for low

temperature. For the lower activation barrier, the rate limiting step was identified to be interface

transport limited. The activation energy obtained at lower temperatures is also too high to be asso-

ciated with a diffusive process (refer to Chapter 3. Table 1). The activation barrier of ∼320kJ/mole

is closer to the bond energies of the three types of bonds present in ethylene( C-H : 410 kJ/mole,

the π and σ bonds of C=C are respectively 264 kJ/mole and 347 kJ/mole ). This suggests that the

rate limiting step for the lower growth temperatures is the dissociation of the precursor molecule.

For the electric field assisted MWNT growth at 0.3V/µm, the normalized growth rates show a single

activation energy of 194 kJ/mole. This implies that for the field assisted case, the rate limiting step

for the MWNT growth is the same as the high temperature mechanism without an electric field.

To summarize, two rate limiting steps were identified for MWNT growth without an electric field.

The activation energies ∼194 kJ/mole and ∼335 kJ/mole are too high to be related to a diffusive

transport of C in the vapor phase or through the iron catalyst particle. Hence, both the rate limiting

steps must be related to interfacial transport. In the kinetic model developed, a first order reaction

was used to describe transport across the vapor-catalyst interface. This first order reaction basically

involves there processes, attachment of the C bearing molecules to the catalyst surface, molecular

dissociation/reaction at the catalyst surface and finally the carbon incorporation into the liquid

catalyst surface. Attachment/physisorption generally has a negative activation barrier. The high

temperature activation barrier, 194 kJ/mole is similar to the activation energy for the dissolution

of C into iron (210 kJ/mole, (76)). The activation energy of the low temperature rate limiting step

corresponds to the bond energies in ethylene, leading to the hypothesis that precursor dissociation

at the interface is the rate limiting step. A schematic of the processes described above is represented

in Fig.5.21. The C flux for the mass transfer step at the vapor-catalyst interface can then be written

as:

J−1VL =

k−11

∆µ1exp (E1/RT) +

k−12

∆µ2exp (E2/RT) (5.27)

where E1 and E2 are the activation barriers for precursor decomposition and C dissolution into the

catalyst particle respectively, and ∆µ1 and ∆µ2 the corresponding changes in chemical potential of

C.

Precursor decomposition on catalyst surface has the higher activation barrier, E1 ≈ 320kJ/mole,

implying it will be the rate limiting step at lower temperature, as is observed in Fig.5.20. With an

increase in growth temperature the process with the lower energy barrier (C incorporation into the

Fe catalyst particle) becomes the rate limiting step. On application of an electric field, we find that

precursor decomposition is no longer the rate limiting step at lower temperatures. From the RGA

analysis we have established dissociation of ethylene in the vapor phase itself on application of an

electric field. Thus the only activation barrier that the C atoms have to overcome in going from the


dissociated C species in the vapor phase to the catalyst particle is that due to C dissolution in Fe,

same as that for the no-field case at higher temperature, Fig.5.21. Thus the enhanced steady state

growth rates at low temperatures on application of an electric field can be explained by a change in

the rate limiting step.Po

tent

ial E

nerg

y

“CHx+catalyst”

“C2H4+catalyst”

vapor vapor-catalyst interface surface/bulk diffusion

Edissol=E2Ediff

Edissc=E1

without fieldwith field

Figure 5.21: Plot of energy of the carbon precursor and CHx (dissociation products of ethylene) asa function of distance form the catalyst interface. The orange, red dotted lines corresponds to theenergetics for a zero bias growth. The blue line represents the energetics of the vapor-catalyst masstransfer step for an electric field assisted growth

The change in rate limiting mechanism at the vapor-catalyst interface also explains the non-

uniform dependence of MWNT heights with the magnitude of applied field, Fig.5.10. The total

flux of the C atoms depends mostly on the chemical potential change of the rate limiting step. For

smaller fields, dissociation of C is the rate limiting step. Hence, increasing the applied electric field

increases the C flux due to the dissociation of the C bearing precursor molecules ,(eqn.5.26), resulting

initially in enhanced height of the MWNTs. But this flux, eventually , becomes larger than the flux

of C atoms dissolving into the catalyst. This makes carbon dissolution the rate limiting step, which

is not influenced by the presence of an electric field. Therefore further increase of applied field has

little or no effect in increasing the growth rates and hence the final MWNT heights.

5.8 Conclusion

To summarize, vertically aligned MWNT growth due to the imposition of an applied DC field was

demonstrated. A FFT based image analysis technique was used to quantify degree of alignment in


the MWNT bundles. An analytical model simulating the CNTs as helical springs was developed to

find the elongation of the CNTs due to tensile stretching by the electrostatic forces. This electrostatic

stretching resulted in straighter CNTs and hence increased alignment. Isolated MWNTs were also

grown from catalyst particles with low spatial coverage under a localized static field. An algorithm

based on the ability to detect edges of the CNTs in SEM images was used to measure the alignment

of the isolated CNTs. Increased alignment for isolated MWNT growth was obtained by orienting the

CNTs vertically along the direction of the imposed field. Three important factors were identified that

control the alignment of the CNTs. The catalyst particle spatial density that controls the probability

of tube-tube interaction, the growth conditions that controls the morphology of the CNTs. Finally,

growth under an applied bias that restricts the growth to Case I regime, taking advantage of its

high axial polarizabilities.

Growth kinetics of field assisted CVD grown MWNT were studied. Application of an electric

field enhances the growth rates. But, the growth enhancement decreased with increasing growth

temperature. Similarly, at the same growth temperature increasing the applied field increased the

height of the CNTs, but for larger fields the height starts leveling off towards a constant value. These

observations were explained in terms of a change in rate limiting step. For an unbiased growth, at

higher temperatures the rate limiting step is the carbon dissolution into the catalyst particle, while

at lower temperatures it is the carbon dissociation at the catalyst-vapor interface which limits the

growth. Application of an electric field enhances the decomposition of the C precursor in the vapor

phase itself, increasing the total carbon flux through the catalyst particles. These increases the

growth rates initially but only to the limit of the growth rates due to the dissolution of carbon into

the iron catalyst particles. These results have potential implications in bringing down the nanotube

growth temperature, on application of an electric field, to levels amenable for CMOS fabrication

procedures.

Chapter 6

Chirality and Diameter Control of

Single-walled Carbon Nanotubes

6.1 Motivation

Carbon nanotubes, particularly SWNTs, have unique transport and elastic properties [1]. Hence

there is considerable interest in using these SWNTs as sensors, composite materials with enhanced

electrical and mechanical properties, electronic components and recently for energy storage and fuel

cell applications. The properties vary as a function of diameter and chirality of the SWNTs. The

bottleneck for the assimilation of the SWNT into devices/materials is the limited control over the

nature of the tube produced and the small laboratory scale production rates. The motivation for this

work was to look for ways to increase production rates. For this, the floating catalyst CVD method

was chosen (please refer to Chapter 1, for other commonly used techniques for SWNT growth) as it

has the largest scope of scalability, since it can be developed as a continuous process as opposed to

batch type processes (e.g. substrate based thermal CVD processes). Simultaneously investigations

for diameter and chirality control were made and is the focus of this chapter.

6.2 Introduction

In the floating catalyst method, catalyst particles are suspended in a flow of a carbon containing

gas, both being continuously fed into the reactor. There has been numerous studies on the produc-

tion of SWNTs by floating catalyst methods; the parameters varied being catalysts (different sizes

and chemical composition), different carbon precursors, different growth temperature and pressure

ranges, introduction of a growth promoter etc (30; 142; 143; 144; 33; 145; 35; 36). One of the more

130

CHAPTER 6. DIAMETER CONTROL OF SWNTS 131

successful techniques was developed by Li. et al (37).They developed a technique to spin continu-

ous fibers and ribbons of carbon nanotubes spun directly from the synthesis zone of a vertical flow

reactor. They used ethanol and ferrocene as the carbon and catalyst precursor respectively, H2 as

the carrier gas and thiophene as a yield promoter. SWNT production rates as high as ∼ 0.5 g/hour

were reported.

In this work, we have used a variation of Lis method for producing SWCNTs. This chapter is

divided such that in the experimental section we talk about the general protocol followed for growing

SWNTs. In the next section we develop a semi-quantitative way of estimating the abundance of the

SWNT diameters based on a combination of transmission electron microscopy, Raman and UV-Vis-

NIR spectroscopy data. Estimating the abundance of SWNT produced (146) has recently gained

a lot of significance with the need for diameter and property selective SWNT growth. We use

the methodology so developed to investigate the reaction space of the vertical furnace for SWNT

production as a function of temperature, carrier gas flow rate and the precursor solution flow rate.

Furthermore we report the sample morphology, catalyst impurities and the nanotube purity as a

function of each of these reaction conditions.

6.3 Experimental Procedure

Ethanol was the chosen carbon source, in which ferrocene and the growth promoter, thiophene, were

dissolved. Various chemical compositions were tried before obtaining the ideal compositions for the

growth of the SWCNTs. For this study, the ferrocene weight percent was varied between 0.25 to

1.0 weight percent (wt%). The thiophene concentration was varied with the amount of ferrocene

in the sample, an atomic S/Fe ratio of 0.2 was experimentally found to be optimum. This solution

was fed into the reactor using a peristaltic pump with flow rates of 0.01 ml/min to 5 ml/min. The

optimum flow rate was found to be approximately 0.1 ml/min. The precursor solution was vaporized

at temperatures of 150 to 200 oC in the delivery tube; the gaseous products were carried directly to

the bottom of the furnace using a controlled H2 flow. The details of the reactor has been mentioned

in Chapter 2. The temperature of the vertical flow reactor was maintained between 900 and 1100oC.

For studying the effect of a particular parameter, all other variables were kept fixed while varying

just the one parameter. Details of these will be mentioned while discussing the effects of individual

parameters on the growth process.

The gaseous mixture is expected to be pyrolized in the first zone/bottom of the furnace with

nucleation and growth of the SWCNTs in the other zones. A typical reaction time was 2 hours,

though it was found that the product mass increased linearly with the reaction time (i.e. constant

production rate). The furnace output runs through ∼4 feet unheated tubing to an exhaust hood, and

hence the entire SWNT production takes place at near atmospheric pressure. The grown nanotubes

were transported out of the reaction zone by the flowing gases and were collected on the cooler parts


of the furnace in the form of very light, diaphanous membrane. These thin films could be easily

peeled off from the reactor walls using tweezers. For characterization of the nature of the CNT

produced, products were collected from the nozzle, the cold portion of the quartz tube protruding

out from the top and bottom ends of the furnace, and the top flange just before the CNT product

entered the exhaust stream. The sample was characterized using transmission electron microscopy

(TEM), thermo-gravimetric analysis (TGA), and Raman and UV-Vis-NIR Absorption spectroscopy.

Raman and TGA were done on the as-prepared sample.

6.4 Results and Discussion

Figure 6.1: Tem images of SWCNT bundles grown at (a) 1000oC and (b) 1050oC with 0.25-wt%ferrocene and 1000 sccm of H2 flow, S/Fe =0.2.

Fig.6.1 is a typical TEM image of the as-synthesized product. The product consists mostly

of bundles of SWCNTs (Fig.6.1(b)). Since the SWNT is lightweight they align along the gas flow

direction and form bundles by adhering to other SWNTs by the Van der Waals forces. This formation

of well-aligned SWNT bundles is characteristic of the floating catalyst method (142) From Fig.6.1

it is observed that particles or particle clusters cling to the surface of the SWNT bundles. These

are mostly either encapsulated Fe catalyst particles or amorphous carbon impurities. It is apparent

that most of the large Fe catalyst particles did not contribute to the growth of the nanotubes, but

rather adhered to the independently formed SWNT bundles during the process.

The purity of the SWNT and also the diameter distribution was found to be very much dependent

on the reaction conditions. The nature of the product was particularly sensitive to the injection rate

of the liquid precursor solution into the carrier gas stream. Higher and very low flow rates resulted

in the formation of soot. There was only a very small window around 0.1 ml/min, which resulted

in the growth of SWCNTs. Similarly, the carrier gas flow rate was found to influence the diameter

of the SWNT produced. Lower flow rates resulted in the growth of larger diameter SWNTs. More


significant influences on the SWNT diameter distribution were observed with varying ferrocene

concentration in the precursor solution and reaction temperature. The detailed influence of these

parameters in determining the carbon nanotube population will be reported in the following sections.

6.4.1 Dependence on the reaction time

(a) (b)

(c)

(d)

150 200 250 300 350 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700

top flangetop of quartz tube

bottom of quartz tubemiddle of quartz tube

nozzle

wavenumber (cm-1) wavenumber (cm-1)

nozzle bottom of tube rope top of tube top flange

nozzle bottom of tube rope top of tube top flange

Inte

nsit

y

Abu

ndan

ce R

atio

I G/I

D

Figure 6.2: Raman of the SWNT samples collected from different parts of the furnace (a)RBMmodes (b)D and G bands (c) Normalized IRBM/IG (d) IG/ID ratio as a function of the furnaceposition

Before discussing the effects of temperature and catalyst metal concentration, the influence of

the reaction time is reported. Also, the semi-quantitative way of estimating SWNT abundance used

throughout this study is described. The as prepared product was collected from different parts of the

quartz tube, with larger distances from the inlet nozzle implying longer reaction times. The reaction

conditions for these set of samples were T = 1000 oC, 1 wt% ferrocene in ethanol, a 1: 5 molar ratio of

thiophene to ferrocene, a precursor solution flow rate of 0.067 ml/min and a H2 gas flow rate of 1000


sccm. Under these conditions, ropes of SWCTs formed that stretched across the entire 6 ft length of

the quartz tube from the nozzle to the top flange. Fig.6.2 shows the Raman spectroscopy data of the

product collected under near IR (NIR) laser (λ =785 nm) excitation. Fig.6.2(a) is a staggered plot

of the radial breathing modes (RBM) of the SWNT samples collected. The RBM Raman features

correspond to the coherent vibration of the carbon atoms in the radial direction, and is a signature

of the CNT product in terms of the nanotube diameter (dt) through its frequency ωRBM and the

electronic structure through its resonant response to the incident laser energy (Resonance Raman

spectroscopy). The diameter distribution of the sample can be found from the position of the RBM

by using the relation ωRBM = A/dt + B, where A and B are empirical fit parameters. A and B

for this set of data had the best fit for A = 230.78 cm−1nm and B = 7.14 cm−1. RBM peaks were

observed at 154, 206, 234 and 266 cm−1, corresponding to nanotube diameters of 1.57, 1.16, 1.02

and 0.89 nm. Fig.6.2(b) is the plot of the corresponding D and G bands. The G-band involves an

optical phonon mode between the two dissimilar C atoms in the graphite unit cell, while the D band

originates from the disorder-induced mode in SWCNT. Therefore the ratio of the G and D band

intensities has long been used as a first estimate of the quality of the SWNT sample. Fig. 6.2(d)

plots the ratio of G and D band. The highest G to D band ratio was obtained for the SWNT sample

collected from the middle of tube, and hence is of the highest quality.

