Structure and Dynamics of Discotic Liquid Crystals in the Bulk and in the Confined State

vorgelegt vonDipl.-Phys.

Christina Krausegeboren in Bergen/Rügen

Von der Fakultät II - Mathematik und Naturwissenschaftender Technischen Universität Berlin

zur Erlangung des akademischen GradesDoktor der Naturwissenschaften

Dr. rer. nat.

genehmigte Dissertation

Promotionsauschuss:

Vorsitzender: Prof. Dr. Reinhard Schomäcker Gutachter: Prof. Dr. Andreas SchönhalsGutachter: Prof. Dr. Regine v. KlitzingGutachter: Prof. Dr. Mario Beiner

Tag der wissenschaftlichen Aussprache: 01. Juni 2015

Berlin 2016

Contents

Contents

1 Abstract 5

2 Inhaltsübersicht 9

3 Motivation 13

4 Introduction 154.1 Rod-like Liquid Crystals and Discotic Liquid Crystals (DLCs) . . . . . . 154.2 The Glass Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3 The Boson Peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 The Effect of Confinement on Arrangement and Phase Transitions . . . 27

5 Experimental Part 295.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1.1 Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . 295.1.2 Confining Hosts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Preparation of the Confined Samples . . . . . . . . . . . . . . . . . . . . . 325.3 Experimental Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3.1 Conventional Differential Scanning Calorimetry . . . . . . . . . . 365.3.2 Dielectric Relaxation Spectroscopy . . . . . . . . . . . . . . . . . . 365.3.3 Specific Heat Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 415.3.4 X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.3.5 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Results and Discussion 516.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal . . . . . . . . . . . . . . 51

6.1.1 Thermal behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.1.2 Molecular Dynamics in the Bulk . . . . . . . . . . . . . . . . . . . 536.1.3 Phase Transitions under Confinement . . . . . . . . . . . . . . . . 636.1.4 Molecular Dynamics under Confinement . . . . . . . . . . . . . . 70

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene(HATn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.2.1 Phase Transitions in the Bulk . . . . . . . . . . . . . . . . . . . . . 756.2.2 Structure in the Different Phases . . . . . . . . . . . . . . . . . . . 776.2.3 Influence of Confinement on the Phase Behavior . . . . . . . . . . 836.2.4 Molecular Dynamics in Dependence of the Chain Length . . . . 966.2.5 Vibrational Density of States (VDOS) in Dependence on the

Chain Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.2.6 Vibrational Density of States (VDOS) under Confinement . . . . 110

1

Nomenclature

6.2.7 Mean Squared Displacement in Dependence on the Chain Length 1156.2.8 Mean Squared Displacement in the Bulk and in the Confined State118

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene(HOTn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.3.1 Structure and Phase Transistions in the bulk . . . . . . . . . . . . 1226.3.2 Structure in the Different phases . . . . . . . . . . . . . . . . . . . 1266.3.3 Molecular Dynamics in Dependence on the Chain Length . . . . 1296.3.4 Vibrational density (VDOS) in Dependence on the Chain Length 1346.3.5 Mean Squared Displacement in Dependence on the Chain Length 136

7 Summary 139

8 Publications 1438.1 List of Peer-Reviewed Publications . . . . . . . . . . . . . . . . . . . . . . 1438.2 List of Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1448.3 List of Posters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

9 List of Abbreviations, Symbols and Constants 145

References 147

List of Figures 156

2

Nomenclature

Acknowledgements

First and foremost, I would like to express my sincere gratitude to Prof. Dr. Andreas

Schönhals for giving me the opportunity to carry out my Ph.D. study on this challeng-

ing and fascinating research topic. His encouragement, support, guidance and patience

throughout these few years, helped me not only to successfully complete this thesis but

also to develop my scientific knowledge, skills and attitude. I also want to acknowledge

the financial support from the German Science Foundation (DFG SCHO-470/20-1).

I would like to thank Prof. Dr. Regine von Klitzing (Technische Universität Berlin) for

being my supervisor at the university and many valuable comments and suggestions.

Furthermore I would like to thank Dr. Bernhard Frick (Institut Laue-Langevin Greno-

ble) and especially PD Dr. Reiner Zorn (Forschungszentrum Jülich) for the extensive

help with the Neutron Scattering experiments, analyis of the hereby obtained data

and many fruitful discussions. Also I would like to thank the Institute Laue-Langevin

Grenoble and the Heinz Maier-Leibnitz Centre for enabling the Neutron Scattering

measurements.

Moreover I would like to thank Prof. Dr. Christoph Schick (Universität Rostock)

and Dr. Andreas Wurm (Universität Rostock) for the experimental assistance in the

TMDSC measurements and discussion on the results.

I would like to thank Dr. Huajie Yin for his help with the AC measurements.

I would also like to thank Dr. Franziska Emmerling and Simone Rolf for the assistance

with X-ray Scattering.

Dietmar Neubert is thanked for his help in the DSC measurements. Furthermore I

would like to thank Christiane Weimann and Sigrid Benemann for the REM pictures

and Dr. Jana Falkenhagen for the MALDI-TOF measurements.

I would also like to thank Professor Dr. Patrick Huber (Universität Hamburg Harburg)

and Dr. Denis Morineau (Université de Rennes) for many inspiring discussions within

the TEMPLDISCO-Project. Furthermore I want to thank Prof. Dr. Mario Beiner

(Universität Halle) for taking over the duty to review my thesis.

I would like to thank all my fellow colleagues at BAM. I appreciate the scientific

help and support from Purv Purohit, Jing Leng, Sherif Madkour, Shereena Said, Alaa

Fahmy Mohamed, Farooq Muhammad and Marieke Füllbrandt. I also would like to

thank Korinna Altmann, Anne Bartel and Frank Milcewski for laughter, breaks as well

as for coffee or green tea whenever I needed it.

I would like to thank my friends, especially Susanne Scholz, Isabelle Fischer and Miriam

Burgauner, for encouragement and moral support.

Most importantly I am extremely grateful to my mother Martina Steger for always

3

Nomenclature

believing in me and her encouragement throughout my life. Her patience, support and

love helped me achieve my goals.

4

1 Abstract

In the course of this work, in order to gain more insight into the structure and dynamics

of discotic liquid crystals (DLCs), selected DLCs in the bulk were investigated in detail:

It was decided to concentrate on the following materials:

1. Pyrene-based discotic liquid crystal (DLC) pyrene-1,3,6,8-tetracarboxylic tetra(2-

ethylhexyl)ester (Py4CEH)

2. Several Hexakis(n-alkoxy)triphenylene (HATn, n=5,6,8,10,12)

3. Several Hexakis(n-alkanoyloxy)triphenylene (HOTn, n=6,8,10,12)

Different techniques were applied such as Differential Scanning Calorimetry, X-ray

Scattering, Dielectric Relaxation Spectroscopy and Neutron Scattering. Furthermore

the impact of confinement on the phase transitions and dynamics for DLCs, Py4CEH

and several HATn (n=5, 6, 10, 12), as an example were studied.

The structure of the HATn and HOTn materials was investigated by differential scan-

ning calorimetry and X-ray Scattering dependent on the length of the aliphatic side

chain. All studied HATn materials have a plastic crystalline phase at low temperatures,

followed by a hexagonally ordered liquid crystalline phase at higher temperatures and

a quasi isotropic phase at even higher temperatures. The X-ray Scattering pattern

in the liquid crystalline phase for all HATn materials showed a sharp Bragg reflection

corresponding to the intracolumnar distance in the lower q-range. Moreover a peak at

higher q-values, linked to the intracolumnar distances between the cores perpendicular

to the columns as well as a broad amorphous halo, related to the disordered structure

of the methylene groups in the side chains in the higher q-range were seen. The in-

tercolumnar distance increases linearly with increasing chain length for the hexagonal

columnar ordered liquid crystalline phase. A similar behaviour is assumed for the plas-

tic crystalline phase.

A comparable structure is obtained for the HOTn materials where the intercolumnar

distance increases linearly with increasing n. However the data obtained by differential

scanning calorimetry revealed several plastic crystalline as well as liquid crystalline

phases indicated by additional peaks in the heat flow.

The phase transitions of HATn (n=5, 6, 10, 12) and Py4CEH embedded to nanoporous

5

1 Abstract

aluminum membranes with different pore sizes were studied by differential scanning

calorimetry. In confinement the two phase transitions of the bulk were also observed

down to the smallest pore size. In addition two different phase structures close to the

wall and in the pore center were identified by two peaks in the heat flow for the phase

transition for the first time. Whereas the temperature of the former is more or less

independent of the pore size, the linear decrease of the latter with decreasing pore

size can be described by means of the Gibbs-Thomson equation. The decrease in the

transition enthalpies for both phase transitions with decreasing pore size implies an

increase in the amount of disordered material inside the pores. A critical pore size for

phase transformations was estimated from the pore size dependence of the transition

enthalpies. This procedure was applied to the phase transition of the material in the

pore center as well as to the phase transition of the complete material inside the pores.

Therefore one can estimate the thickness of the surface layer close to the wall. Alter-

natively, the thickness of the surface layer can be approximated in the framework of a

surface layer model.

The molecular dynamics of Py4CEH was investigated by dielectric relaxation and spe-

cific heat spectroscopy. Dielectric spectroscopy shows three processes, a β-relaxation at

low temperatures, an α-relaxation in the temperature range of the mesophases followed

by conductivity. The dielectric α-relaxation is attributed to a restricted glassy dynam-

ics in the plastic crystal as well as in the liquid crystalline phase. The observed different

Vogel-Fulcher-Tammann laws (different Vogel temperature and fragility) are linked to

the different restrictions of the dipolar fluctuations in the corresponding phases. By

specific heat spectroscopy glassy dynamics was detected also in the plastic crystalline

phase but with a quite different temperature dependence of the relaxation times in

comparison to the results from dielectric spectroscopy. This is discussed considering

the different aspects of the glass transition sensed by the different methods. In the

frame of the fluctuation approach, a correlation length of glassy dynamics is calcu-

lated, which corresponds to the core-core distance estimated by X-ray Scattering.

For Py4CEH an α-relaxation was also investigated in confinement. At the phase transi-

tion the temperature dependence of the relaxation rates changes from which a dielectric

phase transition temperature can be extracted. For temperatures above and below the

phase transition the temperature of the relaxation rate can be approximated by an

Arrhenius equation. The pore size dependence of the estimated apparent activation

energies is ascribed to the interplay between pore size and interaction effects. The co-

operative nature of the underlying molecular dynamics is indicated by the occurrence

of the well-known compensation law.

For all HATn materials three processes can be identified, a β-relaxation at low tem-

peratures, an α-relaxation at higher temperatures and a conductivity process in the

6

“isotropic” phase. The activation energy for the β-relaxation first decreases with in-

creasing n until it increases again and approaches the value found for polyethylene. The

temperature dependence of the α-relaxation changes with increasing chain length from

an Arrhenius type temperature dependence to a polyethylene-like behaviour. Both

results are explained in the framework of a self-organized confinement of the columns

with respect to the alkyl chains. With increasing chain length and therefore increasing

intercolumbar distance the confinement is weakened and released.

Conductivity and β-relaxation were observed for all HOTn under study, however an

α-relaxation was found only for HOT6. The former are described by means of the

Arrhenius equation yielding similar results to HATn, while for the later the curvature

changes from an Arrhenius to a VFT-like behavior with decreasing temperature. This

behavior is characteristic for molecular dynamics under nanoscale confinement. This is

discussed considering the structure of HOT6 and the Cooparativity Approach to glassy

dynamics.

Neutron scattering was employed to investigate the vibrational density of states (VDOS)

for all HATn and all HOTn DLCs. All HATn materials with the exception of HAT8

and all HOTn materials under study exhibit excess contributions to the VDOS which

are called Boson peak. For the HATn materials with increasing chain length, the fre-

quency of the Boson peak decreases and its intensity increases. This can be explained

by a self-organized confinement model. For the HOTn materials, the behavior appears

similar to the HATn materials, however they show an additional fine structure.

For HAT6 confined to the pores of alumina oxide membranes with different pore sizes,

a Boson Peak was observed similar to the bulk. The Boson Peak gains in intensity

and shifts to lower frequencies with decreasing pore diameter. This is discussed in the

framework of a softening of HAT6 induced by the confinement due to a less developed

plastic crystalline state inside the pores compared to the bulk.

Elastic scans were carried out for all HATn and HOTn materials in the bulk as well as

for HAT6 confined to three different pore sizes to monitor the molecular dynamics on

a time scale of nanoseconds. For all HAT materials a comparable molecular dynam-

ics is detected in the plastic crystalline phase whereas the mean-squared displacement

is small compared to the intercolumnar distance. In the liquid crystalline phase the

mean-squared displacement is in the order of the intercolumnar distance and increases

with increasing length of the side chain, because of the release of the self-organized

confinement. The HOT materials show a similar behavior. For HAT6 in confinement

the mean-squared displacement increases in the plastic crystalline phase with decreas-

ing pore size implying a boundary layer. In the liquid crystalline and isotropic phase

the mean-squared displacement is reduced.

