Determination of Local Elastic Modulus of Soft Biomaterial ...

Determination of Local Elastic Modulus of Soft Biomaterial Samples Using

AFM Force Mapping

By

Faieza Saad Ejweada Bodowara

Bachelor of Science, Benghazi University

Master of Science, Benghazi University

A Dissertation

submitted to the Department of Chemistry of

Florida Institute of Technology

in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

In

Chemistry

Melbourne, Florida

January 2018

ii

Determination of Local Elastic Modulus of Soft Biomaterial Samples Using AFM

Force Mapping

a dissertation by


Approved as to style and content

_______________________________________

Boris Akhremitchev, Ph.D. Committee Chairperson

Associate Professor, Department of Chemistry

________________________________________

Joel Olson, Ph.D.


________________________________________

Kurt Winkelmann, Ph.D.


________________________________________

Vipuil Kishore, Ph.D.

Associate Professor, Department of Chemical Engineering

Michael Freund, Ph.D. __________________________

Professor and Head, Department of Chemistry

iii

Abstract

Determination of Local Elastic Modulus of Soft Biomaterial Samples Using

AFM Force Mapping

by


Major Advisor: Boris Akhremitchev, Ph.D.

Conventional methods of mechanical testing cannot measure properties of soft

materials at the nanoscale. In fields such as tissue engineering, it is important to distinguish

the bulk elastic modulus from the surface elastic modulus and to characterize the spatial

distribution of material with non-uniform stiffness. One of the important new methods of

testing is the force mapping using the atomic force microscope. The existing force

mapping approaches often suffer from omitting important effects that might result in

artifacts. The most important effects include taking into account sample’s adhesion and

viscoelasticity and considering more realistic probe shapes. In this work, we have applied

a method that take into consideration probe shape and sample adhesion and developed

elastic modulus mapping. This inclusive approach can be applied to samples with adhesion

that exhibit indentation large enough that requires indenter shape models more

sophisticated than the traditional paraboloid shape model. Sample viscoelasticity can be

revealed by comparing parameters obtained in opposite scanning directions.

The application developed methodology is illustrated with the study of composite

biomaterial scaffolds that are used to support the differentiating cells. Samples are

composed of four groups: uncrosslinked electrochemically aligned collagen (ELAC),

iv

uncrosslinked Bioglass incorporated ELAC (BG-ELAC), genipin crosslinked-ELAC and

crosslinked electrochemically compacted collagen (ECC, unaligned). The force mapping

on BG-ELAC sample did not exhibit any area with high elastic modulus (measured

modulus was around 0.6 MPa), indicating that there is no Bioglass particle protrusion

observed at the BG-ELAC surface. Elastic modulus of ELAC molecules appears softer (~

0.1 MPa) for samples without Bioglass added. Adding genipin crosslinker to collagen

threads made the ELAC and ECC samples stiffer even more than uncrosslinked BG-ELAC

with characteristic values of elastic modulus approximately 0.97 MPa and 1.28 MPa for

crosslinked-ELAC and crosslinked ECC respectively. More extensive studies are

necessary to fully investigate effect of crosslinking ratio and adding Bioglass at different

concentrations on the elastic modulus values of collagen samples. Methodology reported

here is a suitable tool for such studies and can be applied to other soft and potentially

heterogeneous biomaterial samples.

v

Contents

Symbols vii

Abbreviations ix

List of Figures x

List of Tables xvi

Acknowledgement xix

Chapter1 Introduction

1.1 Why are Mechanical Properties Measured? 1

1.2 Mechanical Properties in Nanoscale 2

1.3 Parameters for Studying Mechanical / Nanomechanical Behavior of Materials

4

1.4- Mechanical Properties Measurements 5

1.5 Nanoindentation Techniques 15

1.5.1 Nanoindentation by Atomic Force Microscope 17

1.5.2 Forces during the Tip-Sample Contact 20

1.6. Measurements of Nanomechanical Properties by AFM 22

1.6.1 Tensile/ Bending Testing 24

1.6.2 Applications of Dynamic AFM to Characterize Mechanical

Properties 25

1.6.2.1 Force Modulation AFM 25

1.6.2.2 AFM Phase Imaging 29

1.7 Current Applications of AFM Nanoindentation on Soft Materials and Associated

Challenges 30

1.7.1 Effects of Viscoelasticity in Force-Indentation Measurements 32

vi

1.7.2 Cantilever and Tip Characteristics 34

1.7.3 Effects of Indentation depth 35

1.7.4 Effects of Model Selection 37

1.7.5 Problems with Contact Point Identification 39

1.8 The Aim of Approach 40

1.9 References 45

Chapter 2 Experimental Section 68

2.1 Samples and AFM Setup 68

2.2 Experimental Design 69

2.3 Force Mapping 73

2.4- Data Analysis 74

2.4.1 Calibration of Cantilever Sensitivity and Force Constant 74

2.4.2 Indentation Models 78

2.5 References 83

Chapter 3 Results 85

Chapter 4 Discussion 98

4.1 Elastic Modulus Measurements 98

4.2 Viscoelasticity 102

4.3 Heterogeneity of Surface 107

4.4 Depth Sensing and Tip Shape Artifacts 111

4.5 Conclusion 118

4.6- References 120

vii

Symbols

H Hardness of material

Pmax Maximum load

A Projected area

ν, Poisson ratio

E Elastic ( Young’s modulus)

E* Reduced Young’s modulus

S Stiffness of material

Smax The initial contact stiffness

P Applied load

h The deformation of sample

R Radius of curvature

a Radius of contact area

hf The final depth of the residual hardness impression

hs The drift of the surface at perimeter of contact

hc Vertical displacement during the contact

hmax Total displacement at any time during loading

Vt Photodiode voltage

∆Zp Vertical displacement of piezo actuator

Zp The position of the base of the cantilever

U1 The potential energy of the cantilever spring

U2 The potential energy pf tip-sample interaction

Ut Minimum potential at the equilibrium position of the tip

Us Potential energy due to the sample deformation

viii

Uc The energy resulting from the bending of the cantilever

Ucs Tip-sample potential caused by surface forces

d The cantilever deflection

kc The spring constant of the cantilever

ks Sample stiffness

kinteraction Spring constant of tip-sample interaction

D Tip-sample separation

δ The indentation depth

L The length of the cantilever

w Cantilever width

θ Cantilever thickness

C* A constant related to the selection of tip-sample contact point

α The semivertical angle of the tip

ix

Abbreviations

LH2 Liquid hydrogen

CNTs Carbone nanotubes

ECM Extracellular matrix

SEM Scanning electron microscopy

TEM transmission electron microscopy

AFM Atomic force microscope

ROC Radius of curvature

vdW van der Waals

PEO polyethyleneoxide

LRW London Resin White (plastic)

JKR Johnson, Kendall and Roberts Theory

DMT Derjaguin, Muller and Toporov Theory

ELAC Electrochemically aligned collagen

BG-ELAC Bioglass incorporated ELAC

ECC Electrochemically compacted collagen

Std Standard deviation of values

x

List of Figures

Figure 1.1 shows a stress- strain curve and illustrates different kinds deformation

5

Figure 1.2 shows Hertz model for studying elastic contact between two surfaces with

different radii and elastic constant 6

Figure 1.3 shows a load-displacement indentation curve for typical materials with an

elastic-half space characteristics 8

Figure 1.4 shows a scheme of the across section through the indentation of a typical

sample in the case of elastic-half space 12

Figure 1.5 illustrates the key parameters in Fig. 1.4 for an elastic half space material

13

Figure 1.6 shows a principle scheme of atomic force microscope 18

Figure 1.7 shows a deflection-displacement curve involving different types of tip-sample

interactions 19

Figure 1.8 represents the forces between tip and sample surface as a function of tip-sample

distance 22

Figure 1.9 displays force curves of three different materials: a) elastomer, b) purely plastic

(gold) and c) the most common elastic-half space material (graphite) 23

Figure 1.10 shows the scheme of bending/tensile AFM testing 25

xi

Figure 1.11 shows force-modulation imaging of carbon fiber and epoxy composite.

Panels in the figure show a) topographic image, b) stiffness in the force modulation image.

Here bright spots correspond to stiff areas. Image width is 32 µm 27

Figure 1.12 illustrates topography (A) and elasticity (B) of etched LRW embedded

sample. Panal B shows the difficulties of measuring elastic differences in the

components 29

Figure 1.13 shows the dependence of elastic modulus of polyethylene glycol on indenter

rate and temperature. The elastic modulus changes significantly at high indenter rate and

low temperature 34

Figure 1.14 represents a cross section showing osteons. A unit of cells, an osteocyte, has

a 5-20 µm diameter, is 7µm deep, and contains 40-60cells 42

Figure 1.15 displays a cartoon of an artificial scaffold with cells attaching between

collagen fibrils in microscale 43

Figure 2.1 shows photograph of 1 cm long and 1 mm wide filament of ELAC sample

deposited on a microscopic glass slide 70

Figure 2.2 shows SEM image for the tip of a long wide rectangular cantilever used in the

experiments 71

Figure 2.3 shows images for clean-dry glass surface before fixing the sample. The A

panel shows topographic image and the B panel shows the deflection image 72

xii

Figure 2.4 shows the typical deflection (A) and height (B) image of ELAC sample before

force mapping at scan size 20 μm 73

Figure 2.5 The dependence of voltage value on the cantilever motion. The repulsive force

bends the cantilever up and shifts the laser, and hence the voltage, to the positive value

75

Figure 2.6 shows a deflection vs. Z displacement curve on a hard surface 76

Figure 2.7 shows a typical force-distance curve 78

Figure 2.8 Shows a typical force-indentation curve 79

Figure 2.9 shows comparison of paraboloidal and hyperboloidal shapes that have the same

radius of curvature R. In the figure, α is the semi-vertical angle of hyperboloidal probe

80

Figure 3.1 A-D show deflection (left) and height (right) images at 15 µm scan size. Panels

A-D show images of typical ELAC, 30% BG-ELAC, crosslinked-ELAC, and crosslinked

unaligned collagen samples, respectively 86

Figure 3.2 displays fitting typical approach (A) and withdraw (B) force plots of ELAC

sample using paraboloidal probe shape. Data analyzed to maximum compressive

force of Fmax = 1 nN. 87

xiii

Figure 3.3 shows fitting typical approach (A) and withdraw (B) force plots of BG-ELAC

sample using paraboloidal probe shape. Data analyzed to maximum compressive force of

Fmax= 1 nN 87

Figure 3.4 displays fitting typical approach (A) and withdraw (B) force plots of

crosslinked-ELAC sample using paraboloidal probe shape. Data analyzed at Fmax = 1

nN. 88

Figure 3.5 shows fitting typical approach (A) and withdraw (B) force plots of crosslinked

unaligned collagen sample using paraboloidal probe shape. Data analyzed at

Fmax = 1 nN 88

Figure 3.6 shows the maps of elasticity of crosslinked-ELAC at the three different scan

sizes, and approach and withdraw scan directions using 1 nN maximum force and

paraboloidal probe shape model. Numbers on axes indicate pixel position. Blue pixels

show places were collected force plots could not be analyzed 90

Figure 4.1 displays the average values of Young’s modulus of ELAC, BG-ELAC,

crosslinked-ELAC and crosslinked-ECC collagen threads at A) Fmax = 1 nN, and B) Fmax

= 2 nN. Standard deviations are shown as error bars 99

Figure 4.2 shows the force maps of one spot of crosslinked ECC unaligned sample at the

three different scan sizes 100

xiv

Figure 4.3 displays the approach-withdraw offset for ELAC, BG-ELAC, crosslinked-

ELAC and crosslinked-ECC, unaligned samples at Fmax = 1 nN using paraboloidal tip

model. The numbers inside the chart are the positions of histograms ± one standard

deviation error in this position 104

Figure 4.4 shows the approach-withdraw offset for the different spots using data collected

with 15 μm scan size 105

Figure 4.5 displays the slow increase of viscoelasticity mean value of crosslinked-ELAC

with increasing the scan sizes as more higher modulus areas are tested 107

Figure 4.6 shows force maps and their corresponding histograms of ELAC sample at 15

µm scan size 108

Figure 4.7 shows elastic modulus maps and corresponding histograms measured on ELAC

sample at 640 nm scan size 109

Figure 4.8 shows elastic modulus maps and their corresponding histograms of BG-ELAC

at different scan sizes: a) 640 nm, b) 3 µm, and c) 15 µm 110

Figure 4.9 displays force maps of ELAC and BG-ELAC, crosslinked-ELAC and

crosslinked-ECC, unaligned samples at 640 nm scan size. The higher modulus samples

show sharper features 111

xv

Figure 4.10 Force maps and corresponding histograms of ELAC, BG-ELAC, crosslinked-

ELAC and crosslinked-ECC, unaligned samples using paraboloidal tip at different

indentation depths 114

Figure 4.11 The paraboloidal (gray) and hyperboloidal (blue) probes as expected at small

( Fmax = 1 nN) and large ( Fmax = 2 nN) indentation depths 116

Figure 4.12 in panels a and b show the difference in E values by using paraboloid and

hyperboloid probes over different scan sizes for crosslinked-ELAC sample at Fmax = 1 nN

and 2 nN, respectively 117

xvi

List of Tables

Table 3.1. Elastic modulus values and their corresponding standard deviations (Std) of

sample 1, 1st spot map (1024 force curves) of ELAC sample using maximum compressive

forces of 1 nN and 2 nN, extracted by fitting with JKR model 90


sample 1, 2nd spot map (1024 force curves) of ELAC sample using maximum compressive



sample 2, 1st spot map (1024 force curves) of ELAC sample using maximum compressive



sample 2, 2nd spot map (1024 force curves) of ELAC sample using maximum compressive


Table 3.5. Elastic modulus values and their corresponding standard deviations (Std) of all

spots on ELAC samples using maximum compressive forces of 1 nN and 2 nN, extracted

by fitting with JKR model 92


sample 1, 1st spot map (1024 force curves) of 30% BG-ELAC sample using maximum

compressive forces of 1 nN and 2 nN, extracted by fitting with JKR model 93

xvii


sample 1, 2nd spot map (1024 force curves) of 30% BG-ELAC sample using maximum



sample 2, 1st spot map (1024 force curves) of 30% BG-ELAC sample using maximum



sample 2, 2nd spot map (1024 force curves) of 30% BG-ELAC sample using maximum



all spots on 30% BG-ELAC samples using maximum compressive forces of 1 nN and 2

nN, extracted by fitting with JKR model 95


one force map (1024 force curves) of crosslinked-ELAC sample using maximum


Table 3.12. Elastic modulus values and their corresponding standard deviations(Std) of

1st spot on crosslinked unaligned collagen sample using maximum compressive forces of

1 nN and 2 nN, extracted by fitting with JKR model 96

xviii

Table 3.13 Elastic modulus values and their corresponding standard deviations (Std) of

2nd spot on crosslinked unaligned collagen sample using maximum compressive forces of

1 nN and 2 nN 96


all spots on crosslinked unaligned collagen sample using maximum compressive forces of

1 nN and 2 nN, extracted by fitting with JKR model 97

Table 4.1. Elastic modulus values (MPa) and their standard deviations (Std) for one spot

on crosslinked-ELAC at (Fmax = 1 nN and 2 nN) using paraboloidal and hyperboloidal

models 115

xix

Acknowledgement

I would like to thank Almighty God for giving me the strength and ability to

undertake and accomplish this research satisfactorily. By his blessings, my dream to study

the Ph. D in new and interesting science became reality. The financial support of the

Libyan Ministry of Higher Education played an important role during the first five years

of this study. I would like to thank my country, Libya, for giving me an opportunity to

start my Ph. D program in the United States of America.

I would like to thank Dr. Boris Akhremitchev, my advisor and the source of

valuable scientific insights. Thank you for accepting me in your laboratory, engaging me

in my desirable field and enhancing my ability as a scientific researcher. I would like to

acknowledge the Department of Chemistry at Florida Institute of Technology for providing

me extensive courses and valuable seminars. I would also like to thanks my committee

members, Dr. Joel Olson, Dr. Kurt Winkelmann and Dr. Vipuil Kishore for their interest

in my research, and their wise extensive guidance. I wish to express my deep gratitude to

Dr. Vipuil Kishore, along with Madhura Nijsure and Kori Watkins, for enabling me to

reach my goal of studying a very interesting area by providing me samples, and for being

infinitely patient. I am also grateful to Anad Mohamed Afhaima, my friend and colleague,

for her very useful discussions, advice, and emotional support.