The intensity of the RBMs depend on the chirality of the specific SWCNT, since it determines

the band gap transitions, Sii and Mii, that determine the resonance condition with the incident

laser energy. The band gap energy influences the electron-phonon interaction and the electric-

dipole interaction matrices, which go into the calculation of the Raman intensities (147). The RBM

intensities also depend on the density of SWCNTs in the sample probed and the abundance of

SWNT chiralities. To make an estimate of the abundance of SWCNTs of particular chirality the

two other competing effects have to be corrected for. Normalizing the intensity of the RBM modes

with that of the G band intensities can approximately account for dependence of the sample density.

The best way to correct for the different excitation cross-sections of each chirality present is to find

the theoretical intensity and divide the experimental RBM intensities by it (146). An alternative

way would be to assume a standard and then normalize the IRBM/IG for each RBM peak from a

given sample with the corresponding peak from the standard. These intensity ratios will then give

an estimate of the population abundance of SWNT chiralities in the SWNT sample with respect

to that of the standard. Fig.6.2(c) plots the normalized IRBM/IG ratios that have been described

above, with the samples collected from the nozzle acting as the standard. From Fig.6.2(c) its evident

that population of the larger diameter SWNT(154 cm−1) increases with vertical distance along the

furnace. For example the SWNT product collected from the top flange has twice the number of 1.57

nm SWNTs compared to the nozzle. On the other hand, the abundance of the smaller diameter

SWNT(corresponding to 206-266 cm−1) decreases with height of the furnace.

However, it would be imprudent to come to a conclusion about the population distribution from


Figure 6.3: Kataura plot for the S22, M11 and S33 transitions. Also plotted in the Fig. is theposition of the 785 and 635 laser lines, and a 50 nm shift to account for the bundling of SWNTs.The 2n+m family of the SWCNT are shown for the MOD1 and MOD2 S22 transitions (joined byblack solid line) and for the M11 transitions (joined by green dashed line).

only a single energy excitation resonant Raman study, since it does not probe the entire population

of SWNT chiralities that might be present in a given sample. Fig. 6.3 is a Kataura plot, plotting

the band gap energies as a function of the diameter of the SWNT(and hence the wavenumber).

The values for the interband energies for the S11, S22 and M11 type transitions were obtained from

the model proposed by Strano, et al., (7), while the S33 transition energies were obtained from the

extended tight binding calculations (53). Also shown in the Kataura plot are the 2n+m families of

the SWNT for the MOD1 (n-m mod 3 = 1) and MOD2 (n-m mod 3 =2) S22 transitions (joined

by black solid line) and for the M11 transitions (joined by green dashed line). The solid blue line

gives the energy of the NIR laser. SWNTs having band transitions in this vicinity should give rise

to a RBM peak, due to the resonance Raman effect. However, the 154 and 266 cm−1 RBM peaks

are not in this range. To account for these two peaks we have to include into the Kataura plot the

effects of bundling. For bundled SWNTs, the spectral features are red shifted by 50 to 70 nm with

the magnitude of the shift depending on the extent of bundling and inter-nanotube contact area

(148; 149). Further evidence of the decrease in the transition energies of SWCNTs upon bundling

has been established by Rayleigh Scattering Spectroscopy studies (150). Also due to the broadening

of the electronic transitions the individual RBM spectrum looks less well resolved. One important

note is that the bundling effect has almost no effect on the frequency of the phonon modes (58).

Therefore the dotted blue line, blue shifted from the original position of the NIR laser by 50 nm, with


no change to the wavenumber axis, would be a more appropriate representation of the laser energy

level for bundled SWNT. TEM study of our samples show SWNT bundles of various dimensions

and the actual magnitude of the red shift has not been established, hence instead of establishing a

particular chirality with a given radial peak, we assign the peak to a 2n+m family. This shift now

shows how the 266 cm−1 RBM mode may be excited through the 2n+m = 22 family, MOD2 S22

transitions, and S33 transitions may contribute at or below 150 cm−1. The 150-160 cm−1 region,

however, falls between the M11 and S33 transition energies, with neither being in resonance with

this shifted line. For reasons that will be explained in the next section, we believe that the M11

excitation does not experience the same magnitude of red shift, if any, and thus can be considered

responsible for this peak.

(a) (b)

(c)

wavelength (nm) wavelength (nm)

Abs

orba

nce

%

Abs

orba

nce

Abs

orba

nce

2n+m family

Figure 6.4: UV-Vis-NIR of the samples collected from different parts of the furnace (b) S22 tran-sitions after subtracting the background (c) Comparison of the absorbance % from the spectracorresponding to the peaks obtained from Fig. (b)

Next, to have a better picture of the diameter distribution of the SWNTs, we characterized the

samples using UV-Vis-NIR spectroscopy (Fig. 6.4). This technique has been utilized to estimate

the purity of the nanotubes (151) by comparing the ratio of the area under the S22 peaks with


background intensity, which arises from π-plasmon absorption and particulate scattering from the

SWNT and other carbonaceous impurities. From Fig.6.4(a) it can be seen that the purity of the

SWNT obtained was higher for sample collected from the rope and the top portion of the furnace as

supported by the G to D band ratios from Raman spectroscopy. Further, by noting the positions of

the transition peaks one can also estimate the SWNTs present since the band gap of each SWNT is

unique and has an inverse relation with the diameter. The simplest theoretical treatment predicts

the optical transition wavelengths of semiconducting nanotubes depends linearly on the diameter

according to the relations λ11 = hcdt/2accγo and λ22 = hcdt/4accγo; where acc is the C-C bond

distance and γo the interaction energy between neighboring C atoms [1]. For this paper, the Strano

empirical model was used to estimate the band gaps as in Kataura plot. Similar to the intensity of

the RBM modes, the intensity of the optical transitions is related to the abundance of the SWCNTs

(151; 152). To analyze the peaks, the optical response from the background is subtracted by fitting

to a Lorentzian tail (as expected for a plasmon feature).

For analysis of the UV spectrum we chose a range corresponding to the S22 type transitions. The

M11 features were not used because they were not well resolved, and the S11 transition region was

neglected due to overlap of the solvent (DMF) peaks. Fig. 6.4(b) shows the UV spectrum from the

S22 region after background subtraction. In bundled SWNT systems, intertube interactions broaden

and suppress the van Hove transitions to the extent that the individual features of spectral chiralities

are not resolvable. So instead of trying to identify individual chiralities, the spectral features were

correlated with the 2n+m family corresponding to the S22 transitions. Doing so is straightforward

for the MOD2 S22 transitions, which are very close together in energy, though more questionable

for MOD1 transitions that span a larger, but finite, range. Nevertheless, the approach is useful for a

semi-quantitative interpretation. As shown in Fig. 6.4(b), a multi-peak Lorentzian fit was performed

with the observed peaks assigned to individual 2n + m families as marked in Fig. 6.3 using solid

black lines. The expected location for 2n + m = 28 falls between the major peaks near 810 and

890 nm, thus the dotted vertical lines in the figure are used to assign contributions to the MOD1

2n+m = 29 and 32 families. The areas under the fitted Lorentzian curves were calculated and then

divided by the total area from all the Lorentzian fits for a particular sample to get the absorbance

percentage from each 2n+m family. This was then presented in the form of a bar chart, Fig.6.4(c),

to get a comparison of the SWNT 2n + m families present in each sample. Fig.6.4(c) agrees with

what was observed by comparing the normalized RBM intensities in Fig.6.2(c). Absorbance peaks

were observed from 2n+m families of higher magnitude for samples collected from the top regions

of the furnace. These peaks were almost entirely absent for the sample collected from the bottom

part of the furnace (e.g. the spectral feature corresponding to 2n+m = 37, which also corresponds

to the diameter range for the RBM peak at 154 cm−1). We also note the relatively lower percentage

of the lower 2n+m families from the samples collected from the top part of the furnace. This again

shows that samples collected from the top regions of the furnace have a higher range of diameters,


with a larger fraction of larger diameter SWNTs.

(a)

(b)

Wei

ght %

Wei

ght %

nozzle rope top flange

Figure 6.5: TGA of the samples from different parts of the furnace

Finally, TGA analysis of the samples collected from various parts of the furnace was used to

estimate the SWNT and impurity fractions (Fig.6.5). The initial weight loss on ramping up the

temperature is attributed to amorphous carbon and the residual weight at the end of the temperature

ramp is due to Fe-oxide. The remaining weight loss in between 400 to 900oC is attributed to SWNTs.

While the boundary between SWNT and amorphous carbon may not be distinguished with absolute

certainty via TGA measurement, this metric is used to provide approximations of the SWNT purity

in the sample. On this basis, the fraction of SWNT increases with height as seen from Fig.6.5(b).

The residual Fe-oxide percentage in the samples is relatively high, and will be further discussed in

the following sections.

To summarize, the percentage of larger SWNT diameter in the samples collected increases with

height of the furnace. The higher position in the furnace corresponds to a larger distance from the

nozzle where the precursors enter the reaction zone, and hence a longer residence time. Longer

residence times result in a greater opportunity for the smaller Fe catalyst particles to collide and

agglomerate to bigger particles, as observed in TEM studies. The larger catalyst particles result in

the formation of SWNTs with larger diameter. This explains the increasing diameters of SWNT

samples with position in furnace. The higher purity observed may be attributed to an annealing

effect due to greater exposure to elevated temperature. Also, impurities and amorphous carbon may


form early in the process and thus be preferentially collected near the inlet rather than the outlet.

The rope formed in the middle of the furnace experiences longest exposure to high temperature

conditions and therefore displays the highest purity of all the samples.

6.4.2 Effects of Ferrocene concentration

Catalyst particles are known to influence the nature of the SWNT product (83). The iron catalyst

precursor (ferrocene) concentration in the solution was systematically varied to study the influence

of the metal concentration on this particular process of SWNT growth. Ferrocene concentrations of

0.25wt%, 0.5wt% and 1.0 wt% were used in the precursor solution. Also, for each set of ferrocene

wt% studied, two sets of samples were collected from the top and bottom of the quartz tube. The

other growth parameters held constant for this study were: growth temperature of 1000oC, H2 gas

flow rate of 1000 sccm, solution flow rate of 0.66 ml/min and S/Fe atomic ratio of 0.2.

Fig.6.6(a) plots the RBM intensities under 785 nm laser excitation for all three weight percentages

of ferrocene tried. The two dominant RBM Modes from the 785 laser for all these samples are at 154

and 206 cm−1 wavenumbers. The intensity of the Raman modes for the 206 cm−1 wavenumber did

not vary much with the ferrocene wt%, but there was a noticeably large increase in the intensity of

the 154 cm−1 wavenumber as a function of the ferrocene wt%. In fact, for the sample collected from

the top of the quartz tube prepared from 1wt% of ferrocene, the intensity of the 154 cm−1 RBM mode

was greater than that of the corresponding G band. To extract semi-quantitative information about

the SWNT abundance in the sample from the Raman data, the data was normalized as described

above. The normalized IRBM/IG data are plotted in Fig. 6.6(c), with the sample collected from

the bottom of the tube for 0.25wt% ferrocene concentration being the reference. There is a 10-fold

increase in the abundance of the 1.57 nm (corresponding to a wavenumber of 154 cm−1) nanotubes

for samples with higher ferrocene concentrations, implying that higher metal concentrations spawn

larger quantities of larger diameter SWNTs. This trend is also observed using 633 nm excitation.

The inset of Fig. (a) shows the RBM modes with 633 nm laser excitation. The 633 nm laser probes a

different band gap energy region than the 785 nm laser as shown on the Kataura plot (Fig. 6.3). The

red line and the dotted red line in Fig. 6.3 shows the position of the 633 laser and the approximate

effective position of the laser after the red shift due to bundling effects have been accounted for. The

0.25 wt% and the 0.5 wt% sample exhibits RBM peaks at 190 and 210 cm−1. The 1.0-wt% sample

gives rise to an additional RBM peak at 150 cm-1also weakly present for 0.5wt% sample. This again

implies that a larger metal concentration also results in the formation of larger diameter SWNTs.

The normalized D and G bands for these sets of samples are shown in Fig. 6.6(c). Fig. 6.6(d)

compares the ratio of the G band and D band intensities and shows no particular trend. However,

the shape of the G band changes significantly with ferrocene weight percentage. The more intense

G+ feature ( at 1585 cm−1) is associated with the C atom vibrations along the direction of the

tube axis, while the overlapping lower wavenumber G- band is associated with the vibrations of the


(a) (b)

(c)

(d)

120 140 160 180 200 220 240 260 280 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700

wavenumber (cm-1) wavenumber (cm-1)

bottom(0.25) top(0.25) bottom(0.5) top(0.5) bottom(1.0) top (1.0)

Inte

nsit

y

Abu

ndan

ce R

atio

I G/I

D

bottom(0.25) top(0.25) bottom(0.5) top(0.5) bottom(1.0) top (1.0)

Figure 6.6: Raman of the SWCNT samples as a function of ferrocene concentration. (a) RBM modeswith 785 nm laser, 635 nm laser (inset). (b) D and G bands from 785 nm laser. (c) NormalizedIRBM/IG (d) IG/ID ratio and the extent of G split as a function of temperature. The labels for Fig.(a) and (b) are the same. The label for Fig. (d) is also true for Fig. (a).

C atoms along the circumferential direction of the SWCNT. The G- line shape is highly sensitive to

whether the SWNTis metallic (Breit-Wigner-Fano (BWF) line shape) or semiconducting (Lorentzian

line shape)(53). The samples from 0.5% and 1.0wt% ferrocene have the BWF line-shape while the

0.25wt% sample has the Lorentzian line shape. This implies that the resonant chiralities at 785

nm are primarily metallic for the SWNT prepared from 1.0 wt% ferrocene. Comparison with the

RBM trends suggests this arises from the CNTs contributing the 154 cm−1 feature. Referring back

to Fig. 6.3, we observe that the CNTs contributing to the 154 cm−1 RBM are resonant between

800-900 nm excitation. That this is higher than the effective excitation wavelengths suggest that

bundling effects are different for these SWNTs than the other SWNTs previously described. The

data suggests that red shifting might be completely absent in metallic SWNTs, though tunable laser

Raman spectroscopy will be required to demonstrate this unambiguously. The 150cm-1 RBM for


the 1.0wt% sample with the 633 laser, on the other hand, may be attributed to the S33 transitions

shown in Fig. 6.3, which is corroborated by the Lorentzian shape of the corresponding G band (not

shown here).

Figure 6.7: TEM images of the samples. Fig. (a) and (b) are TEM images from 1.0 wt% samplewhile (c) is the image from SWCNTs formed with 0.25 wt% ferrocene.