7

1 Abstract

8

2 Inhaltsübersicht

Um mehr Einblick in die Struktur und Dynamik von diskotischen Flüssigkristallen

zu erlangen, wurden im Verlauf dieser Arbeit ausgewählte Diskoten im Detail unter-

sucht:

1. Pyrene-1,3,6,8-tetracarboxylic tetra(2-ethylhexyl)ester (Py4CEH)

2. Hexakis(n-alkoxy)triphenylene (HATn, n=5,6,8,10,12)

3. Hexakis(n-alkanoyloxy)triphenylene (HOTn, n=6,8,10,12)

Hierfür wurden unterschiedliche experimentelle Methoden wie Differential Scanning

Calorimetry (DSC), Röntgenstreuung, dielektrische Spektroskopie und Neutronenstreu-

ung angewandt.

Darüber hinaus wurden die Auswirkungen eines Nanoconfinements in Hinblick auf die

Dynamik und Phasenübergänge für ausgewählte Beispiele, Py4CEH und verschiedene

HATn (n=5, 6, 10, 12) Materialien betrachtet.

Die Struktur der HATn und HOTn Flüssigkristalle wurde in Abhängigkeit von der

Länge der aliphatischen Seitenketten durch DSC und Röntgenstreuung ermittelt. Alle

untersuchten HATn Materialien weisen eine plastisch-kristalline Phase bei niedrigen

Temperaturen, gefolgt von einer hexagonal geordneten flüssigkristallinen Phase bei

höheren Temperaturen, sowie einer “isotropen” Phase bei noch höheren Tempera-

turen auf. Das Diffraktogramm der flüssigkristallinen Phase zeigt für alle Materialien

eine scharfe Bragg-Reflexion im unteren q-Bereich, die dem interkolumnaren Abstand

zwischen den Molekülen entspricht, sowie einen Peak bei höheren q-Werten, der im

Zusammenhang mit dem interkolumnaren Abstand senkrecht zu den Säulen steht und

einen breiten amorphen Halo als Resultat der ungeordneten Methyl-Gruppen. Der in-

terkolumnare Abstand nimmt linear mit n zu.

Die HOT-Materialen weisen eine ähnliche Struktur auf. Die DSC-Daten zeigen zusät-

zliche Maxima im Heizfluss, die auf mehrere plastisch-kristalline sowie mehrere flüs-

sigkristalline Phasen hindeuten.

Die Phasenübergänge von HAT5, HAT6, HAT10, HAT12 und Py4CEH, welche in

nanoporöse Aluminium-Membranen mit verschiedenen Porendurchmessern (180 nm,

9

2 Inhaltsübersicht

80 nm, 40 nm, 25 nm) eingebettet wurden, wurden mit DSC untersucht. Auch im Con-

finement sind die im Bulkmaterial auftretenden Phasenübergänge sichtbar. Zum ersten

Mal konnten durch zwei Maxima im Heizfluss zwei unterschiedliche Phasenstrukturen

am Rand und in der Mitte der Pore identifiziert werden. Die Phasenübergangstem-

peratur am Rand ist mehr oder weniger unabhängig vom Porendurchmesser. Hinge-

gen nimmt die Phasenübergangstemperatur des Materials in der Mitte der Pore mit

kleinerer Porengröße linear ab, was durch die Gibbs-Thomson-Gleichung beschrieben

werden kann. Die Abnahme der Phasenübergangsenthalpie mit abnehmendem Poren-

durchmesser deutet auf einen Anstieg ungeordneten Materials innerhalb der Pore hin.

Hieraus wurde eine kritische Porengröße für das Auftreten der Phasenübergänge be-

stimmt. Dieses Verfahren wurde für das sich sowohl in der Mitte der Pore als auch

das sich in der gesamten Pore befindliche Material angewandt um hieraus die Dicke

der Randschicht abschätzen zu können. Alternativ kann diese Dicke auch im Rahmen

eines Randschicht-Modells angenähert werden.

Die molekulare Dynamik von Py4CEH im Volumen wurde mit Hilfe von dielektrischer

und spezifischer Wärme-Spektroskopie untersucht. Im dielektrischen Spektrum wur-

den drei Prozesse beobachtet: eine β-Relaxation bei niedrigen Temperaturen, eine

α-Relaxation im Temperaturbereich der Mesophasen gefolgt von Leitfähigkeit bei ho-

hen Temperaturen. Die dielektrische α-Relaxation wurde auf eine eingeschränkte

glasige Dynamik sowohl im plastisch-kristallinen als auch im flüssigkristallinen Zu-

stand zurückgeführt. Die ermittelten verschiedenen Vogel-Fulcher-Tammann Gesetze

(mit unterschiedlichen Vogel-Temperaturen und Fragility-Parametern) wurden durch

die verschiedenen Beschränkungen der dipolaren Fluktuationen in den entsprechen-

den Phasen erklärt. Mit der spezifischen Wärme-Spektroskopie wurde die glasige Dy-

namik auch in der plastisch-kristallinen Phase beobachtet, aber mit einer veränderten

Temperaturabhängigkeit. Dies wurde unter Berücksichtigung der unterschiedlichen

Aspekte des Glasübergangs, die von den verschiedenen Methoden detektiert werden,

erörtert. Im Rahmen des Fluktuations-Ansatzes des Glasübergangs wurde eine Kor-

relationslänge für die glasige Dynamik berechnet, welche dem aus den Röntgenstreu-

ungsdaten geschätzten interkolumnaren Abstand entspricht.

Für Py4CEH wurde auch im Confinement eine α-Relaxation festgestellt. Am Phasenüber-

gang ändert sich die Temperaturabhängigkeit der Relaxationsrate. Hieraus lässt sich

eine dielektrische Phasenübergangstemperatur abschätzen. Bei Temperaturen ober-

halb und unterhalb des Phasenübergangs kann die Temperaturabhängigkeit der Relax-

ationsrate durch eine Arrhenius-Gleichung angenähert werden. Die Abhängigkeit der

geschätzten scheinbaren Aktivierungsenergien von den Porengrößen wurde durch das

Zusammenspiel zwischen Porengröße und Interaktionseffekten erklärt. Das Auftreten

des bekannten Kompensationsgesetzes deutet auf eine kooperative Natur der zugrunde

10

liegenden molekularen Dynamik hin.

Für alle HATn Materialien wurden drei Prozesse beobachtet: eine β-Relaxation bei

niedrigen Temperaturen, eine α-Relaxation bei höheren Temperaturen und Leitfähigkeit

in der “isotropen” Phase. Die Aktivierungsenergie der β-Relaxation nimmt zunächst

mit n zu um wieder abzunehmen und sich an den Wert von Polyethylene anzunä-

hern. Die Temperaturabhängigkeit der α-Relaxation ändert sich mit zunehmender

Kettenlänge von einer Temperaturabhängigkeit, die der Arrhenius-Gleichung folgt,

zu einer Annährung an das Verhalten, das für Polyethylene beobachtet wird. Beide

Ergebnisse wurden im Rahmen eines selbstorganisierten Confinement der Säulen in

Bezug auf die Alkylketten erörtert. Mit zunehmender Kettenlänge und daraus resul-

tierendem interkolumnaren Abstand wird das Confinement geschwächt. Leitfähigkeit

und β-Relaxation werden für alle HOTn Materialien beobachtet, eine α-Relaxation

hingegen nur für HOT6. Die Temperaturabhängigkeit der Relaxationsrate von Leit-

fähigkeit und β-Relaxation wurden durch die Arrhenius-Gleichung mit ähnlichen Ak-

tivierungsenergien wie für die HATn Materialien beschrieben, die von α-Relaxation

durch eine Arrhenius-Gleichung bei höheren Temperaturen und eine VFT-Gleichung

bei niedrigeren Temperaturen. Dieses Verhalten ist typisch für molekulare Dynamiken

in einem nanoskaligen Confinement. Dies wurde erörtert unter Berücksichtigung der

Struktur von HOT6 sowie eines Kooperativitätsansatzes für glasige Dynamik.

Neutronenstreuung wurde eingesetzt, um die Schwingungszustandsdichte (VDOS) für

alle HATn und alle HOTn Diskoten zu ermitteln. Mit Ausnahme von HAT8 zeigen

alle untersuchten HAT und HOTn Materialien zusätzliche Beiträge im VDOS, welche

Boson-Peak genannt werden. Für die HATn Materialien verringert sich die Frequenz

des Boson Peaks mit zunehmender Kettenlänge, wobei sich seine Intensität erhöht.

Dies kann durch ein Modell des selbstorganisierten Confinements erklärt werden. Das

Verhalten der HOTn Materialien ähnelt dem der HATn-Materialien, sie zeigen jedoch

eine zusätzliche Feinstruktur.

Für HAT6 eingebettet in Aluminiumoxidmembranen mit verschiedenen Porengrößen

(80 nm, 40 nm, 25 nm) wurde ein Boson-Peak ähnlich wie im Bulkmaterial beobachtet.

Der Boson-Peak gewinnt an Intensität und verschiebt sich mit abnehmendem Poren-

durchmesser zu niedrigeren Frequenzen. Dies wurde im Rahmen eines Aufweichens des

plastisch kristallinen Zustandes von HAT6 in den Poren durch das Confinement im

Vergleich zum Bulkmaterial diskutiert.

Elastische Scans wurden für alle HATn und HOTn Materialien im Volumen sowie für

HAT6 im Confinement durchgeführt, um die verschiedenen molekularen Prozesse auf

einer Zeitskala von Nanosekunden zu identifizieren. In der plastisch kristallinen Phase

wurde für alle HAT Materialien eine vergleichbare molekulare Dynamik beobachtet.

Hier ist das mittlere Verschiebungsquadrat klein im Vergleich zum interkolumnaren

11

2 Inhaltsübersicht

Abstand. In der flüssigkristallinen Phase ist das mittlere Verschiebungsquadrat in

der gleichen Größenordnung wie der interkolumnare Abstand und nimmt durch die

Aufweichung des selbstorganisierten Confinements mit größerer Kettenlänge zu. Die

HOT Materialien zeigen ein ähnliches Verhalten. Für HAT6 im Confinement nimmt

das mittlere Verschiebungsquadrat in der plastisch-kristallinen Phase mit abnehmender

Porengröße zu, was auf eine Grenzschicht hindeutet. In der flüssigkristallinen sowie in

der isotropen Phase ist das mittlere Verschiebungsquadrat reduziert.

12

3 Motivation

Discotic liquid crystals appear very promising in the field of organic electronics, which

can meet today’s dire need for effective, low-cost, portable and disposable elements

such as tunable organic light-emitting diodes (OLEDS), thin film field-effect transis-

tors (OTFTs) or photovoltaic chips (OVPs). These unique soft matter materials exhibit

aspects both of a solid crystal and of a conventional fluid. Due to their highly ordered

columnar structures these materials outperform many photoconductive polymers (e.

g. in terms of charge transport or short-lived excitonic response) thereby giving them

highful potential for the use in molecular electronic devices.

The structure of discotic liquid crystals has been extensively studied by many different

methods (X-ray diffraction, calorimetry and polarized optical microscopy).[1] However

when aiming at applications such as advanced electronic devices a fundamental un-

derstanding of their molecuclar mobility is indespensable. Furthermore, as a result

of their inherent counterplay between order and mobility, discotic liquid crystals can

be interesting materials when adressing fundamental questions, e.g. about the glass

transition, which is a controversially discussed problem of soft matter physics or the

Boson Peak exhibited by many glasses which is not fully understood yet. Moreover for

both pursuits, designing efficent electronic elements and understanding the underlying

processes, studying the influence of spatial nanoscale confinement on the properties

and dynamics of these materials, is essential.

In this thesis differential scanning spectroscopy, X-ray and neutron scattering, dielectric

relaxation and specific heat spectroscopy are employed to elucidate the structure as

well as the dynamics of one pyrene-based and two series of triphenylene-based discotic

liquid crystals in the bulk and when confined to self-ordered alumina membranes.

Structure and phase behavior of all samples were determined and confirmed by X-ray

scattering and differential scanning calorimetry. The molecular dynamics of the bulk

materials was investigated by means of dielectric relaxation spectroscopy. The impact

of confinement on the phase behavior on several selected liquid crystals was studied by

differential scanning calorimtery. Neutron scattering experiments were carried out on

both bulk and confined samples by two different techniques, (1) time of flight neutron

13

3 Motivation

scattering to measure the vibrational density of states and (2) backscattering to gain

an overview about the molecular dynamics on a time scale of nanoseconds.

14

4 Introduction

4.1 Rod-like Liquid Crystals and Discotic Liquid

Crystals (DLCs)

Liquid crystals are unique soft matter materials which exhibit aspects both of a solid

crystal and of a conventional fluid. Since the introduction of liquid crystalline states of

matter into science by Otto Lehmann, Friedrich Reinitzer and others, the relationship

between the formation of liquid crystalline phases and the structure of the correspond-

ing molecules has been under discussion.[2, 3]

In different temperature ranges different phases are observed (see Figure 4.1): at

low temperatures in the crystalline phase the molecules are completely ordered. With

increasing temperature and after undergoing a phase transition to a liquid crystalline

phase disordered molecules in ordered layers (smectic phases) and disordered molecules

with ordered orientations (nematic phases) can be found. In the high temperature range

in the isotropic phase the molecules are supposed to be completely disordered.

Whereas during the first decades liquid crystalline mesophases were mainly accepted

for linear rod-like shaped molecules, they were theoretically predicted also for disc-

like molecules. In 1977 Chandrasekhar et al. reported “mesomorphism in pure single-

component systems of relatively simple plate-like, or more appropiately disc-like, mole-

cules” and hereby delivered the first clear-cut evidence for “Liquid Crystals of disc-like

molecules”. Further liquid crystals by disk-like molecules were observed by Dubois[4]

and Levelut[5].