I would like to express my thanks to my Dean, Dr. Hamid Rassoul, who is a source

of much wisdom and endless encouragement. He was wonderful at solving problems,

removing obstacles, and offering good suggestions. I will never forget Dr. Mary Sohn for

xx

her help and support while was serving as the head of the Chemistry Department. Her

good attitudes were continued by Dr. Michael Freund, who took over that position and

continuously encouraged and supported my work.

My family has always been most supportive and encouraging. I would like to take

this opportunity to thank them all, my mother, brothers and sisters, whose love and

guidance were my motivation to pursue my goal, especially my mother, her prayer and

sacrifices for me was what made me brave enough to accept the challenges. Last, but

certainly not least, I am extremely grateful to my husband, who has stood by me throughout

this endeavor and who has never doubted my ability to succeed, your love has sustained

me.

1

Chapter 1 Introduction

1.1 Why are Mechanical Properties Measured?

The use of different kinds of materials depends on their mechanical properties, from

hard structural materials to soft biomaterials. Knowing the mechanical properties of

materials can facilitate their improvement [1]. For example, the cross linking process is

sometimes recommended in plastics for improving their resistance to mechanical and

chemical influences [2]. Here are several examples of processes where knowing the

mechanical properties of polymeric materials is essential for successful development.

Because of the rapid development of plastics and its derivatives, the plastic recycling

process has become one of the largest global concerns over the last several decades. To

prevent pollution and to recover both energy and material, mechanical properties of plastic

materials have been manipulated to produce easily recycled plastics. To achieve this goal,

investigation of the properties that are responsible for plastic degradation, e.g. the ability

to granulate, and hence to reuse the reground materials have definitely been successful [3].

In the space field, a tank made from thin polymer is used to store liquid hydrogen LH2,

which is used to protect the astronauts from the high level of cosmic radiation at cryogenic

temperatures. Investigation of mechanical properties such as permeability and Young's

modulus of the film has been performed at cryogenic temperatures to monitor the stiffness

of the LH2 container and hence to preserve the LH2 level [4]. In membrane manufacturing,

mechanical properties for membranes used for water filtration, methanol fuel cells, coating

and other important applications are undoubtedly worthwhile. Membranes should exhibit

a proper strength that keeps their integrity during the achievement of their role even in

2

critical environments such as high pressure or temperatures [5]. Lastly, it was recently

demonstrated that stiffness of substrates affects development and locomotion of cells [6,

7]. Therefore, knowing the local elastic modulus is important for the development of

approaches aiming at controlling cell behavior.

1.2 Mechanical Properties at Nanoscale

Development of the nanocomposite industry has provided new functional materials.

Mechanical performance can be controlled by adjusting the mechanical properties of

material in nanoscale [8], even better than those of micro-particle-filled composites [9].

For example, the interfacial strength between the fiber and matrix in nanocomposite

polymeric material is responsible for the general behavior of this material [8]. Carbon

nanotubes (CNTs) have the highest strength and stiffness and the lowest density among all

known materials [10]. Mixing polymeric material with CNTs creates smart (damage

resistant with high surface to volume ratio) polymer matrix nanocomposites and improves

the material mechanics [11]. CNTs are also widely used in polymer reinforcement and

coating surfaces that require a robust mechanical performance such as in gears, drive shafts,

body panels in airplanes [12,13], and instrumentation sensors such as probes in atomic

force microscopy [14].

Decreasing sizes of materials to nanoscopic scale has become desirable to achieve

durability and strength [15]. Over the last several years, understanding and probing

nanomechanical properties have become of significant interest. In the biological field, the

investigation of nanomechanical properties can lead to identifying biofunctions and

3

diagnosing many health problems [16]. For example, decreased rigidity is a marker for

cancer cells, in addition to other diseases such as Alzheimer's dementia, and vascular and

kidney diseases that occur due to losing the elasticity of cells [17], while stiffening of red

blood cells in malaria is correlated with the deaths due to this disease [18]. Therefore,

changes in mechanical properties of cells may affect disease progression.

One important recent application of nanoscience technology is in the field of tissue

engineering, where substrates called scaffolds are tailored to support growing cells. The

scaffolds are designed to mimic the in vivo chemical, topographical, and mechanical

properties of the organ [19]. To build a strong tissue, scaffolds first should be mechanically

strong to be easily handled. Second, the scaffold and tissue site in which the former is to

be implanted have to be mechanically consistent with each other. Third, scaffolds should

promote cell adhesion, which also strongly depends on consistency of the mechanical

properties between cells and scaffolds that should be similar to that between cells and the

extracellular matrix, ECM [20-30].

Development of materials with new and improved functions by manipulating

nanoscale characteristics requires quantification of the mechanical properties of materials

in that scale. This requires knowledge of important parameters, methods and theories that

have been used to determine nanomechanical properties of materials.

1.3 Parameters for Studying Mechanical / Nanomechanical Behavior of Materials

One of the first quantities that has been determined as a mechanical characteristic

of material is the hardness, H, which is a measure of material resistance to indentation, or

4

how much the material will deform under a load [31]. When a hard ball is pressed with a

fixed normal load into a smooth hard surface and equilibrium has been reached, the

indenter and hence the load are removed and the diameter of the permanent impression is

measured. Then, the hardness of the smooth surface is the ratio of the maximum load (at

the equilibrium Pmax) to the projected area, A, of the indentation [32]

H = 𝑃𝑚𝑎𝑥

𝐴 (1.1).

One more mechanical property of materials is the Poisson’s ratio, ν, which

expresses how much the material extends orthogonally to the direction of applied force. It

is the ratio of the transverse / orthogonal strain to the strain along the direction of elongation

[33]. The Poisson’s ratio for soft materials approximately equals 0.5 [9].

The elasticity (elastic modulus) of material, E, is the ratio of stress to strain, where

stress is the deformation force per contact area, and the strain is the amount of the

deformation relative to the unperturbed state [34]. The elastic modulus is the material's

resistance to being elongated or compressed elastically. It is a constant value which can be

extracted from the linear portion of a stress-strain diagram. Figure 1.1 illustrates the stress

/ strain relationship for different kinds of materials. The deformation is elastic as long as

the relation is linear.

5

Str

ess

Strain0

A

B

C

D

E

Elastic region

Plastic region

A – Elastic limit

B – Yield strength

D – Ultimate strength

E – Fracture pointYoung Modulus

Stress

Strain

Figure 1.1 shows the stress- strain curve and illustrates different kinds of deformation. The slope

of the linear region is the elastic (or Young’s) modulus [http://www.totalmateria.com/]

The stiffness, S, of material is an amount of force, P, that is required to deform the material

structure [35]

S = 𝑃

ℎ (1.2)

where h is the deformation of the sample caused by the force along the same degree of

freedom.

1.4 Mechanical Properties Measurements

One of the first analytical approaches to study mechanical properties of materials

was by Boussinesq in 1885 [36]. He first used potential theory to compute stresses and

displacements for a homogenous-elastic body loaded vertically by a rigid-axisymmetric

6

indenter [36]. Then, the same procedure was used to derive solutions for other common

indenter geometries such as conical and cylindrical [37, 38]. In 1896, Hertz recognized

that the elastic contact plays a key role in mechanical properties determination [31] since

the first response to interactions of two objects is elastic deformation [39]. He considered

two elastic bodies with different radii of curvature and different elastic constants in contact

at a point. Figure 1.2, [39] illustrates Hertz’s model for the elastic response when R1= ∞

for a flat surface and R2 = R for a spherical indenter [39].

h

a

Sample

RP

Indenter

Figure 1.2 shows Hertz model for studying elastic contact between two surfaces with different radii

and elastic constant [39].

By applying the load P, the bodies deform and create a contact area with radius of contact,

a, which increases with the penetration depth, h, according to the equation:

𝑎 = √𝑅ℎ (1.3)

7

For elastic sample, removal of the load decreases the contact area back to the initial point

contact. For an applied load, P, and the indenter radius R, the reduced elastic modulus E*

can be obtained from the contact area radius – load dependency:

𝐸∗ = 3𝑃𝑅

4𝑎3 (1.4)

where

1

𝐸∗=

(1 − 𝜈12)

𝐸1+

(1 − 𝜈22)

𝐸2 (1.5)

E1 and ν1 are the elastic modulus and the Poisson ratio of the flat surface, and E2 and ν2 are

the elastic modulus and the Poisson ratio for the indenter. Unlike Boussinesq's model,

Hertz's model can be used to analyze the effects of non-rigid indenters, since it can deal

with a wide range of indenter elastic constants [31]. Hertz's approach is a basis for many

experimental and theoretical works in contact mechanics [40]. However, Hertz's model

can be used only in the case of a very low surface energy (surface adhesion), and the

indenter load should be much higher than surface forces so the latter can be neglected.

Meanwhile, the load should be limited to prevent wear and plastic deformation [41, 42].

Most materials exhibit a mixture of elastic and plastic behavior, and the indentation

process might exhibit inelastic deformation. Moreover, application of the Hertzian model

is limited to few simple shapes of indenters. Consequently, this approach has been replaced

by elastic-half-space analysis, which was introduced by Sneddon [43]. He developed the

Hertizian theory further by using general indenters of axisymmetric shape that can also be

8

described as a solid of revolution of a smooth function (e,g, a flat ended cylindrical punch,

a parabolic of revolution, and a cone, and other shapes) to indent elastic half-space.

In the early 1970s, as an extension of Sneddon’s work, Bulychev, Alkhin, and co-

workers [44-48] were interested in measuring the elastic modulus from load-displacement

indentation. They used a microhardness testing machine to obtain load-displacement

curves, Figure 1.3 [35], and determined the elastic modulus by using the equation:

S = d𝑃

dℎ =

2

√𝜋 𝐸𝑟 √𝐴 (1.6)

hf

Displacement

Lo

ad

hmax

Pmax

S = dP / dhloading

unloading

Figure 1.3 shows the load- displacement indentation curve for typical materials with an elastic-

half-space characteristic. hf represents the final depth of the residual hardness impression [31].

where S is the stiffness of the upper linear portion (the elastic behavior) of the unloading

data, Er is the reduced modulus, and A is the projected area of elastic contact, which is the

optically measured area of hardness impression. Therefore, the modulus of material can

9

be determined by measuring the initial unloading stiffness from the slope of the unloading

curve and the contact area [31]. This equation was originally established for a conical

indenter in elastic contact theory, though Bulychev et al. obtained reasonable results with

this equation using spherical and cylindrical indenters, and expected the same applicability

for other indenter geometries with square and triangular cross sections. Parr, Oliver and

Brotzen also emphasized that the equation is suitable for any indenters with a body of

revolution of smooth function (spherical and cylindrical) [49]. In turn, King in 1987

confirmed by the finite element calculation that this equation can be applied also on

indenters of square and triangular cross sections, which are not bodies of revolution of a

smooth function [50].

Due to the fact that thin film industries and hence mechanical investigations on a

very small scale have become one of the foremost concerns during 1980's, instruments of

submicron indentations, which are called traditional indenters, have been developed [51-

54]. However, imaging a hardness impression for a very small indentation as a procedure

to obtain the contact area was very difficult and time consuming. Focusing on this problem,

Oliver, Hutching and Pethica proposed a simple method to determine the contact area in

terms of the indenter area function; it is a cross-section area of the indenter as a function

of the distance from its tip (contact depth) [55,56]. At the peak load, the material deforms

and takes the shape of the indenter at some depth, which can be obtained from the load-

displacement data in Figure. 1.3. There are two obvious depths that can easily be

extrapolated from the load-displacement curve, the maximum displacement at the

10

maximum load, hmax, and the residual depth after final unloading, hf. Then, the projected

area of contact can be estimated from the shape function [56].

In 1986, Doerner and Nix provided an approach, which was considered as the most

comprehensive method until 1992, interpreting the load-displacement data acquired from

deep-sensing indentation instruments to determine the elastic modulus of thin films.

According to this approach, the elastic indentation can be subtracted from the total

displacement to calculate the hardness of material, and the elastic modulus is extracted

from the initial unloading stages (unloading stiffness) [57]. By extrapolating the depth at

zero load, the area of contact can also be calculated using the Oliver, Hutching, and Pethica

approach [55, 56] to find the resolution. The authors observed in some materials that the

elastic behavior of the initial unloading stages is similar to that of a flat cylindrical punch.

In other words, during this stage the area of contact remains unchanged and hence its

unloading portion is linear. Therefore, the slope of the linear portion dP / dh (unloading

stiffness) can be determined. However, the flat-punch approximation is not completely

suitable for real material behavior. It was found that a large number of materials do not

have any linear part in their unloading curve. In 1992 [31], the indentation load-

displacement data for fused silica, soda-lime glass, a single crystal of aluminum, tungsten,

quartz, and sapphire were obtained using Berkovich (a three sided pyramid) indenters, and

the nonlinearity in unloading curves for each material was observed. Dynamic

measurements of contact stiffness proved that the reason for this curvature reflects changes

in the contact area continuously as the indenter is withdrawn [31].

11

To analyze these complex data, modeling Berkovich indenters, a method of taking

into account the curvature in unloading curves and determining the depth in the absence of

linear portions have been reported by Oliver and Pharr [31]. Based on the Sneddon theory,

which had derived analytical solutions for several indenter geometries, conical and

paraboloid of revolution shapes were selected to compare with elastic unloading of

Berkovich indenters. Like Berkovich indenter, the conical indenter has a cross section area

that is a function of h2. Additionally, the conical indenter tip is similar to that of the

Berkovich indenter; they have similar geometries at a small indentation depth. The

paraboloid of revolution was chosen as a realistic indenter (the real indenters are rounded

at the apex because it is impossible for indenter to be perfectly sharp). Previous methods

had attempted to manipulate the unloading curvature, in which a straight line of the upper

portion of the unloading curve was taken to measure the slope (the stiffness). However,

the stiffness value depends on how much of the data points are in this line. Further, the

stiffness obtained from the first and final unloading are very different because of the creep

in the first curve. Attempts have been made to minimize the creep by holding the indenter

for a period of time before the final unloading, yet a problem related to the data point-line

fitting still exists.

It was found that the stiffness obtained from the power law, Sneddon's expression,

for the first unloading data is only a little greater than that for the final curve. This indicates

that the creep is not observed and hence the power law is recommended to be used for

analyzing data. Parameters used in this analysis are shown in Figure 1.4 [31], which is a

scheme of a cross section of indentation.

12

a

P

hf

hc

hs

hmax

Surface profile after

load removalIndenter

Surface profile under load

Initial surface

Figure 1.4 shows a scheme of the across section through the indentation of a typical sample in the

case of elastic half space [31].

In this figure, hmax is the total displacement at any time during loading, hc is the vertical

displacement during the contact, hs is the drift of the surface at the perimeter of contact,

and hf is the final depth of the residual hardness impression after the indenter is fully

withdrawn and the surface has elastically recovered. Another scheme that illustrates the

key parameters is given in Figure 1.5 [31]. Based on Sneddon's model, the loading-

unloading data were analyzed in the elastic response region. Because of the nonlinearity,

the initial contact stiffness, Smax, was measured only at the peak load, Pmax,

Smax = 𝑃𝑚𝑎𝑥

ℎ𝑚𝑎𝑥 (1.7)

Then, the elastic modulus can be determined by

Er = 𝑆𝑚𝑎𝑥√𝜋

2 √𝐴 (1.8)

13

Load

hmax

Pmax

S = dP / dhloading

unloading S

hc forE = 1

hc forE = 0.72

Possible range

for hc

Figure 1.5 illustrates the key parameters in Fig. 1.4 for an elastic half space material [31].