TEM on the 0.25wt% and 1.0wt% sample was performed to investigate the validity of the diam-

eter trends from the Raman studies and also to elucidate reasons behind these trends. Fig.6.7(a-b)

are TEM images of SWNT samples that were grown with 1.0 wt% ferrocene, while Fig.(c) is the

TEM image of SWNT sample collected from the 0.25 wt% sample. Fig. 6.8 (a) is a histogram of the

diameter distribution of the SWNT samples obtained from the TEM analysis. The 0.25wt% sample,

on average, has lower diameters compared with the 1.0-wt% sample. The population density for the

former has a maximum at 1.3 nm with a mean value of 1.36 nm (std. deviation = 0.2 nm), while the

percentage distribution for the 1.0 wt% sample peaks at 1.7 nm (mean = 1.86 nm, std. deviation

=0.19 nm). This compares well with the Raman data.

Other groups have reported similar results. Kim, et al., (153)grew CNTs by filling the pores

of well-ordered porous anodic oxide with a metal ion solution. They reported that increasing con-

centration of the metal ion resulted in the formation of larger diameter multiwall CNTs. SWNTs

were grown by Jeong, et al., (154) using methane as the C precursor and ferritin as a source for the

catalysts. They reported that decreasing the Fe concentration resulted in a smaller diameter range

of the SWNTs and also a smaller mean diameter. Singh, et al., (155) did a similar study for the in-

jection CVD growth of aligned CNTs, and observed that decreasing the Fe concentration resulted in

smaller tube diameters, a decrease in CNT purity and width of the diameter distribution. They also

reported that concentration of the encapsulated particles increased with an increase in the ferrocene

concentration. Nasibulin, et al., (83) reported that increasing the metal concentration resulted in


the formation of larger bundles of SWNT, a fact that was substantiated from TEM studies.

(a)

(b)

Abu

ndan

ce %

Abu

ndan

ce %

Figure 6.8: SWCNT diameter and (b) Fe catalyst particle size distribution for sample prepared with0.25 and 1.0 wt% ferrocene respectively, obtained from the TEM images.

The reason for all the above observations was that higher catalyst concentration resulted in the

formation of larger catalyst particles. To check this we did an analysis of the catalyst particle size

for the lower and higher concentration of the ferrocene concentration in the samples (Fig.6.8(b)).

The average particle size for the 1.0 wt% sample (8.65 nm) was found to be larger than that for

the 0.25wt% sample (mean = 3.40 nm). Considering that the CNT diameter bears a certain ratio

with that of the particle size, (reported ratios vary from 2 to 3, (156)) it is not expected that these

large particles are contributing to the growth of the SWNT bundles. This can be verified from the

TEM images of the samples. Both small and large particles are seen in Fig.6.7(a) for the 1.0-wt%

sample. It is apparent that the largest particle is not terminating the growth of any SWNTs and is

in fact coated with an amorphous carbon shell. Therefore, it is not acting as a catalyst for nanotube

growth. On the other hand, a bundle of SWNTs can be observed to terminate at the smaller particle,

implying it is serving as a catalyst.

Fig.6.7(b) is another example of a larger particle forming a carbon onion rather than SWNT

bundles, while a TEM image from the 0.25 wt% sample, Fig. 6.7(c), shows the growth of SWNT from

a smaller catalyst particle. This suggests that there is an optimum concentration of Fe that aids in the

growth of the SWNT by forming catalyst particles. Beyond this level, the Fe particles agglomerate


to form larger particles that do not aid in the growth of SWCNT. This result in the formation of

carbon impurities, thus decreasing the quality of the products formed. This interpretation is also

consistent with the residence time dependencies discussed previously.

(a) (b)

(c)wavelength (nm) wavelength (nm)

Abs

orba

nce

%

Abs

orba

nce

Abs

orba

nce

2n+m family

400 600 800 1000 1200 1400 600 700 800 900 1000

Figure 6.9: UV-Vis-NIR of the samples collected as a function of ferrocene concentration. (b) S22

transitions after subtracting the background (c) Comparison of the absorbance % from the spectracorresponding to the peaks obtained from Fig (b)

UV-Vis-NIR spectroscopy data may provide a larger picture than that given by Raman and

TEM alone. Fig.6.9 plots the absorbance as a function of the weight percentage of the samples.

We concentrate only in the 650-1050 nm region that corresponds to the S22 transition region. Fig.

6.9(b) plots the background subtracted absorbance data, along with the fitted Lorentzian peaks.

Each of the peaks is identified to the 2n+m family; solid lines mark the MOD2 2n + m families.

The two most intense peaks of the absorption spectrum, observed around 815 nm for all samples

and near 885 nm for the higher wt% samples cannot be accounted for using the MOD2 families.

Since Raman spectroscopy suggests that a large fraction of the SWNT near 785 nm are metallic in

nature, the peaks can be identified with the M11 type 2n+m = 33 and 36/39 families respectively.

The 645 nm peak for the 0.25 wt% sample was identified with 2n + m = 23 family of MOD1 S22

transitions. The absorbance percentages for each of the three samples are plotted in Fig.6.9(c). We

see that the abundance of the higher order families are greater for the samples grown with 1 wt%

ferrocene than for the 0.25 wt% sample, consistent with the Raman and TEM data. Thus we can


say that increasing the ferrocene percentage increase the diameter range of the SWNT produced

and also results in preferable growth of the higher diameter SWNTs.

(a)

(b)

Wei

ght %

Wei

ght

frac

tion

Figure 6.10: TGA of the samples prepared with different amount of ferrocene in the precursorsolution. For the fit data x is the wt% of ferrocene in the sample.

Finally, TGA analysis of the samples as a function of the ferrocene concentration was done

(Fig.6.10). The percentage of the SWNT decreases linearly with increasing ferrocene concentra-

tion in the sample. 30% by weight of the product collected is the metal oxide for 0.25% ferrocene

in precursor solution, (comparable with values reported by other groups for oxide content in the

sample (151)) while the 1.0-wt% sample has a residual weight of 65%. The trend of residual iron

content is consistent with first order reaction kinetics for iron formation and constant carbon pro-

duction, i.e. if rFe = knFerrocene and rC+CNT = C, then, wFe = wFerrocene

wFerrocene+C/kM where wFe is the

weight percentage of iron in the product, wFerrocene is the percentage of ferrocene in solution, and

M is a constant conversion factor to convert mass percent to number density. Using C/kM as

the fitting parameter, we find that the above expression reflects the experimental data well for a

value of C/kM = 0.5 (Fig.6.10(b)). Another interesting point is that ratio of the two carbon mass

fractions, Mamorphous/MCNT , decreases with greater ferrocene percentage. This implies that the


two competing processes for formation of amorphous carbon and SWNT are impacted in favor of

SWNT formation when more ferrocene is present. But it is noteworthy that a sizable portion of

the catalyst particles do not contribute to the growth process, as observed in TEM for the 1.0 wt%

ferrocence, due to formation of larger particles from a high concentration of catalyst particles in

solution. Therefore, there is a large metal impurity product, even though the SWCNTs may be of

higher quality, as shown by Raman and TGA. This tradeoff thus points to an optimum value for

catalyst concentrations for SWNT growth.

6.5 Temperature Effects

The effect of the temperature on the growth of the SWNTs was also studied, for this has been

reported to be perhaps the most important factor determining the nature of the CNTs formed

(157; 158; 159; 35; 160). SWNT were grown at temperatures of 900, 1000, 1050 and 1100oC. The

other growth parameters for these set of samples were fixed at 0.25 wt% ferrocene with atomic S/Fe

= 0.2, 1000 sccm of H2 gas flow and a precursor solution flow rate of 0.067 ml/min.

RBMs were observed at 150 cm−1 wavenumber and also in the 200-250 cm−1 wavenumber range

(Fig. 6.11a). As discussed previously, it is probable that the M11 transitions gave rise to the 150

cm−1 RBM mode because the distinct BWF line-shape for the G- band in the 900oC sample (Fig.

6.11(c)). The most important observation from this plot is that, as the SWNT growth temperature

is increased, the intensity of the RBM modes corresponding to the 200-250 cm−1 become more

prominent, implying a definite increase in the range of the SWNT diameters produced with a greater

abundance of the smaller diameter semi-conducting SWCNT. The RBM modes due to the 633 nm

laser (Fig. 6.11b) show an increase in RBM intensity at 190 cm−1, probably due to the (15,0) metallic

M11 transition, based on the position of the RBM mode and the shape of the G band (not shown).

Note that this RBM mode resonance is predicted to be near 720 nm, yet is not observed under 785

nm excitation; again suggesting that the metallic SWCNTs are not red shifted by bundling, and

may even blue shift. Fig. 6.11(d) compares the intensity of the RBMs normalized by the G band

intensity, with the SWNT sample grown at 900oC being the reference. The corresponding histogram

shows that the abundance of the higher diameter SWNTs does not vary much with an increase in

the growth temperature. Contrary to that, the abundance of the smaller diameter semiconducting

SWNTs, corresponding to those exhibiting RBM at 206 and 234 cm−1 wavenumber, increased by 3

and 5 fold respectively when the growth temperature was increased from 900oC to 1100oC.

Fig.6.11 (c) plots the Raman spectrum in the D and G band region. The 900oC sample shows a

distinct metallic BWF line-shape, while the 1100oC sample shows a distinct splitting of the G band

to the two symmetric G+ and G- bands, a signature of semiconducting SWNTs. This supports the

observations made in discussion of the RBM. The G bands of the samples grown at intermediate

temperatures feature a combination of these two types of line-shapes. Furthermore, the quality of


wavenumber (cm-1)

Inte

nsit

y

wavenumber (cm-1)

wavenumber (cm-1)

150 200 250

1300 1400 1500 1600 1700

120 140 160 180 200 220 240 260 280 300

900oC 1000oC 1050oC 1100oC(bot) 1100oC(top)

900oC 1000oC 1050oC 1100oC(bot) 1100oC(top)

IG/ID

G split

I R B

M /I G

Figure 6.11: Raman of the SWNT samples synthesized at different temperatures. (a) RBM modeswith 785 nm laser and (b) 635 nm laser. (c) D and G bands from 785 nm laser. (d) NormalizedIRBM/IG as a function of temperature (e) Shows the variation of IG/ID and the extent of G splitwith temperature. The color legend for Fig. (a) and (c) is the same.

the SWNT produced increases as a function of the growth temperature, evidenced by the increase

in the intensity ratio of the G to D band for the higher temperature samples (Fig. 6.11(d)). This is

to be expected because it is well known that processing at higher temperature anneals away defects

resulting in the formation of more crystalline graphitic nanotube walls (151). Fig.6.11(e) also plots

the G split, defined as the difference between the G+ and G- band wavenumbers, as a function

of the growth temperature. The position of the G- band varies as the inverse of diameter of he

tube, while the extent of G split varies as the inverse of the square of the diameter of the SWNTs

(161) Specifically the relation for the position of the G- band is ωG− = 1591 − C/d2t , the values of

the constant C being different for semi-conducting and metallic SWNT(Cs= 47.7 cm−1nm2; Cm=

79.5 cm−1nm2). This relation can be used to estimate the average diameter of the SWNTs. The

magnitude of the G split for the 900 and 1100oC samples is nearly identical at 29 cm−1, and these


samples are predominantly metallic and semiconducting, respectively. Thus, we have the average

diameter for the 900 and 1100 oC samples to be 1.65 nm and 1.28 nm, respectively. Such an estimate

cannot be made for the sample grown at intermediate temperatures as they show a mixture of the

semi-conducting and the metallic character.

(a) (b)

wavelength (nm)

Abs

orba

nce

Abs

orba

nce

Abs

orba

nce

wavelength (nm)

wavelength (nm)

400 600 800 1000 1200 1400 650 700 750 800 850 900 950 1000

Figure 6.12: UV-Vis-NIR of the samples collected as a function of SWNT growth temperature.(inset, a) M11 and S33 transitions.(b) S22 transitions after subtracting the background. The colorlegend for all the Figures is the same.

Next, absorption spectroscopy was used to estimate the overall diameter distribution of the

samples. As can be seen from Fig. 6.12(a) the absorption peaks for the 1100 oC are present over a

wider range and are also better defined than for the SWNT samples grown at lower temperatures. A

wider range of spread of the absorption peaks implies a wider range of diameter distribution for the

1100oC case. Both smaller and larger diameter SWNTs as compared to the 900oC sample show up

for the higher temperature sample. The larger area under the peaks implies a larger ratio of SWNT

absorption to impurity scattering, meaning a higher purity of SWNT(83), consistent with the Raman

data. To look into more detail at the 2n + m families that gives rise to the absorption peaks, we

plotted the absorption data corresponding to the S22 transition (650-1100 nm) in Fig.6.12(b). As

in previous sections, the first attempt was to correlate the spectra with 2n + m MOD2 families,

because of their distinct inter-band transition wavelengths, marked in bold lines. From Raman

spectroscopy data for the 785 nm laser we had concluded that the higher temperature samples

were predominantly semiconducting in nature near 785 nm and hence the remaining peaks were

identified with the MOD1 S22 families rather than the M11 families. These peaks were assigned

to be MOD2 S22 2n + m = 26,29,32,35 families, the dotted lines identifying the mean value of the

interband transition wavelengths for their respective families. Raman data for the 900oC grown


sample suggested more metallic SWNTs near 633 and 785 nm. Hence the absorption spectra for the

900oC sample could be identified with the 2n + m = 30 and 39 M11 families. It should be noted

that the absorption spectrum for the 1100oC sample exhibits a much wider distribution of transition

wavelengths. Also with increasing temperature, the intensity of the peaks and the resolution of the

interband transition features increases. This point to higher quality SWNTs, which can be attributed

to higher temperatures facilitating the kinetics of the SWNT growth process and simultaneously

annealing defects resulting in tubes with high crystalline quality.

(a)

(b)

Abu

ndan

ce %

Diameter of tubes (nm)

Diameter of nanocatalyst particles (nm)

Figure 6.13: (a) SWCNT diameter and (b) Fe catalyst particle size distribution for SWCNTs,obtained from TEM analysis, grown at 900oC and 1100oC.

Extensive TEM studies of the SWNT grown at 900oC and 1100oC were conducted to verify the

relationships noted. The SWNT diameter distribution is plotted in Fig. 6.13(a). At 900oC, SWNT

with diameters in the range of 1.6-1.8 nm are most abundant, with a mean of 2.03 nm (std. deviation

= 0.27 nm). For the 1100oC sample, the TEM data shows a bi-modal distribution for the SWNTs,

with peak values at 1.3 and 1.9 nm. The mean of the diameter distributions was 1.625 nm, with a

standard deviation of 0.19 nm. The TEM data thus supports the spectroscopic observations. Next,

the size distribution of the catalyst particles was investigated (Fig. 6.13(b)). The overall catalyst

particle size distribution for growth temperatures of 900oC and 1100oC were similar, though the

high temperature case appears to have bimodal characteristics. Therefore, from the known values

of catalyst particle size to tube diameter ratio, the catalyst particle size optimum for the growth of

SWNTs of diameter ranges reported here will be 3.0-4.0 nm. There are a larger fraction of catalysts

for the 1100oC sample in this range. This might partially account for the increased yield of SWNTat


this temperature.