As can be seen from Figure 4.2 discotic liquid crystals consist of a stiff disk-like core

surrounded by flexible alkyl side chains. At low temperatures discotic liquid crystals

can show a plastic crystalline phase, followed by a hexagonal columnar mesophase at

higher temperatures. At even higher temperatures they undergo a phase transition to

a more or less isotropic liquid. Possible other phases include nematic phases or plastic

crystalline phases. In a plastic crystal the molecules weakly interact with each other

and have some orienational or conformational degree of freedom.

The length and specific structure of the side chains determine the isotropization tem-

15

4 Introduction

Figure 4.1: Different Phases of liquid crystals

Figure 4.2: Discotic liquid crystals in the columnar phase

16

4.1 Rod-like Liquid Crystals and Discotic Liquid Crystals (DLCs)

perature and the temperature range of the hexagonal columnar mesophase. Columnar

phases ocurr in pyrene and triphenylene systems which are in the focus of this work

as well as in many others (perylenes, triphenyltriazines, benzoperylenes, coronenes,

ovalenes etc.). The self-assembly of these materials is directed through non-covalent

molecular interactions: the disc-shaped molecules arrange themselves into columns

which further assemble into two-dimensional arrays with a hexagonal mesophase. The

side chains fill the intercolumnar space giving rise to a nanophase separated state.

The formation of the disc-shaped molecules into columns is inherent to the different

columnar phases: there are different types of stacking in dependence on the corre-

sponding irregular interactions:

1. “disordered columns” (irregular stacking of the disks)

2. “ordered columns” (cores are stacked in a regular ordered (equidistant) fashion

while the flexible tails are still disordered)

3. “tilted columns” (cores of the disks are tilted with respect to the columns)

whereas none of these types has translational order. Therefore they can generally be

regarded as 1D fluids. These columns arrange in a 2D lattice while their axes are

parellel to each other. As a result the different columnar phases can be considered as a

1D fluid along the columns and 2D crystalline structures along the 2 D lattice vectors.

Their molecular oder can be disordered, ordered or tilted and their symmetry of the

2D intercolumnar lattice can be hexagonal, rectangular or oblique.

In liquid crystals and especially in discotic liquid crystals order and mobility compete,

providing the possibilty to investigate fundamental problems like the glass transition

or the boson peak. Moreover they look promising for applications in the field of organic

electronics. However for applications such as advanced electronic materials, the intrin-

sic disc mobility as well as the mobility of the alkyl chains can influence the charge

carrier mobility. Therefore the molecular mobility has to be explored in detail.

By covering an extensive frequency and temperature range, dielectric relaxation spec-

troscopy is a powerful tool to investigate the molecular dynamics in different soft matter

systems including discotic liquid crystals.[6] A detailed theory for dielectric relaxation

of calamitic (rod-like) liquid crystals was developed by by Nordio et al.[7] Based on

these considerations Araki et al.[8] developed an approach without prior specifications

of the character of the involved molecular fluctuations. Different relaxation processes

are predicted which are assigned to specified molecular motions. An overview is given

in reference [6]. However, for discotic liquid crystals such a general theoretical approach

does not exist and so a detailed assignement of the observed relaxation processes to a

molecular mechanism is not possible. The nomenclature of the processes follows more

17

4 Introduction

or less that of glass forming materials, e. g. one relaxation process in the hexagonal

columnar mesophase is assigned to glassy dynamics.[9] A study of the dynamics of three

dipole functionalized hexa-peri-hexabenzocoronenes by means of NMR techniques and

dielectric spectroscopy elucidated the origin of two dielectric processes with different

glass transition temperatures and delivered the first phase diagram for this kind of

materials.[10]

The design of applicable devices requires columnar formation over rather large length

scales (monodomains) at room temperature as well as the control and adjustment of

the parameters that influence the alignment when the discotic liquid crystals interact

with solid interfaces (nanostructures, contacts).

18

4.2 The Glass Transition

4.2 The Glass Transition

Man has been producing and using glassy materials since prehistoric times. Nowa-

days, glasses have become indispensable in modern technology as well as in daily life.

However, a quantitative physical understanding of their nature and formation remains

controversial and an open problem of condensed matter physics.[11, 12, 13, 14, 15]

The glass transistion is characterized for instance by the glass transition temperature

Tg where step-like changes in material properties, e. g. the specfic heat cp or the

thermal expansion coefficient, are detected by thermal methods such as Differential

Scannning Calorimetry (see section 5.3). Tg can also be defined as the temperature

where the relaxation time is 100 s. On microscopic level, upon continously cooling

down, the molecular mobility gradually decreases until the cooling rate does not al-

low sufficient time for configural sampling and the material appears "frozen" on the

experimental time scale. Hence, whether the material under study exhibits solid-like

or liquid-like behaviour depends on the time-scale of the experiment. With increasing

cooling rate the material under study loses time to attain equilibrium condition and the

glass transition temperature Tg increases by 10 Kelvin or higher.[16, 17, 18] Therefore,

the glass transition temperature is not a well-defined property.

The structural relaxation time is the key to understanding the dynamic glass transi-

tion. According to Maxwell the solid-like behaviour of an elastic liquid can be described

by:[19]

γ = σ

η+ σ

G(4.1)

where γ is the time derivative of the shear displacement, η the viscosity, G the shear

modulus and σ the shear stress. Assuming a sudden shear displacement beginning

from equilibrium conditions, γ = γ0δ(t), and integrating equation (4.1) delivers a link

between the relaxation time and the viscosity:

τ = η

G∞(4.2)

where G∞ is the “instantaneous” shear modulus. With decreasing temperature the

shear modulus increases from a liquid-like behaviour first to a rubbery plateau (G ∼ 106

Pa) followed by a strong increase below the glass transition temperature Tg to 109 to

1010 Pa.

Numerous experimental methods including Dynamical Mechanical spectroscopy (DMS),

Nuclear Magnetic Spectroscopy (NMR), Neutron Scattering, Dynamic Light Scat-

tering, Ultrasonic Attenuation, Photon Correlation Spectroscopy (PCS), Differential

Scanning Calorimetry (DCS), AC Calorimetry, and especially Broadband Dielectric

Spectroscopy [11] have been employed to study the glass transition.

19

4 Introduction

Glassy dynamics have been detected for manifold materials such as organic small

molecules, synthetic as well as side chain liquid crystalline polymers, metallic com-

pounds, biomaterials but also inorganic substances of different constitution. Seki and

Suga observed a glass transition in plastic crystals for the first time.[20] The glassy dy-

namics of a nematic mixture were investigated by by broadband dielectric and specific

heat spectroscopy.[21]

Figure 4.3 shows an overview over the different processes which are observed in poly-

mers and other glass-forming substances in the dielectric loss (see section 5.3):

The pronounced process on the low frequency side (see Figure a) is the α-relaxation

which is also referred to as dynamic glass transition. In the high temperature limit

the representative dielectric relaxation time typically is τ∞ ≅ 10−13 s, due to local ori-

entational fluctuations. In this region the viscosity of the liquid varies between 10−3

to 10−2 Pa s. The strong increase of the relaxation time (and therefore decrease in the

maximum frequency, see Figure 4.3b) as well as the viscosity observed with decreasing

temperature can be approximated by the empirical Vogel-Fulcher-Tammann (VFT)

equation:[22, 23, 24]

log1

2πτ(T ) = log fmax = log f∞ − A

T − T0

= log f∞ − ln(10)DT0

T − T0

(4.3)

where f∞ is a pre-exponential factor, A is a constant and T0 the so-called Vogel or

ideal glass transition temperature(30-70 K below the thermal glass transition) and D

is the so-called fragility parameter or fragility strength. A dependence according to the

Vogel-Fulcher-Tammann equation (4.3) will show up as a straight line in the following

representation:

(d log fmax

dT)−1/2 = A−1/2(T − T0) (4.4)

The singularity in equation (4.3) at T = T0 is attributed to the Kauzmann paradox

observed in calorimetric measurements: by extrapolation the liquids entropy decreases

with decreasing temperature, below a certain temperature TK termed the Kauzmann

temperature even beneath the crystal entropy. However, the physcial interpretation

remains unclear. It should be pointed out that equation (4.3) cannot be applied at

high viscosities because when compared to experimental data the obtained relaxation

times are too high.

As already mentioned and can be seen from Figure 4.3c, the α-relaxation shows up as

a step-like change in the specfic heat capacity (thermal glass transition).

An approach by Avramov [25] (also see reference [19]) which represents an alternative

20

4.2 The Glass Transition

Figure 4.3: Overview on the dynamics ocurring at the glass transition. a) Dielectric lossǫ′′

versus frequencies for two different temperatures T1 and T2 b) Relaxationmap (maximum frequency versus inverse temperature) for the different pro-cesses c) specific heat capacity cp versus inverse temperature (thermal glasstransition). Adapted from [6].

21

4 Introduction

approach to fit the data with the same parameters, is given by

τ = τ0 exp

⎡⎢⎢⎢⎢⎣C

T n

⎤⎥⎥⎥⎥⎦(4.5)

Equation (4.5) does not provide remarkable advancement over Equation (4.3). Ther-

fore in the absence of a better theory of the dynamic glass transition, equation (4.3) is

still commonly used despite its restrictions.

The existence of non-Debye relaxation is another remarkable charcteristic of glassy

dynamics. The exposure of the material under study to an immediate thermal, me-

chanical or electrical perturbation results in a slow relaxation towards the steady state

whereas in most cases the response shows a non-exponential time dependence. The re-

sponse function φ(τ) follows the “stretched exponential” Kohlrausch-Williams-Watts

function written as:

φ(τ) = exp

⎡⎢⎢⎢⎢⎣−⎛⎝

t

τKW W

⎞⎠

βKW W ⎤⎥⎥⎥⎥⎦(4.6)

where βKW W (0 ≪ βKW W ≤ 1) is the stretching parameter attributed to an asymmet-

ric broadening of φ(τ) at short times compared to the exponetial decay and τKW W is

linked to the relaxation time. Glarum derived one of the earliest models to interpret

the molecular basis of equation (4.6) [26] and recently further approaches have been

introduced.[27] There are two possible theories of the KWW-behaviour under current

discussion: one approach assumes a homogenous system consisting of exponentially

relaxing molecules, whereas the other suggests a heterogenous system composed of re-

gions, each of them displaying different dynamics following an exponential relaxation

with a different characteristic time. The latter hypothesis is supported by studies uti-

lizing techniques such as multidimensional NMR, dielectric non-resonant hole-burning,

and optical photo-bleaching.[15] While glassy dynamics is still a controversially dis-

cussed soft matter topic, nonetheless there is predominant consensus about the coop-

erative nature of the underlying motional process.[28]

Adam and Gibbs [29] introduced the Cooperativity Rearranging Regions (CRR). A

CRR is defined as the smallest volume which can change its configuration indepen-

dently from the neighbouring regions. The size of a CRR is small at high temperatures

and increases with decreasing temperature approaching Tg. Within this approach a

temperature dependence according to the VFT law can be derived. Donth developed

a fluctuation approach to the glass transition in order to enhance this idea.[28] Within

his approach a correlation length ξ (or volume VCRR) at the glass transition can be

calculated as

ξ3 = VCRR = kBTg∆(1/cp)ρ(δT )2

(4.7)

22

4.2 The Glass Transition

where Tg is the dynamic glass transition temperature, ρ is the density at Tg and

∆(1/Cp) = 1/cp,Glass − 1/cp,Liquid the step of the reciprocal specific heat capacity at

the glass transition where cV ∼ cp is assumed. δT is the width of the glass transition

and can be extracted experimentally from the temperature dependence of the spe-

cific heat capacity which can be estimated from broadband specific heat spectroscopy

data.[30, 28, 31]. Moreover within the fluctuation approach the temperature depen-

dence of the correlation approach can be derived to ξ ∼ (T − T0)−2/3.[28] This implies

that the degree of cooperativity decreases with decreasing T0 at a given temperature.

Please note that the four point correlation function approach to the glass transition

delivers a similar result.[32].

At temperatures below the glass transition temperatures (and higher frequencies) many

materials show localized motions (e.g. localized fluctuations of the sidechains) often

referred to as β-relaxation (see Figure 4.3a). For this process an Arrhenius-type tem-

perature dependence is observed (see Figure 4.3b):

fmax,β = fmax,∞ exp [− EA

R ⋅ T ] (4.8)

where f∞ denotes the relaxation rate at infinite temperature, EA the activation energy

and R the ideal gas constant. The values found for the activation energy of the β-

relaxtion vary in dependence on the environment of the involved molecules between 20

and 60 kJ mol−1): a value of 23 kJmol−1 found for a triphenylene derivate with five CH2

groups [33], 50 kJ mol−1 for discotic liquid crystalline hexabenzocoronene derivatives

with even longer alkyl side chains and 37 kJ mol−1 for polyethylene.[34, 35] However the

origin and nature of secondary relaxations in general is not fully understood yet as they

occur besides in polymers also in glass-forming liquids [36] lacking internal modes of

motion (e.g. ionic liquids [37, 38]). At even higher frequencies and lower temperatures

in the THz region (see Figure 4.3a) a further process occurs which is called Boson peak

[39] and will be discussed in more detail in the following section (section 4.3).