To obtain the contact area, A, the indenter geometry and hence its area function, f (h),

should be known. Then, the projected area can be calculated at the peak load by

A = f (hc) (1.9)

where

hc = hmax – hs (1.10)

The hmax can be experimentally measured at the peak load. According to Sneddon's

expression for the shape of the surface outside the contact area [44], hs for the conical

indenter is given by:

hs = (𝜋 –2) (ℎ – ℎ𝑓)

𝜋 (1.11)

14

where (h – hf) represents only the elastic displacement. The Sneddon's expression of the

stiffness, S, over this distance for the conical indenter is:

S = 2 𝑃

(ℎ – ℎ𝑓) (1.12)

Therefore: for the projected area at the peak load Pmax

hs = ɛ 𝑃𝑚𝑎𝑥

𝑆𝑚𝑎𝑥 (1.13)

where ɛ equals to 2(π –2) /π ≈ 0.72, 0.75 or 1 for a conical indenter, a paraboloid of

revolution indenter or a flat punch indenter, respectively. Hence, hs for the flat punch

equals Pmax / Smax, then hc is given by:

hc = hmax – 𝑃𝑚𝑎𝑥

𝑆𝑚𝑎𝑥 (1.14)

which is the same as that in the Doerner and Nix expression for a flat punch. For a conical

indenter:

hc = hmax – 0.72 𝑃𝑚𝑎𝑥

𝑆𝑚𝑎𝑥 (1.15)

and for a paraboloid of revolution:

hc = hmax – 0.75 𝑃𝑚𝑎𝑥

𝑆𝑚𝑎𝑥 (1.16)

15

Using ɛ = 0.72 or 0.75 depends on which of the indenter geometries are the best for

describing the experimental data. Depending on the power law exponent, m, values that

fit in the unloading curve, the unloading was best described by a paraboloid of revolution

[31]. Although the difference with the conical ɛ is insignificant, there are other reasons for

selecting paraboloid geometry to represent the Berkovich indenter in this experiment. The

pressure distribution around the tip of the paraboloid is more realistic. Second, it is

relatively difficult to deal with a conical indenter because any plastic deformation on the

apex leads to complete loss of important characteristics, especially the elastic properties

[31].

1.5 Nanoindentation Techniques

Traditional indentations for measuring mechanical properties have additional

indirect steps; they are restricted by imaging the surface after the experiment in order to

determine the area of hardness impression (the plastically deformed area) [58]. Scanning

electron microscopy (SEM) or transmission electron microscopy (TEM) is required after

microindentation experiments. Further, imaging the shallow indenters by these techniques

is often unclear and leads to inaccurate measurements. For these reasons, traditional

indentation measurements have become inconvenient and time consuming. After

development of nanoscale science, traditional indentation measurements became more

tedious and difficult for acquiring reliable results since microindenters do not allow for the

investigation of nanomechanical properties. In the last 20 years, it was realized that there

is a deep relationship between nanoscale interactions and the macroscale behavior of

materials [9]. This implication has been used to improve and develop materials in the

16

engineering and biological fields [9]. For example, dispersing nanoparticles uniformly in

polymer matrices improves their mechanical properties such as modulus, hardness, and

even damage resistance.

Nanoindentation technique has been developed and widely used to determine

elastic modulus, hardness, and other mechanical properties at nanoscale, e. g. in studying

properties of thin-films [59]. Its applications have dramatically grown during the past 20

years in medical and microbiological fields to diagnose and monitor the mechanical

properties of cells that are linked to disease progression [60]. In the nanoindentation

approach, an indenter with a known tip geometry and nanoscale radius is loaded with

gradually increasing tiny forces to penetrate the sample by a small amount of depth, and

the mechanical properties can be estimated using the indentation force-displacement data

[60, 58]. The advantage of this technique over traditional indentations is the ability to

directly determine mechanical properties by analyses of indentation load-displacement

data alone, without the need for imaging the hardness impression [61]. It was found that

using nanoindenters with soft materials results in the “skin effect”, which is the

overestimation of modulus at small indentation depth [62]. This occurs because of the

existence of viscoelastic behavior or sample creep (especially when a sharp probe is used),

which leads to an error in the surface detection and hence to the use of an incorrect

projection contact area in the calculation of the modulus. In addition to the nonlinearity of

the stress-strain relationship, the skin effect can also originate from analyzing the data by

using a model that does not take surface adhesion into the account [62]. Indentations by

nanoindenters can only be analyzed by the Oliver and Pharr method, in which a small

17

indentation is made by an arbitrary sharp indenter (e.g. Berkovich indenter), and does not

take surface adhesion into account [63].

1.5.1 Nanoindentation by Atomic Force Microscope, AFM

A number of investigations of nanomechanical properties for soft materials and thin

layers, as in biomaterial, biological, and microbiological studies, by non-destructive and in

situ measurements have dramatically increased during the last decades [64-70]. In the

diagnostic field, measuring nanomechanical properties of cells is becoming a useful tool to

monitor disease progression [71].

At present, the direct local probing of mechanical properties of hard, soft, thin layer,

and complex materials non-destructively and in situ with nanoscale resolution has become

a reality after the development of the atomic force microscope, AFM [72]. It is considered

to be the most accurate technique for quantitative measurements of mechanical and

dynamic properties at nanoscale [17]. A small tip diameter (radius of curvature down to

<10 nm) makes the AFM instrument able to apply small loads (<1 nN) locally and for

relatively hard samples produces very small deformation (0.02 nm) [17]. Consequently, a

very high spatial image resolution can be obtained by AFM [17] and local topographic

information can be gained. Spatial resolution in topographic imaging is related to the

mechanical properties. AFM is a versatile tool that can be used for variety of materials

whether conducting or insulating, and under variety of conditions (vacuum, air or liquid

medium) [58, 60, 71, 72].

18

The general principle of AFM technique is fairly simple as illustrated in Figure 1.6.

The sample mounted on a piezo-ceramic electric scanner is contacted by a sharp tip fixed

at the end of a flexible cantilever that is held in the probe holder. During indentation

measurements, the tip first goes down to contact with the sample and then indents into the

surface until a previously specified value of compressive force is applied to the sample

[67]. This part of the motion cycle is called “approach”. Then the probe reverses its motion

and brings the probe to the initial position. This part of the motion is called “withdraw”.

Once the tip senses the surface forces, the flexible cantilever bends, and its deflection is

measured with high precision by the optical lever method. It is based on focusing a laser

beam on the top of the probe, so the cantilever deflection causes the laser reflection to a

new position on a segmented photodiode as shown in Figure 1.6.

Piezo scanner

Sample

AFM cantilever, kc

Laser

diode

Segmented

photodiode

Cantilever

deflection

measurement

Force

Deflection

DV

Figure 1.6 shows the principle scheme of the atomic force microscope.

19

Thus the deflection changes the photodiode voltage, Vt, which is monitored as a

function of the vertical displacement of the piezo actuator, ΔZp as shown as deflection vs.

displacement graph in Figure 1.7 [67]. During the probe approach the deflection voltage

remains constant (in the absence of long-range forces) until the tip jumps to contact with

the surface under influence of short-range (nanometer scale) surface attractive forces [67].

This results in a rapid decrease in deflection voltage (region B-C in Figure 1.7). A further

displacement of the piezo actuator increases the repulsive forces that deflect cantilever in

the opposite direction, causing an increase in the Vt signal (region C-D in Figure 1.7).

When the repulsion reaches the maximum, the unloading process starts, and the cantilever

deflection will gradually decrease until the tip separates from the surface. In many cases,

during the unloading process the tip adheres to the surface, leading to an increase in the

attractive forces (negative value) until the force reaches maximum tensile value (point E in

Figure 1.7). Then the tip separates from the sample (region E-F in Figure 1.7).

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

Repulsive

region

3002001000 400 500Tip

def

lect

ion

vo

ltag

e, V

t

ΔZp, (nm)

D

C

BF

A

E

Attractive

region

Transition

region

Figure 1.7 shows deflection-displacement curve involving different types of tip-sample interactions

[67]

1.5.2 Forces during the Tip-Sample Contact

20

In AFM measurements surface forces play a major role in forming nanometer scale

contacts between the two surfaces [58]. Therefore, to achieve nondestructive

characterization with high spatial resolutions, the AFM operation should be within the

limited range of attractive and repulsive forces. Two major forces during tip-sample

interactions are the repulsive force and the attractive van der Waals (vdW) force [73, 74].

The repulsive force results from the overlap of electrons between the tip and sample atoms;

therefore, it is a short range (~ angstroms) and localized force. The long-range vdW force

(typical range 5-15 nm) originates from induced dipoles (polar molecules attract nonpolar

molecules by changing the arrangement of their electrons and thus inducing the dipole

moment) and/or dispersion force interactions and, unlike the repulsive force, it is not very

localized and can include hundreds of the nearest atoms [75]. This force is responsible for

the nanoscale jump to contact and for the same pair of materials varies depending on

surface roughness. Therefore, especially for biological and soft samples, to keep the

sample undamaged and to minimize the error in measurements of elastic parameters, the

vdW force should be controlled. This can be achieved for example by performing

experiments in a liquid medium. It was found that the AFM measurements have higher

signal to noise ratio in water than in a vacuum or air because of the significant reduction

of vdW force [76, 77]. This substantial decrease in vdW force is mainly attributed to

increasing the uniformity of the polarizable system created during the tip-sample contact

in a liquid medium [75].

There is another type of attractive force when performing AFM measurements in

ambient air at considerable humidity that is called the capillary force. It results from

21

condensation of water at the place of tip-sample contact, thus creating a liquid meniscus

bridging the tip and sample surfaces [78]. It might lead to excessive attraction and hence,

inaccurate measurements. One convenient way to eliminate capillary force is to perform

the experiment in a liquid medium [79].

The tip-sample interaction forces acting between the tip and the surface during the

approach-withdraw cycle are illustrated in Figure 1.8. The cantilever, which is considered

as a Hookean spring, has a potential energy of U1 = 1

2 kc d

2, where kc is the spring constant

and d is the deflection of the cantilever. The tip-sample interaction has a potential energy

U2 that includes the sum of energies of the attractive and repulsive forces. The second

derivative of this potential with respect to the tip-sample separation D is the spring constant

of interaction k interaction= -dU22 / d2D.This spring constant is positive for repulsive forces

and negative for attractive forces. The equilibrium position of the tip corresponds to the

minimum of total potential, Ut=U1 + U2. If kc<-kinteraction, the cantilever will jump in contact

with the sample surface, and if kc > -kinteraction, the cantilever will jump out of contact with

sample surface [39]. For elastic deformation, the total potential of the system can be

described by:

Ut = Ucs(D) + Uc (Zc) + Us (δ) (1.17)

= Ucs (D) + 1

2 kc Zc

2+ 1

2 ks δ

2 (1.18)

22

where Ucs represents the tip-sample interaction potential caused by surface forces, Uc is the

energy resulting from the bending of the cantilever, Us is the potential energy due to the

sample deformation, ks is the sample stiffness, which is a resistance to the sample

deformation, δ is the indentation depth, and D is the actual tip-sample separation D = Zp–

(Zc + δ ) where Zp is the position of the base of the cantilever (piezo position). At the

contact point, D equals 0 and Zp = Zc + δ. At equilibrium, maximum indentation, we have

ks δ = kc Zc [71].

Figure 1.8 represents the forces between tip and sample surface as a function of tip-sample distance

[https://www.researchgate.net/].

1.6 Measurements of Nanomechanical Properties by AFM

The first investigation of mechanical properties using AFM was by Burnham and

Cotton in 1989 [80]. They used the force mode of AFM for three different materials. Pure

https://www.researchgate.net/figure/27477827%20fig1

23

elastic (elastomer), pure plastic (gold), and a material in between (graphite) were indented

by a tungsten tip with radius R = 100-200 nm and attached to cantilever with kc = 50 ± 10

N/m. If such a cantilever is bent by 20 nm, then the applied load can be as large as 1000

nN. The characteristic force curves of the three materials are shown in Figure 1.9 [80].

Sneddon's solution for a flat-ended cylindrical indenter [43] was used to calculate the

elastic modulus values, which were comparable with what had been obtained by other

methods. This work started application of AFM as a method to directly determine the

mechanical properties of a wide range of materials.

Ideally elastic deformation

Penetration depth (um)

UnloadingNo

rmal

lo

ad (

N)

Elastic-plastic deformation


Loading

No

rmal

lo

ad (

N)

Plastic deformation


Loading

No

rmal

lo

ad (

N)

UnloadingLoading

Unloading

Figure 1.9 displays the force curves of three different materials: a) elastomer, b) purely plastic

(gold) and c) the most common elastic half-space material (graphite) [44].

Later, different AFM methods were developed to measure mechanical properties

of materials. These methods are bending/tensile test [81-85], dynamic AFM [86-90], as

well as nanoindentation methods [91-96].

24

1.6.1 Bending / Tensile Testing

In a bending / tensile test, the tensile load is applied on the fibrous specimen and the

resulting elongation is measured. The sample is mounted on a microscope stage equipped

with a camera to determine the deformation and geometrical dimensions of the sample

[85]. The load acting on the sample is determined by a piezo resistive AFM cantilever

whose tip is placed at the free end of the specimen. Then, the elastic modulus of the sample

can be determined using standard beam theory [84] assuming a uniform rectangular cross

section cantilever:

E = 4 𝐿3

𝐹

𝛿

𝑤 𝜃3 (1.19)

where L is the length of the cantilever, w is the cantilever width, 𝜃 is the cantilever

thickness, and F/δ is the slope of load-displacement curve. This method is suitable for in

situ applications; however, it has significant drawbacks [84]. First, while the force

measurements are carried out by the piezo resistive AFM cantilever, the displacement

cannot be measured by AFM because of the hysteresis in the piezoelectric AFM cantilever;

hence, an additional device such as SEM is needed to measure the displacement accurately

[84]. Even with additional accessories, accurate and reproducible results are limited to

measurements only in a vacuum state [84] and for only stretched materials such as

polyethyleneoxide (PEO) nanofiber as illustrated in Figure 1.10 [85].

25

Piezo-resistive

AFM cantilever

tip

Glass

fiber

Super

glue

UV glueMasking

tape

Microscope

stage

Coverslip

Stretched PEO

nanofiber

Microscope lens

Figure 1.10 shows the scheme of bending / tensile AFM testing [85].

1.6.2 Applications of Dynamic AFM to Characterize Mechanical Properties

Dynamic atomic force microscope techniques have been developed to obtain high

resolution topographic images and compositional information about sample surfaces in

gentle and non-destructive ways [86]. This method is especially suitable for soft samples

that can be easily damaged by high adhesion, friction or high electrostatic forces, or for

materials that cannot be tightly fixed on their substrates. Dynamic AFM methods include

the amplitude modulation AFM (tapping mode) and the non-contact mode.

1.6.2.1 Force Modulation-AFM, FM-AFM

The dynamic mode technique called force-modulation, AFM, allows the imaging

of areas on hard surfaces. In this technique the sample height is modulated when measuring

a topographic image and a map of surface elasticities is created (force modulation image)

by observing the modulation of cantilever amplitude at the frequency of sample modulation

26

[97]. After keeping the tip-sample force constant by the feedback loop, a small motion

(~1-10 nm amplitude) ΔZm, is introduced to the sample surface in Z direction. This leads

to an additional cantilever deflection, d, and hence a variation in the tip-sample force. The

upper and lower positions of the cantilever are measured to calculate the cantilever

deflection d. Then, the quantity d / ΔZm is used to build the force modulation image. The

amount of variation of the average force depends on the dynamic response represented in

the viscoelastic properties of the sample. This response is characterized by the sample

spring constant, ks, as follows:

ks = 𝛥𝐹

𝛥𝑍m–𝑑 (1.20)

where (ΔZm - d ) is the sample deformation by the acting force ΔF. In the absence of

adhesion forces (no energy dissipation) we have:

kc d = ks (ΔZm–d) (1.21)

ΔZm / d = 𝑘𝑐

𝑘𝑠 +1 (1.22)

If kc /ks << 1, the sample is much stiffer to be deformed and the contrast based on

surface elasticities cannot be obtained. Therefore, stiff cantilevers (depending on the

elastic modulus of the sample, kc > 1 N /m for polymeric samples and up to ~1000 N/m for

hard samples) are necessary for acquiring the force modulation images. During force

modulation imaging the soft areas deform more than hard areas on the sample surface (the

27

cantilever deflection d is less over the soft area). According to the Hertz model (with no

adhesion force), the force ΔF acting on a surface of modulus Es, and required to deform it

by pressing a spherical indenter of radius R to the depth δ is expressed as:

ΔF = ( Es2R δ3)1/2 (1.23)

The first application of force modulation model was by P. Maivald et al. in 1991

[97], in which a contrast resulting from variations in local surface elasticity and

topographic images were obtained for carbon fibers and epoxy composite, E ranges from

3.5 GPa to 2.3 × 102 GPa. Figure 1.11 [97] displays these images, for which a stiff

cantilever (kc = 3000 N /m) was fabricated with a diamond tip of radius (R = 10 μm) to

apply a repulsive force of 10–3 N in air.