Temperature effects on the type of SWNT produced have been investigated in some detail.

Bandow, et al., (159) did so for pulsed laser vaporization process and found temperatures of 750oC

resulted in formation of 0.81 nm SWNTs, while 1050 oC resulted in average diameter of 1.51 nm.

Kataura et al.,(157), while using the laser furnace technique, noticed that the purity of the SWNT

increased with temperature up to 1300 oC, beyond which it dropped rapidly. Perhaps most studies

for the temperature effects on SWNT growth have been done for CVD processes. Kumar, et al.,

(160) found that the diameter of the SWNTs, irrespective of them being SWNT or MWNT, increase

with temperature. Above 850oC, SWNT were found to coexist with the MWNT. They also noticed

the formation of metal encapsulated C fibers and other carbon impurities at temperatures greater

than 1000 oC. Singh, et al. (155), in addition to above, noticed that the range of tube diameters

increased with increasing temperature. Nasibulin, et al., (83) studied the diameter dependence

between SWNTs and the catalyst particles in a laminar flow aerosol reactor. They reported an

increase in catalyst diameter with temperature, which resulted in the formation of larger diameter

SWNTs. Similar results were observed for the floating catalyst method of growing SWCNTs and

while using alcohol precursors (35; 156). Our results, as indicated by the Raman and absorption

studies, support the above-mentioned trends with one notable exception. Though we also notice

an increase in the range of production diameters with increasing temperatures, there is a relative

increase in both larger and smaller diameter SWNTs. This is in contrast to observation of other

groups that the average diameter increases with temperature. In all these prior works, this trend

was attributed to the formation of larger catalyst particles at high temperature.

However, the variations in the catalyst sizes by themselves may not fully account for the growth

of smaller diameter SWNTs at higher temperatures. While the kinetics of Fe agglomeration will

control the particle size distribution, thermodynamics suggests an increased preference for smaller

diameter SWNTs at high temperature. Curvature plays an important role in determining the ther-

modynamically favorable product. For smaller diameter SWNTs, the larger curvature leads to

a greater bending energy required to form the SWNTs relative to graphene sheet. Therefore, a

larger energy barrier exists to form smaller SWNTs, thus requiring higher temperatures to nucleate

SWNTs out of smaller diameter particles. To get an approximate idea about the dependence of the

critical SWNT radius on the growth temperature, we have adapted the simple model proposed by

Kuznetsov. (162). The change in Gibbs free energy for the formation of a nucleus is given by the

summation of the energy required to precipitate out carbon from iron-carbon solution, the energy

required to create new surfaces and the strain energy that arises from bending the graphene layer

during bonding with the metal surface (curvature dependent). Our formalism is same as that of

Kuznetsov, except, instead of comparing the volume of the nucleus with the molar volume of the

graphene to calculate the number of moles of carbon, we have compared surface area with respect

to the molar area for graphene. This approach is more appropriate because the SWNT is essentially


a curved 2D surface instead of a solid volume. Hence, for a 2D nucleus with perimeter l and height

h we have:

∆G =γl2 + lh

Am∆Gnucleus + γl2(σnucleus−gas + σnucleus−surface − σsurface−gas)+

lε+ Estr

where γl2 is the surface area (γ being a geometric factor),ε is the specific edge free energy. Next, the

change in free energy for formation of the nucleus is equated with the saturation coefficient of the

solution (∆Gnucleus = −RT ln(x/xo)) and expressing the strain energy, Estr, as Estr = Qcl4.4h , with

Qc = 4.5 eV, as in (162). Since the critical size of the nucleus corresponds to a maximum of ∆G,

the change in free energy is differentiated with respect to l and equated to zero. After simplification

and noting that l = 2πr, the corresponding expression for the critical radius takes the form:

rcrit =−(ε+Qc/4.5h− hRT ln(x/xo)/Am)

−RT ln(x/xo)/Am + (σnucleus−gas + σnucleus−surface − σsurface−gas)(6.1)

Figure 6.14: Theoretical plot to show the temperature dependence for the critical radius for SWC-NTs. The solid circles show the mean for the diameter distribution from TEM analysis at 900 and1000oC. The arrows mark the most abundant range for the SWNT from absorption spectroscopy.

Fig.6.14, which plots the temperature dependence of critical radius, shows that, at higher tem-

peratures it is thermodynamically possible to obtain smaller diameter SWCNTs. For comparison,

the plot also charts the SWNT radii distribution from the current study as a function of temperature.

The actual presence of these smaller diameter SWNTs at higher temperatures, though, depends on


the presence of the right size of catalyst particles, which in turn is controlled by the kinetics of the

agglomeration of the Fe particles. The other groups that have reported an increase in diameter of

the SWNTs with temperature have also reported an increase in the diameter of the catalyst parti-

cles. In contrast, TEM studies for the current study show a similar distribution of particle sizes at

both temperatures, with an overlap in the diameters of the particle suitable for growth of SWNTs

in the range observed, thereby permitting thermodynamic factors to alter the size distribution in

the low diameter range. Further work is required to understand the kinetics of the catalyst particle

formation in this reactor.

(a)

(b) (c)

2n+m =26

(n)

(m)

2n+m =26

2n+m =29

2n+m =30

2n+m =34

Figure 6.15: Abundance maps for SWCNT grown at 900oC (a) and 1100oC (b). For comparison theabundance map for HIPCO characterized using a similar procedure is shown. A darker color impliesa larger abundance of SWCNT, from absorbance studies. The red dotted line shows the positionsof the SWCNT diameter distributions obtained from TEM study.

Fig.6.15 maps the abundance of the SWCNTs grown at 900 and 1100oC, by combining the

TEM and UV-Vis-NIR spectroscopy results together. For comparison, the HIPCO 2n + m family

abundances are also shown as characterized by the same approach in our lab. Thus, we see that

increasing the temperature from 900 to 1100oC significantly increases the range of SWNTs produced.

The diameter distribution for the samples grown by this process is different from that for the HIPCO

sample. The average diameter of the HIPCO SWNTs are in the range of 0.9-1.25 nm, while the

SWNTs grown by this process are in the range of 1.3-1.8 nm. SWNTs in this diameter range are


sought for various applications. Simply varying the temperature also results in some control over

the nanotube size.

6.6 Conclusion

To summarize the work in this chapter, we developed a method of analysis via combined two wave-

lengths Raman and Absorption spectroscopy with TEM validation for diameter and chirality family

populations. Next we used the method developed to report the influence of three important growth

parameters namely reaction time, temperature and metal catalyst concentration on the nature of

product obtained by using a floating catalyst method to grow SWNT from ethanol and ferrocene

using a vertical flow reactor. Larger residence time forms larger catalyst particles resulting in for-

mation of larger diameter SWNTs. Increased residence time also increases the purity of the SWNTs

due to annealing for longer time in the hot zone of the furnace. Greater ferrocene percentage, in

the precursor solution, led to the formation of larger particles and hence larger SWNTs. While

analyzing the corresponding Raman spectrum, we came across experimental evidence that suggest

that the shift due to bundling of SWNTs could be different for metallic SWNTs when compared

to the smaller diameter semiconducting SWNTs. Also the percentage of iron content in the sample

scales with ferrocene percentage in the solution, suggesting constant carbon production rate. Also

increased ferrocene gives less amorphous carbon, suggesting that there are two competing pathways

for pyrolized iron and carbon: carbon and metal to form amorphous carbon and carbon diffusing out

of a supersaturated iron-carbon solution to form carbon nanotubes. We also observed that increasing

the metal concentration and the growth temperature increase the purity of the SWNT produced.

We report that higher temperature leads to the formation of smaller diameter SWNTs, in contrast

to other literature reports. Thermodynamics of SWNT formation suggest that it is feasible to form

smaller diameter SWNTs at higher temperatures if catalyst particle sizes of adequate dimensions

are present. Larger ferrocene concentration and higher temperatures increase the range of SWNT

produced. A larger concentration of metal catalyst increases the diameter of the SWNTs. While,

higher temperature increases the range by forming both smaller and larger diameter SWNTs, but

with a bias for the smaller tubes. These contrasting trends along with optimum levels of carrier gas

and precursor solution flow rate can be used to control the diameter of the SWNTs produced.

Chapter 7

Hydrogen Storage in Pt-Single

walled Carbon Nanotube

Composites

7.1 Introduction

In this chapter we investigate the ”spillover mechanism” of hydrogen storage in SWNT-Pt compos-

ites. The spillover mechanism proposes that hydrogen molecule can be spontaneously dissociated on

the surface of Pt. The dissociated hydrogen atoms can then spill onto the underlying carbon nan-

otube structure. The hydrogen atoms can then find favorable sites on the nanotube surface through

surface diffusion ultimately forming bonds. Pt was the catalyst of choice since Pt does not store

hydrogen or form a bulk platinum hydride phase under ambient conditions(163; 164). Thus the hy-

drogen uptake enhancement of SWNTs can be simply calculated by calibrating the mass fraction of

Pt in a composite sample. ”Spillover” mechanism has been exploited by several groups for enhanced

hydrogen uptake in SWNTs and other carbon based materials such as MWNTs, Carbon nanofibers,

activated carbon etc(40; 44; 45; 46; 47). Despite this, there is a healthy amount of speculation about

the validity of the spillover mechanism. Also further investigations need to be done to improve the

low uptake capacity and slow kinetics. These were the motivation for the current study.

In the first part of this chapter we discuss briefly our previous work on Pt-SWNT composites

and insights obtained from that work. This is followed by a description of the samples used for this

study and the conductivity and XPS studies done on the SWNT-Pt composite samples before and

after hydrogenation.

153

CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 154

7.2 Prior studies on hydrogen storage in Pt-SWNT compos-

ites

One of the important factors for increased hydrogen uptake is the optimal distribution of Pt particles

on the SWNT matter. Hence the effect of Pt nominal thickness on hydrogen uptake was investigated.

Nominal thickness is the deposited thickness of a film on an ideally smooth substrate. Figure 7.1(a-

d) shows the TEM morphological evolution of deposited Pt catalyst nanoparticles in the SP-Pt

hybrids with nominal film thickness varying from 0.2 to 3.0 nm. The Pt film does not wet the

nanotube surface, resulting in small nanoparticles from thin Pt layers. It is observed that the size

of the deposited Pt nanoparticles becomes larger from 0.2 to 0.5 nm thickness, while the number

density on the bundle does not increase substantially. For hybrids with 1.0 nm or thicker nominal

thickness, the particles tend to agglomerate with each other resulting in large island formation on

nanotube bundles during deposition. Significant decrease in the particle number density due to

impingement is observed for SWNT-Pt hybrids with 1.0 and 3.0 nm nominal thickness as shown in

figure 7.1 (c) and (d), respectively. Hydrogen uptake was estimated by measuring small pressure

changes arising from hydrogen uptake, using a modified Sievert’s apparatus (44), and equating it

to the change in the samples hydrogen content using the gas law equation. The isotherms were

measured for the samples at room temperature with a pressure increment of 4 Bar. The uptake

capacity of the hybrids increases with Pt thickness to 0.5 nm and then decreases for samples with

greater thickness.

The number density of nanoparticles was measured for SWNT-Pt hybrids with 0.2 and 0.5 nm of

Pt nominal thickness. It is reasonable to compare the particle density between these two composites

because the Pt particles tend to form agglomerated islands for thicker films. For simplicity, a

cylindrical geometry of SWCNT bundle is assumed as shown in the inset of figure 7.1(f). The

assumption is valid because the particle density was measured from relatively straight portion of

nanotube bundles, and the deposited catalyst particles are presumably outside of bundles. The

number of Pt particles was counted from several HR TEM images in terms of the calculated surface

area of corresponding carbon nanotube bundle. The numerical density of the particles for the 0.2

and 0.5 nm sputter deposited films were 0.023 and 0.031 particle#/nm2 respectively, Table 7.1. The

Table also shows that the relative ratio of measured uptake capacities at 30 Bar is similar to the

particle density ratio. Therefore it can be concluded that the hydrogen uptake of the total sample

or the uptake enhancement by the nanoparticles is proportional to the number of catalyst particles

in a unit area.

Knowing the total hydrogen uptake for the composite samples, particle density and average size

of the Pt particle (the Pt particle shape on the SWNT surface is assumed to be hemispherical),

an estimate of the H diffusion length on SWNT surface that accounts for the amount of hydrogen

uptake can be made. For this estimate, we further assume that all the C atoms in the affected


10 nm 10 nm

10 nm 10 nm

(a)

(c)

(b)

(d)

Figure 7.1: TEM morphologies of deposited Pt nanoparticles on SWNTs as a function of the nom-inal thickness of the deposited films: (a) 0.2nm, (b) 0.5nm, (c) 1.0nm and (d) 3.0nm. (e) Roomtemperature isotherms for Sp-Pt SWCNT hybrids with different nominal thickness of the sputteredcatalyst. (f) Pt catalyst number density for Sp Pt hybrids with 0.2 and 0.5 nm thick films. (Inset)Schematic of SWCNT bundle decorated with Pt nanoparticles, for the density calculation.

region forms a C-H bond giving the absorbed hydrogen density on the basal plane of graphene to be

76.32/nm2. The radius of the H diffusion circle thus estimated from the assumed and experimental

values are 1.0 and 1.32 nm for the 0.2 and 0.5 nm sputter deposited films respectively. This implies

that the hydrogen diffusion length in either case is less than 0.5nm. The other source for hydrogen

uptake for the Pt-SWNT hybrid could be surface hydride formation on Pt. It would be interesting

to make an estimate of the amount of surface H coverage on Pt required to account for the reported

uptake values in Table 7.1. For this calculation we assume a Pt (111) surface and 1:1 H:Pt ratio

(H density of 15.05/nm2). To account for 0.37 and 0.52 wt% hydrogen uptake by the 0.2nm and

0.5nm Pt-SWNT composite the surface hydride forming on the Pt has to be respectively 5.5 and

3.0 layers thick. Theoretical calculations show that the maximum surface coverage for H on Pt is


Table 7.1: Hydrogen uptake with catalyst particle density.

Pt thickness 2A 5A Ratio

Numerical Density 0.023 0.031 1.35(particle #/ nm2)

Avg. particle φ (nm) 1.14± 0.28 2.05± 0.36Htotal at 30 bar (wt%) 0.37 0.52 1.38HCNT at 30 bar (wt%) 0.41 0.57 1.39

Avg. radius of CHx (nm) 1.00 1.32Avg. #ML (if PtHx) 5.46 3.04

two monolayers (one surface and one sub-surface layer)(163).