23

4 Introduction

4.3 The Boson Peak

For crystalline materials the vibrational density of states (VDOS) g(ω) (see section

5.3.5) follows the Debye model of sound waves g(ω) ∼ ω2. In contrast amorphous

materials exhibit excess contributions in the frequency range ω = 0.2...1 THz (energy

range 1...5 meV). For these materials in the reduced representation g(ω)/ω2 a peak is

detected. This peak is generally called Boson Peak (BP) which is a universal but con-

troversially discussed feature of glasses and other materials with a complete or partial

disorder.[39] Furthermore it is equivalent to the excess contributions commonly ob-

served for glasses in the specific heat and in thermal conductivity at low temperatures.

Although the time scales of the thermal glass transition (∼ 100 s at Tg), and the BP

(terahertz range) differ, there are strong signs of a relevance of the BP for the glass

transition.

In fact many materials exhibiting a BP also show a glass transition. Materials catego-

rized as “strong glasses” exhibit a well-pronounced BP whereas “weak” ones show only

a weak BP. Moreover the BP rarely depends on temperature. [40]

However the origin of the BP is still unclear. Different theoretical approaches are

discussed and they can be classified into two categories:

1. The modes of the BP differ from sound waves and emerge from (quasi) localized

modes. These result from peculiarities of the interatomic forces in the material

(e. g. group of atoms subject to a soft potential).

2. The BP of the amorphous system is a broadened version of the Van Hove sin-

gularity which is a well-known phenomenon in crystalline systems : For a linear

chain as a model system the frequency is proportional to the sine of the wave

vector. Therefore frequencies close to the maximum occur more often than low

frequency sound frequencies. Under the assumption that this singularity exists

also in amorphous materials to a given extent, the VDOS of an amorphous ma-

terial is only a modification of the VDOS of the corresponding crystalline system

due to random fluctuations of force constants.

Numerous different methods like Fourier transform infrared spectroscopy, inelastic X-

ray Scattering, Neutron Scattering, Mössbauer spectroscopy, low frequency Raman

spectroscopy and light scattering have been employed to study the Boson Peak in

conventional glass formers as low molecular weight liquids and polymers as well as

biologically active systems (e. g. proteins) which are also considered to undergo a

glass transition. In investigations on plastic crystals by means of THz dielectric spec-

troscopy a Boson peak was observed implying that these materials can also undergo a

24

4.3 The Boson Peak

glass transition.[20]

The Boson Peak has been linked to fluctuations of elastic constants in reference [41]

where sound waves in a disordered environment were considered. In this environment

the local elastic constants are subjected to fluctuations whose spatial correlation is

denoted by a correlation length. Sokolov et al. studied the correlation between the

dynamic heterogeneity length scale ζ of glasses estimated from the boson peak and

the activation volume for the dynamic glass transition ∆V # in a number of molecular,

hydrogen bond and polymeric glass formers. They observed that ζ3(Tg) ∼ ∆V #(Tg)holds regardless of chemical structure, molecular weight and pressure (density) of the

studied materials.[42]

When impregnating materials into nanostructures both surface and confinement size

play a role. This can be a useful procedure to distinguish between the two theoretical

approaches.

Confinement can be categorized into two classes, hard and soft confinement.

For organic glass-forming systems embedded in a hard confinement (e.g. nanopores),

with decreasing pore size the low frequeny wing is supressed whereas the high frequency

range does not change. This results in a sharper BP which is shifted to higher frequen-

cies as shown for poly(methylphenylsiloxane) (PMPS) confined to Sol/Gel-Glasses in

Figure 4.4. This was observed also for other conventional low molecular weight (sa-

lol) and polymeric glass-forming systems (poly(dimethyl siloxane), poly(phenylmethyl

siloxane), poly(propylene glycol)) [43, 44, 45, 46] and for the glass forming liquid crys-

tal E7 confined to the pores of a molecular sieve.[47] These findings might support the

hypothesis of a collective nature of the BP.

As an example for a study on the influence of soft confinement, Propylene glycol was

embedded to microemulsion droplets. In this case, the boson peak of the bulk material

is completely washed out under the soft confinement.

25

4 Introduction

0 2 4 6 8 10

0.0

2.0x10-4

4.0x10-4

6.0x10-4

8.0x10-4

1.0x10-3

Bulk

5.0 nm

2.5 nm

g(ω

) /

ω2 [ps

-3]

ω [ps-1]

Figure 4.4: Vibrational density of states of poly(methylphenylsiloxane) (PMPS) in thebulk and confined to Sol/Gel-Glasses with different pore sizes as indicatedtaken at T=80 K at IN6. Taken from [48].

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Bulk

Confinement (2.5 nm)

g(ω

)/ω

2 [10

-3 p

s3]

ω [ps-1]

Figure 4.5: Vibrational density of states of the nematic liquid crystal E7 in the bulkand confined to a molecular sieve (MCM) with a pore size of 2.5 nm. Takenfrom [47].

26

4.4 The Effect of Confinement on Arrangement and Phase Transitions

4.4 The Effect of Confinement on Arrangement and

Phase Transitions

Confining materials on nanoscale can fundamentally influence their properties and

phase behavior. This applies especially to discotic liquid crystals where order and

mobility compete. Synthesizing nanowires by impregnating organic materials into

nanoporous template membranes is one possible breakthrough in the field of organic

(nano-) electronics. The formation of DLC nanowires in self-ordered anodic aluminum

oxide (AAO) was reported by Steinhart et al.[49] However, the supramolecular order

in nanowires is difficult to control because the the long-range order of the bulk cannot

be maintained in the wires. A different approach is producing molecular nanorods by

chemical modification of the pore wall and controlling the packing structure by apply-

ing a magnetic field.[50]

Although the phase behavior and the molecular mobility of discotic liquid crystals have

been studied in detail [2, 51, 52, 53, 54, 10, 33, 55] the impact of a nanoscale confine-

ment on the properties of these unique soft matter materials has been investigated only

scarcely.

For discotic liquid crystals there are two possibilities to arrange with regard to a surface

[56]:

(1) planarly (edge-on orientations of the molecules) as found for columns in thin films

(2) homeotropically (face-on orientation of the molecules) when the material is confined

between two solid substrates.

As the π − π-system has to be electrically contacted by macroscopic electrodes, only

the homeotropic alignment can be used for efficient photovoltaic devices and other

applications.[57] A competition between homeotropic and planar arrangement results

from different interfacial tensions between air and the liquid crystal as well as between

the liquid crystal and a substrate. Homeotropic arrangement organization can be ob-

tained by thermal annealing of the material in open films, when confined between two

interfaces or by combining two miscible mesogens with different mesophases.

For polymers and polymorphs confined to nanopores and porous glasses crystalline

phases which are inaccessible, metastable or transient in the bulk material were re-

ported. [58, 59, 60, 61, 62] The stability and developement of a certain crystalline

phase depends on the size of the confinement. Furthermore a supression of crystalliza-

tion for small pore diameter is observed. Accordingly, one can define a critical diameter

for the development of a certain crystalline state: if the size of the confining space is

smaller than the crystal size of the stable crystalline state, a different metastable crys-

talline state can develop.[63, 64, 65] Moreover confining a material to a pore size smaller

than the crystal size of any possible crystalline phase can result in a stable amorphous

27

4 Introduction

phase. This can also be pictured that enhanced by the interaction of the molecules

with the wall the crystallization dynamics have slowed down drastically so that they

have become undetectable on experimental time scale.

For nanocrystals a metastable crystalline phase can emerge if the sum of the surface en-

ergy contributions is higher than the energetic advantage of a transition to a more stable

crystalline phase. In the case of calamitic rodlike liquid crystals a supression of phase

transitions and new paranematic, short-range ordered smectic, or low-temperature lay-

ered structures have been found.[49, 66, 67, 68, 69, 70, 71, 72] For the nematic liquid

crystal 5CB confined to anodic aluminum membranes, Floudas et el. observed that

the phase transition temperatures shift to lower values with decreasing pore sizes and

a complete supression of the crystallization for pore sizes smaller than 35 nm.[73]

For a variety of materials the decrease of the phase transition temperatures with de-

creasing pore size under confinement can be described by the Gibbs-Thomson formula:

[65, 74]

∆T = TmB

4σ

∆Hρsd(4.9)

where TmB denotes the bulk phase transition temperature, σ is the solid liquid interface

energy per unit area (surface tension), ∆H is the transition enthalpy of the bulk

material, ρS is the density, and d is the pore diameter. The surface tension is mainly a

molecular quantity related to the interaction of the molecule with a surface. [75, 76] In a

recent study [77] it was concluded that while for larger pore sizes due to the existance of

long range translational order T ∼ 1/d = 2/R holds, no signs for such an order has been

found for pore sizes smaller than 10 nm. In the latter case a Landau-de Gennes model

with elastic splay deformations in cylindrical layers of radially arranged molecular

columns is assumed. As a result of the increasing impact of splay deformations with

descreasing pore size T ∼ 1/(R2) is more suitable.

28

5 Experimental Part

5.1 Materials

5.1.1 Discotic Liquid Crystals

Py4CEH-a Pyrene-based Discotic Liquid Crystal

Pyrene-1,3,6,8-tetracarboxylictetra(2-ethylhexyl)ester (Py4CEH) consists of the aro-

matic Pyrene core surrounded by aliphatic chains as shown in Figure 5.1. Py4CEH

exhibits a plastic crystalline phase below 246 K, between 246 K and 369 K it has

a hexagonal columnar liquid crystalline phase and undergoes the clearing transition

above 369 K. The synthesis of this material is given in [78].

Figure 5.1: Chemical structure of Py4CEH

29

5 Experimental Part

Figure 5.2: Chemical structure of Hexakis(n-alkyloxy)triphenylene HATn. The lengthn of the side chains is varied: n=5, 6, 8, 10, 12.

Figure 5.3: Chemical structure of Hexakis(n-alkanoyloxy)triphenylene HOTn. Thelength n of the side chains is varied: n=6, 8, 10, 12.

Triphenylene-based Disoctic Liquid Crystals

Two series of triphenylene-based discotic liquid crystals were investigated in this study.

The first considered homologous series of Hexakis(n-alkyloxy)triphenylene (HATn)

DLCs is based on an aromatic triphenylene core where the length of the side chain

n is varied (n=5, 6, 8, 10, 12). Figure 5.2 gives their chemical structure.

The stucture of the second series of triphenylene-based disoctic liquid crystals Hexakis(n-

alkanoyloxy)triphenylene (HOTn) as seen in Figure 5.3 is similar, but here the alkyl

chains are linked via an ester group to the triphenylene core. The HOTn materials

were investigated for four different side chains: n=6,8,10,12.

All materials were purchased by Synthon Chemicals (Bitterfeld, Germany) and used

30

5.1 Materials

820 830 840

14C

13C

Inte

nsity [a

.u]

m/z [Da]

12C

MHAT6

=829.24 g/mol

Figure 5.4: MALDI-TOF spectrum of HAT6 (C54H84O6). The spectra were collectedemploying a Bruker Autoflex III (Bruker Daltonik GmbH, Bremen, Ger-many) spectrometer equipped with a SmartbeamT M laser (356 nm, fre-quency 200 Hz).

as received. Their chemical structure was confirmed by MALDI-TOF mass spectrome-

try. The MALDI-TOF MS spectrum of HAT6 is shown in Figure 5.4. In the theoretical

molar mass range of 828 g/mol of HAT6 pronounced peaks were detected while only

the mass of 12C is considered. As carbon has different stable and unstable isotopes

where the most common are 12C, 13C, and 14C several peaks are observed. The mass

difference between the different peaks is as expected 1 Da. Considering the natural

occurrence of the isotopes this leads to a molar mass of HAT6 of 829.24 g/mol. For

the other materials corresponding results are obtained.

5.1.2 Confining Hosts

For the investigations of discotic liquid crystals in confinement porous alumina oxide

membranes are used as hosts. Two types of alumina membranes have been tested:

Anapore Membranes (Whatman)

In order to optimize the filling conditions anopore inorganic membranes with differ-

ent pore sizes (25 nm, 100 nm, 200 nm) were purchased by Whatman. Due to the

non-uniform pore shapes of these membranes, they are not suitable to investigate the

31

5 Experimental Part

a b c

Figure 5.5: Electron microscopy (REM) pictures (Zeiss Gemini Supra 40 courtesy toBAM 6.4) of Smart Membranes with a pore size of (a) 25 nm, (b) 180 nm(c) 180 nm breaking edge.

Experimental Differential Scanning Dielectric Relaxation NeutronMethods Calorimetry Spectroscopy Scattering

Membrane Diameter [mm] 13 15Membrane Thickness [μm] 80

Pore Diameter [nm] 25 40 80 180 25 40 80 180 25 40 80Porosity [%] 10 45 50 10 10 45 50 10 10 45 50

Table 5.1: Properties of the membranes used in the course of this study.

influence of confinement on properties and dynamics of the materials under study here

and are only employed to adjust the filling conditions.

Smart Membranes

Alumina Membranes [79] with different four different pore diameters for dielectric re-

laxation spectroscopy (25 nm, 40 nm, 80 nm, 180 nm) as well as differential scanning

calorimetry and three different pore sizes for neutron scattering (25 nm, 40 nm, 80

nm) were purchased by Smart Membranes GmBH (Halle). The properties of the mem-

branes used are summarized in Table 5.1. Due to their more regular pore shapes, pore

diameters respectively (see Figure 5.5) they can be used as confining porous hosts. The

membranes were filled according to the procedure described in section 2.3.