Figure 1.11 shows force-modulation imaging of carbon fiber and epoxy composite. Panels in the

figure show a) topographic image, b) stiffness in the force modulation image. Here bright spots

correspond to stiff areas. Image width is 32 µm. The figure reproduced with permission from IOP

science [97].

28

As illustrated in the topographic image in Figure 1.11, carbon fibers show up higher

than the surrounding epoxy. The force modulation image exhibits the variation in local

surface elasticity and also reveals this structure across the cross section of fibers. Features

in the force modulation image generally do not match perfectly with features in the

topographic image confirming that each image has its own information source [97]. This

technique can be used to characterize nanoscale heterogeneity of mechanical properties

and surface defects. However, application of this technique is limited to relatively hard

samples [98]. On soft samples and samples with adhesion, force-modulation imaging

might produce excessive lateral forces that will damage samples. Moreover, on sticky

samples, the adhesive force adds to the average compressive force. Consequently this

might produce false contrast in the image. Force modulation measurements were

previously carried out on tissue embedded in London Resin White, LRW (a hydrophilic

acrylic resin used for embedding biological samples) [99], which have modulus values

almost equal 0.5 GPa. The image of elasticity was damaged during measurements as

shown in Figure 1.12 [99].

29

Figure 1.12 illustrates topography (A) and elasticity (B) of etched LRW embedded sample. Panal

B shows the difficulties of measuring elastic differences in the components [98].

1.6.2.2 AFM Phase Imaging

Tapping mode imaging is performed by exciting cantilever oscillation at or near its

resonance frequency. Then the tip at the end of the oscillating cantilever interacts with the

sample surface, and the local force gradient shifts the resonance frequency of the cantilever.

This in turn changes the amplitude of the cantilever oscillation. Imaging is performed by

scanning across the sample surface and using a feedback loop to maintain the amplitude of

the cantilever oscillation. It is noticed that the phase of the oscillating cantilever depends

on the mechanical and adhesive properties of the sample. More specifically, the phase shift

for the cantilever excited at its resonance frequency is proportional to the energy dissipated

during each contact of the tip with the sample. Phase shift can be measured along with the

topographic image. Contrast in the phase image indicates the variation in elastic and/or

30

adhesive properties of the sample surface [100]. Therefore, phase imaging cannot be used

to obtain quantitative information about the elastic modulus.

1.7 Current Applications of AFM Nanoindentation on Soft Materials and Associated

Challenges

The ability to continuously and accurately measure stiffness at various indentation

depths [101] nominates Nanoindentation methods to be used in determination of

nanomechanical properties of a wide variety of materials [102]. However, the relatively

large indentation forces (several μN) applied in this technique restricts it from being used

with soft materials, on which the nonlinear stress-strain relationship likely occurs. For

example, the strong indentation of biological cells can cause a disruption of cellular

components [103]. Furthermore, the skin effect, which is the overestimation of modulus

at small indentation depth and hence exceeding the elastic limit, occurs with soft samples

measured by nanoindenters, in which the data are analyzed by the Oliver-Pharr model

[104]. Another downside in nanoindenters is the need of additional optical device to

complete the measurements. This external procedure causes time consuming and decreases

the accuracy of measurements, which became depend on the resolution of this device [101].

The recent applications on soft materials, such as tissue engineering and biological

fields, concern with investigation of nanomechanical properties and submicro features on

the outermost surface. Further, imaging and concurrently determining nanomechanical

characterization under physiological conditions became very important for either

monitoring cell progression or improving biomaterials [101]. These multiple purposes, in

31

addition to the versatility of using different models to analyze data, demand the using of

AFM nanoindentation for applying forces of a few piconewton and achieve very small

deformation (~ 0.1 nm) [101], and to simultaneously image the indentation site under

desirable conditions [ 051 ]. Recently, AFM nanoindentation has been used to study the

skin effect of different polymers using probes with different radii (22, 810 and 1030 nm)

and analyzing the data by different models (Oliver-Pharr, JKR, Hertz and DMT) [ 041 ].

This report stated that the skin effect disappeared by using the large radius probes and

analyzing the data by either JKR or DMT, which take the adhesion into account. When

using the dull probes, the results started to be close to the bulk moduli at indentations 2-3

nm, which considered as the smallest depth for soft samples to reach the bulk modulus.

However, in the case of sharp tip the bulk moduli could not be reached until the indentation

was 90 nm. Consequently, the skin effect originates from either using a sharp tip that can

break the stress-strain linearity, or using improper model such as Oliver-Pharr to extract

modulus values [104]. In biological field, AFM nanoindentation was applied to distinguish

between healthy and disease cells and also monitor the disease progression [106]. Intensive

studies have been made by AFM nanoindentation on normal, benign and tumor cells [107.

108]. It was found that the flexibility of tumor cell diffusion can be attributed to its lower

stiffness with respect to normal cell [108, 106]. Because of the AFM ability to characterize

micro and nanoscale feature sizes, AFM nanoindentation has widely applied to study

microorganisms and viruses. Mechanical heterogeneity of bacterial surface and its biofilm

have been examined [109]. Determination of local stiffness on viral surfaces demonstrated

that their elasticity related to the virus inactivation reaction [110]. Additionally, this

approach has been used to determine elastic modulus of hydrogels and thin layers of soft

32

materials [68, 111, 104,112, 113], and some of the results were agree with macroscopically

measured values [68, 121]. More developed AFM nanoindentation method has been

performed using force-volume mode [114], which also called force mapping, in which a

matrix of force curves are collected across the sample surface. It has been widely used

with soft samples as a solution to avoid the lateral forces that result from contact-imaging

[115]. During force mapping, the tip is completely separated from the surface before

indenting the other point. Some of its recent applications are to produce maps of elasticity

and topographic images for human cells at different stages of disease progression.

Nonetheless, challenges for AFM nanoindentation to achieve accurate

measurements on soft samples still exist. These difficulties are related to either sample

nature such as viscoelasticity and adhesion phenomena, or experimental setup represented

in probe geometry and size, the cantilever stiffness, identification of probe-sample contact

point [104], and using improper model to extract the Young's modulus of materials [101].

1.7.1 Effects of Viscoelasticity in Force-Indentation Measurements

Viscoelastic materials have important applications as adhesives, coatings,

biosensors and lubricants [111]. Therefore, determining the viscoelastic behavior

accurately for these materials has recently a considerable concern. Attempts have been

made to access the viscoelastic property of soft materials; one of them is the study the

dependence of tip-sample adhesion on loading speed and also on temperature, but these

procedures have lack of quantitative information regards the viscoelastic characterization

[116]. To investigate the interfacial viscoelasticity of materials, microparticles were

attached to a tipless AFM to study the adhesion with mica surface [117, 118] and then

33

analyzing the data by different theories to explore the adhesion contributions [117,

120,121]. Recently, Cappella et al proposed an approach to determine the viscoelasticity

by studying the variation of elastic modulus with changing both time and temperature of

the experiment [122]. Yet, these attempts used indirect ways to investigate the viscoelastic

behavior. It used the frequency of voltage instead of piezo displacement rate, which directly

related to the complete travel of the piezo that can reflect the irreversible sample

deformation [122, 123]. Another suggestion to provide information about viscoelasticity

was the strain rate. Using a conical probe in AFM nanoindentation to explore the

viscoelasticity in term of the strain rate was arguable procedure. Although the self-

similarity of the conical probe as an axisymmetric shape, the stress field from this tip is

highly complicated because the surface points located in the tip domain are not

experiencing the same strain during the indentation process [111]. For this reason, indenter

rate was introduced instead of strain rate to characterize viscoelastic behavior and its

repeatability. In this work [111], the variations of Young's modulus with both temperature

and the indenter rate changes were identified, which reflected the viscoelastic behavior of

poly propylene glycol material. Figure 1.13 shows the dependence of evaluated Young's

modulus on both temperature and indenter rates.

34

Temperature, K

Ela

stic

Modulu

s, M

Pa

0

10

20

30

40

50

60

290 295 300 305 310 315

8400 nm/s

2790 nm/s

897 nm/s

Figure 1.13 shows the dependence of elastic modulus of polyethylene glycol on indenter rate and

temperature. The elastic modulus changes significantly at high indenter rate and low temperature

[111].

The plots illustrate the high dependence of modulus on the indenter rate at low

temperature. It was found that the viscoelastic property is reproducible as long as the basic

AFM steps have achieved [111].

1.7.2 Cantilever and Tip Characteristics

Even though the sharp tip with ROC~ 10 nm provides high resolution and can sense

the supported cellular membranes [124], the tip of large ROC is recommended for soft and/

or thin [74] samples to minimize plastic deformation and reduce damaging [125, 126]. The

large tip radius exerts a slight pressure and contact gently with soft samples. However, in

many cases the dull probes likely provided incorrect values of elastic modulus if the sample

roughness would not be taken into account [101]. Spherical tips have ROC similar or even

larger than the roughness of biological surfaces. This leads to the incorrect estimation of

35

the tip-sample contact point. Therefore, a relatively sharp probe with ROC smaller than

sample roughness should be considered [127]. The Geometrical changes in the tip shape

have significant effects on elastic modulus values. Using spherical probe with (ROC ~ 2)

μm causes a dramatic decrease in modulus compared to that using pyramidal probe (ROC

~ 50 nm) [128]. On the other hand, using probes with the same ROC but different spring

constants can affect Young's moduli. The spring constant is a marker to what extent the

cantilever can deflect, and by this deflection the mechanical properties of samples will be

detected [101]. To achieve an accurate detection for surface elasticity, the cantilever

stiffness should be close to that of sample. Indentation of soft materials by stiff cantilever

can exceed the elastic limit and damage the sample. Soft cantilever will be damaged if it

scans a much stiffer surface.

1.7.3 Effects of Indentation depth

There are two main effects related to the penetration depth and lead to obvious errors in

elastic modulus values. First, the indentation that similar or less than sample roughness

affects the true tip-sample contact area. In other words, very small indentation in biological

surfaces leads to miss contact with many points beneath the tip curvature and hence large

error in elastic modulus calculations [101]. To solve this problem, the penetration depth

must be much larger than sample roughness [129]. The rule of thumb can be applied in

this case, which stated that the roughness / indentation depth ratio should be ≤ 1

10 [101].

The second reason is represented in the substrate effect, which is the overestimation of

Young's modulus [101], and can be seen in the case of compliant material with small

36

thickness [130, 131]. This effect appears at the indentation site that either pile-up when

the tip indents the soft thin film deposited on a hard surface, or sink-in when the indentation

occurs at a hard material fixed on soft substrate [132]. To eliminate the substrate effect,

the indentation depth must be less than 10% of the entire sample thickness [31, 133]. Based

on Oliver and Pharr's, models have been developed to improve the accuracy of modulus.

Hay and Crawford [134] were enabled to eliminate the substrate effect and accurately

determine elastic modulus through an indentation depth up to 25% from the sample

thickness. However, it was noted that in AFM indentation measurements substrate effects

might be expected when the radius of contact area is similar to the sample thickness, even

though sample indentation might still be small in comparison to the sample thickness [135].

Therefore estimation of geometry of tip-sample contact is necessary in order to understand

whether the substrate effect can be avoided in particular experiment. Overall, the main

steps to deal with soft thin materials in AFM nanoindentation technique are to examine the

sample roughness and its total thickness, then perform an indentation ten times more than

roughness scale. For thin samples using sharp probe and low indentation force might be

necessary to avoid systematic error associated with hard substrate. For analyzing data of

thin films, using infinite thickness models may cause large errors in elastic modulus values

[135, 136, 137]. In the latter reference, Akhremitchev and Walker used Dhaliwal and Rau

model [138] to calculate elastic modulus for finite sample thickness and indicate that the

errors result from models of linear elasticity can be an order of magnitude.

1.7.4 Effects of Model Selection

37

Models that do not take into account the obvious phenomena of materials cannot

provide accurate values of modulus. Even though Hertzian and Oliver-Pharr models are

considered as conventional methods for many materials, challenges occur when applying

these methods on compliant and hydrated biomaterials [113]. For example, the Oliver

Pharr model can only deal with the elastic-plastic response of the sample without taking

the adhesion into account [139], resulting in large errors in modulus values of adhesive

biological samples. Other viscoelastic models have been proposed to calculate the storage

modulus of viscoelastic materials under a very low load to achieve only Hertzian

interactions [140], but the very small indentation can increase the error in modulus values.

Applying load much higher than adhesion forces or performing the experiments under

water can also minimize the adhesion and facilitate using the viscoelastic models.

However, using high load or water might damage the sample or change its physical

properties, respectively. Therefore, a comprehensive model that compromise between all

significant phenomena is required to diminish the error ratio. In fact, it is still complicated

to develop a model that can deal with both viscoelastic and adhesion properties of material

[141]. This can be attributed to the dependence of both adhesion and viscoelastic properties

on frequency.

The obstacle to use Hertz model with adhesive samples is that the adhesion property

of biological samples enlarges the contact area between tip and sample surface, which

conflicts with Hertzian concept that requires a very small contact area to ignore the

adhesion. The JKR model can be applied to model the indentation by a large spherical

probe that creates a large contact area, and then the adhesion can be taken into account.

38

However, the JKR model has some limitations since it cannot be valid for a wide range of

materials such as visoelastic samples, and works only with a perfectly spherical tip

[113].To develop this model and make it more versatile, a model which based on the

adhesive interaction between AFM tips and samples, called two-point method, has been

proposed in previous work [142]. Many problems related to soft thin films and large

adhesive materials have been overcome by modeling the induced adhesive tip-sample

interactions. In this method, only a passive indentation is induced by tip-sample adhesion,

minimizing the interference from the substrate compared to what is found using the

indentation method [142]. Furthermore, it does not require locating the tip-sample contact

point, which is a challenge in adhesive soft samples, since the adhesive interactions are

represented by fitting the whole retraction force curves. In this report, the two point method

was tested on a series of poly (dimethyl siloxane) polymer samples with different degrees

of crosslinking, and the results were consistent with macroscopic data [143]. Because of

the high accuracy of this model [144, 140], it was later applied in several researches. One

of them was for calculating the elastic modulus of poly (vinyl acetate), PVAc, films in both

glassy and rubbery states. First, elastic modulus values were calculated from measured

force curves by using Hertz equation. Then, the modulus values were used to get the JKR

theoretical curves, which exhibited a good agreement with the experimental data in the

case of glassy samples, indicating the validation of two-point method for calculating the

elastic modulus of glassy polymers. On the other hand, a little deviation between the

experimental data of rubbery samples and the theoretical curves can be observed. This

inconsistency might be attributed to the viscoelastic interaction between the probe and

sample, indicating that the two-point method works only with elastic manner [140, 142]

39

1.7.5 Problems with Contact Point Identification

One of the most common problems during nanoindentation of soft materials is

misidentification of contact point, Guo and Akhremitchev [145] stated that almost 10% of

systemic errors are related to incorrect selection of contact point. Missing the contact point

can result from either the high level of noise in the instrument or the high adhesion on the

sample surface, which considerably exists in biological materials [144]. Attempts have

been made to correctly identify the tip-sample contact point on soft and adhesive samples.

Jaasma et al [146] extracted the contact point from the linear relationship of derivative of

cantilever deflection to its base position. Extrapolation data to zero value yields the point

at contact or separation position. However, this method requires data to be in the elastic

limit (very small indentation). On the other hand, at this position the interactive forces are

significant and cause high level of noise that can affect the accuracy of derivation. To

manipulate this situation, measurements might be performed at sufficiently large

indentation to minimize the level of noise [146]. Yet, this leads definitely to damage the

soft biological surfaces. Another suggestion has been introduced by Guo and

Akhremitchev [145], their idea start from the fact that accurately determination of Young’s

modulus from Hertizian expression (equation 1.24) is limited with a correct value of the

indentation depth, δ.