Two important observations can be made from the above study on the dependance of hydrogen

uptake as a function of nominal thickness of the sputter deposited Pt. One, surface hydrogenation

of Pt cannot solely account for all the hydrogen uptake, hence providing circumstantial evidence for

the spillover mechanism. Secondly, the diffusion length scales for the spill over process are in the

sub-nm range, implying slow kinetics. Thus, there is need to investigate optimal hydrogen charging

conditions to hasten the process and optimal Pt coverage of SWNT surface so that a larger surface

area can be made available for hydrogen uptake.

7.3 Sample Preparation

A rigorous investigation of the sample space dependance on hydrogen uptake was performed. For

these, SWNTs from different sources were used to prepare films of different thicknesses and different

catalyst concentration. The SWNTs used were from two different sources : (i) as grown SWNT and

(ii) commercially procured HiPCO SWNTs.

The as grown CVD mat samples used in both the XPS measurements and the conductivity

measurements were grown in an atmospheric CVD system utilizing isopropanol as the carbon source.

The growth temperature was varied from 700oC to 800oC in order to change the density of SWNTs

in the mat and the overall mat thickness. The gas flow rates were also used to influence the density

and thickness of the mats produced. All of the samples were grown on ∼ 2A thick film of cobalt

metal deposited on silicon oxide wafers with 50 nm of oxide, Fig.7.2(a,b). The advantage of using

these samples was that these samples did not undergo any treatment procedure: i.e. were not mixed

with any alcohol or surfactant to obtain a well dispersed film.

The HiPCO SWNTs were used to prepare samples by two different methods. For the ticker

samples, the SWNTs were dispersed in isopropanol (1mg/10ml), sonicated for 15 minutes, and

then spin cast on a quartz slide, Fig.7.2(c). Before Pt deposition the samples were annealed in

an evacuated chamber at 250oC for one hour to get rid of the alcohol. To maintain uniformity

of the samples the same deposition steps were rigorously followed each time. These samples were


extensively used for the conductivity studies. The advantage of these samples was preparatory ease.

But, this technique resulted in the formation of thick films made of bundled SWNTs and hence had

the worst Pt to SWNT coverage of all the films studied.

The optimal SWNT mat for hydrogen storage will be a compact but uniform distribution of a

monolayer of unbundled SWNTs. This will have the highest Pt to SWNT coverage and also have

the lowest weight. To de-bundle the SWNTs a density gradient centrifugation (DGC) rate (zonal)

separation for sodium-cholate suspended SWNTs through an iodixanol step-gradient at 300,000

g was performed. This method separates nanotubes by mass, with fractions rich in single CNTs

floating on top of the column and bundles settling at the lower parts of the centrifuge column. Long,

individual SWNTs are obtained and characterized by spectroscopic methods. Xiaolin et al. (165)

used these individual SWNTs to prepare monolayer assemblies of SWNT films by the Langmuir-

Blodgett (LB) method. This LB method involved dispersing of SWNT functionalized by PmPV in

an organic solvent 1,2-dichloroethane (DCE). Pressure cycling during LB film compression facilitates

high-degree alignment and packing of SWNTs. Fig.7.2(d,e) are SEM and AFM images of the SWNT

films prepared by this technique. Once the LB films formed they were calcined to get rid of the

organic solvents/surfactants etc. One disadvantage of this technique is that the SWNT undergoes a

number of processing steps and is contaminated with other organic compounds (residual following

the calcination step). Hence extreme care has to be taken in interpreting spectroscopic data.

Fig.7.2(f) is a representative Raman spectrum obtained from the HiPCO SWNT. Comparing the

spectra obtained using three different excitation lasers with the Kataura plot, the diameter range

of SWNT samples was found to be within the limit 0.8-1.6 nm. The as grown SWNTs also had

a similar diameter range. The 514 nm Raman spectrum shows a distinct BWF line-shape. This

implies that the SWNT samples used have a high fraction of metallic nanotubes. The presence of

these metallic nanotubes are important for the 4-probe conductivity tests.

7.4 Conductivity Tests on Pt-SWNT composite samples dur-

ing hydrogen charging

Anton et al.(43) performed X-ray Absorption spectroscopy (XAS) on SWNT samples to show the

presence of two prominent spectral features corresponding to π∗ and σ∗ resonances as expected

of π conjugated C materials. After exposing the SWNT to an atomic hydrogen source, the π∗

resonance spectra was seen to loose intensity. Subsequent theoretical calculations showed that C

atoms to which a H atom is attached have a structural geometry and a chemical bonding that have a

substantial component from sp3 hybrids. As a result the π and π∗ components to the electronic DOS

vanish, resulting in a complete disappearance of the corresponding features in a XA spectrum(166).

Further evidence of decrease in conductance due to C-H bond formation was obtained from electrical

transport measurements of individual SWNT field effect transistors. Zhang et al.(42) consistently


1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Inte

nsity

1800160014001200

wavenumber(cm-1)

0.4

0.3

0.2

0.1

0.0280240200160

wavenumber(cm-1)

514 nm 632 nm 785 nm

Figure 7.2: SEM images of SWNT films used for the conductivity and spectroscopy studies. (a,b)Dense and sparse distribution of as grown SWNT films. (c) Spin cast HiPCO SWNT films (d)Monolayer coverage of SWNT films prepared by LB technique (e) AFM scan of the LB films. (f)Representative Raman spectrum obtained from the HiPCO SWNT samples.


observed a drastic decrease in conductance for SWNT devices after room temperature H-plasma

treatment. The conductance decrease upon hydrogenation can be attributed to the sp2 → sp3

structure change of an SWNT, leading to localization of π-electrons. Hence, conductivity tests were

performed to study the change in conductivity of the Pt doped SWNT film on being exposed to a

molecular hydrogen source.

80

60

40

20

0

pres

sure

(psi

)

50004000300020001000time(secs)

1.00

0.98

0.96

0.94

0.92

curr

ent (

norm

aliz

ed)

norm

aliz

ed c

urre

nt

Figure 7.3: Change in current passing through a Pt-doped SWNT film (nominal thickness = 0.5nm) on repeated exposure to hydrogen. Also plotted is the change in hydrogen pressure inside thechamber

Fig. 7.3 plots the change in current across a Pt doped SWNT film (a steady voltage was main-

tained across the two probes) on exposure to hydrogen. Initially a constant current flowed through

the SWNT film, but on exposure to 80 psi of hydrogen the current decreased. On evacuating the

chamber the current was approximately constant, while on re-exposing the film to hydrogen the

conductance of the film decreased further, though the drop in conductivity was relatively small.

Similar response was observed for one more hydrogen exposure. Thus it was established that the

exposure to hydrogen resulted in a definite decrease in conductance of the SWNT film. But from

a two probe experiment it is hard to determine whether the change is due to a change in contact

resistance or due to change in the intrinsic property of the film. Hence for subsequent conductivity

tests a 4-probe set-up was used, since it eliminates the contact resistance between the probes and the

material, and hence any change in resistance of the sample is solely due to the change in resistivity

of the material.

7.4.1 In-situ 4 probe conductivity tests

The details of the 4-probe setup has been described in Chapter 2. A constant current is passed

through the sample via the outer two probes, and the potential difference between the inner two


1.0

0.8

0.6

0.4

0.2

0.030x1032520151050

time (secs)

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

∆R/Ro

150010005000

0.20

0.15

0.10

0.05

0.00

∆R/R

o

302520151050

x103

-50

-40

-30

-20

-10

0

10x10

-3 150010005000

H2, 7

00 T

orr

expo

sed

to a

ir

pum

ping

expo

sed

to a

ir

no p

umpi

ng

H2 c

harg

ing

0.6 Pt (charging) 0.6 Pt (cycling)

HiPCO (charging) HiPCO + 0.6 nm Pt (charging) HiPCO + 0.6 nm Pt (cycling)

Figure 7.4: Resistance change as function of hydrogen charging for as-deposited and Pt sputteredSWNT samples. Also shown is the change in resistance of the Pt-SWNT hybrid film on exposure toair. For comparison, changes to a 0.6 nm thick sputtered Pt film on quartz on exposure to hydrogenis also plotted.

probes was constantly monitored as a function of time. The pressure inside the 4-probe chamber is

limited to atmospheric pressure, hence all the conductivity studies reported here were performed at

a pressure of 700 Torr. Before exposing the films to air the chamber was evacuated using a turbo

pump. SWNT films for the tests were prepared as mentioned in a previous section. Metal pads were

sputter deposited on the films to facilitate good electrical contact with the 4 probes. The resistance

of the as-deposited film was measured. Subsequent to which a desired amount of Pt was sputter

deposited on the film with the contact pads. These sputter deposited Pt-SWNT films were then

used for the in-situ conductivity tests.

Fig.7.4 plots the change in resistance (normalised by the resistance of the Pt-SWNT hybrid film

at the onset of exposure to hydrogen) as a function of hydrogen charging time before and after

sputtering Pt on the thin SWNT films. The films were exposed to 700 Torr of hydrogen pressure,

after evacuating the chamber down mTorr. The change in resistance of the Pt-SWNT composite

film is approximately 4 times the resistance change for the un-doped film. The increase in resistance


is directly related to the change in intrinsic property of the SWNT film and can be attributed to the

formation of C-H bonds on exposure to hydrogen. The higher change in resistivity of the doped films

then is due to enhanced C-H bond formation a direct consequence of spillover of H atoms obtained

by dissociative chemisorption of hydrogen molecules on the Pt nano catalyst particle surface.

Of, special note is the plot of the resistance change of a bare 0.6 nm Pt thin film exposed to

hydrogen. Similar to the SWNT-Pt composite films, the resistance of the Pt film increases probably

due to the change in Fermi level of Pt on exposure to hydrogen. But, the time scale for the change

in resistance of the Pt film is much smaller than the SWNT-Pt composites. In fact, the bare Pt film

undergoes a drastic resistance change and reaches a plateau level within a short interval of the onset

of hydrogen flow. On the other hand the resistivity of the Pt-SWNT hybrid did not reach a steady

state even after 8 hours of hydrogen charging. This implies that for most of the hydrogen uptake

process for SWNT-Pt hybrid the surface hydrogenation reaction of Pt has reached steady state.

Thus the molecular hydrogen in the gas phase is in equilibrium with the chemisorbed hydrogen on

the Pt sites and chemisorption is certainly not the rate determining step.

H2(gas) + 2ch ↔ [2H]ch (7.1)

where ch denotes an empty chemisorbtion site on the Pt surface.

0.20

0.15

0.10

0.05

0.00

∆R/

R

30x103252015105

Time(secs)

0.2nm Pt 0.4nm Pt 0.6nm Pt1.0nm Pt1.5nm Pt

Figure 7.5: Resistivity changes with hydrogen exposure for CNTs with different Pt loadings


Fig.7.4 also plots the resistance change in the 0.6nm P film and the Pt-SWNT hybrid sample

when air is leaked into the 4 probe chamber. On exposure to air the resistance of the Pt film

increases further, probably due to the higher affinity for oxygen of the hydrogenated Pt surface

(167). The resistance of the Pt film shows further changes on subsequent evacuation, hydrogen

charging and re-entry of air into the chamber. On the other hand, the resistance of the Pt-SWNT

film remains relatively unchanged while undergoing the same processes. Actually on exposure to air

there is a small decrease in resistivity of the film, in contrast to the bare Pt film. These studies thus

establish that the change in resistivity of the Pt-SWNT film is not due to changes in resistivity of

the Pt catalyst particles but is due to intrinsic change in SWNT film itself, and hence consolidate

the evidence for spillover mechanism of hydrogen storage.

Function of nominal thickness of Pt on SWNT mats

Next we studied the increase in resistance of the films as a function of the nominal thickness of

the sputter deposited Pt films. This is shown in Fig.7.5. The sputtered Pt film does not wet the

SWNT surface, but as mentioned before, it balls up forming particles. The size and distribution of

the particles formed depend on the thickness of the sputtered Pt. This study was done to find the

optimal catalyst particle size.

With increase in nominal thickness of the catalyst particles the normalized resistance initially

increases to an optimal level, beyond which it decreases. The optimal thickness of the deposited

Pt film is 0.6 nm. This supports the hydrogen uptake measurements with the Sieverts apparatus,

mentioned in Section 2 of this chapter, where it was observed that the hydrogen uptake by a Pt-

SWNT composite film varies linearly with the density of the Pt particles. With an increase in the

nominal thickness of the Pt film, the density as well as the size of the catalyst particles increase. But,

beyond a certain thickness of sputtered film, the Pt particles start agglomerating, thus decreasing

the number density of the particles and hence decreasing the extent of H spillover onto the SWNT

surface.

Function of SWNT film thickness

For the next experimental set, the nominal thickness of the sputtered Pt film was kept constant

(0.6 nm, the optimal nominal thickness determined from the previous set of experiments), but the

thickness of the SWNT film was varied. For this study five different SWNT films were used: HiPCO

SWNT dispersed in iso-propanol and spin cast on glass, dense and sparse distributions of horizontal

SWNT mats grown from Co catalysts on glass, and finally two monolayer thick SWNT films of

varying densities assembled by the Langmuir Blodgett (LB) method. The resistance of the films

so prepared are inversely proportional to the thicknesses, Fig.7.6(b). It is to be noted that the

resistances of the films before and after Pt deposition remains almost the same implying that the

sputtered Pt even for the LB films are not continuous but are in the form of catalyst particles


2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Norm

aliz

ed in

crea

se in

resis

tivity

30x1032520151050time(secs)

LB film (sparse) LB film (dense) as grown SWNT (sparse) HiPCO spun on glass as grown SWNT (dense)

100

101

102

103

104

105

106

107

Res

istan

ce (Ω)

as grown SWNT

dense

sparse

LB films

sparsedense

as deposited SWNT SWNT + 0.6nm Pt

Figure 7.6: Hydrogen uptake efficiency for SWNT films with varying thickness. The Pt loading waskept identical for all samples.


0.4

0.3

0.2

0.1

0.0

∆R/

R

30x1032520151050 time (secs)

-5oC 25oC 45oC 69oC 94oC 127oC

0.8

0.6

0.4

0.2

0.0

∆R/R

(no

rmal

ized

)

500040003000200010000 time (secs)

-5oC 25oC 45oC 69oC 127oC

Figure 7.7: Hydrogen uptake measured at different temperatures. The Pt loading and the filmthicknesses are the same for all the runs.

dispersed on the nanotube surface.

Hydrogen uptake by the Pt-SWNT composites has a strong dependence on the thickness of the

SWNT mats; the sparse SWNT LB films show an increment of more than an order of magnitude

in normalized change in resistance values compared to the HiPCO SWNT films spun cast on glass.

This dependence is attributed to the numerical density of Pt particles per area of the SWNT film

exposed to hydrogenation, which is the least for the thick HiPCO films and highest for the LB films.