5.2 Preparation of the Confined Samples

In order to obtain reproducible and well-defined samples, a procedure to fill the mem-

branes was developed. The alumina membranes were outgassed in vaccum of 10−4

mbar at 453 K for 12 h to remove water and other impurities. Under vacuum the

membranes were transferred into a glove box filled with argon. The membranes were

heated up again to a temperature above the discotic to isotropic phase transition of

the bulk material. Then some amount of liquid crystal was put on the surface of the

32

5.2 Preparation of the Confined Samples

a

0

100

200

T [K]

d m

/ d

T [

µg

/K]

weight loss

400 600 800 1000

0

20

40

60

80

100

m [%

]

b

400 600 800 1000

0

20

40

60

80

100

m [%

]

T [K]

weight loss

due to LC

residue 69.3%

(Membrane)

0

200

400

600

800

triphenylene core

d m

/ d

T [

µg

/K]

arms

Figure 5.6: TG-curve of a) HAT6 in the bulk state b) Anopore Membrane (pore size100 nm) filled with HAT6 (filling time of 24 hours at 393 K)

membrane to fill it by capillary wetting. For dielectric relaxation spectroscopy and

differential scanning calorimetry only one sample per measurement was prepared. In

the case of neutron scattering in order to have a sufficient mass inside the sample cells,

the following numbers of membranes were prepared for the different pore sizes: 80 nm

(12 - filled and 12 - empty membranes), 40 nm (24-filled and 24 - empty membranes);

25 nm (60-filled and 30- empty membranes). In order to ascertain adequate filling con-

ditions membranes with different pore sizes were filled with HAT6. They were kept at

different temperatures above the isotropization temperature for different time scales.

The filling degree of the alumina oxide membranes filled with discotic liquid crystal

is controlled by thermo-gravimetric measurements (TGA). These measurements were

performed by a SEIKO TG/DTA 220 apparatus under dry synthetic air atmosphere

at the BAM Federal Institute for Materials Research and Testing. The weight loss due

to the burning and decomposition of the organic molecules is measured up to 900K

with a heating rate of 10 K/min while the membranes remain thermally stable up to

higher temperatures. Figure 5.6a shows the decomposition of the HAT6 bulk material

whereas the weight loss consists of two steps. The weight loss of a membrane filled

with HAT6 is presented in Figure 5.6b. The final weight loss for membranes filled

with HAT6 for 2 different pore sizes in dependence on filling time is shown in Figure

5.7. Whereas for short times the data show a large scatter and the filling is incomplete

and undefined, for longer times (t>24 hours) stable pore filling is accomplished. When

converting the percentage of the weight loss to a mass mLC one can calculate the filling

degree Θ as follows:

Θ = mass measured

maximal mass for complete pore filling= mLC

Vp ∗ ρconf0

(5.1)

33

5 Experimental Part

0 20 40 60 80

0

10

20

30

40

50 200 nm

20 nm

weig

ht lo

ss [%

]

Filling Time [h]

Figure 5.7: Final weight loss in dependence on filling time for Anopore Membranes(filling temperature 393 K, filling material HAT6) with different pore sizesas indicated.

Figure 5.8: Electron microscopy (REM) pictures (Zeiss Gemini Supra 40 courtesy toBAM 6.4) of a Smart Membrane with a pore size of 180 nm filled withHAT6 breaking edge.

with Vp as the overall pore volume of the membrane and ρconf0 as the density of the

liquid crystal in confinement.

A membrane with a pore size of 180 nm filled with the DLC HAT6 is depicted in Figure

34

5.2 Preparation of the Confined Samples

5.8.

35

5 Experimental Part

5.3 Experimental Techniques

5.3.1 Conventional Differential Scanning Calorimetry

Conventional Differential Scanning Calorimetry (DSC) was carried out on the heat

flow using a Seiko DSC 7020. The samples (∼ 10 mg) were measured in appropiate

temperature ranges with a heating and cooling rate of 10 Kmin−1. Nitrogen was used

as the protection gas.

5.3.2 Dielectric Relaxation Spectroscopy

Dielectric Relaxation Spectroscopy (DRS) investigates the interaction of electromag-

netic fields with matter in a wide frequency interval ranging from 106 Hz to 1012 Hz.

A combination of several measurement systems based on different principles has to be

employed in order to cover this extensive frequency range. A schematical overview of

these techniques is given in Figure 5.9.

The complex dielectric function for a capacitor filled with a material is given by

ǫ∗ = ǫ′ − iǫ′′ = C(ω)C0

(5.2)

where C∗ is the complex capacitance of the filled capacitor, ω denotes the angular

frequency ω = 2πf = τ−1 with τ as the time for one period and C0 is the vacuum

capacitance. ǫ′and ǫ′′ are the real respectively imaginary part of the complex dielectric

function. For a periodic external field E = E0 exp (−iωt) in the linear regime (for many

materials E0 ≤ 106Vm−1) with ω as the angular frequency, the dielectric function can

be determined by measurements of the complex impedance Z∗ of the sample:

ǫ∗(ω) = J∗(ω)iωǫ0E∗(ω) = 1

iωZ∗(ω)C0

(5.3)

In the frequency range from 10−2 to 107 Hz the complex dielectric function is measured

by a Novocontrol high resolution alpha dielectric analyser with an active sample cell.

The sample was prepared in parallel plate geometry between two brass-plated elec-

trodes with a diameter of 20 mm and a spacing of 50 μm maintained by fused silica

spacers.

From 106 to 109 Hz measurements are performed on a coaxial reflectometer based on

the Agilent E4991 RF Impedance/Material Analyser. For both setups the temperature

of the sample was controlled by a Quatro temperature controller (Novocontrol) with

36

5.3 Experimental Techniques

Figure 5.9: Measurement techniques applied in the frequency range from 10−6 Hz to1015 Hz. Taken from [11]

37

5 Experimental Part

log (f)

ε'

log ε

''

Figure 5.10: Real ǫ′ and imaginary part ǫ′′ of the complex dielectric function ǫ∗ independence on frequency.

nitrogen as a heating agent providing a temperature stability that was better than 0.1

K.

Py4CEH confined to the self-ordered AAO was measured only in the low frequency

range. The disklike membrane was prepared between two gold-plated electrodes with

a diameter of 10 mm. A spacing of 80 μm was maintained by the thickness of the

membrane. Please note in that configuration the cylindrical pores are oriented perpen-

dicular to the electrode, thus in parallel to the electric field. Therefore, the filled AAO

membranes can be considered as two capacitors in parallel arrangement composed of

ǫ∗LC and ǫ∗AAO , and the contribution of the empty membranes can be simply subtracted

from the dielectric loss of the filled membranes.

Analysis of Dielectric Spectra

Figure 5.10 gives the real ǫ′ (energy storage) and imaginary part ǫ′′ (energy loss) of the

complex dielectric function. Relaxation processes typically successively decrease with

increasing frequency in the real part of the complex dielectric function ǫ′ and a peak

in the imaginary part of the complex dielectric function ǫ′′. Relaxations as a result

of molecular fluctuations are related to the whole molecule or at least parts of it, e.g.

functional side groups. Therefore, by analysis of the complex dielectric function, one

can acquire information about the dynamics of the molecular configuration. From the

step in ǫ′ respectively the area beneath the loss peak in ǫ′′ one can deduce the dielec-

38

5.3 Experimental Techniques

tric strength ∆ǫ of the corresponding process. The frequency of the loss peak fmax is

also connected to the characteristic relaxation rate ωmax = 2πfmax or relaxation time

τp = 1/ωmax. The distribution of relaxation times can be determined from the shape of

the loss peak.

Neglecting inertia effects and under the assumption that the polarization changes pro-

portional to its actual value, a simple approach to determine the time dependence of

dielectric behaviour is as follows:

d P (t)dt

= − 1

τD

P (t) (5.4)

where τD denotes the characteristic relaxation time. Equation (5.4) results in an expo-

nential decay for the correlation φ(τ) = exp(−t/τD) delivering for the complex dielectric

function ǫ∗(ω):ǫ∗(ω) = ǫ∞ + ∆ǫ

1 + iωτD

(5.5)

where ∆ǫ = ǫS − ǫ∞ represents the dielectric strength with ǫS = limωτ≪1 ǫ′(ω) and

ǫ∞ = limωτ≫1 ǫ′(ω). The Debye relaxation time is connected to the frequency of the

maximal loss fmax by ωp = 2πfp = 1/τD. The real and imaginary parts of the complex

dielectric function are expressed as follows:

ǫ′(ω) = 1

1 + (ωτD)2ǫ′′(ω) = ωτD

1 + (ωτD)2(5.6)

The Debye function predicts a symmetric loss peak with a half width wD of 1.14

decades.[11] Only very few materials exhibit Debye behaviour, typically one observes

much broader peaks (up to 6 decades) and furthermore an asymmetric relaxation curve

with a high frequency tail in many cases. Therefore, a number of generalizations of the

Debye function have been made to be able to describe broadened as well as asymmetric

loss peaks. The Cole/Cole(CC)-function includes a broadening of the dielectric function

ǫ∗CC(ω) = ǫ∞ + ∆ǫ

1 + (iωτCC)β(5.7)

where 0 < β ≤ 1 denotes the symmetrical broadening of ǫ∗, β = 1 delivers the Debye

function again. The position of the maximum of ǫ′′ is obtained by the Cole-/Cole

relaxation time τCC = 1/ωmax = 1/(2πfmax). The asymmetric broadening observed in

many measurements, mainly those of liquids or low molecular glass forming materials,

can be described by the Cole/Davidson(CD)-function written as:

ǫ∗CD(ω) = ǫ∞ + ∆ǫ

(1 + iωτCD)γ(5.8)

39

5 Experimental Part

where 0 < γ ≤ 1 results in an asymmetrical broadening of ǫ∗ for ω > 1/τCD with

τCD as the Cole-Davidson relaxation time. For γ = 1 the Debye-function ist obtained

again. It is important to note that for the asymmetrical Cole-Davidson function, the

characteristic relaxation time differs from the relaxation time corresponding to the

peak position ωp in ǫ′′. The relationship between both values is determined by the

shape parameter:

ωp = 1

τCD

tan

⎡⎢⎢⎢⎢⎣π

2γ + 2

⎤⎥⎥⎥⎥⎦(5.9)

Havriliak and Negami [80] suggested a more generalized model function (HN-function)

in including a symmetric as well as an asymmetric broadening:

ǫ∗HN = ǫ∞ + ∆ǫ

(1 + (iωτHN)β)γ(5.10)

where β and γ describe the symmetric respectively the asymmetric broadening of the

complex dielectric function. The real and imaginary parts of the Havrilak-Negami-

function are expressed as:

ǫ′(ω) = ǫ∞ + (ǫs − ǫ∞) cos γφ

1 + 2(ωτ0)β sin(π2)(1 − β) + (ωτ0)2β

ǫ′′(ω) = (ǫs − ǫ∞)sinγφ

1 + 2(ωτ0)β sin(π2)(1 − β) + (ωτ0)2β

φ = tan−1(ωτHN)β cos(π

2)(1 − β)

1 + (ωτHN)β sin(π2)(1 − β)

(5.11)

The peak position fmax in ǫ′′ is given by

fmax = ωmax

2π= 1

2πτHN

⎡⎢⎢⎢⎢⎣sin

βπ

2 + 2γ

⎤⎥⎥⎥⎥⎦1/β⎡⎢⎢⎢⎢⎣

sinβγπ

2 + 2γ

⎤⎥⎥⎥⎥⎦−1/β

(5.12)

These shape paramaters are linked to the restricting behaviour of ǫ∗ at low and high

frequencies:

ǫS − ǫ′(ω) ∼ ωm; ǫ′′ ∼ ωm for ω ≪ 1/τHN with m = β (5.13)

ǫ′ω − ǫ∞ ∼ ω−n; ǫ′′ω ∼ ω−n ω ≫ 1/τHN with n = βγ (5.14)

40

5.3 Experimental Techniques

The Debye theory of dielectric relaxation generalized by Kirkwood and Fröhlich gives

for the dielectric relaxation strength

∆ǫ = 1

3ǫ0

gμ2

kBT

N

V(5.15)

where μ is the dipole moment related to the process under consideration and N/V

is the number density of the dipoles involved. g is the Kirkwood-Fröhlich correlation

factor which describes the static correlation between the dipoles. kB is the Boltzmann’s

constant. The Onsager factor covering internal field effects is omitted for the sake of

simplicity.

Charge transport process at higher temperatures and lower frequencies can analyzed

by considering the complex modulus

M∗ = 1

ǫ∗= M ′′ + iM ′′ (5.16)

where M′

is the real part and M ′′ loss or imaginary part. For conductivity a peak is

observed in the imaginary part M′′[6]. Similar to the relaxation processes it can be

analyzed by fitting the loss part of HNequation to corresponding data. One obtains

a characteristic rate fmax,con for the conductivity which can be compared to the other

relaxation rates.