F = 4 𝐸 𝑅

12

3(1−𝜈2) 𝛿

3

2 (1.24)

Where F is the load, R is the probe’s radius of curvature, δ is the indentation, ν is the

Poisson ratio of the elastic solid, E is the Young’s modulus. Yet, it is difficult to obtain

40

the accurate value of δ because of the hardly determine the tip-sample contact point.

Therefore, Guo and Akhremitchev wrote the Hertzian equation in a way by which the

Young’s modulus can be calculated from the dependence of applied force on the tip-sample

distance, D, regardless their contact point. They states that the relation between D and δ

can be written as:

δ = C − D (1.25)

Therefore, the Hertzian equation can be expressed in terms of equation (1.25) as follows:

𝐹2

3 = C* − [4𝐸𝑅

12

3(1−𝜎2)]

2

3

(1.26)

C* is another constant that reflects the selection of tip-sample contact point.

From this linear equation, the post contact region points can be plotted and then the

Young’s modulus can be extracted from the slope of the line. Noticeable, a systematic error

of only ~ 10% might occur, which results from either the probe radius of curvature or the

estimated Poisson’s ratio. This uncertainty is found to be less than that of cantilever spring

constant [145]. Yet, this approach can be used only in elastic limit where the indentation

is non-interactive [144].

1.8 The Aim of Research

Methods of measuring elastic properties of materials described above suffer from

different limitations that prevent comprehensive characterization of mechanical properties

of soft samples. Specifically, techniques capable of mapping mechanical and adhesive

properties often provide only a relative map of elastic properties (e.g. force modulation and

41

phase imaging described above). Techniques capable of extracting the absolute value of

the local modulus (force-indentation measurements) often report only statistical values of

the elastic modulus without providing information regarding the spatial distribution of

moduli values [147-150]. More advanced studies that generate maps of elastic moduli of

soft samples do not consider the effects of adhesion and viscoelasticity [151,152]. It is the

goal of the current study to develop and test methodology that is capable of measuring

mechanical and adhesive properties of soft materials and to simultaneously report

heterogeneity and spatial distribution (mapping) of the measured parameters, including the

effects of depth sensing, adhesion, and viscoelasticity.

The developed approach is used to characterize the elastic properties of collagen-

Bioglass samples that are important substrates in tissue engineering efforts [153]. Selection

of these samples for testing measurement methodology is rationalized below.

The rational design of artificial scaffolds for tissue engineering requires inclusive

studies of the extracellular matrixes (ECMs) to successfully mimic their characteristics.

ECMs are natural scaffolds that provide structural support to cells and surrounding tissues

[152]. Figure 1.14 shows an image of the natural ECM of bone tissue.

42

Figure 1.14 represents a cross section showing osteons. A unit of cells, an osteocyte, has a 5-20

µm diameter, is 7 µm deep, and contains 40-60 cells [https://www.78stepshealth.us/].

ECMs mainly contain bioactive molecules such as proteins, glycosaminoglycans

and glycoproteins. Quantities and local distribution of the ECM components determine

the mechanical properties, shape, and function of the whole organ. For example, collagen

is the most common component in bone and skin tissues [154]. Therefore, collagen can be

the main component for designing an artificial scaffold in bone engineering. However,

collagen concentration must be controlled since it can affect both cell-cell adhesion and

scaffold porosity, which has basic roles in cell-scaffold adhesion. Moreover, an increase

in collagen concentration results in high crosslinking of ECM, which leads to a limitation

in the supply of gases and nutrients to the cells and release of a hypoxia-related signaling

process [155]. Scaffold stiffness should also be controlled, since it is responsible for

mechanical strength during and after implantation [156]. Meanwhile, ECM stiffness values

are different from one tissue to another. The stiffness values of osteogenic, myogenic, and

neuronal tissues are 34 kPa, 11 kPa, and 0.1 kPa, respectively [156]. Therefore, the

artificial scaffold should have a stiffness value compatible with that kind of tissue.

https://www.78stepshealth.us/

43

Moreover, cells interacting with scaffolds interact with the superficial layer of the

biomaterial, while the mechanical testing of scaffold materials typically measures the total

modulus. Thus, it is important to compare the elastic properties at the surface with the bulk

values. In addition, the spatial heterogeneity of mechanical properties on a biologically-

relevant length scale should be characterized to provide additional information for scaffold

design.

Experimental testing will be performed on collagen samples loaded with different

amounts of Bioglass, to mimic the ECM of bone tissue. Figure 1.14 shows a cartoon of an

artificial scaffold as expected at microscale.

Figure1.15. displays a cartoon of an artificial scaffold with cells attaching between collagen fibrils

in microscale

Elastic properties of collagen samples will be mapped using the AFM force

mapping technique. The variation of the elastic modulus with depth will be sensed by

analyzing portions of the force curves corresponding to different penetration depths

44

(different levels of maximum applied force). The spatial heterogeneity of the modulus will

be characterized by using different scan sizes, corresponding to the pixel-to-pixel distances

of 20, 95, and 470 nm. This will allow the separation of systematic variations in the elastic

modulus with characteristic dimensions from random point-to-point variations.

In order to perform depth sensing, relatively sharp AFM probes will be used.

Therefore the tip of the probe might indent the sample to a depth noticeably exceeding the

radius of curvature of the probe. However, standard methods of extracting elastic

properties in indentation measurements utilize very simple probe shape models (e.g.

conical or paraboloidal tip models). The tip of the AFM probe is usually somewhat

rounded at the apex and then transitions to a conical shape. Consequently, if a simple probe

shape model is used in data analysis, then the effects of the probe shape might be perceived

as the depth dependence of the elastic modulus. To test and correct for this possible artifact,

the hyperboloidal tip shape model will be used because it has both of these features:

rounded tip shape that transitions into cone [137]. Data analysis will explicitly take into

account sample’s adhesion to avoid artifacts related to testing mechanical properties for

sticky samples [142].

45

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Chapter 2. Experimental Section

2.1 Samples and AFM setup

In this study, four different collagen-based biomaterial samples were prepared: 1)

uncrosslinked electrochemically aligned collagen (ELAC), 2) uncrosslinked Bioglass

incorporated ELAC (BG-ELAC), 3) crosslinked-ELAC and 4) crosslinked

electrochemically compacted collagen (ECC; unaligned). ELAC and BG-ELAC were

synthesized based on previously published protocol [1]. Briefly, acid soluble monomeric

collagen solution (Purecol, 3.1 mg/mL, Advanced Biomatrix, CA) was first dialyzed

against water for 24 hrs. Bioglass particles (GLO160P/-20; ~ 20 µm particle size; MO-

SCI Corporation, MO) were suspended at 200 mg / ml in water. Then, the Bioglass

particles were mixed with dialyzed collagen at the desired ratio, 30% Bioglass : 70%

collagen (w / w). This mixture was then applied between two stainless steel wire electrodes

( electrode spacing: 1.8 mm), and electric field was applied (3 V, 30 min). Electric field

triggers the formation of a pH gradient that in turn imparts a positive charge to the collagen

molecules close to the anode and negative charge to the collagen molecules close to the

cathode. Because of their repulsion with the same charge on the electrodes, the collagen

molecules self-assemble along the isoelectric point. During this process, the Bioglass

particles become entrapped within the collagen framework to form a highly aligned and

densely packed Bioglass incorporated ELAC thread (BG-ELAC) [1]. Collagen only

threads (ELAC) were made by the same way but without adding Bioglass particles. For

the third group of samples, ELAC threads (without Bioglass) were crosslinked via

incubation in 0.625% genipin solution (in 90% ethanol) for four hours at 37 ⁰C [2]. The

69

last group of samples were the crosslinked unaligned ECC collagen matrices which were

prepared in a similar manner but by replacing the stainless steel wire electrodes with planar

graphite electrodes [3].

2.2 Experimental Design

For AFM measurements, the samples were fixed on clean clipped corner plain

microscope slides [Thermo Fisher Scientific ESCO]. The thread diameter of ELAC

samples ranged from 250 µm to 300 µm, but appeared wider when deposited on the

substrate. The ECC unaligned samples are flat with a width of almost 5 mm. The cover

glasses were fixed with epoxy glue on plain glass microscope slides. Figure 2.1 shows a

photograph for a filament of the ELAC sample after fixing on the slide.

All AFM measurements were performed on fresh samples using a Molecular Force

Probe 3D AFM (MFP-3D, Asylum Research, Santa Barbara, CA). Samples were placed

on the AFM scanner, and two separate positions of the xy scanner were identified such that

AFM probe can be moved to these positions for force indentation measurements. Before

the AFM measurements, the samples were re-hydrated in a phosphate buffer saline (PBS)

pH ~ 7, to mimic the physiological environment. Then, the AFM head was placed properly

on the scanner and the measurements started from one of the identified positions. The

scanning was performed at two different spots for each sample (two samples for the

uncrosslinked and two for crosslinked collagen) and three different scan sizes to investigate

the large scale and short scale heterogeneity, respectively.

70

Figure 2.1 shows photograph of 1 cm long filament of ELAC sample deposited on a microscopic

glass slide. After deposition on glass apparent width is 1 mm.

All AFM measurements were performed using silicon nitride probes model NP-

S20 (Veeco, Santa Barbara, CA). To quantify force acting on the probe the cantilever

spring constant was measured by the thermal noise method [4], and the typical value was

approximately 100 pN / nm. Because of the heterogeneity of the Si3N4 cantilever material,

it might be suspected that the spring constant of cantilevers might vary significantly [5].

Therefore the spring constant was measured for each cantilever used in the measurements.

The manufacturer specifies radius of curvature of the AFM tip as approximately 20

nm. If the tip radius is very sharp it might damage the soft surface; if it is very dull, no

high spatial resolution can be obtained. The tip of AFM probe used in the elastic modulus

measurements was imaged using scanning electron microscope (SEM, Philips XL30).

Figure 2.2 shows the SEM image of the typical tip used in this research. The resolution of

this image is not sufficient to resolve features on a scale of 10 nm, but the image allows to

see that the probe has a sharp tip with a radius of curvature < 50 nm. This dimension

indicates that the probe was not significantly damaged during the AFM measurements.

71

Figure 2.2 shows SEM image for the tip of a long wide rectangular cantilever used in the

experiments.

The AFM measurements followed standard measurement procedure. After fixing

the cantilever in the probe holder and then in the AFM head, the laser beam was focused

on the back of cantilever close to the tip position to give the maximum reflection signal,

and the deflection was adjusted to zero. Then, the deflection sensitivity was calibrated on

the glass surface, and afterwards the spring constant was also calibrated using the built-in

thermal motion analysis procedure.

The measurements were carried out at three different spots that were previously

selected. One spot was selected on the glass area that was not covered with biomaterial.

This spot was used for measuring the optical lever sensitivity in PBS (typical values of

inverse sensitivity range from 27 nm / V to 31 nm / V) and to image the bare glass surface

for comparison. Figure 2.3 shows the glass surface image after cleaning by deionized water

and drying with a flow of N2.

72

Deflection

range = 10 nm

-200

200

nm

A B

Figure 2.3 shows images for clean-dry glass surface before fixing the sample. The A panel shows

deflection image and the B panel shows the topographic image. The topographic image is flat

because this scale is typical for collagen samples.

The other two spots were on the collagen sample with a distance of ~ 2 mm in

between. Two spots are selected to investigate the large scale heterogeneity of elastic

properties. At each spot, first, a contact mode image of a square area of 20 × 20 μm2 was

obtained to ensure the tip is scanning over the sample (not substrate) surface. Figure 2.4

shows typical image on ELAC sample in contact mode at a relatively low set point of 0.5

V. Low setpoint is selected to maintain the integrity of the sample surface.

Optical lever sensitivity was calibrated after each scan to perform accurate

indentation measurements [5].

73

Figure 2.4 shows the typical deflection (A) and height (B) image of ELAC sample with scan size

of 20 μm × 20 μm obtained before force mapping.

2.3 Force Mapping

Force curves were collected by moving the AFM probe towards and away from the

sample surface. Motion towards the sample surface was reversed once the deflection of

the cantilever reached the pre-determined trigger value. After each measurement, the

position of the sample was changed to a new location. Measurements continued until a

map of 32 × 32 force plots were collected [6]. The resulting force volume is a two-

dimensional grid across a specific area of sample surface, which can be used to extract a

map of the mechanical, adhesive, and viscoelastic properties over this area. During the

force mapping, the relative trigger was selected at 25 nm, meaning that the maximum

compressive force will be limited to 25·kc.≈ 2.5 nN for all force curves. The force curve

before the trigger is reached is called the approach force curve and after the trigger the

74

retracting curve starts. Collected data are stored on the computer and then analyzed using

custom software written for Matlab.

At each spot, the force mapping is performed over three different scan sizes, 640

nm × 640 nm, 3 μm × 3 μm, and 15 μm × 15 μm, corresponding to 20 nm, 95 nm, and 470

nm distances between two nearby force plots. The rationale for mapping small scan sizes

is to investigate the small scale heterogeneity of elastic modulus and to maintain the optical

lever sensitivity, since it might vary for large scan sizes.

2.4 Data Analysis

The AFM instrument measures cantilever deflection voltage and sample

displacement. To extract information about the local mechanical properties of materials

these data should be converted to force and indentation values. The experimentally

measured force vs. indentation dependence is compared with predictions of theoretical

models. In this section instrument calibration and several theoretical models are

considered.

2.4.1 Calibration of cantilever sensitivity and force constant

The AFM instrument measures cantilever deflection voltage and sample

displacement. To extract information about the local mechanical properties of materials

these data should be converted to force and indentation values. To obtain force and

indentation values, the cantilever deflection sensitivity should be calibrated.

When the laser beam reflects off the cantilever, it goes to the split photodiode and

produced the deflection voltage. When the end of the cantilever moves the deflection

75

voltage changes as illustrated in Figure 2.5. The sensitivity tells us how much the voltage

changes with a cantilever motion (the slope of ΔV vs. ΔZ), where ΔZ is the change in piezo

position, the deflection [7].

Calibration of optical lever sensitivity was carried out by changing the z piezo

position until the tip reached a hard surface (the deflection occurs) and change in the

deflection voltage was recorded. Figure 2.6 shows the relationship between changes in

deflection voltage and displacement, and the calibration of the optical lever sensitivity.

Figure 2.5 shows the dependence of voltage value on the cantilever motion. The repulsive force

bends the cantilever up and shifts the laser, and hence the voltage, to the positive value (Figure

adapted from http://www.nanophys.kth.se/)

Optical lever sensitivity is measured on a hard surface:

OLS (optical lever sensitivity) = ∆𝑉

𝑑 (2.1)

76

where ∆V is the change in the deflection voltage and d is the cantilever deflection.

Figure 2.6 shows a deflection vs. z displacement curve on a hard surface.

The measured value is used to convert the deflection voltage to the deflection distance at

other positions on the sample:

d = ∆𝑉

OLS= ∆𝑉 × Inv. OLS (2.2)

where Inv.OLS is the inverse optical lever sensitivity. Displacement of the base of

cantilever is the sum of the cantilever deflection d and the indentation δ.

Z = d + δ (2.3)

Then

∆Z = ∆V × Inv.OLS + δ (2.4)

77

Therefore, the cantilever sensitivity should be calibrated on surface that is much harder

than the samples (such as mica or a glass slide) to ensure that δ is close to zero in equation

(2.4) so that for calibration

Inv. OLS =∆𝑍

∆𝑉 (2.5)

The value of Inv.OLS should be relatively low (less than 100 nm / V); higher values

lead to a weak sensitivity, meaning that a large cantilever deflection is needed to achieve a

little change in voltage. Consequently, low sensitivity results in considerable contribution

of electronics noise to the measured signal, degrading performance of the instrument. Also,

low sensitivity might indicate that the AFM probe got damaged by handling or during

experiments. When the cantilever deflection is calibrated, the sample indentation can be

calculated as.

𝛿 = 𝑍 − ∆𝑉 × Inv. OLS (2.6)

The applied force can be calculated as follows:

F = kc × d (2.7)

where d is the cantilever deflection. Selecting cantilever with particular spring constant

requires taking into account several considerations. The most sensitive measurements can

be obtained when the cantilever spring constant is comparable to that for the sample.