Thus for maximum hydrogen storage it is necessary to obtain a uniform dispersion of monolayer

thick unbundled SWNTs, doped with optimal size and density of Pt catalyst particles. This will

ensure a high specific hydrogen uptake per weight of Pt-SWNT composite.

Function of hydrogen charging temperature

The time for all the hydrogenation experiments mentioned so far is approximately 8 hours. It was

observed that even after 8 hours the resistance plots do not reach a plateau region, implying very

slow kinetics. If the hydrogen uptake is via the spill over mechanism, then the kinetics will be limited

by the diffusion of C over the SWNT surface. In that case, the temperature of the charging process

would influence the kinetics and possibly result in an uptake increment with temperature. Fig. 7.7

plots the temperature dependence of resistance change for a film on exposure to 700 Torr of hydrogen.

An embedded heater was used to set the temperature for the hydrogen charging experiments. The

maximum substrate temperature attained by the heater is 127oC.

It is observed that the rate of change in resistance increased on ramping up the hydrogenation


temperature from −5oC to 127oC (Fig.7.7(b), shows that with increasing temperature the resistivity

changes reaches a plateau region faster). This again provides indirect evidence for the spillover

process. But, interestingly the net change in resistance of the films decreased on ramping up the

temperature. The net change in resistance and hence the amount of hydrogen uptake is largest for

−5oC and kept on decreasing monotonically on increasing the hydrogenation temperature. This

behavior can be attributed to the exothermic nature of the hydrogen dissociation reaction on Pt.

Increasing the temperature will decrease the Pt- surface hydride formation (163) and hence the

amount of H spilling over onto the SWNT surface.

7.5 XPS characterization of SWNT films

Ex-situ XPS measurements were performed on SWNT- Pt composites before and after hydrogena-

tion. The experiment was performed based upon the observation that the hydrogen release from

the composite sample took a long time even under ∼mTorr level vacuum. Hence XPS can be used

to establish the presence/absence of C-H bond subsequent to hydrogen charging. LB films and as

grown SWNT mats were chosen for the XPS studies, as they showed the most promise from the

thickness dependence studies mentioned in the last section. After depositing 0.6nm Pt of nominal

thickness on the SWNT films, the samples were baked overnight in an evacuated chamber at 250oC.

XPS spectra was collected. Next following another anneal, the hybrid samples were exposed to a

hydrogen pressure of 120 psi for 6 hours. Subsequent to which, XPS spectra of the hydrogenated

samples were collected. A glove bag containing forming gas was used during the sample transfer,

hence the hydrogenated samples were not exposed to air before the measurements were performed.

100

80

60

40

20

0

Cou

nts

[a.u

.]

700600500400300200100Kinetic Energy [eV]

O2

C Auger N2

Pt 4d

C 1s

O Auger

Pt 4f LB films + 6A Pt hydrogenated LB films + 6A Pt

Figure 7.8: XPS overview of the samples before and after hydrogenation. 0.6nm Pt+ LB SWNTfilm composite


Fig.7.8 plots XPS overview spectrum from 0.6 nm Pt doped LB film before and after hydrogena-

tion obtained using 700 eV incident photon energy. The spectral features include C 1s and C Auger

from the SWNT, Pt 4f and 4d peaks from the catalyst particles decorating the LB films, and O and

N spectral features most probably from the organic residues generated during the calcination step.

The Pt 4f peak is used to calibrate the XP spectrum.

The XPS of the samples before and after hydrogen exposure was measured, Fig.(7.9,7.10). For

comparison, the signal intensities were normalized through linear background subtraction of the

lower binding energy side.The strongest component at 284.8 eV binding energy is the C 1s peak and

is assigned to sp2 hybridized C atoms in the nanotubes. After exposure to hydrogen at a pressure

of 120 psi, the spectra of the hydrogenated samples showed a different peak profile particularly

in the higher binding energy side of the primary carbon C1s peak. From Fig.7.9,7.10(a) we can

observe a significant shoulder at 285.6 eV binding energy . This new contribution is assigned to the

re-hybridization of C atoms to sp3 due to the breaking of π-bonds and C-H bond formation and can

be seen as a direct evidence for the proposed spillover effect.

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Inte

nsity

294292290288286284282280

Binding energy(eV)

As grown SWNT+6A Pt As grown SWNT+6A Pt (hydrogenated)

Figure 7.9: (a)XPS before and after hydrogenation of As-grown films. Fitted XPS peaks of as-grownsamples, before (b); and after Hydrogen exposure(c)

Furthermore, an additional new peak at 288 eV can be detected for both hydrogenated samples.

We conjecture that this peak arises from a metal-to-semiconductor transition of the nanotubes that

is induced by the hydrogenation. The accompanying decrease of the electric conductivity can cause a

reduction of the core hole screening, resulting in a ∼4 eV higher final state energy (41). Alternatively,

the creation of a band gap can give rise to a shake-up line.

By de convoluting the XP spectra as shown in Fig.7.9,7.10(b,c), we can estimate the amount of

carbon atoms that has undergone a change from sp2 to sp3 hybridization, which corresponds to the


1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Inte

nsity

294292290288286284282280

Binding energy (eV)

LB film + 6A Pt LB film + 6A Pt (hydrogenated)

Figure 7.10: (a)XPS before and after hydrogenation of 0.6 nm Pt-LB film hybrids. Fitted XPSpeaks of as-grown samples, before (b); and after hydrogen charging(c)

amount of stored hydrogen. The asymmetric C1s principal peak was fitted with a Voigt line shape

with a tail. The same relative amplitudes for the Voigt line-shape and the accompanying tail were

maintained for fits before and after exposure. The shoulder that appears on hydrogenation were

fitted with Lorentzian line shapes at 285.6 and 288 eV. The relative weights of the sp2(sp3) peaks

are 0.84 (0.17) for the LB film and 0.87 (0.13) for the as-grown film. The third peak at 288 eV

has a relative weight of 0.05 in both samples. Since the fraction of hydrogenated carbon atoms is

proportional to the relative peak intensity, we obtain atomic hydrogen percentages of 16% for the LB

film and 12% for the as-grown film. If all carbon atoms were hydrogenated, the hydrogenation will

be 7.7 weight percent. Therefore in this experiment the weight percentage hydrogen uptake is 1.2%

for LB films and 1 % for the as-grown films. This is consistent with the conductivity experiments

where we also observed a higher percentage of hydrogen uptake for the LB films. Similar trends

were observed from the 4A Pt samples for the LB and as-grown SWNT films. This leads us to the

conclusion that the exposure of Pt-modified SWNTs to molecular hydrogen results in the formation

of stable C-H bonds.

7.6 Conclusion

In this chapter, hydrogen uptake of the Pt catalyst doped SWNT composites were investigated.

Qualitatively the results are analogous to previous reports of hydrogen uptake by doped SWNT

samples. 4-probe conductivity was used to study in-situ hydrogen uptake properties. Hydrogen


uptake capacity of sputtered Pt composite showed significant increases by a factor of four over un-

doped SWNT films. Very different timescales and nature of the resistivity change of the doped

SWNT films and thin Pt films during the conductivity tests established that hydrogen uptake in the

composites is solely due to formation of C-H bonds. The 4-probe conductivity plots were used to

identify optimal nominal thicknesses of the sputtered Pt and SWNT film thicknesses for enhanced

hydrogen uptake. Finally temperature dependent charging experiments showed that kinetics of

the hydrogen uptake process is fastened at higher temperature, providing evidence of the diffusion

limited nature of the process. Most importantly, the above sets of experiments show that 4-probe

studies can be used as a simple, sensitive probe to optimize the hydrogen uptake conditions for

doped SWNT films. XPS experiments evidenced the possible switch from sp2 orbital structure

of the carbon nanotube to the sp3-type structure upon the formation of C-H bonds. Our results

demonstrate that the hydrogenation mechanism is a spillover process where hydrogen molecules first

dissociatively adsorb on the Pt surface, and the chemisorbed H atoms subsequently diffuse onto the

nanotube surface where they form C-H bonds.

Chapter 8

Conclusions and Future Work

8.1 MWNT growth model and in-situ tracking of tube height

A generic model for growth of 1-d nano structures via VLS mechanism is applied to the nanotube

growth. The model formulated steady state flux in terms of change/drop in chemical potential for

the basic four mass transfer steps identified. The flux is then written in terms of the total change

in chemical potential in going from the vapor state to the nanotube and in terms of the diffusive

and/or interface reaction rates. The growth rates of the MWNT was then measured using time

resolved reflectivity data obtained from the interferometer set up as a function of temperature and

pressure. The idea is to identify the rate limiting step by interpreting the experimental conditions

and results in terms of the model. Once the rate limiting step is identified growth rates, final heights

etc can be and was predicted as a function of growth time, temperature, pressure, gas flow rates

etc. provided the limiting step remains unchanged. Further experiments can also be designed to

further the understanding of the rate limiting step. For example, study of MWNT growth under the

influence of an electric field was used to identify two different limiting reaction mechanisms within

the purview of the vapor-catalyst interfacial transport limited growth. Thus, we have developed a

protocol/template which can be used to understand and predict growth of 1D materials.

The model was tested for different growth conditions using ethylene as a hydrogen source. To

further validate the model more studies need to be performed using different C precursors, in par-

ticular higher molecular weight carbon precursor sources. This is because the decomposition of

these hydrocarbons and incorporation of the C or the C- bearing species into the growing SWNTs

could be very different from the simpler molecules used for this study. Further the interferometry

technique could be complimented by other techniques (e.g the time-lapse photography) so that the

maximum limit of film heights studied can be increased. This will also help to investigate in detail

the important catalyst deactivation/growth termination step. A good case study, could be the incor-

poration of controlled amount of water into the growth process which is supposed to delay catalyst

169

CHAPTER 8. CONCLUSIONS AND FUTURE WORK 170

deactivation by etching away the carbon soot formed on catalyst particles.

8.2 Catalyst size and nanotube morphology

The catalyst particle size is one of the key parameters that determine the morphology of the 1D car-

bon nanostructures. The diameter controls the diameter of the nanotube formed. Gibbs Thompson

effect predicts a size dependent suppression of melting point, determining the phase of the particle

at the time of growth which in turn was shown to affect the 1D structure formed. In the CVD

process, higher annealing pressures were found to form larger particle sizes which led to nanofiber

growth. At these diameters, the melting point suppression puts the Fe-C particle in a dual solid-

liquid phase. Carbon flux accumulates in the dual phase during growth until the dual phase becomes

energetically unfavorable because of the growing contribution of the surface energy. At this point,

the particle reverts to a single solid phase regime by discarding excess carbon, resulting in a discon-

tinuous graphitic structure characteristic of Carbon nanofibers. Ex-situ TEM studies was used to

determine the morphology of growth. Though convincing, the experimental evidence for the model

proposed is circumstantial. In-situ TEM characterization of MWNT during growth from a range of

diameters will resolve the ambiguity. So environmental TEM in situ studies should be performed to

study the particle diameter dependence of the 1D morphology.

8.3 Electric-field assisted MWNT growth

Application of an electric field during MWNT growth enhanced the growth rate and alignment of

the MWNTs. It was observed that increasing the magnitude of the field enhanced the growth rate

but the growth rates leveled off to a constant value on increasing the field. On the other hand,

for the same magnitude of bias, the height enhancement on application of an electric field was

largest for the lower growth temperatures. Further analysis of temperature dependent studies in

the presence and absence of the electric field reveal that there are actually two activated processes

involved, with rate-limiting step being independent of applied field at high temperature. At higher

temperatures, the rate-limiting step is the carbon dissolution into the catalyst particle, while at lower

temperatures it is the carbon dissociation at the catalyst-vapor interface that limits the growth.

Application of an electric field enhances the decomposition of the C precursor in the vapor phase,

thus circumventing this low temperature activation barrier. The main advantage of an imposed field,

that took advantage of the high polarizability of the CNTs along the axial direction, was to restrict

the tube-tube interaction. Calculations show that this benefit is obtained at a minimum field level,

with no benefit arising from further increase in field strength. The enhanced alignment of the CNTs

in the dense MWNT films with the electric field is explained by tensile stretching overcoming the

defect-induced kinking of the MWNTs.


Two other factors found to be important for enhanced alignment were, spatial density and the

growth induced kink formation that resulted in the formation of defective MWNTs. Future studies

are needed to identify growth conditions that will decrease the defect concentration in the CNTs

and also identify catalyst preparation techniques to further reduce their spatial density. Subsequent

application of an electric field for those conditions should result in formation of an array of vertically

aligned nanotubes.

8.4 Chirality, Diameter control of SWNT

The bottleneck for the assimilation of the SWCNT into devices/materials is the limited control over

the nature of the tube produced and the small laboratory scale production rates. In this work we

reported the influence of three important growth parameters namely reaction time, temperature and

metal catalyst concentration on the nature of product obtained by using a floating catalyst method

to grow SWCNT. Larger residence time forms larger catalyst particles resulting in formation of

larger diameter CNTs. Greater ferrocene percentage, in the precursor solution, led to the formation

of larger particles and hence larger CNTs. Thus particle size has a direct relation to the diameter of

the SWNT formed. Temperature increase increased the diameter range of the SWNTs synthesized

but with a bias for the smaller diameter tubes. These conditions were tried independent of each

other, but, in future studies, a combination of two or more of these trends can be used to narrow

down further the chirality/diameter range. In the process, we developed a method of analysis via

combined two wavelengths Raman and Absorption spectroscopy with TEM validation for diameter

and chirality family populations.

One further knob in controlling the chirality of the SWNTs could be the use of different types of C

precursors, which is being studied by Cara Beasely from Prof. B. M. Clemen’s and Prof. P.Wong’s

group. Another future avenue could be to use the growth model developed for 1D nanomaterial

growth to identify growth conditions for which the catalyst-CNT interface is the rate limiting case.

Under these rate limiting conditions, any changes to the catalyst, carbon precursor and growth

parameters should reflect in the nature of the SWNT formed. It is worth putting an effort to come

up with a method to control the diameter and chirality of the SWNTs during the growth process

itself, rather than isolating nanotubes via post growth techniques. This is because most of the post

SWNT separation techniques involve functionalization of the SWNTs or use of a surfactant which

could change the physical properties of the SWNT.

8.5 Hydrogen Storage in Pt-doped SWNT

The mechanism of hydrogen uptake in transition metal-doped SWNT was studied. In-situ 4-probe

conductivity tests were performed on mats of Pt doped SWNT during hydrogen uptake. On hydrogen


charging the resistivity of the Pt doped SWNT mat increased. This is due to the formation of C-H

bonds, which consumes the π and π∗ electrons from the affected SWNT regions, thereby increasing

the resistivity. Initial studies of the temporal dependence of hydrogen uptake suggest a diffusion-

limited process. XPS was employed to measure the extent of sp3 C-H bonding.