5.3.3 Specific Heat Spectroscopy

The thermal fluctuations of the discotic liquid crystal Py4CEH were studied by a

combination of Temperature Modulated DSC (TMDSC) and AC chip calorimetry. The

temperature is periodically varied with a frequency f. If relaxation processes take place

in the sample a phase shift between the heating and heat flow rate is observed.The

measurements result in a complex heat capacity

c∗p(f) = c′p(f) − ic′′p(f) (5.17)

where c′ and c′′ represent the real, imaginary respectively part of the complex heat

capacity.[81, 82, 83, 84, 85, 86] At low frequencies cp(f) was obtained by step scan

calorimetry, a special variant of TMDSC using a Perkin Elmer Diamond DSC. These

measurements were carried out in the Polymer Physics group of Professor Christoph

Schick at the University of Rostock. The sample (sample mass = 30.17 mg) was

quenched from room temperature, where the material is in the liquid crystalline phase,

to 178 K to avoid crystallization. The step length duration in TMDSC measurements

41

5 Experimental Part

correspond to the frequency range from 10−3 to 4.8 × 10−2 Hz from a base frequency

(f = 10−3 Hz) with available harmonics.[87] Nitrogen was used as the protection gas to

avoid degradation. The dynamic glass transition temperature was estimated by fitting

Gaussians to the data of the phase angle tan δ = c′′p/c′p which has to be corrected for

heat conductivity effects. For details see references [88] and [89].

At higher frequencies specific heat spectroscopy was performed using a differential AC

chip calorimeter [81] with a sensitivity of pJK−1. Because of this high sensitivity only

a low sample mass (∼ ng) of material is required. The differential setup developed by

Schick et al. [81] is employed where the calorimeter chip XEN 39390 (Xensor Inte-

gration, Nl) is used as the measuring cell. The differential approach will minimize the

contribution of the heat capacity of the empty sensor to the measured data. In the

approximation of thin films (submicron) the heat capacity of the sample CS is then

given by

CS = iωC(∆U − ∆U0)/P0S (5.18)

where C = C0 + G/iω denotes the effective heat capacity of the empty sensor where

G/iω is the heat loss through the surrounding atmosphere, S is the sensitivity of the

thermopile, P0 is the applied heating power, ∆U is the complex differential thermopile

signal for an empty and a sensor with a sample, and ∆U0 is the complex differential

voltage measured for two empty sensors. For identical sensors, ∆U0 = 0 holds.

The measured complex differential voltage ∆U is taken as a measure for c∗p(f) compared

with the complex dielectric function. On the AC calorimeter chip, heaters as well as

thermopiles are arranged as described in [90]. The heat capacity of the system is

measured by the temperature change sensed by the thermopiles in a lock-in approach

(complex voltage). For details see references [84] and [86]. The frequency was swept

from 1 Hz to 1000 Hz under isothermal conditions; this means the mean temperature

was kept constant during the sweep. The temperature was changed from 193 K to

243 K in steps of 2 K. The sample was also kept in a nitrogen atmosphere to avoid

degradation. The amplitude of the complex differential voltage is analyzed as a function

of temperature at a fixed frequency. At the glass transition the real part shows a step-

like change and a dynamic glass transition temperature can be determined by the half

step position of amplitude as a function of the frequency.[91]

5.3.4 X-ray Scattering

Figure 5.11 gives the geometry of a typical scattering experiment. Interaction of radia-

tion with a material leads to scattering or diffraction as result of spatial and temporal

correlations in the sample.[92] kf and ki denote the scattered and incident vector and

42

5.3 Experimental Techniques

θ is the scattering angle between the both vectors. The scattering vector q is the dif-

ference between kf and ki and a reciprocal of the correlation length. The norm of the

Figure 5.11: Scheme of the scattering process due to interaction of radiation with thesample.

scattering vector is given by

q = 4πn

λsin

θ

2(5.19)

where λ is the wavelength of the radiation, n the refractive index in the scattering

medium and θ the scattering angle.

For the X-ray scattering experiments, the sample was filled into borosilicate glass capil-

laries (WJM-Glas Glastechnik & Konstruktion, Germany) with a diameter of 0.3 mm.

The measurements were performed on the synchrotron micro focus beamline μSpot

(BESSY II of the Helmholtz Centre Berlin for Materials and Energy).

With a divergence of less than 1 mrad (horizontally and vertically), the focusing scheme

of the beamline is designed to provide a beam diameter of 100 μm at a flux of 1 × 109

photons s−1 at a ring current of 100 mA. A wavelength of 1.03358 A was applied

by a double crystal monochromator (Si 111). Scattered intensities were collected 820

mm behind the sample position with a two dimensional X-ray detector (MarMosaic,

CCD 3072 × 3072 pixel with a point spread function width of about 100 μm). For the

materials a heating rate of 10 Kmin−1 was applied in order to be consistent with the

DSC measurements. A more detailed description of the beamline is given in reference

[93].

The obtained scattering images were processed, converted into diagrams of scattered

43

5 Experimental Part

intensities versus scattering vector q and employing an algorithm of the computer pro-

gram FIT2D.[94]

Taking the maximum position qmax the core-core distance dcc is calculated according

to [95, 2]

dcc = 4π√3qmax

(5.20)

44

5.3 Experimental Techniques

5.3.5 Neutron Scattering

Neutron Scattering can monitor the movements of atoms and molecules on microscopic

time scale. The energy and momentum exchanged during the experiment between

neutrons and the sample gives information about space and time.

The double differential cross section is written as

d2Ω/dΩdω = 1/4πkf/ki(σcohScoh(q, ω) + σincSinc(q, ω)) (5.21)

where ki and kf are the incident and final wave vectors of the neutron beam, q the

momentum transfer vector, Ω the space angle of detection, S(q, ω) the so-called scat-

tering function, σ the scattering cross-sections for coherent and incoherent scattering,

ω the angular frequency to energy transfer ∆E which reads

ω = ∆E

h(5.22)

This law can be also written in terms of correlation functions. S(q, ω) is linked by

Fourier transformation (FT) to the intermediate scattering function S(q, t):S(q, ω) = 1/2π ∫ ∞

−∞S(q, t) exp−iωt dt (5.23)

One has to distinguish between a coherent and an incoherent variant of the scattering

function. The coherent variant corresponding to the pair correlation reads

Scoh = 1/N N∑i=1

N∑j=1

⟨expiqri(0) exp−iqrj(t)⟩ (5.24)

where ⟨ ⟩ denotes the thermal averages. The incoherent scattering function dominat-

ing most experiments on polymers and organic liquids is given by

Sinc = 1/N N∑i=1

⟨expiqri(0) exp−iqri(t)⟩ (5.25)

By inverse Fourier Transformation Scoh(q, t) is linked to the van Hove pair correlation

function

G(r, t) = 1

(2π)3 ∫ ∞

−∞e−i(qr−ωt)Scoh(q, t)d3qdω = 1

N

N∑i,j=1

δ(r−ri(0))δ(r−rj(t)) = ⟨ρ(0, 0)ρ(r, t)⟩(5.26)

45

5 Experimental Part

and the self correlation function

G(r, t) = 1

(2π)3 ∫ ∞

−∞e−i(qr−ωt)Sinc(q, t)d3qdω = 1

N

N∑i=1

δ(r − ri(0))δ(r − ri(t)) (5.27)

Measurement of the Vibrational Density of states by Time of Flight

Spectroscopy

Time of Flight Spectroscopy is used to determine the vibrational density of states,

measurements were carried out at IN6 at the ILL Grenoble and FOCUS at the Paul

Scherrer Institute. As an example for a TOF spectrometer the layout of IN6 is given

in Figure 5.12. The wavelength λ of the neutrons analogously to photons according to

the de Broglie relationship is

λ = h

mv(5.28)

where h is the Planck constant, m the neutron mass and v the velocity. The higher the

veleocity of a beam of neutrons created at the same time, the lower is their wavelength.

The kinetic energy is determined via a chopper system. The neutrons are scattered

at the sample and then collected by an array of detectors. The time it takes the

neutrons to cross the distance between the sample and the detector is measured and

gives information about the energy exchange (resolution meV) between the neutron

and the sample. The program INX [96] was used to correct the data for background

and adsorption. The VDOS was measured at 80 K. The resolution of the instrument

was obtained by measuring the sample under investigation at 2 K where all molecular

motion and vibrations are frozen. To correct the data of the filled membranes for the

scattering of the host materials the empty membranes were also measured at 2 and 80

K. The membranes were cleaned as described in 5.2 and sealed into the measuring cell

used for neutron scattering under Argon atmosphere.

Figure 5.13 gives the spectra of HAT10 as measured by IN6 normalized to the height

of the elastic peak. In order to separate the parts from the resolution and from low-

energy vibrations the standard expression for the one-phonon scattering function is

applied :

S(q, ω) = exp−2W (q) (δ(ω) + hq2

2m

g(ω)−ω

× 1 − exp( hω

kBT)−1) (5.29)

where exp−2W q is the Debye-Waller factor and m the average mass of an atom. The

observed scattering law is the convolution of (5.21)with the resolution function of the

instrument. The convolution effect of the inelastic term can be omitted because the

46

5.3 Experimental Techniques

Figure 5.12: The Time of Flight spectrometer IN6, picture taken from [97]

-2 0 2 4 6 8 10

0.0000

0.0005

0.0010

S(q

,∆E

) / S

(q,∆

E=

0)

∆E [meV]

Boson Peak

Figure 5.13: IN6 spectra of HAT6 in the bulk normalized to the height of the elas-tic peak (averaged over the detector range 54...108, corresponding to a

q range of 1.1...2.0 A−1 for elastic scattering): open squares - HAT6 inthe bulk at T=80 K; open circles correspond to a measurement at 2Krepresenting the instrumental resolution.

47

5 Experimental Part

boson peak is broad when compared to the resolution. Therefore it holds[98]:

Sobs(q, ω) = R(q, ω) ⊗ S(q, ω) ≈ exp−2W (q)(R(ω) + hq2

2m

g(ω)−ω

× 1 − exp( hω

kBT)−1)(5.30)

When applied to spectra at two different temperatures, Equation (5.30) gives a system

of two linear equations from which the vibrational density of states (VDOS) g(ω) and

R(q, ω) can be calculated.

Measurement of the Elastic Scans by Neutron Backscattering

To obtain an overview about the molecular dynamics elastic scans were carried out on

the neutron backscattering spectrocmeters IN10 and IN16 at the ILL Grenoble and

SPHERES at MLZ Garching.

As example a scheme of IN10 is given in Figure 5.14. IN10 (time scale 4 ns, resolution

∼ 1μeV) was used in standard configuration (“ unpolished” Si-111) with a wave length

of 6.271 A. To correct the data for the confined samples, elastic scans were carried

out on the empty host membranes. Furthermore the scattering of the empty can was

measured and substracted from the data for all samples.

Under backscattering conditions the neutrons traverse the sample before they are

backscattered again to the sample after which they reach the He-detector. A chop-

per is employed in order to dispose of neutrons which are scattered directly from the

sample into the detector.

A fixed window scan is applied: a certain energy transfer ∆E is chosen (∆E = 0 for

Figure 5.14: The Neutron Backscattering spectrometer IN10, picture taken from [97]

“elastic scan”) and furthermore the scattered intensity depending on a physical control

48

5.3 Experimental Techniques

parameters (e.g. the temperature T) is documented.

The incoherent scattering function can be divided into an elastic and an inelastic part.

S(q, E) = A(q, δE) + Sinel(q, E) (5.31)

In this representation A(q, δE) is the elastic incoherent structure factor (EISF) and

the Fourier transform of the spatial self-correlation function of the scattering particles

in the limit t → ∞. As a result it gives a large part of the spatial information about

a dynamical mechanism, e.g. it is possible to distinguish between a jumping process

between fixed sites and a continuous diffusion in the same spatial range.

The instrumental resolution broadens the observed spectral intensity of the scattering:

I(q, E) = R(q, E) ⊗ S(q, E) = A(q)R(q, E) + R(q, E) ⊗ Sinel(q, E) (5.32)

where R(q, E) is the instrumental resolution and ⊗ a convolution. If the width of the

resolution function is much smaller than the width of the inelastic scattering, S(q, E)near E = 0 can be omitted and therefore holds:

I(q, 0) = A(q)R(q, 0) (5.33)

In the classical approximation at T = 0 K only elastic scattering occurs: A(q) = 1.

The temperature dependence of A(q) can be obtained by normalising the temperature

dependent elastic scattering Iel(q) = I(q, E = 0, T ) to its low temperature limit I0(q) =I(q, E = 0, T = 0). For elastic scattering (E = 0) for the scattering vector q holds if the

scattering angle is 2θ: q = 4πλ

sin θ = 2k sin θ where λ is the de Broglie wavelength of the

neutrons respectively k = 2π/λ their wave vector.

The elastic scattered intensities can be approximated by a Gaussian. Then the effective

mean squared displacement ⟨u2⟩eff is extracted by

Iel

I0

= exp−q2⟨u2⟩

eff

3 (5.34)

where Iel is the elastically scattered intensity and I0 is the low temperature limit of

the scattered intensity which is generally measured below 2 K.