However, the deflection voltage of a very soft cantilever in presence of adhesive forces

might exceed the voltage range of the photodiode. On the other hand, deflection of too

stiff cantilever will have significant contribution from the system electronic noise [4]. In

78

measurements spring constant of cantilevers was calibrated using the built-in thermal noise

method [4].

During the experiments, the Inv.OLS values in PBS were between 24 nm / V and

31 nm / V. The spring constant determined by the thermal noise method for a long wide

cantilever ranges from 98 pN / nm to 125 pN / nm, so the maximum applied forces

calculated by Eq. (2.6) range from 2.4 nN to 3.8 nN. After calibration, the force-

displacement curve can be obtained as shown in Figure 2.7.

Figure 2.7 shows a typical force-displacement curve

2.4.2 Indentation Models

Indentation values were obtained as described in eq. 2.6. However, it should be

noted that the displacement Z does not have zero corresponding to the sample surface, but

is determined up to some constant. Therefore the extracted indentation will also have some

offset. This issue in detail is discussed in section 1.7.5. This problem can be particularly

79

significant for soft samples [8]. Therefore, initially indentation is determined with an offset

(as shown in Figure 2.8) and the position of the contact point is used as an adjustable

parameter during data reduction.

-500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0

0

0.5

1

1.5

2

2.5

3

Fo

rce,

nN

Indentation, nm

Surface

Figure 2.8 shows a typical force-indentation curve

For example, the force-indentation dependence without adhesion for paraboloidal

probe is fitted using the model [8]:

F = 4

3

𝐸

1–𝜎2 √𝑅 𝛿3 (2.7)

where δ is the indentation determined with offset as in Figure 2.8 with an added offset (𝛿 =

𝛿𝑒𝑥𝑝 + 𝛿𝑜𝑓𝑓), F is the applied force, R is the probe’s radius of curvature, σ is the Poisson

ratio of the sample and E is the elastic (Young’s) modulus of the sample. Then off is used

as a fitting parameter. The Poisson ratio cannot be obtained separately from the elastic

modulus in indentation measurements. Therefore another fitting parameter in this model

is the modified elastic modulus E*

80

𝐸∗ =𝐸

1–𝜎2 (2.8)

As can be seen from SEM image of the AFM probe, the initial curved apex then

transitions into somewhat conical shape. Therefore, if indentation is large then

paraboloidal shape model given by eq. 2.8 might be inaccurate. Therefore probe shape that

contains both the rounded apex and conical body can be considered. One of such shapes

is the hyperboloidal shape [8] that is shown in Figure 2.9.

Paraboloidal

Hyperboloidal

R

a

Figure 2.9 shows comparison of paraboloidal and hyperboloidal shapes that have the same radius

of curvature R. In the figure a is the semi-vertical angle of hyperboloidal probe.

For a hyperboloid probe profile force-indentation dependence cannot be derived as

a closed-form expression. However, this dependence can be calculated using the radius of

contact area as a parameter [8]:

𝐹 =𝐸𝑎3

(1−𝜎2)𝑅[𝜁2 +

𝜉

2 (1 − 𝜉2) {

𝜋

2 + 𝑎𝑟𝑐𝑡𝑎𝑛 (

1

2𝜉 −

𝜉

2)}] (2.9)

81

𝛿 = 𝑎2

2𝑅 𝜁 [

𝜋

2 + 𝑎𝑟𝑐𝑡𝑎𝑛 (

1

2𝜁−

𝜁

2)] (2.10)

where

𝜁 =𝑅 𝑐𝑜𝑡 (𝛼)

𝑎 (2.11)

Here a is the radius of contact area, α is the semi-vertical angle of the tip and other

parameters as described for the paraboloidal probe model eq. 3.7.

The modified elastic modulus values obtained from data analysis with the above

models that do not include adhesion are used as an initial guess to fit the data with models

that consider adhesion [6]. In fitting models with adhesion one more fitting parameter is

used: the energy of adhesion, . Here for both probe shape model the equations use the

radius of contact area, a, that connects force and indentation. For the paraboloidal probe

the JKR theory (after Johnson, Kendall and Roberts [9]) gives force and indentation as:

3 *3 *4

83

a EF a E

R (2.12)

2

*

2a a

R E

(2.13)

The JKR model takes into account elastic deformation of the sample surface, but it

ignores the long range attractive forces. Samples used in this study are soft and elastic

deformation is significant. Moreover measurements do not detect long range attractive

forces. Therefore it is reasonable to apply this model to analyze indentation data on

82

samples studied here. Similar model that takes adhesion into account can be derived for

the hyperboloidal probe model [6]:

* 2 2 2 2* 3

2 22arcsin 8

4

E A a A a AF a A E a

R a A

(2.14)

2 2

2 2 *

22arcsin

4

a A a A a

R a A E

(2.15)

Here a is radius of contact area, cot( )A R a , and other parameters as described above.

83

2.5 References

[1] Nijsure, M. P.; Pastakia, M.; Spano, J.; Fenn, M. B.; Kishore, V., Bioglass incorporation

improves mechanical properties and enhances cell-mediated mineralization on

electrochemically aligned collagen threads, Journal of Biomedical Materials Research

Part A, 2017, 105A, 2429-2440.

[2] Uquillas, J. A.; Kishore, V.; Akkus, O., Optimized crosslinking elevates the strength of

electrochemically aligned collagen to the level of tendons, Journal of Mechanical Behavior

for Biomedical Materials 2012, 15C, 176-189.

[3] Kishore, V.; Iyer, R.; Frandsen, A.; Nguyen, T-U., In vitro characterization of

electrochemically compacted collagen matrices for corneal applications, Biomedical

Materials 2016, 11, 055008.

[4] Proksch, R.; Schȁffer, T. E.; Cleveland, J. P.; Callahan, r. C.; Viani, M. B., Finite optical

spot size and position corrections in thermal spring constant calibration, Nanotechnology

2004,15, 1344-1350.

[5] Ducker, W. A.; Senden, T. J.; Pashley, R. M., Direct measurement of colloidal forces

using an atomic force microscope, Nature 1991, 353, 239-241.

[6] Sun, Y.; Akhremitchev, B. B.; and Walker, G. C., Using the adhesive interaction

between Atomic Force Microscopy tips and polymer surfaces to measure the elastic

modulus of compliant samples, Langmuir 2004, 20, 5837-5845.

84

[7] Attard, P., Measurement and interpretation of elastic and viscoelastic properties with

the atomic force microscope, Journal of Physics: Condensed Matter 2007, 19, 1-30.

[8] Akhremitchev, B. B.; Walker, C. G., Finite sample thickness effect on elasticity

determination using Atomic Force Microscopy, Langmuir 1999, 15, 5630-5634.

[9] Johnson, K. L.; Kendall, K.; Roberts, A. D., Surface energy and contact of elastic solids,

Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences

1971, 324, 301-313.

85

Chapter 3. Results

AFM images for all samples, ELAC, 30% BG-ELAC, crosslinked ELAC and

crosslinked unaligned collagen have been collected before and after force mapping to

confirm the integrity of measured surface after force mapping. Figure 3.1 shows the height

(right panel) and deflection (left panel) images for the typical sample of each type collected

after performing the force mapping measurements; scan size in all four images was 15 µm

× 15 µm. If there was any damage during the mapping, squares of 640 nm and 3 µm would

be visible in the middle of images below. Absence of such squares indicates no damage to

the sample surface using the selected range of forces during indentation measurements.

A

B

86

Figure 3.1A-D show deflection (left) and height (right) images at 15 µm scan size. Panels A-D

show images of typical ELAC, 30% BG-ELAC, crosslinked-ELAC, and crosslinked unaligned

collagen samples, respectively.

Approach and withdraw force plots have been acquired for each point in the map

(32 × 32 = 1024 force plot). The force-indentation data were analyzed using custom

software written for Matlab. Figures 3.3-3.6 show typical approach and withdraw force

curves for each sample. Force curves were analyzed using the least squares fit of the JKR

model eq. 2.12 and 2.13 to the data. For each force curve analysis provides elastic modulus

(E*, see eq. 2.8), position of the surface and for curves exhibiting adhesion, energy of

adhesion parameter as well.

C

D

87

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

500

0

1

2

3

For

ce,n

NMaximum

forceSurfac

e

A

-500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0

0

1

2

3

Fo

rce,

nN

Relative Indentation, nm

B

Surfac

e

Maximum

force

Figure 3.2 displays fitting typical approach (A) and withdraw (B) force plots of ELAC sample using

paraboloidal probe shape. Data analyzed to maximum compressive force of Fmax = 1 nN.

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

500

0

1

2

3

For

ce,n

N

A

-

500-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

500

0

1

2

3

For

ce,n

N


B

Maximum force

Maximum force

Surface

Surface

Figure 3.3 shows fitting typical approach (A) and withdraw (B) force plots of BG-ELAC sample

using paraboloidal probe shape. Data analyzed to maximum compressive force of Fmax= 1 nN.

88

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

50 0

0

1

2

3

For

ce,n

N

A

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

50 0

0

1

2

3

For

ce,n

N


B

Maximum force

Surface

Surface

Maximum force

Figure 3.4 displays fitting typical approach (A) and withdraw (B) force plots of crosslinked-ELAC

sample using paraboloidal probe shape. Data analyzed at Fmax = 1 nN.

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

500

0

1

2

3

Forc

e,nN

A

-

500

-

450

-

400

-

350

-

300

-

250

-

200

-

150

-

100

-

500

0

1

2

3

Forc

e,nN


B

Maximum

force

Surfac

e

Surfac

e

Maximum

force

Figure 3.5 shows fitting typical approach (A) and withdraw (B) force plots of crosslinked unaligned

collagen sample using paraboloidal probe shape. Data analyzed at Fmax = 1 nN.

89

Analysis of all force plots (1024 analyzed for each map) provides maps of elastic

modulus (E*) for each sample at two spots and three different scan sizes to characterize

local elastic modulus and investigate the large range and short range heterogeneity. As an

example, Figure 3.7 illustrates the heterogeneity in maps of elasticity over three scan sizes:

640 nm, 3 µm and 15 µm for crosslinked-ELAC sample. Separate maps are shown for

approach and withdraw scan direction. In analysis range of compressive forces was limited

to 1 nN maximum force; the JKR paraboloidal probe shape model was used.

5 10 15 20 25 30

5

10

15

20

25

30

Approach

Elastic modulus [MPa]; Mean 0.609 Std 0.133 Elastic modulus [MPa]; Mean 0.580 Std 0.119

5 10 15 20 25 30

5

10

15

20

25

30

Withdraw

640 nm

scan size

0.25 MPa

1.35 MPa

Elastic modulus [MPa]; Mean 1.340 Std 1.060

5 10 15 20 25 30

5

10

15

20

25

30

3 um

scan size


5 10 15 20 25 30

5

10

15

20

25

30

0.25 MPa

4.6 MPa

90


5 10 15 20 25 30

5

10

15

20

25

30


5 10 15 20 25 30

5

10

15

20

25

30

15 um scan size

0.1 MPa

5.6 MPa

Figure 3.6 shows the maps of elasticity of crosslinked-ELAC at the three different scan sizes, and

approach and withdraw scan directions using 1 nN maximum force and paraboloidal probe shape

model. Numbers on axes indicate pixel position. Blue pixels show places were collected force

plots could not be analyzed.

The average of elastic modulus values for each map with the corresponding

standard deviation were calculated using Matlab program. Tables 3.1 to 3.14 display these

values for the four different samples.

Table 3.1. Elastic modulus values and their corresponding standard deviations (Std) of sample 1, 1st spot map (1024 force curves) of ELAC sample using maximum compressive forces of 1 nN and 2 nN, extracted by fitting with JKR model.

Scan

sizes

Scan

direction

E*, MPa

Fmax 1 nN Fmax 2 nN

640 nm

Approach

Std

0.112

0.058

0.317

0.053

Withdraw

Std

0.319

0.099

0.569

0.151

3 um

Approach

Std

0.077

0.040

0.155

0.069

Withdraw

Std

0.156

0.076

0.219

0.139

15 um

Approach

Std

0.165

0.079

0.227

0.105

Withdraw

Std

0.176

0.082

0.253

0.110

91

Table 3.2. Elastic modulus values and their corresponding standard deviations (Std) of sample 1,

2nd spot map (1024 force curves) of ELAC sample using maximum compressive forces of 1 nN and

2 nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa

Fmax 1 nN Fmax 2 nN

640 nm

Approach

Std

0.104

0.063

0.151

0.091

Withdraw

Std

0.135

0.102

0.221

0.148

3 um

Approach

Std

0.098

0.028

0.124

0.036

Withdraw

Std

0.111

0.041

0.149

0.054

15 um

Approach

Std

0.091

0.032

0.117

0.048

Withdraw

Std

0.116

0.054

0.145

0.082


1st spot map (1024 force curves) of ELAC sample using maximum compressive forces of 1 nN and


Scan

sizes

Std, Scan

direction

E*, MPa

Fmax 1 nN Fmax 2 nN

640 nm

Approach

Std

0.139

0.007

0.146

0.005

Withdraw

Std

0.129

0.010

0.140

0.006

3 um

Approach

Std

0.141

0.052

0.132

0.034

Withdraw

Std

0.122

0.044

0.128

0.037

15 um

Approach

Std

0.114

0.031

0.116

0.027

Withdraw

Std

0.111

0.035

0.114

0.032

92


2nd spot map (1024 force curves) of ELAC sample using maximum compressive forces of 1 nN and


Scan

sizes

Std, Scan

direction

E*, MPa

Fmax 1 nN Fmax 2 nN

640 nm

Approach

Std

0.090

0.006

0.075

0.003

Withdraw

Std

0.094

0.006

0.081

0.005

3 um

Approach

Std

0.103

0.008

0.087

0.007

Withdraw

Std

0.103

0.008

0.095

0.009

15 um

Approach

Std

0.118

0.011

0.109

0.019

Withdraw

Std

0.113

0.013

0.132

0.037

Table 3.5. The average of elastic modulus values and their corresponding standard deviations (Std)

of all spots on ELAC samples using maximum compressive forces of 1 nN and 2 nN, extracted by

fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa

Fmax 1 nN Fmax 2 nN

640 nm

Approach

Std

0.111

0.034

0.172

0.038

Withdraw

Std

0.166

0.054

0.253

0.077

3 um

Approach

Std

0.105

0.045

0.125

0.036

Withdraw

Std

0.122

0.038

0.148

0.061

15 um

Approach

Std

0.122

0.038

0.142

0.049

Withdraw

Std

0.114

0.076

0.161

0.065

93


1st spot map (1024 force curves) of 30% BG-ELAC sample using maximum compressive forces of

1 nN and 2 nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa

Fmax= 1 nN Fmax = 2 nN

640 nm

Approach

Std

0.510

0.112

0.533

0.093

Withdraw

Std

0.488

0.111

0.563

0.101

3 um

Approach

Std

0.572

0.199

0.578

0.181

Withdraw

Std

0.534

0.197

0.601

0.212

15 um

Approach

Std

0.527

0.131

0.538

0.111

Withdraw

Std

0.499

0.130

0.564

0.118


2nd spot map (1024 force curves) of 30% BG-ELAC sample using maximum compressive forces

of 1 nN and 2 nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa


640 nm

Approach

Std

0.529

0.101

0.587

0.094

Withdraw

Std

0.463

0.107

0.612

0.100

3 um

Approach

Std

0.570

0.149

0.625

0.129

Withdraw

Std

0.525

0.132

0.643

0.132

15 um

Approach

Std

0.605

0.199

0.676

0.173

Withdraw

Std

0.590

0.169

0.736

0.280

94


1st spot map (1024 force curves) of 30% BG-ELAC sample using maximum compressive forces of

1 nN and 2 nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa


640 nm

Approach

Std

0.578

0.058

0.709

0.068

Withdraw

Std

0.719

0.106

0.852

0.106

3 um

Approach

Std

0.542

0.154

0.761

0.210

Withdraw

Std

0.804

0.296

1.020

0.340

15 um

Approach

Std

0.392

0.198

0.568

0.299

Withdraw

Std

0.593

0.373

0.796

0.371


2nd spot map (1024 force curves) of 30% BG-ELAC sample using maximum compressive forces

of 1 nN and 2 nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa


640 nm

Approach

Std

0.777

0.164

0.756

0.137

Withdraw

Std

0.704

0.136

0.771

0.123

3 um

Approach

Std

0.826

0.225

0.792

0.178

Withdraw

Std

0.731

0.187

0.786

0.171

15 um

Approach

Std

0.778

0.205

0.780

0.173

Withdraw

Std

0.770

0.155

0.782

0.162

95

Table 3.10. The average of elastic modulus values and their corresponding standard deviations

(Std) of all spots on 30% BG-ELAC samples using maximum compressive forces of 1 nN and 2

nN, extracted by fitting with JKR model.