Future studies should completely avoid the use of molecular hydrogen in the energy storage /

transport /release cycle, thus making it more practical. The electrochemical hydrogen reduction at

pure carbon nanotube surfaces involves electron tunneling between the nanotube surface and the

outer Helmholtz plane, and thus a significant over-potential. Hydrogen atoms will thus be generated

at a greater distance from the nanotube, and will likely recombine to form molecular hydrogen

before they could reach the nanotube surface. Therefore electrochemical hydrogen reduction at

pure nanotube electrodes will merely lead to the production of hydrogen gas. If SWNTs were to be

replaced with Pt-SWNT composites then the molecular hydrogen formed above can be dissociatively

chemisorbed to the Pt surface, from where it will spillover to the SWNT surface, same as the

process described for a gaseous H2 source. The amount of stored hydrogen could be determined

either by 4-probe conductivity or XPS measurements. Prof Nilsson’s group at SLAC is studying

this electrochemical route for hydrogen storage.

Appendix A

Derivation of tip amplitude of a

vibrating carbon nanotube under

the influence of an electrical field

The carbon nanotube is simulated as a cantilever beam, fixed at one end. For small deflections,

the amplitude of a vibrating cantilever beam under the influence of an electric field is given by the

equation:

ρAδ2y

δt2+ YI

δ4y

δx4− αE2

2

δ2y

δx2= 0 (A.1)

where ρ is the density of the material, I is the second moment of inertia of the cross-sectional area

A, Y the Youngs modulus , α the polarizability coefficient, and E the electric field acting on the rod.

Solving A.1 is cumbersome, so previous efforts to describe the amplitude of the nanotube under a

localized applied field involved simplifying assumptions. Hongo et al.(28) assumed that the second

term in A.1 which describes the potential energy due to the bending of the nanotube can be ignored

and its influence approximated by an effective polarizability term. The effective polarizability term

approaches the actual polarizability values only in the limit of dipole-field interaction being more

dominant than the bending. Hence it was necessary to estimate the effective polarizability values

from the experimental dataset. Here we present a more rigorous solution for the partial differential

equation described in A.1. Assuming that the nanotube vibrations are in equilibrium with the

ambient temperature the solution is of the form: y = f(x) sin(ωt); f(x) = exp(λx).

Substituting in A.1 we get the relation

−ρAω2 + YIλ4 − αE2

2λ2 = 0 (A.2)

173

APPENDIX A. TIP AMPLITUDE OF MWNT 174

Solving for the quadratic, in ’λ’ we get,

λ2 =

αE2

2 ±√

α2E4

4 + 4ρAω2YI

2YI(A.3)

.

Hence the solution of the partial differential equation, A.1, should be of the form

f = sin(ωt)[A sinh(mx) + B cosh(mx) + C sin(nx) + D cos(nx)] (A.4)

where the roots of A.3 are, ± m, ± in, are given by the relation:

m2 =αE2

4YI+

√α2E4

16Y2I2+ρAω2

YI(A.5)

n2 =

√α2E4

16Y 2I2+ρAω2

Y I− αE2

4Y I(A.6)

The boundary conditions for a cantilever beam of length,L, clamped at one end is given by the

relations:

f|x=0 =δf

δx|x=0 =

δ2f

δx2|x=L =

δ3f

δx3|x=L = 0 (A.7)

This leads to the following solution for the nth harmonic

yn =un

2sin(ωt)sinh(mnL)− mn

nnsin(nnx)− m2

n sinh(mnL) + mnnn sin(nnL)

m2n cosh(mnL) + n2

n cos(nnL)[cosh(mnx)− cos(nnx)]

(A.8)

with un being the amplitude of the nth harmonic at the tip x=L. The constraints on the possible

values of mn and nn are given by the two equations below.

m4n + n4

n + 2m2nn2

n cosh(mnL) cos(nnL) + (mnn3n −m3

nnn) sinh(mnL) sin(nnL) = 0 (A.9)

m2n − n2

n =αE2

2YI(A.10)

This can be simplified realizing:

m4n + n4

n = 4A2 + 2B2

m2nn

2n = B2

(mnn3n −m3

nnn) = B(n2n −m2

n) = −2AB


where

A =αE2

4YIB = ω

√ρA

YI(A.11)

Substituting A.11 in A.9 and A.10 , we solved for the frequency, ω. An analytical solution for

A.9 and A.10 is not possible and hence the above equations were numerically solved to obtain the

allowed eigenvalues, ωn, for a given height and applied field. The allowed values of frequencies are

plotted as a function of field strengths and lengths in Fig.A.1. The energy in the mode n is therefore

quantized in units of ~ωn. In the limit of large bias, cosh(mL) = sinh(mL) = exp(mL/2), m >> n,

cos(nL) = (1− nL) and sin(nL) = nL. This results in n2 = 2m exp(−mL)/L, or

ω = [YI

ρA]1/2[

αE2

2YI]3/4√

2

Lexp[−1

2

√αE2

2YIL] (A.12)

103

104

105

106

107

108

109

1010

1011

1012

Freq

uenc

y(H

z)

108642

Height of tubes

wo(0) w1(0) w2(0) wo(10V/m) w1(10V/m) w2(10V/m) wo(100V/m) w1(100V/m) w2(100V/m) wo(10e3V/m) w1(10e3V/m)_ w2(10e3V/m) wo(10e4V/m) w1(10e4V/m) wo(10e5V/m) w1(10e5V/m) wo(10e6V/m) w1(10e6V/m)

Figure A.1: Allowed frequencies for the lower order modes as a function of height and strength ofapplied electric field during growth.

This solution differs from that of Hongo et al. and other papers mentioned therein, because

the approximation of neglecting the 4th derivative in results in a solution that does not satisfy two

of the four boundary conditions. Retaining the 4th order term to properly satisfy the boundary

condition changes the solution significantly. The plot reveals some interesting trends. The allowed

frequencies decrease as a function of height of the CNTs. The allowed frequencies of the higher order


modes increase with increasing bias magnitudes. In contrast the fundamental mode frequencies

decrease with an increase in magnitude of the applied field, as expected from A.12. For applied

fields > 1000V/m , the ω values approach zero, which will lead to a trivial solution (as can be seen

from A.9 and A.10). Hence for larger fields the next higher mode is considered the fundamental

mode. The total elastic energy contained in the vibration mode n can be obtained at the instant of

maximum deflection when the cantilever is momentarily stationary, sin(ωt) = 1.

Eelasticn = |YI

2

∫ L

0

(δ2yn

δx2)2dx|sin(ωt)=1 =

1

2celasticn u2

n (A.13)

The elastic energy in the absence of an applied bias simplifies to Eelasticn =

YILu2nn4

8 , the same as

obtained in (86). In the limit of large bias the relation is Eelasticn = YI

16 m3n . The average energy of

the nth mode is < En >= kT , half of which comes form the elastic energy degree of freedom. Thus

comparing A.13 with kT, the amplitude of each vibrational mode can be determined.

δn = (kBT

celasticn

)1/2 (A.14)

This is unlike (86) where the authors were looking for the root mean square amplitude, since here

we are concerned about the maximum amplitude for a given length and biasing magnitude, which

in turn determines the growth mode for the nanotubes. The vibration amplitude for the lower order

modes are plotted in Fig. 5.16 as a function of the length of the multi-walled carbon nanotubes and

the strength of the electric field.

Appendix B

Algorithm for analyzing

interferometer scans

There were two methods that were developed for analyzing the interferometer scans. The first one

fitted the attenuating background signal using a Savitzky-Golay (SG) filter. The second removed

the background by taking a Fourier Transform of the signal and removing the contributions from

the low frequency components. An inverse transform was performed to obtain the interfering signal.

B.1 Savitzky-Golay filter

Following is the algorithm written for Igor Pro 6 and above. It is to be noted that the algorithm

does not work on a lower platform since the number of averaging points required for the SG filter

are much more than 25 (the maximum number of points handled by the older platforms).

# pragma rtGlobals=1 // Use modern global access method.

Variable/G gStartPt, gEndPt, gNpeak // global variables to hold parameters from previous

execution of ’Smooth F indPeaks’

Variable/G gBkgndSmoothWidth, gNumBkgSmooths

Variable/G gFirstTime=1 // flag to indicate if function has been called previously

****************************************************

Menu ”Macros”

”Analyze CNT Data”,Smooth F indPeaks()

177

APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 178

End

****************************************************

Function Smooth F indPeaks()

WAVE Timex, Signal

NVAR gStartPt, gEndPt, gNpeaks

NVAR gBkgndSmoothWidth, gNumBkgSmooths

NVAR gFirstTime

Variable Tstart, Tend, StartPt, EndPt, Npts, Npeaks=10

Variable index

————————————————————————————-

Variable peakToValleyDistance=425

// physical distance (in nm) corresponding to peak-to-valley separation in the interferogram

————————————————————————————–

Variable ptsPerCyc, oneEighthCyc

Variable hiFreqSmoothWidth, bkgndSmoothWidth

Variable numBkgSmooths

Variable numHiFreqSmooths=6

// Kill graphs or tables left from previous execution of this Function

DoWindow/K Signal Graph

DoWindow/K Rate Table

DoWindow/K Rate Graph

// Make graph of raw signal vs time

Display /W=(9,49,493,374) Signal vs Timex as ”Graph of Signal vs Time”

DoWindow/C Signal Graph

ModifyGraph lSize=0.5

ModifyGraph grid=1

ModifyGraph tick=2

ModifyGraph mirror=1

ModifyGraph fSize=12

ModifyGraph standoff=0

Label left ”Signal x”

Label bottom ”Time, s”

SetAxis/A/N=1

ShowInfo

If (gFirstTime == 0) // check to see if the function has already been executed – if so, replace the

cursors and reset Npeaks

Cursor/P A,Signal,gStartPt


Cursor/P B,Signal,gEndPt

Npeaks = gNpeaks

// Pause to let the user place or adjust cursors on the graph of signal vs time.

// Cursors should span the region with oscillations, such

// that only the ”real” oscillations” are included.

// The following ’If’ statement is used only to call the special function ’PlaceCursors’, which

// places a small window beneath the graph, and suspends all operations other than changes

// to the main graph, until the user clicks ’Continue’.

If (PlaceCursors(”Signal Graph”,”Set the Cursors ”,”Adjust cursors ’A’ and ’B’”,” to span the

region of interest.”,”When finished,

click on CONTINUE.”) != 0)

return -1;

Endif

Else If (PlaceCursors(”Signal Graph”,”Set the Cursors ”,”Place cursors ’A’ and ’B’ on the Raw

Signal trace,”,” spanning the region of

interest.”,”When finished, click on CONTINUE.”) != 0)

return -1;

Endif

Endif

// Prompt user for the input parameters:

Prompt Npeaks,”Approximate number of Peaks (cycles) between the cursors?”

DoPrompt ”Inputs”,Npeaks //,loCutoff,hiCutoff,windowChoice

gNpeaks = Npeaks // save in global variable for next execution of function

// Figure the times (Timex) corresponding to the cursor locations.

StartPt=pcsr(A)

EndPt=pcsr(B)

gStartPt = StartPt // save the StartPt in a global variable so it can be resurrected for subsequent

calls to this function

gEndPt = EndPt // same for EndPt

Tstart=Timex[StartPt]

Tend=Timex[EndPt]

// Figure the number of pts between the cursors.

Npts=1+EndPt - StartPt

ptsPerCyc=trunc(Npts/Npeaks)

oneEighthCyc = trunc(ptsPerCyc/8)

Print ”Pts per cycle = ”,ptsPerCyc

If (gFirstTime==1)


bkgndSmoothWidth = trunc(Npts/3)

numBkgSmooths = 3

gFirstTime = 0

Else

bkgndSmoothWidth = gBkgndSmoothWidth

numBkgSmooths = gNumBkgSmooths

Endif

Prompt bkgndSmoothWidth,”Width (in points) of Background smooth?”

Prompt numBkgSmooths,”Number of Background smoothing passes?”

DoPrompt ”Background Smoothing:”,bkgndSmoothWidth,numBkgSmooths

gBkgndSmoothWidth = bkgndSmoothWidth

gNumBkgSmooths = numBkgSmooths

Duplicate/O signal,background,netSignal

// First, extend the signal to the right, past the location of the right-hand cursor, to

// avoid end-region problems with the Savitsky-Golay smoothing.

background[EndPt + 1,]=background[EndPt]

// Determine the ”background” by over-smoothing the ”signal” to eliminate oscillations

////bkgndSmoothWidth = trunc(2*ptsPerCyc) // set the width for the S-V smoothing; make sure

it’s ODD

If (mod(bkgndSmoothWidth,2)==0) // if it’s EVEN

bkgndSmoothWidth += 1 // make it ODD

Endif

// Now, do the smoothing

For (index=1;index¡=numBkgSmooths;index+=1)

smooth/S=2 bkgndSmoothWidth,background

EndFor

netSignal = signal - background // subtract the ”background” from the original signal

Duplicate/O netSignal,smoothedNetSignal // make a wave to hold the result of hi-freq filtering

// Filter out the high-frequency noise by S-V smoothing

hiFreqSmoothWidth = trunc(ptsPerCyc/2) // set the width for the S-V smoothing; make sure it’s

ODD

If (mod(hiFreqSmoothWidth,2)==0) // if it’s EVEN

hiFreqSmoothWidth += 1 // make it ODD

Endif

// Now, do the smoothing

For (index=1;index¡=numHiFreqSmooths;index+=1)

smooth/S=2 hiFreqSmoothWidth,smoothedNetSignal


EndFor

// Add the background and the final smoothed net signal to the Signal Graph

DoWindow/F Signal Graph

AppendToGraph background vs Timex

ModifyGraph lsize(background)=1,rgb(background)=(3,52428,1) // green

AppendToGraph smoothedNetSignal vs Timex


ModifyGraph rgb(smoothedNetSignal)=(1,4,52428) // blue

HideInfo

******************************

// Find Peaks and Valleys

******************************

Make/O/n=0 PVpointNum

Variable numPVsFound

Variable noPeaks,noValleys

Variable firstValleyLoc=0,firstPeakLoc=0,lastPVloc

FindPeak/Q/B=(oneEighthCyc)/R=[startPt,endPt] smoothedNetSignal // find first Peak

If (V flag == 0) // i.e., found a peak first

firstPeakLoc = V peakLoc

Else

DoAlert 0,”Didn’t find any peaks !!!”

Endif

FindPeak/Q/N/B=(oneEighthCyc)/R=[startPt,endPt] smoothedNetSignal // find first Valley

If (V flag == 0) // i.e., found a peak first

firstValleyLoc =V peakLoc Else

DoAlert 0,”Didn’t find any valleys !!!”

Endif

If (noPeaks ‖ noValleys)

DoAlert 0, ”No peaks or valleys were found – must abort!!”