49

5 Experimental Part

50

6 Results and Discussion

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

6.1.1 Thermal behaviour

The heat flow of Py4CEH versus temperature for a heating and a cooling cycle in a

DSC measurement is shown in Figure 6.1. The phase transition temperatures were

estimated from the maximum positions of the peaks in the heat flow and summarized

in Table 6.1. The corresponding transition enthalpies for the heating cycle are 10.6 J/g

200 250 300 350 400-1.0

-0.5

0.0

0.5

1.0

1.5

120 140 160 180 200-0.1

0.0

0.1

0.2

Tcol

h,iso

Tcry, col

h

Tcol

h,iso

Hea

t flo

w [

W/g

]

T [K]

Tcry, col

h

exo

Hea

t Flo

w [

mg/

mW

]

T [K]

Tg ?

exo

Figure 6.1: DSC thermogram of Py4CEH during cooling (dashed line) and heating(solid line) with a cooling/heating rate of 10 K/min. The inset enlargesthe temperature range between 120 K and 210 K.

and 8.62 J/g respectively and for the cooling cycle 7.4 J/g and 8.1 J/g. At the phase

transitions this corresponds to entropy changes of 0.047 J/(gK) and 0.023 J/(gK) for

heating and 0.033 J/(gK) and 0.022 J/(gK) for cooling. These numbers might indicate

larger structural changes during the phase transition between plastic crystalline and

51

6 Results and Discussion

Tcry,col[K] Tcry,col[K]Heating 247 369Cooling 221 365

Table 6.1: Phase transition temperatures from plastic crystalline to hexagonal colum-nar mesophase Tcry,col and from hexagonal columnar mesophase to isotropicphase Tcol,iso at a rate of ±10 K/min.

liquid crystalline phase. This is in agreement with the larger hysteresis values found for

the transition from the plastic crystal to the hexagonal columnar mesophase. A more

careful inspection of the DSC trace for cooling reveals a small step at low temperature

(see inset Figure 6.1). Such a step might indicate a glass transition. This will be

discussed in more detail the course of this section.

The structure of Py4CEH in the liquid crystalline phase has been investigated by

Grelet et. al. [95]: They detected the Bragg reflections denoting the hexagonal packing

of columns. An amorphous halo around around 1.4 A−1 corresponds to the disordered

aliphatic side-chains and the (001) broad peak at ∼ 1.8 A−1 to the π − π-stacking of the

cores within the columns.

52

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

-10

12

34

56

-3

-2

-1

0

1

150

200250

300350

400

β-Relaxation

α-Relaxation in thedifferent Phases

Conductivity

Iso.Hexagonal Columnar

log

ε''

T [K]

log (f [Hz])

Crys.

Figure 6.2: Dielectric loss of Py4CEH in dependence on frequency and temperatureduring cooling. Taken from own publication [99].

6.1.2 Molecular Dynamics in the Bulk

Investigations by means of dielectric relaxation spectroscopy

Figure 6.3 presents the dielectric loss of Py4CEH in dependence on frequency and

temperature in a 3D representation. There are two peaks in the dielectric loss cor-

responding to two relaxation processes: a β-relaxation at low temperatures (or high

frequencies) and a process which will be further referred to as α-relaxation at higher

temperatures (or low frequencies). The latter occurs in both the plastic crystalline as

well as in the liquid crystalline phase. At the phase transition temperature a change in

the temperature dependence of this process is observed. This becomes more obvious in

the frequency dependence of the dielectric loss at fixed temperatures (see Figure 6.3).

For charge transport at higher temperatures and lower frequencies a peak is observed

in the imaginary part of the complex Modulus M′′

(see the inset of Figure 6.3). The

data is analyzed quantitavely by means of the Havriliak-Negami equation (5.10) for

α-relaxation and β-relaxation by considering the dielectric loss ǫ′′

and for charge trans-

port by the imaginary part of the complex Modulus M′′.

The relaxation rates in dependence on temperature are shown in Figure 6.4 (relax-

ation map). For the β-relaxation the temperature dependence of the relaxation rate

fmax,β follows the Arrhenius equation (4.8) and might be linked to localized fluctua-

tions of the methylene groups. The activation energy is estimated to be (10.3 ± 0.2)

kJ mol−1. The value of the activation energy obtained for Py4CEH is relatively low

53

6 Results and Discussion

-2 0 2 4 6 8 10

-3

-2

-1

0

1

2

-2 0 2 4 6

-3

-2

-1

log

ε''

log (f [Hz])

log

M''

log (f[Hz])

Figure 6.3: Dielectric loss in dependence on frequency at different temperatures (T=331K (downward triangles), 303 K (pentagrams), 255 K squares), 233 K (cir-cles), 221 K (upward triangles), 207 K (stars), 185 K (right triangles)).Lines denote fits by the Havriliak-Negami equation to the correspondingdata. Inset: Imaginary Part of the complex modulus M

′′at different tem-

peratures (353 K (squares), 357 K(circles), 361 K (upward triangles), 365K (downward triangles), 369 K (stars), 373 K(pentagons))

3 4 5 6 7

-2

0

2

4

6

8

1/TCol

h, iso

log

(fm

ax [

Hz]

)

1000/T [K-1]

1/TCry, Col

h

Figure 6.4: Relaxation map of Py4CEH: stars (dielectric β-relaxation), circles (dielec-tric α-relaxation), squares (conductivity). The dashed-dotted line repre-sents the α-relaxation of Polyethylene ([35]). The figure is taken from ownpublication.[99]

54

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

when compared to those of other disoctic liquid crystals which exhibit a similar process

(see section 4.2). These values are more in the range of those observed for localized

molecular motions of polyethylene.[34, 35] However, a closer look at the structure of

Py4CEH (see Figure 5.1), reveals firstly a shorter side chain and secondly the location

of the ethyl groups at the ester group. Both effects lead to a reduced packing structure

of the methylene groups compared to polyethylene which ease localized fluctuations.

This results in a lower activation energy. For the conductivity process fmax,con increases

with temperature while its slope changes in the vicinity of T= 365 K corresponding

to the transition temperature from the hexagonal columnar liquid crystalline to the

isotropic liquid phase. The corresponding activation energies estimated according to

equation (4.8) are (110±2) kJ mol−1 for the columnar hexagonal liquid crystalline and

(62 ± 2) kJ mol−1 for the isotropic phase. This is in contrast to what is observed for a

series of liquid crystalline phthalocyanine derivatives.[52]

The relaxation rate of the dielectric α-relaxation fmax,α is curved when plotted versus

inverse temperature. Hence it might be described by the Vogel-Fulcher-Tammann equa-

tion (4.3). A more detailed inspection of the temperature dependence of fmax,α reveals

that close to the phase transition temperature measured by DSC changes in fmax,α(T )take place. This is analyzed in more detail by means of the derivative technique.[6]

(d log fmax

dT) versus temperature is plotted in Figure 6.5. In this representation according

to equation (4.4) a dependence according to the Vogel-Fulcher-Tammann equation (4.3)

should appear as a straight line. Here the data show two different regimes for temper-

atures below and above Tcry,col which can be well described by straight lines. Therefore

the temperature dependence of the dielectric relaxation rate has to be described by

the VFT equation in both regimes. This type of dependence indicates a kind of glassy

dynamics. Accordingly a process related to glassy dynamics takes place in the plastic

crystalline as well as the columnar hexagonal liquid crystalline phase. At approxi-

mately the phase transition temperature Tcry,colh the slopes of the lines change. This

suggests different glassy dynamics in both the phases. From linear regression to the

data in the different regions according to equation (4.3) both the Vogel temperature T0

and the fragility parameter D can be obtained. For the Vogel temperatures,T0,cry = 62.5

K is estimated for the plastic crystal and T0,colh = 140.1 K for the columnar hexagonal

liquid crystalline phase. Fragility parameters Dcry=13.73 for the plastic crystal and

Dcolh=2.25 for the hexagonal liquid crystalline phase are obtained. Hence in the latter

phase the material behaves more fragile than in the plastic crystal phase. This is in

agreement with the discussion given in reference [100]. A similar behaviour but with

a less extended data analysis is also reported in reference [54]. Later these results will

be compared to data obtained by a different technique namely temperature modulated

differential scanning calorimetry. This more detailed discussion will be given later.

55

6 Results and Discussion

50 100 150 200 250 300 3500

2

4

6

8

T0,colh

d lo

g (f

max

,α [

Hz]

) / d

T [

K]

-1/2

T [K]

T0,cry

TCry,Col

Figure 6.5: (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of Py4CEHin the crystalline as well as the columnar hexagonal liquid crystalline phase- circles. The solid and the dashed lines are linear regressions to the cor-responding dielectric data in the different regions. T0 (arrows) denote theestimated Vogel-temperatures. The dotted vertical line indicates the phasetransition temperature taken from DSC measurements with a cooling rateof 10 K min−1. Taken from own publication.[99]

Figure 6.6 presents the temperature dependence of the dielectric strength ∆ǫα for the

dielectric α-relaxation. In agreement with the DSC measurements (see Figure 6.1) the

dielectric strength of the α-relaxation reveals the hysteresis between the heating and

the cooling run.

The dielectric strength decreases with increasing temperature in the columnar hexag-

onal liquid crystalline phase. However this dependence is stronger than predicted by

equation (5.15) which besides the VFT behaviour of the relaxation rate is typical for

glassy dynamics [6] In the plastic crystalline phase ∆ǫα is more or less independent of

temperature. Moreover in this phase ∆ǫα much lower than for the columnar hexag-

onal liquid crystalline phase. As the dipole moment should not change at the phase

transition this indicates a smaller number densitiy of fluctuating dipoles according to

equation (5.15). Therefore in the plastic crystal phase, the molecular fluctuations are

more restricted.

The temperature dependence of the dielectric strength for the β-relaxation ∆ǫβ is

shown in the inset of Figure 6.6. Generally ∆ǫβ decreases with increasing temperature.

This difference in the temperature dependence of ∆ǫ of conventional glass forming

materials might be the result of an increasing order with increasing temperature in

56

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

150 160 170 180 190 2000.00

0.05

0.10

150 180 210 240 270 300 3300

1

2

∆ε β

T [K]

Tg

T Cool

Cry; Colh

T Heat

Cry; Colh

∆ε α

T [K]

Plastic crystal

Columnar hexagonalliquid crystal

Figure 6.6: Temperature dependence of the dielectric strength ∆ǫα for heating (opencircles) and cooling (open triangles) for the α-relaxation. The dashed linesare guides for the eyes. The dashed-dotted vertical lines indicate the phasetransition temperatures measured for heating and cooling by DSC. Theinset: dielectric strength ∆ǫβ for the β-relaxation. The line is a guide forthe eyes.

the plastic crystalline phase. At Tg a change of the temperature dependence of the

dielectric strength of the β-relaxation is observed.

57

6 Results and Discussion

210 220 230 240

1.00

1.01

1.02

1.03

180 185 190 195 200 205 210 215 220 225

0.9

1.0

1.1

1.2

1.3

1.4

1.5

T [K]

cp' [

J/g

K]

0.00

0.02

0.04

0.06

0.08

0.10

0.12

δco

rr [de

gre

e]

Tdyn

g

Tdyn

g

∆U

/∆U

T=

-343 K

T [K]

Figure 6.7: Real part C′p (open squares) and corrected phase angle dcorr (open circles)

of the complex heat capacity versus temperature at f = 1.499 × 10−2 Hz ofa TMDSC measurement. The solid line is a fit of a Gaussian to the dataof the phase angle to estimate its maximum position. The width of theglass transition is taken from the variance of the Gaussian. Inset: Normal-ized amplitude of the complex differential voltage ofPy4CEH for heatingat different frequencies: open stars=720 Hz, open diamonds=560 Hz, opensquares=360 Hz. Dashed-dotted vertical lines denote the correspondingdynamic glass transition temperatures (halfstep height).

Investigations by means of Specific Heat Spectroscopy (SHS)

Thermal measurements are considered a true evidence for a glass transition, therefore

it was decided to study the α-relaxation in more detail by means of specific heat

spectroscopy. Figure 6.7 shows the real part of the complex heat capacity C′p and phase

angle dcorr corrected for heat transfer processes as obtained by a TMDSC measurement.

It shows a steplike increase in c′p while in parallel the phase angle exhibits a peak. Such

a behavior indicates a dynamic glass transition.[81] A corresponding dynamic glass

transition temperature can be determined from the half step position of the step in c′p.

An alternative procedure to determine Tg is fitting a Gaussian to dcorr and taking the

maximum position of the fit curve as Tg (see Figure 6.7). The normalized amplitude

of the complex differential voltage of Py4CEH at different frequencies as obtained by

AC chip calorimetry is shown in the inset of Figure 6.7. Similar to the temperature

dependence of C′p a step-like increase with increasing temperature is observed. This

step shifts to higher temperatures with increasing frequency. Analogously to above the

corresponding dynamic glass transition temperature is determined from the half step

58

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

3.0 3.5 4.0 4.5 5.0 5.5 6.0

-2

0

2

4

6

8

10

log

(fm

ax [

Hz]

)

1000/T [K-1]

1/TCry, Col

h

Figure 6.8: Temperature dependence of the α-relaxation, obtained by dielectric relax-ation spectroscopy (circles) and by specific heat spectroscopy (triangles).Dashed lines are fits of the VFT-equation (4.3) to the different branches ofthe dielectric α-relaxation and to the specific heat spectroscopy data. Thedashed-dotted line denotes data of the dielectric α-relaxation of polyethy-lene (PE) taken from reference [35].

position of the amplitude of the complex differential voltage.