Scan

sizes

Std, Scan

direction

E*, MPa


640 nm

Approach

Std

0.600

0.109

0.646

0.098

Withdraw

Std

0.594

0.115

0.700

0.107

3 um

Approach

Std

0.628

0.182

0.689

0.175

Withdraw

Std

0.649

0.203

0.762

0.213

15 um

Approach

Std

0.575

0.183

0.640

0.189

Withdraw

Std

0.613

0.206

0.715

0.231

Table 3.11. Elastic modulus values and their corresponding standard deviations (Std) of map (1024

force curves) of crosslinked-ELAC sample using maximum compressive forces of 1 nN and 2 nN,

extracted by fitting with JKR model.

Scan

sizes

Std, scan

direction

E*, MPa

Fmax= 1 nN Fmax= 2 nN

640 nm

Approach

Std

0.609

0.133

0.715

0.126

Withdraw

Std

0.580

0.119

0.769

0..145

3 um

Approach

Std

0.881

0.520

1.490

1.210

Withdraw

Std

1.340

1.060

2.240

1.940

15 um

Approach

Std

0.924

0.470

1.670

1.190

Withdraw

Std

1.480

0.962

2.450

1.860

96

Table 3.12. Elastic modulus values and their corresponding standard deviations (Std) of 1st spot on

crosslinked unaligned collagen sample using maximum compressive forces of 1 nN and 2 nN,


Scan

sizes

Std, scan

direction

E*, MPa


640 nm

Approach

Std

0.922

0.226

1.390

0.251

Withdraw

Std

2.470

0.628

3.100

0.521

3 um

Approach

Std

0.732

0.187

1.220

0.219

Withdraw

Std

1.790

0.587

2.640

0.473

15 um

Approach

Std

0.570

0.316

0.887

0.449

Withdraw

Std

1.280

0.730

1.890

0.886

Table 3.13 Elastic modulus values and their corresponding standard deviations (Std) of 2nd spot

on crosslinked unaligned collagen sample using maximum compressive forces of 1 nN and 2 nN,


Scan

sizes

Std, scan

direction

E*, MPa


640 nm

Approach

Std

1.040

0.196

1.760

0.329

Withdraw

Std

2.120

0.650

2.990

0.710

3 um

Approach

Std

0.842

0.241

1.360

0.361

Withdraw

Std

1.530

0.538

2.230

0.560

15 um

Approach

Std

0.772

0.253

1.140

0.343

Withdraw

Std

1.320

0.466

1.980

0.510

97

Table 3.14 Elastic modulus values and their corresponding standard deviations (Std) of all spots

on crosslinked unaligned collagen sample using maximum compressive forces of 1 nN and 2 nN,


Scan

sizes

Std, scan

direction

E*, MPa


640 nm

Approach

Std

0.981

0.211

1.575

0.290

Withdraw

Std

2.295

0.639

3.040

0.616

3 um

Approach

Std

0.787

0.214

1.290

0.290

Withdraw

Std

1.660

0.562

2.435

0.517

15 um

Approach

Std

0.671

0.285

1.014

0.396

Withdraw

Std

1.300

0.600

1.930

0.698

Results shown in these tables indicate that the samples are relatively soft with

modulus E* in are range from approximately 0.1 MPa to approximately 3 MPa. It should

be noted that to obtain values of corresponding elastic modulus, results for modulus E*

should be multiplied by factor (1 - 2). The Poisson ratio ranges from 0.5 to 0, so the

factor ranges from 0.75 to 1. This represents the inherent uncertainty in extracting elastic

modulus using this method. This uncertainty can be reduced if reasonable guess about

Poisson ratio can be made.

98

Chapter 4. Discussion

4.1 Elastic modulus measurements

Previous section shows parameters obtained by fitting the JKR model to data

collected on four different types of samples. Results show that for ELAC, BG-ELAC,

crosslinked-ELAC and crosslinked-ECC samples the average extracted moduli obtained

from approach curves using 1 nN maximum compressive force are 0.12 MPa, 0.61 MPa,

0.97 MPa and 1.28 MPa with 0.05 MPa, 0.17 MPa, 0.54 MPa and 0.41 MPa standard

deviation, respectively. The same order was found at Fmax = 2 nN. Figure 4.1 shows these

average data with their standard deviations shown as error bars. In previous work, it was

found that Bioglass incorporated within ELAC threads improves the elastic modulus

significantly [1]. The higher standard deviation value of BG-ELAC than for ELAC sample

indicates less uniformity of the former. Crosslinked samples have higher Young’s modulus

than uncrosslinked collagen threads. The same observation has been reported in previous

work [2], which stated that the modulus value of soft materials decrease with decreasing

the crosslink ratio [2]. Kishore and coworkers determined the ultimate tensile stress (UTS)

for ECC material with and without treatment with genipin crosslinker [3]. They observed

a significant increase in UTS by adding genipin to the ECC matrices [3]. The crosslinked-

ECC unaligned exhibits higher modulus than crosslinked aligned, crosslinked-ELAC

sample. The higher std value of elastic modulus for cosslinked-ELAC than that of

crosslinked ECC unaligned sample might be attributed to the presence of regions with

significantly different values of the modulus as shown in Figure 3.6. No such regions are

99

observed for unaligned sample. Figure 4.2 shows the force maps of one spot of crosslinked

ECC unaligned sample at the three different scan sizes.

E, MPa

ELAC BG-ELAC Crosslinked-

ELAC

Crosslinked-

ECC

0

0.4

0.8

1.2

1.6 A

ELAC BG-ELAC Crosslinked-ELAC Crosslinked-

ECC

0

1

2

3

E, MPa

B

Figure 4.1 displays the average values of Young’s modulus of ELAC, BG-ELAC, crosslinked-

ELAC and crosslinked-ECC collagen threads at A) Fmax = 1 nN, and B) Fmax = 2 nN. Standard

deviations are shown as error bars.

100


Approach

5 10 15 20 25 30

5

10

15

20

25

30


5 10 15 20 25 30

5

10

15

20

25

30

Withdraw


5 10 15 20 25 30

5

10

15

20

25

30


5 10 15 20 25 30

5

10

15

20

25

30


5 10 15 20 25 30

5

10

15

20

25

30


5 10 15 20 25 30

5

10

15

20

25

30

640 nm

3 um

15 um

100 nm 100 nm

1 um 1 um

5 um 5 um

0.65 MPa

3.35 MPa

0.20 MPa

2.75 MPa

0.20 MPa

2.50 MPa

Figure 4.2 shows the force maps of one spot of crosslinked ECC unaligned sample at the three

different scan sizes.

Elastic modulus values measured here can be compared with elastic modulus values

of collagen gels, in which collagen molecules are organized in hydrogels with a lot of

empty space between individual molecules, and with the elastic modulus is in the sub-kPa

101

range [4]. Therefore, the densification-alignment and unalignment processes of the

investigated samples very significantly increases modulus in comparison with hydrogels.

The measured values are close to the elastic modulus of stiffer biological materials like

cartilage and meniscus (100 kPa – 1 MPa range) [5, 6]. However, this value is significantly

(about two orders of magnitude) lower than the elastic modulus of protein materials in

crystalline state [7].

The elastic modulus of similarly prepared BG-ELAC samples was reported earlier

in paper by Kishore and co-workers [1]. Results for the bulk modulus obtained using the

dynamic mechanical analyzer were approximately 10 times higher than values reported

here. It might be suggested that in part the observed difference results from uncertainty in

the radius of curvature of the AFM probe. However, the nominal value of the tip radius

was specified with 5 nm uncertainty. This means that if the extreme values of 15 nm and

25 nm were used, they would provide modulus values different by ~13% from the value

obtained using the expected radius. The measured elastic modulus is proportional to R–½

(see eq. 2.7). Therefore the radius should be approximately 100 times lower to reconcile

the observed difference, making the probe unrealistically sharp with 0.2 nm radius of

curvature. Therefore other explanation for observed difference is needed. This difference

in modulus values can be attributed to the testing direction. The modulus value of

anisotropic material depends on the direction of the applied force. In the previous work

[1], the applied force of the tensile test used to determine the elastic modulus is parallel to

collagen alignments, whereas the force applied by AFM is perpendicular to the alignments.

Furthermore, the observed difference can be explained by noting that AFM tests elastic

102

modulus of the near-surface layer. Therefore it can be suggested that the surface of samples

is considerably softer than the middle part of material. From the typical force-indentation

curves shown in Figure 3.2 – 3.6, it can be seen that the soft surface layer extends to at

least several tens of nanometers into the sample surface because after some relatively short

distance (about 50 nm – 150 nm) the fit curves start to deviate noticeably from the data. It

appears that samples are stiffer beyond the surface layer. For ELAC sample the elastic

half-space model fits the indentation data reasonably well up to the depth of approximately

150 nm (Figure 3.2) and for BG-ELAC sample the range of good fit is approximately 50

nm (Figure 3.4). For crosslinked-ELAC, the reasonable fitting is at depth up to

approximately 35 nm while that for crosslinked-ECC (unaligned) at ~ 25 nm. The

consistence of these depths coincides with that order in Figure 4.1. By applying a specific

force the tip travels largest distance into the softest, and the shortest into the stiffest

material. The upturn of the force-indentation data from the fit lines generated using the

JKR model can be observed for all samples.

4.2 Viscoelasticity

As with most biological and soft materials [8, 9, 10], our samples exhibit viscoelastic

behavior that can be seen as hysteresis between the approach and the withdraw force curves

when the probe applies compressive force to the sample (hysteresis at tensile forces is

caused by adhesion) [9, 11, 12]. Generally such hysteresis in the region of compressive

forces can be attributed to either plastic or viscoelastic behavior [13]. After the sample is

deformed plastically, the deformation persists after removal of the force. However, the

viscoelastic behavior is a time dependent deformation that occurs after the force is

103

applied/removed to/from the sample [14]. Therefore, if force curves collected on the same

spot continue to exhibit hysteresis then observed hysteresis is of viscoelastic nature. For

all samples tested here the continuously reproduced hysteresis indicates the viscoelastic

behavior. Figures 3.3 – 3.6 show this hysteresis as a difference in slope and offset between

approach and withdraw curves for ELAC, BG-ELAC, crosslinked-ELAC and crosslinked-

ECC, unaligned, samples in the region of compressive (positive) forces.

The model that is used here to analyze indentation data does not explicitly include

viscoelastic effects. The observed viscoelasticity can be quantified as differences in the

elastic modulus obtained for the approach and withdraw force curves. Such difference

would mainly manifest itself as difference in the slope of force-indentation curves near the

point of reversal of probe’s motion. Therefore higher-force regions of force curves should

be considered to compare viscoelastic behavior across the samples. This type of hysteresis

is typical for viscoelastic polymeric materials [15] and biomaterials [16].It can be noticed

that the approach and withdraw force curves shown in Figures 3.3 – 3.6 have similar slopes

for low compressive forces (below ~1 nN). Consequently effects of viscoelasticity can be

quantified as horizontal offset between approach and withdraw curves. Such offset is zero

for purely elastic samples. Figures 4.3 and 4.4 show histograms of approach-withdraw

offsets obtained for different samples at different scan sizes, as indicated in corresponding

panels.

Figure 4.3 compares force curve offsets at different scan sizes and Figure 4.4

compares values obtained at different spots on the sample surface. Offsets seem to be

similar at different scan sizes with BG-ELAC samples exhibiting lower offset than the

104

other two samples. Large offset observed on ELAC sample might be expected because

this sample is not crosslinked. Somewhat surprising is the low offsets measured for BG-

ELAC sample observed at different scan sizes and at different spots.

-50 0 50 100 150 200 250 3000

20

40

60

80

100

120

-50 0 50 100 150 200 250 3000

20

40

60

80

100

120

-50 0 50 100 150 200 250 3000

50

100

150

200

250

-50 0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

300

Oc

cu

ran

ce

Occ

ura

nce

Approach-withdraw offset, nm Approach-withdraw offset, nm



58.7 ± 8.6ELAC (3 um scan size)

6.4 ± 1.7ELAC (15 um scan size)

8.0 ± 0.3BG-ELAC (3 um scan size)

9.5 ± 0.3BG-ELAC (15 um scan size)

Oc

cu

ran

ce

Oc

cu

ran

ce

-50 0 50 100 150 200 2500

50

100

150

200

250

Crosslinked-ECC(3 um scan size)

Occ

ura

nce

-50 0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

180

17.8 ± 0.6Crosslinked-ECC

( 15 um scan size)

Occ

ura

nce

15.2 ± 0.3

Figure 4.3 displays the approach-withdraw offset for ELAC, BG-ELAC and crosslinked-ECC,

unaligned samples at Fmax = 1 nN using paraboloidal tip model. The numbers inside the chart are

the positions of histograms ± one standard deviation error in this position.

105

1 st spot 2 nd spot

-50 0 50 100 1500

20

40

60

80

100

120

-50 0 50 100 1500

20

40

60

80

100

120

140

160

-50 0 50 100 1500

20

40

60

80

100

120

140

160

-50 0 50 100 1500

50

100

150

200

250

-50 0 50 100 1500

50

100

150

200

250

25.3 ± 0.2

Crosslinked-ECC

-50 0 50 100 1500

20

40

60

80

100

120

140

160

180

6.4 ± 1.7

ELAC (15 um scan size)

10.6 ± 0.5

ELAC

9.5 ± 0.3

BG-ELAC

3.3 ± 0.3

BG-ELAC

17.8 ± 0.6

Crosslinked-ECC

Occ

ura

nce

Occ

ura

nce

Occ

ura

nce


Figure 4.4 shows the approach-withdraw offset for the different spots using data collected with 15

μm scan size.

This reveals that the Bioglass particles affect the viscoelastic behavior of collagen

threads: It appears that samples with added Bioglass exhibit more elastic-like behavior.

For ELAC sample, it can be seen that the offset distribution dramatically changed

106

throughout the short scale of the scan size (from 58.7 − 8.6 to 6.4 + 1.7 from 3 μm to 15

μm, respectively).

For crosslinked-ECC, the viscoelasticity is larger than for BG-ELAC sample and

this is consistent at different scan sizes and spots. In the case of crosslinked-ELAC a

continuous change in viscoelastic offset was observed throughout changing the scan scales.

Figure 4.5 shows the slow increase of the mean value of approach-withdraw offset for

crosslinked-ELAC sample over the three different scan sizes, 640 nm, 3 μm and 15 μm.

This regularity might be attributed to the fact that this sample consists of regions with

relatively low and high elastic modulus, as seen in Figure 3.8. Only “low” modulus region

was tested at scan size of 640 nm, and this region corresponds to lower viscoelastic offset

that is shown on the left panel of Figure 4.5. As higher modulus areas appear in the image,

so the more pronounced is the right hand side shoulder in the histograms. These

observations are consistent with earlier notion that crosslinking increases elastic modulus

but also increases viscoelastic offset between approach-withdraw curves.

107

50

13.2 ± 0.3

15 um scan size

50

Approach-withdraw offset, nm

-20 -10 0 10 20 30 400

20

40

60

80

100

120

140

160

180

200

8.4 ± 0.1

Occ

ura

nce


100

120

140

160

180

-20 -10 0 10 20 30 400

20

40

60

80

10.7 ± 0.8Crosslinked-


-20 -10 0 10 20 30 40 500

20

40

60

80

100

120

140

160

Crosslinked-ELACELAC

3 um scan sizeCrosslinked-ELAC

640 nm scan size

Figure 4.5 displays the slow increase of viscoelasticity mean value of crosslinked-ELAC with

increasing the scan sizes as higher modulus areas are included in testing.