Abort

Endif

numPVsfound = 1

If (firstPeakLoc < firstValleyLoc)

insertpoints (numpnts(PVpointNum)),1,PVpointNum // NOTE: this statement increases

numpnts(PVpointNum) by 1.

PVpointNum[numpnts(PVpointNum)-1] = firstPeakLoc


lastPVLoc = firstPeakLoc

Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, firstPeakLoc,” ”

Else

lastPVLoc = firstValleyLoc

Endif

DO

// Look for next VALLEY

FindPeak/Q/N/B=(oneEighthCyc)/R=[lastPVloc,endPt] smoothedNetSignal // look for next

VALLEY

If (numtype(V TrailingEdgeLoc)==0)

insertpoints (numpnts(PVpointNum)),1,PVpointNum

PVpointNum[numpnts(PVpointNum)-1] = V peakLoc

lastPVloc = V peakLoc

numPVsFound +=1

Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, V peakloc,” ”

Else

Break // break out of loop when there are no more extrema

Endif

// Look for next PEAK

FindPeak/Q/B=(oneEighthCyc)/R=[lastPVloc,endPt] smoothedNetSignal // look for next PEAK

If (numtype(V TrailingEdgeLoc)==0)

insertpoints (numpnts(PVpointNum)),1,PVpointNum

PVpointNum[numpnts(PVpointNum)-1] = V peakLoc

lastPVloc = V peakLoc

numPVsFound +=1

Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, V peakloc,” ”

Else

Break // break out of loop when there are no more Peaks or Valleys

Endif

WHILE(1)

Make/O/n=(numpnts(PVpointNum)),PVtimes

PVtimes = Timex[PVpointNum]

Make/O/n=(numpnts(PVtimes)-1) PVavgTimes,PVrates

PVavgTimes = (PVtimes[p]+PVtimes[p+1])/2 // mid-way between peak and valley times

PVrates = peakToValleyDistance/(PVtimes[p+1]-PVtimes[p])

// Make graph of rates vs time

Display /W=(497,49,981,375) PVrates vs PVavgTimes


DoWindow/C Rate Graph

ModifyGraph mode=4

ModifyGraph marker=8

ModifyGraph lSize=2

ModifyGraph msize=4

ModifyGraph grid=1

ModifyGraph tick=2




Label left ”Growth Rate, nm/s”

Label bottom ”Elapsed Time, s”

SetAxis/A/N=1/E=1 left

SetAxis/A/N=1/E=1 bottom

// Make a Table with the Peak and Valley locations, avg times, and rates

Edit/W=(999,49,1342,437) PVpointNum,PVavgTimes,PVrates

DoWindow/C Rate Table

END // end of Function ’Smooth F indPeaks’

*****************************************************

Function PlaceCursors(grfName, ctrlName,str1, str2, str3)

String grfName, ctrlName, str1, str2, str3

DoWindow/F $grfName // Bring graph to front

if (V F lag == 0) // Verify that graph exists

Abort ”No such graph.”

return -1

endif

NewPanel/K=2 /W=(139,341,550,432) as ctrlName

DoWindow/C tmp PauseforCursor // Set to an unlikely name

AutoPositionWindow/E/M=1/R=$grfName // Put panel near the graph

DrawText 21,20,str1

DrawText 21,35,str2

DrawText 21,50,str3

Button button0,pos=80,58,size=92,20,title=”Continue”

Button button0,proc=UserCursorAdjust ContButtonProc

PauseForUser tmp PauseforCursor,$grfName

return 0


End

************************************************ Function

UserCursorAdjust ContButtonProc(ctrlName) : ButtonControl

String ctrlName

DoWindow/Ktmp PauseforCursor // Kill self

End

************************************************


B.2 Fourier Transform Method

The next code uses a Hanning function to do a FFT of the interfering signal, and then subtracts

off the low frequency components to eliminate the attenuating background. The rest of the code is

same as that of the SG filter algorithm. Here only the first part of the code pertaining to the FFT

approach is given.

# pragma rtGlobals=1 // Use modern global access method.

Variable/G gStartPt,gEndPt Menu ”Macros”

”Analyze CNT Data”,FFT FindPeaks()

****************************************************

Function FFT FindPeaks()

WAVE Timex,Signal

NVAR gStartPt,gEndPt

Variable peakToValleyDistance=425 // physical distance corresponding to the peak-to-valley

separation in the interferogram

Variable hiCutoff,loCutoff

// Kill any graphs or tables left over from previous execution

// of this Function

DoWindow/K Raw Graph

DoWindow/K Rate Table

DoWindow/K Rate Graph

// Make graph of raw signal vs time

Display /W=(9,49,493,374) Signal vs Timex as ”Graph of Raw Signal vs Time”

DoWindow/C Raw Graph


ModifyGraph grid=1

ModifyGraph tick=2




Label left ”Raw Signal, x”

Label bottom ”Time, s”

SetAxis/A/N=1/E=1

ShowInfo

If (gStartPt>0) // check to see if the function has already been executed – if so, replace the cursors

Cursor/P A, Signal, gStartPt


Cursor/P B, Signal, gEndPt // Pause to let the user place or adjust cursors on the graph of signal

vs time.

// Cursors should span (include) the region with oscillations, such

// that only the ”real” oscillations” are included.

// The following ’If’ statement is used only to call the special function ’PlaceCursors’, which

// places a small window beneath the graph, and suspends all operations other than changes

// to the main graph, until the user clicks ’Continue’.

If (PlaceCursors(”Raw Graph”,”Set the Cursors ”,”Adjust cursors ’A’ and ’B’”,” to span the

region of interest.”,”When finished, click on CONTINUE.”) != 0)

return -1;

Endif

Else

If (PlaceCursors(”Raw Graph”,”Set the Cursors ”,”Place cursors ’A’ and ’B’ on the Raw Signal

trace,”,” spanning the region of interest.”,”When finished, click on CONTINUE.”) != 0)

return -1;

Endif Endif

Variable Tstart,Tend,StartPt,EndPt,Npts,Npow,Npeaks,Save DC

String windowChoice

// Set default values for the input parameters:

Npeaks = 6

loCutoff = (Npeaks/2)

hiCutoff = (2*Npeaks)

// Prompt user for the input parameters:

Prompt Npeaks,”Approximate number of Peaks (cycles)?”

Prompt loCutoff,”Low-freq Cutoff in Cycles:”

Prompt hiCutoff,”High-freq Cutoff in Cycles:”

Prompt windowChoice,”Type of FFT window function:”,popup,”Hanning;Hamming;Cosine;None”

DoPrompt ”Inputs”,Npeaks,loCutoff,hiCutoff,windowChoice

Print ”Npeaks = ”,Npeaks,”, loCutoff = ”,loCutoff,”, hiCutoff = ”,hiCutoff,”, Window Type =

”,windowChoice

// Figure the times (Timex) corresponding to the cursor locations.

StartPt=pcsr(A)

EndPt=pcsr(B)

gStartPt = StartPt // save the StartPt in a global variable so it can be resurrected for subsequent

calls to this function

gEndPt = EndPt // same for EndPt

Tstart=Timex[StartPt]


Tend=Timex[EndPt]

// Figure the number of pts between the cursors.

Npts=1+EndPt - StartPt

// Make sure the number of points is EVEN (FFT requires EVEN)

If (mod(Npts,2))

EndPt += 1 // add a point at the end, if necessary

Npts += 1

EndIf

Make/O/n=(Npts) filteredSignal,filteredTime // prepare waves to hold the FFT’d output

// Figure the average value (DC level) between the cursors.

// Save for later so it can be added back after the FFT.

WaveStats /Q/R=[StartPt,EndPt] Signal

Save DC = V avg

// Take the FFT.

// Use a ”Window Filter Function” to minimize the effects

// of the data values at the start and end not being equal, as nominally

// required for a good Fourier transform. The user gets to select

// the specific window funtion that will be used to pre-multiply

// the ”signal” data.

StrSwitch (windowChoice)

Case ”None”:

FFT/OUT=1/RP=[StartPt,EndPt]/DEST=Signal FFTSignal

Break

Case ”Hanning”:

FFT/OUT=1/WINF=Hanning/RP=[StartPt,EndPt]/DEST=Signal FFTSignal

Break

Case ”Hamming”:

FFT/OUT=1/WINF=Hamming/RP=[StartPt,EndPt]/DEST=Signal FFTSignal

Break

Case ”Cosine”:

FFT/OUT=1/WINF=Cos1/RP=[StartPt,EndPt]/DEST=Signal FFTSignal

Break

EndSwitch

// Set the DC component to zero.

Signal FFT [0]=0

// NOTE: The nth point in the FFT corresponds to that many cycles

// in the original wave; i.e., filter above point 10 if you


// want to keep 10 peaks.

// FILTER to leave only freq’s below ’hiCutoff’ (cycles)

Signal FFT [hiCutoff,]=0

// FILTER to leave only freq’s above ’loCutoff’ (cycles)

Signal FFT [0,loCutoff]=0

// Now take the Inverse FFT.

IFFT/DEST=Signal FFT IFFTSignal FFT

filteredSignal=Signal FFT IFFT

filteredTime = Timex[p+startPt]

// Shift it up and add back the DC component.

filteredSignal += Save DC

// Display the result in the raw data graph.

DoWindow/F raw Graph

AppendToGraph filteredSignal vs filteredTime


ModifyGraph rgb(filteredSignal)=(1,4,52428)

HideInfo

Appendix C

Quantifying alignment of Carbon

Nanotubes

C.1 Orientation Analysis of nanotubes in MWNT forests

To quantify alignment of the CNTs a Fast Fourier Transform (FFT) based image analysis technique

was developed. High magnification SEM images were taken of the cross section of the vertical

nanotube forests. All SEM images were of the same magnification and size to avoid introducing

artifacts.. To prevent edge effects in the FFT data, the edges were blurred using a Gaussian low-pass

filter. The FFT was then performed on the edge-blurred images. The intensities of this transformed

image are used to quantify alignment using the Hermans orientation factor, f . The Matlab R2008a

image analysis code is given below.

% call the images

im=imread(’hipco.TIF’);

% select part of the image for the FFT s=size(im);

im=imcrop(im,[100,100,s(2)-200,s(1)-200]);

figure,imshow(im);

% blurr the edges using a Gaussian filter

PSF = fspecial(’gaussian’,60,10);

edgeblurred = edgetaper(im, PSF);

figure,imshow(edgeblurred,[]);

% do a FFT on the edge blurred image, and shift the zero-frequency component of the FFT image

to the center of the spectrum

F = fftshift(fft2(edgeblurred));

F1 = log(abs(F));

189

APPENDIX C. QUANTIFYING ALIGNMENT OF CARBON NANOTUBES 190

figure, imshow(F1,[0,10]);colormap(jet);colorbar

% determine the absolute intensity corresponding to a point on the transformed image and also

calculate the angle made by a straight line joining the point to the center of the FFT.

i = 1;

for x = 225:446

for y = 1:161

angle(i)= atan(abs((y-162)/(x-224)));

I(i) = abs(F(y,x));

i = i+1;

end

end

Inum =0;

Iden =0;

% determine the Herman’s parameter f from the intensity and the azimuthal angle so obtained

for i = 1:length(I)

Inum = Inum + I(i) ∗ (cos(angle(i))2) ∗ sin(angle(i));

Iden = Iden + I(i)*sin(angle(i));

end

avgcos2phi = Inum/Iden;

f = 0.5 ∗ (3 ∗ avgcos2phi− 1);

C.2 Orientation Analysis of isolated MWNTs

To quantify alignment of isolated MWNTs an edge tracking method was developed based on the

approach of Kovesi et al. (132). Please go to his website to download the relevant part of the code

corresponding to different embedded functions used below. The first step is to detect the edges of

the CNTs. This is done by looking for local maxima in the gradient of intensities of the SEM images

of the isolated nanotubes. The co-ordinates of the maxima positions are listed and linked together

to obtain the nanotube edges. Straight segments are then fitted to each edge after defining minimum

length specifications. Next, the angles made by the straight edges with respect to the substrate are

obtained.

% call the image and select section of the image on which orientation analysis has to be performed

im=imread(’deep.jpg’);

im=rgb2gray(im);

imshow(im); axis on;

s=size(im);

im=imcrop(im,[25,25,s(2)-50,s(1)-50]);


% detect edges of the MWNTs

edgeim=edge(im,’canny’,[0.01 0.3],1);

imshow(edgeim);

% link the edge points detected from the images into lists; connect the points to draw just the

edges of the MWNTs

[edgelist, labelededgeim] = edgelink(edgeim,10);

drawedgelist(edgelist, size(im), 1, ’rand’, 2); axis on;

figure;

imshow(im);

hold on;

% form edge line segments from the edge list; draw the straight line segments and superimpose

them on the image showing the MWNT edges.

tol=2;

seglist = lineseg(edgelist, tol);

drawedgelist(seglist, size(im), 2, ’rand’,3); axis on;

hold on;

for r=1:length(seglist)

plot(seglist(r)(:,2),seglist(r)(:,1),’sr’)

end

% determine and plot the angles made by the straight line segments with the substrate

k=0;

for i=1:length(seglist)

for j=1:length(seglist(i))-1

k=k+1;

angle(k) = atan((seglist(i)(j, 1)− seglist(i)(j + 1, 1))/(seglist(i)(j, 2)− seglist(i)(j + 1, 2)));

if angle(k) < 0

angle(k) = angle(k) + π;

end

dist(k) = sqrt((seglist(i)(j, 1)− seglist(i)(j + 1, 1))2 + (seglist(i)(j, 2)− seglist(i)(j + 1, 2))2);

end

k=k+1;

angle(k) = atan((seglist(i)(length(seglist(i)), 1)− seglist(i)(1, 1))/(seglist(i)(length(seglist(i)), 2)−seglist(i)(1, 2)));

if angle(k) < 0

angle(k) = angle(k) + π;

end


dist(k) = sqrt((seglist(i)(length(seglist(i)), 1)− seglist(i)(1, 1))2 + (seglist(i)(length(seglist(i)), 2)−seglist(i)(1, 2))2);

end

figure;

s=0;

for p=1:length(angle)

for q=1:round(dist(p))

s=s+1;

a(s)=angle(p);

end

end

hist(a,90);

[N,X]=hist(a,90);

filledPixles=sum(N);

xlim([0 pi])

set(gca,’XTick’,0:pi/4:pi)

set(gca,’XTickLabel’,’0’,’pi/4’,’pi/2’,’3pi/4’,’pi’)

h = findobj(gca,’Type’,’patch’);

set(h,’FaceColor’,[.6 .6 .6],’EdgeColor’,’w’)

plotsizey=ylim;

textsetpoint1=plotsizey(2)*2/3;

textsetpoint2=plotsizey(2)*1.8/3;

title(’Distribution of Angles’)

xlabel(’Angles (radians)’)

ylabel(’Number of pixles contributing to specified angle’)

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