In the comparison of mean values of offset for the four types of sample at 15 μm scan size,

the offset distribution is overlapped within the two spot ranges of ELAC and BG-ELAC

samples, revealing the similar manner in viscoelasticity at the given scan size. On the other

hand, crosslinked materials show clearly increase in the offset most probable values from

each other and the first two samples.

4.3 Heterogeneity of Surface

The topographic map of ELAC sample in Figure 2.4 shows variations that could be

associated with local organization of collagen threads. The corresponding map and

histogram of elastic modulus are shown in Figure 4.6. It can be observed that the

distribution of elastic modulus is not wide with clear peak around the most probable value.

As discussed in the previous sub-section, the elastic modulus extracted from the withdraw

force curves is shifted towards higher values. Distance between force plots collected in

this map is approximately 0.5 µm, and considerable point-to-point variation in the elastic

108

modus observed in the modulus maps here indicate that the characteristic scale for variation

in the elastic modulus for this sample is less than 0.5 µm. The force maps collected at 640

nm scan size shown in Figure 4.7 exhibit considerably smoother variation in the modulus

with characteristic scale of modulus variation of 100 nm. This scale is similar in size with

the size of the tip-sample contact area estimated as 2(R·δ) ½ which reaches value of ~110

nm at maximum indentation. Figures 4.6, and 4.7 show the maps and histograms for both

scan directions, approach and withdraw. The withdraw maps show slightly higher

variation in distribution of modulus and thus higher standard deviations. Higher width of

distribution of the withdraw curves can be attributed to the higher uncertainty in the

modulus extracted by simultaneously taking into account the adhesion of samples.

5 10 15 20 25 30

5

10

15

20

25

30

5 10 15 20 25 30

5

10

15

20

25

30

Elastic modulus [MPa]; Mean 0.109 Std

0.019

Elastic modulus [MPa]; Mean 0.132 Std

0.037

Approach Withdraw

5 um 5 um

0 0.1 0.2 0.30

50

100

150

200

250

300 Elastic modulus [MPa]

0 0.1 0.2 0.30

50

100

150

200

250


0.08 MPa

0.34 MPa

Figure 4.6 shows force maps and their corresponding histograms of ELAC sample at 15 µm scan

size

109

Unlike the ELAC sample, which does not have a significant increase of

heterogeneity with increasing scan size, the standard deviation of elastic modulus for BG-

ELAC is considerably higher and it increases with increasing the scan size, as shown in

Figure 4.8. This is expected for composite materials since the larger scan size can include

more and more features with various mechanical properties. This consistence has been

shown in previous report [18], in which the samples appears to be strongly heterogeneous

with increasing the scan size.

Elastic modulus [MPa]

Mean 0. 075 Std 0.004

5 10 15 20 25 30

5

10

15

20

25

30


Mean 0.081 Std 0.005

5 10 15 20 25 300

5

10

15

20

25

30

Approach Withdraw

100 nm 100 nm

0.07 0.08 0.09 0.100

20

40

60

80

100Elastic modulus [MPa]

0.07 0.08 0.09 0.100

20

40

60

80

100


0.035 MPa

0.079 MPa

Figure 4.7 shows elastic modulus maps and corresponding histograms measured on ELAC sample

at 640 nm scan size.

110

5 10 15 20 25 30

5

10

15

20

25

30

5 10 15 20 25 30

5

10

15

20

25

30

5 10 15 20 25 30

5

10

15

20

25

30

a)

b)

c)

100 nm

1 um

5 um

.

Elastic modulus Mean 0.570 MPa, Std 0.149


0 0.5 1 1.5 20

20

40

60

80


0 0.5 1 1.5 20

20

40

60

80

100


0 0.5 1 1.50

50

100


2

Std = 0.10 MPa

Scan size= 640 nm

Std = 0.15 MPa

Scan size = 3 um

Std = 0.2 MPa

Scan size = 15 um

0.23 MPa

0.91 MPa

0.20 MPa

1.10 MPa


0.2 MPa

1.70 MPa

Figure 4.8 shows elastic modulus maps and their corresponding histograms of BG-ELAC at

different scan sizes: a) 640 nm, b) 3 µm, and c) 15 µm.

Elastic map with scan size 640 nm for BG-ELAC shows noticeably sharper variation of

features than for ELAC sample. This can be attributed to the considerably lower size of

the contact area; here characteristic size 2(R·δ) ½ is approximately 60 nm. Crosslinked-

ECC sample, which has a resolution of approximately 45 nm shows features with more

sharp dimensions than BG-ELACs’. Figure 4.9 characterizes some features of the four

types of sample at the smallest scan size, 640 nm, in which the point to point distance

equals 20 nm. The small features reflect the high modulus of surface, on which the tip-

111

sample contact area is smaller than that on the lower modulus materials. Even though

crosslinked-ELAC has a characteristic size even less than BG-ELACs’ (approximately 53

nm), it exhibits sudden variations in force the map, indicating that the feature dimensions

are smaller than 53 nm.

5 10 15 20 25 30

5

10

15

20

25

30

ELAC threads at 640 nm scan size

5 10 15 20 25 300

5

10

15

20

25

30

BG-ELAC at 640 nm scan size

5 10 15 20 25 30

5

10

15

20

25

30

5 10 15 20 25 30

5

10

15

20

25

30

Crosslinked-ELAC at 640 nm scan size Crosslinked-ECC, at 640 nm scan size

100 nm100 nm 100 nm 100 nm

0.34 MPa

0.16 MPa 0.20 MPa

0.87 MPa

0.25 MPa

1.35 MPa

0.65 MPa

3.35 MPa

Figure 4.9 displays force maps of ELAC and BG-ELAC, crosslinked-ELAC and crosslinked-

ECC, unaligned samples at 640 nm scan size. The higher modulus samples show sharper features.

4.4 Depth Sensing and Tip Shape Artifacts

Tables 3.5, 3.10, 3.11 and 3.14 display the elastic modulus values of samples,

ELAC, BG-ELAC, crosslinked-ELAC and crosslinked-ECC, unaligned samples at

maximum forces of 1 nN and 2 nN, using a JKR model for paraboloidal tip shape [18]. For

all samples there are differences in elastic modulus values determined at different level of

compressive forces. By using the t-test these differences are significant although their

elastic maps exhibit unobvious differences. In a previous study [19], there was a slight

difference in modulus values between the core and shell of the collagen fibril, and both

showed similar morphological structures [20, 15]. However, findings for individual

collagen fibrils cannot be directly applied here because of difference in preparation

112

conditions and modification procedures of these materials. Figure 4.10 displays 15 µm ×

15 µm elastic modulus maps for ELAC, BG-ELAC, crosslinked-ELAC and crosslinked-

ECC, unaligned samples obtained using a paraboloidal tip model at different levels of

maximum (depth) applied force. First, The BG-ELAC maps show essentially no different

topographic features indicating absence of objects with different elastic moduli at depth up

to ~250 nm.


5 10 15 20 25 30

5

10

15

20

25

30

0 0.200 0.400 0.6000

20

40

60

80

100


0 0.100 0.200 0.300 0.400 0.500 0.6000

20

40

60

80

100



5 10 15 20 25 30

5

10

15

20

25

30

ELACF

max = 1 nN F

max = 2 nN

113


5 10 15 20 25 30

5

10

15

20

25

30

5 10 15 20 25 30

5

10

15

20

25

30


Fmax

= 1 nN Fmax

= 2 nN

BG-ELAC

0 0.5 1 1.5 20

20

40

60

80

100

120

Elastic modulus

[MPa]

0 0.5 1 1.5 20

20

40

60

80

100

120

140


5

10

15

20

25

30


5 10 15 20 25 30

Crosslinked-ELAC


5 10 15 20 25 30

5

10

15

20

25

30

Fmax

= 2 nNFmax

= 1 nN

0 1 2 3 4 5 60

20

40

60

80

100

120

140

160


60 1 2 3 4 50

20

40

60

80

100

120

140


114

Crosslinked-ECC, unaligned


5 10 15 20 25 30

5

10

15

20

25

30

100

Fmax

= 1 nN Fmax

= 2 nN


5 10 15 20 25 30

5

10

15

20

25

30

0 0.500 1.00 1.50 2.00 2.500

20

40

60

80

100


0 0.50 1.00 1.50 2.00 2.500

20

40

60

80


Figure 4.10 Force maps and corresponding histograms of ELAC, BG-ELAC, crosslinked-ELAC

and crosslinked-ECC, unaligned samples using paraboloidal tip at different indentation depths.

Data in the previously mentioned tables and histograms indicate that the samples

appear stiffer and with higher variation (higher std) at higher indentation force. The higher

standard deviation with increasing indentation depths might reflect higher heterogeneity in

direction perpendicular to sample’s surface within the sample. Increase in the elastic

modulus with increase of the applied force has observed when measuring elasticity of

living cells [21]. However, for soft sample such as corneal membrane, the indentation

profiles indicated considerable uniformity of material with depth [20]. The increase of

modulus values with the indentation depth in part can be attributed to the tip shape artifact

and not to actual increase of elastic modulus with increase of depth sensing. The AFM tip

115

does not have ideal shape of paraboloid of revolution, but rather shape with rounded apex

that becomes a cone, similar to shape of hyperboloid [22]. To avoid this tip shape artifact

in the depth sensing, studies the hyperboloid probe with adhesion model [18] was applied.

As an example, the results of crosslinked-ELAC samples are shown in Table 4.1.

Table 4.1. Elastic modulus values (MPa) and their standard deviations (Std) for one spot on

crosslinked-ELAC at (Fmax = 1 nN and 2 nN) using paraboloidal and hyperboloidal models.

Scan sizes

And

directions

E, MPa,

Standard

deviation

Fmax, JKR Fmax, Hyperboloid

1 nN 2 nN 1 nN 2 nN

Approach

640 nm

withdraw

Mean

Std 0.609

0.133

0.715

0.126

0.604

0.133

0.701

0.135 Mean

Std 0.580

0.119

0.769

0..145

0.593

0.118

0.720

0.146

Approach

3 μm

withdraw

Mean

Std 0.881

0.520

1.490

1.210

0.836

0.433

0.989

0.587 Mean

Std 1.340

1.060

2.240

1.940

0.864

0.362

0.959

0.495

Approach

15 μm

withdraw

Mean

Std 0.924

0.470

1.670

1.190

0.879

0.478

1.160

0.776 Mean

Std 1.480

0.962

2.450

1.860

0.868

0.560

1.200

0.739

To achieve the same indentation by both paraboloid and hyperboloid probe shapes

with the same radius of curvature, the higher force should be applied with the hyperboloidal

probe because the former shape displaces more material as illustrated in Figure 4.11.

116

Figure 4.11 compares shapes of the paraboloidal (gray) and hyperboloidal (blue) probes and

indicates expected indentation depths at two different force levels, as indicated in the figure.

However, the results in Table 4.1 show that using hyperboloid probe model

decreases the modulus values obtained at different indentation forces, indicating that the

paraboloidal tip underestimated the modulus values. This artifact has increased with

increasing the applied force. By using t-test, there are insignificant differences between

paraboloid and hyperboloid modulus values in the case of Fmax = 1 nN, whereas the

differences became significant at Fmax = 2 nN. Figures 4.12 a and b show the increase of

modulus difference between paraboloidal and hyperboloidal model at Fmax = 2 nN over the

given scan sizes on crosslinked-ELAC sample.

117

Figure 4.12 in panels a and b show the difference in E values by using paraboloid and hyperboloid

probes over different scan sizes for crosslinked-ELAC sample at Fmax = 1 nN and 2 nN,

respectively.

The same effect was also found in ELAC material. The reason for increasing the

tip artifact with increasing the indentation depth can be attributed to the considerable

118

change in the tip shape at larger indentation corresponding to Fmax = 2 nN as illustrated in

Figure 4.11.

4.5 Conclusion

A comprehensive approach was developed to determine and characterize surface

distribution of elastic modulus for soft biomaterials at nanoscale under physiological

conditions. The developed method takes into account sample adhesion and can be used for

probes with geometry that deviates from simple paraboloid of revolution geometry. The

hyperboloidal probe shape is added into the analysis in order to test for probe shape

artifacts. Elastic modulus values obtained for modified collagen threads are in the range

of hundreds of kilopascals. The characteristic dimensions of surface features visible in

elastic maps are consistent with estimated size of the tip-sample contact area. Even though

the visual differences between modulus maps at different maximum forces are

unobservable, difference of mechanical properties measured at the surface layer and at the

deeper probe penetration are significant as confirmed by the t-test.

No Bioglass protrusions at the surface were detected for BG-ELAC sample,

however elastic modulus of surface collagen molecules appear stiffer than for ELAC-

sample. It appears that Bioglass affects packing order of the surface collagen molecules

even though it is not present at the top sample layer. Crosslinked materials showed higher

elastic modulus than BG-ELAC threads, however crosslinking also increases viscoelastic

features observable in indentation experiments. Further more extensive studies are

necessary to determine the concentration dependence of the Bioglass, or crosslinker,

affecting the elastic modulus of the surface of BG-ELAC threads. This can be extended

119

with comprehensive multi-disciplinary study of effects of crosslinking ratio or adding

Bioglass on cell response [1, 3]. The rationale for using this method is its ability to separate

the elastic modulus in microscale dimensions and of superficial layer that is sensed by cells

from the elastic modulus of the bulk of substrate.

The developed technique allows the detection of viscoelasticity of the surface layer

of the material. This opens an opportunity to determine to what degree viscoelastic

properties (in contrast to the purely elastic) of the surface layer affect cell differentiation

and growth. However, to fully explore this idea the data analysis should be extended to

take viscoelastic properties into account explicitly. To start, it can be performed by

adopting viscoelastic models that do not take adhesion into account [21-23], and then

utilize much more complex models that includes both adhesion and viscoelasticity [24-26].

120

4.6 References

[1] Madhura P. Nijsure, Meet Pastakia, Joseph Spano, Michael B. Fenn, Vipuil Kishore

Bioglass incorporation improves mechanical properties and enhances cell-mediated

mineralization on electrochemically aligned collagen threads, Journal of Biomedical

Materials Research Part A, 2017, 105A, 2429-2440.

[2] Kohn JC1, Ebenstein DM., Eliminating adhesion errors in nanoindentation of compliant

polymers and hydrogels, Journal of the Mechanical Behavior of Biomedical Materials

2013, 20, 316-326.

[3] Kishore, V.; Iyer, R.; Frandsen, A.; Nguyen, T-U., In vitro characterization of

electrochemically compacted collagen matrices for corneal applications, Biomedical

Materials 2016, 11, 055008.

[4] Nama, S.; Hub, K. H.; Buttec, M. J.; Chaudhuria, O. Strain-enhanced stress relaxation

impacts nonlinear elasticity in collagen gels, Proceedings of the National Academy of

Sciences 2016, 113, 5492-5497.

[5] Kilpatrick, J. I.; Revenko, I.; Rodriguez, B. J., Nanomechanics of Cells and

Biomaterials Studied by Atomic Force Microscopy, Advanced Healthcare Materials 2015,

4, 2456-2474.

[6] Han, B.; Nia, H. T.; Wang, C.; Chandrasekaran, P.; Li, Q.; Chery, D. R.; Li, H.;

Grodzinsky, A. J.; Han, L., AFM-Nanomechanical Test: An Interdisciplinary Tool That

Links the Understanding of Cartilage and Meniscus Biomechanics, Osteoarthritis

https://www.ncbi.nlm.nih.gov/pubmed/?term=Kohn%20JC%5BAuthor%5D&cauthor=true&cauthor_uid=23517775

https://www.ncbi.nlm.nih.gov/pubmed/?term=Ebenstein%20DM%5BAuthor%5D&cauthor=true&cauthor_uid=23517775


121

Degeneration, and Tissue Engineering, ACS Biomaterials Science & Engineering 2017, 3,

2033-2049.

[7] Guo, S.; Akhremitchev, B. B., Investigation of Mechanical Properties of Insulin

Crystals by Atomic Force Microscopy, Langmuir 2008, 24, 880-887.

[8] Vanlandingham, M. R., et al., Nanoindentation of polymers: An overview,

Macromolecule 2001, 167, 15-43.

[9] Dagastine, R. R.; et al., Dynamic forces between two deformable oil droplets in water,

Science 2006, 313, 210-213.

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Determination of Local Elastic Modulus of Soft Biomaterial ...

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