Comparison of the data obtained by DRS and SHS

The data data from specific heat spectroscopy is compared to the dielectric data in

Figure 6.8. A direct comparison with the dielectric data as shown in Figure 6.8 can

be made because of the fact that both methods measure a generalized compliance.[84]

Similar to the dielectric data the temperature dependence of the relaxation rates is

curved versus inverse temperature but they are shifted to higher temperatures. Pro-

nounced deviations are observed for lower temperatures in the plastic crystal phase.

This is attributed to the fact that while dielectric spectroscopy is sensitive to the molec-

ular fluctuations of dipoles more close to the columns, specific heat spectroscopy senses

entropy (or enthalpy) fluctuations more in the intracolumnar space. This is discussed

in more detail by means of the derivative technique. Please note that the thermal

data are subjected to a larger error than the dielectric ones. As can be seen in Figure

6.9, the data obtained by both AC chip calorimetry and by TMDSC collapse into one

plot. Moreover, a straight line can be used to desribe the whole chart. This proves a

VFT temperature dependence also for the thermal data and therefore indicates glassy

59

6 Results and Discussion

50 100 150 200 250 300 3500

2

4

6

8

T0,colh

d lo

g (f

max

,α [

Hz]

) / d

T [

K]

-1/2

T [K]

T0,cry

TCry,Col

T0,therm

Figure 6.9: (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation presented inFigure 6.8 of Py4CEH in the crystalline as well as the columnar hexagonalliquid crystalline phase: circles - dielectric data; triangles - thermal data.The solid and the dashed lines are linear regressions to the correspondingdielectric data in the different regions. The dashed dotted line correspondsto the derivative of the dielectric relaxation rate of polyethylene taken fromreference [35]. T0 -arrows denote the estimated Vogel-temperatures. Thedotted vertical line indicates the phase transition temperature taken fromDSC measurements with a cooling rate of 10 K min−1. Please note thatthe effective cooling rate for the dielectric measurements is ca. two decadeslower.

dynamics. However, the estimated Vogel temperature T0,therm= 192 K is much higher

than the values obtained by dielectric spectroscopy for both the phases. The sequence

of the Vogel temperatures is as follows T0,cry < T0,colh < T0,therm.

For further discussion the following assumptions are made:

(1) The α-relaxation observed by both techniques (dielectric and specific heat spec-

troscopy) is related to molecular fluctuations of the side chains filling the intercolumnar

space.

(2) Dielectric spectroscopy is sensitive to the fluctuations of dipoles whereas specific

heat spectroscopy detects entropy fluctuations (see above).

For Py4CEH the main dipole moment is found in the ester group and located close to

the stiff core of the molecule (see Figure 5.1). The core structures are incorporated

into the columns in both the hexagonal columnar liquid crystalline and the plastic

crystalline phases. This will result in a restriction of the molecular mobility of the

attached groups, e. g. the ester group. This restriction will be stronger for a more

60

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

ordered than a less ordered phase.

In the framework of the cooperativity approach of the glass transition developed by

Donth (see section 4.2), the difference in the Vogel temperatures obtained by dielectric

spectroscopy (T0,colh = 140.1 K, T0,cry = 62.5 K) can be understood by considering the

higher restriction of the ester groups in the plastic crystalline phase. As a result of this

restriction, it is not possible for the ester groups to take part freely in the cooperative

process of the α-relaxation. In the columnar hexagonal liquid crystalline phase a part

of the restriction is released due to the change in structure. For that reason the ester

groups sensed by dielectric spectroscopy can participate more freely in the coopera-

tive α-relaxation.This leads to a higher Vogel temperature and a more fragile behavior

when compared to the plastic crystalline phase. The decrease of the restriction of the

ester groups in the columnar hexagonal liquid crystalline phase is in agreement with

the increase of the dielectric strengths at the phase transition and its changed temper-

ature dependence (see Figure 6.6). In contrast to dielectric spectroscopy which senses

the dipolar fluctuations close to the core, specific heat spectroscopy is sensitive to the

whole amount of material located in the intercolumnar space. This includes, besides

the ester groups, mainly the CH2 and CH3 units (see Figure 5.1). These units are much

less affected by the rigid columnar structures. Therefore they take part completely in a

cooperative process which results in a considerably increased Vogel temperature. The

data from specific heat spectroscopy can be compared to data measured for polyethy-

lene because the arms of Py4CEH consist mainly of CH2 and CH3 units. Thus for the

dielectric relaxation rate of polyethylene (see reference[35]) the derivative according to

equation (4.4) was calculated.

Figure 6.9 gives a comparison of this result to the data measured by specific heat

spectroscopy for Py4CEH. The calculated line (dashed-dotted line) and the data mea-

sured by specific heat spectroscopy coincide completely. This means that firstly, both

datasets have to be described by the same Vogel temperature (T0,therm). Secondly, the

α-process measured for Py4CEH by specific heat spectroscopy is due to similar molec-

ular fluctuations occuring also in polyethylene.

The correlation length for glassy dynamics can be calculated according to equation (4.7)

by using the data obtained by TMDSC shown in Figure 6.7(δT=7.58 K, cp,Liquid = 1.10

J(g ⋅ K)−1, cp,Glass = 1.05 J(g ⋅ K)−1 for Tg = 203 K. A value of 0.78 nm is obtained for

the correlation length of glassy dynamics.

In order to compare this to structural data, Small Angle X-ray Scattering was carried

out. Figure 6.10 shows Small Angle X-ray Scattering data at 303 K. This temperature

corresponds to the hexagonal columnar mesophase. Unfortunately, due to experimen-

tal reasons it was not possible achieve temperatures below the phase transition of the

plastic crystalline phase. A peak at q=3.54 nm−1 which corresponds to the core-core

61

6 Results and Discussion

distance is observed. By calculating the core-core distance dcc according to equation

0.1 1 10

1E-4

1E-3

0.01

0.1

Inte

nsity

[a.

u.]

q [nm-1]

Figure 6.10: X-ray diffractogram in the small angle range (SAXS) of Py4CEH at T=303K. Taken from own publication [99].

(5.20) one obtaines a value of 2.05 nm. Considering the fact that a part of this distance

has to be assigned to ordered columns on both sites (0.4 nm - 0.5 nm per site) ca. 0.8

nm is estimated for the intercolumnar space. A distance of ca. 0.8 nm can also be

estimated for the all-trans conformation of the alkyl chains. [101] One can conclude

that the length scale calculated from the thermal data (dynamic data) corresponds

very well to the structural data.

62

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

6.1.3 Phase Transitions under Confinement

Differential Scanning Caloriemtry was employed to investigate the phase transitions

of confined Py4CEH. Figure 6.11 shows DSC thermograms (heating rate 10 K/min;

second heating run) of Py4CEH in the bulk state and confined to the nanoporous

channels with three different pore sizes as indicated. The values of the heat flow were

recalculated according to the actual mass of the organic material inside the pores. It is

observed, that Py4CEH undergoes the phase transition from the plastic crystalline to

the hexagonal ordered liquid crystalline and to the isotropic state also when confined

and to the smallest pore diameter used in this study. The effect of the nanoscaled

confinement on the phase transition is threefold:

1. With decreasing pore diameter there is a shift of the phase transition tempera-

tures to lower temperatures for both phase transitions.

2. The phase transition enthalpies decrease with smaller pore size.

3. For the two lowest pore sizes the peak splits up for both phase transitions.

Similar to the bulk material Py4CEH confined to the pores exhibits a glass transition

around 200 K. The glass transition temperature seems to be independent of the pore

size down to 25 nm as expected from results obtained on confined molecular liquids

and amorphous polymers.[102, 103, 104]

Figure 6.12 shows the phase transition temperature from the plastic crystalline to the

liquid crystalline phase versus inverse pore size. As already mentioned above, for pores

with 40 and 25 nm in diameter the phase transition from the plastic crystalline to the

liquid crystalline phase splits of into two peaks (satellite peaks, see arrows in Figure

6.11).

The phase transition temperature for the peak located at higher temperatures remains

more or less independent of the pore size. For the peak at lower temperatures there is

a decrease of the phase transition temperature from plastic crystalline to liquid crys-

talline versus inverse pore size.

For the phase transition between the liquid crystalline and the isotropic liquid phase,

while the phase transition temperature for the peak located at higher temperatures

is more or less independent of the pore size, for the peak at lower temperatures, a

continuous decrease in the phase transition temperatures with decreasing pore size is

observed. (see Figure 6.13).

Similar to other materials for Py4CEH the change in the phase transition temperatures

63

6 Results and Discussion

150 200 250 300 350 400 450

Tg

exo

Tcry, col

h

Tcol

h,iso

40 nm

25 nm

80 nm

Hea

t Flo

w [

a.u.

]

T [K]

bulk

Tg

Figure 6.11: DSC Thermograms of bulk Py4CEH and Py4CEH located inside self-ordered AAO membranes with different pore diameters as indicated (Heat-ing rate 10 K/min, second heating scan). The dashed lines indicate thephase transitions of the bulk.

0.00 0.01 0.02 0.03 0.04

234

236

238

240

242

244

246

Phas

e T

rans

ition

Tem

pera

ture

[K

]

1/d [nm-1]

Figure 6.12: Phase transition temperatures between the plastic crystalline and the liq-uid crystalline phase versus inverse pore size as obtained by DSC (Solidsquares - main peak; Solid circles - satellite peak. The solid line is a linearregression to the corresponding data where the line is a guide for the eyes.

under confinement for both phase transitions can be described by the Gibbs-Thomson

formula (4.9). Using equation (4.9) the surface tension was estimated to ca. (3.16±0.31)

64

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

0.00 0.01 0.02 0.03 0.04

345

350

355

360

365

370

Phas

e T

rans

ition

Tem

pera

ture

[K

]

1/d [nm-1]

Figure 6.13: Phase transition temperatures between liquid crystalline and isotropicphase as obtained by DSC versus inverse pore size. Solid squares - mainpeak; Solid circles - satellite peak. The solid line is a linear regression tothe data of the main peak. The dashed line is a guide for the eyes forthe satellite peak. The open data points corresponds to literature data ofPy4CEH in AAO membranes with a pore diameter of 50 nm: star - DSC;triangle - X-ray; diamond - SANS. Taken from own publication [99]

.

mJm−2 for the plastic crystalline phase and to ca. of (3.03±0.15) mJm−2 for the liquid

crystalline phase. As σ is linked to the interaction of the molecule with a surface, for

both phase transitions a comparable value for the surface tension is found.

For the transition between the liquid crystalline and the isotropic liquid phase for

Py4CEH confined to self-ordered AAO with a pore diameter of 50 nm a decrease of

-5 K (SANS), -7 K (X-ray) and (-7.5 K DSC) was obtained in reference [105]. This

difference might be explained by the use of another host system with different pores

surfaces. For liquid crystals, in addition to the interfacial energy, the elastic energy

and/or the formation of dipoles can be of significance. Moreover elastic distortion and/

or the formation of defects which are essential in the formation of a columnar order in

the channels with a homeotropic anchoring result in a lower phase transition tempera-

ture. An increase in the phase transition temperature due to surface ordering has been

reported for the rodlike liquid crystal 5CB.[73]

As discussed above when taking a closer look at the measured heat flow in confined

Py4CEH (see Figure 6.11) additional to the pronounced peaks for each phase transition

peaks with a smaller transition enthalpy than the main peaks are observed for pore

sizes 40 and 25 nm. These additional satellite peaks are located at higher temperatures

65

6 Results and Discussion

Figure 6.14: Schematic representation of the possible organization of Py4CEH insidethe pores

than the main peaks and only weakly depend on the pore size. When extrapolating

this pore size dependence to larger pore sizes, it intersects with the Gibbs-Thomson

regression line at approximately 180 nm. Therefore, these additional satellite peaks

are attributed to the confinement and to two slightly different phase structures.

As discussed in references [105] and [49] the molecules will be more or less planarly ori-

ented in the pore center. The extent of this phase strongly depends on the pore size and

consequently the phase transition temperatures should follow the Gibbs-Thomson pre-

diction as found. Close to the pore wall the orientation of the both phases is attributed

to the interaction of the molecules with the pore wall. Therefore, a homeotropic ori-

entation is observed for Py4CEH close to the walls.[105]

As a summary, the different arrangement of the molecules inside the pores results in

two different phases with different phase transition temperatures for the material near

66

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

the center of the pores and the material close to the walls. As the latter moelcules

are stabilized by the pore walls, during heating first the material in the pore center

undergoes the phase transition and then at higher temperatures the liquid crystals at

the pore walls.

Figure 6.14 gives a simplified possible arrangement of the discotic liquid crystal inside

there pores. It has to be kept in mind, that these findings are based solely on results

from differential scanning calorimetry whereas only scattering methods provide the

means for a more straightforward discussion.

Figure 6.15 gives the pore size dependence of the transition enthalpies for both phase

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

5

10

0.00 0.01 0.02 0.03 0.04 0.050

5

10

∆H

[J/g

]

1/d [nm-1]

∆H=0

∆Hcry, colh=0

∆H

Py

4C

EH [J/g

]

1/d [nm-1

]

Figure 6.15: Transition enthalpies at the transition from the liquid crystalline to theisotropic phase versus inverse pore diameter: full circles - sum of main andsatellite peak, empty circles -main peak. The lines are a linear regressionto the data. Inset: Transition enthalpies from the plastic crystalline to theliquid crystalline phase versus inverse pore diameter. The line is a linearregression to the data.

transitions. The transition enthalpies are reduced to the amount of organic material

confined to the pores. In the case of satellite peaks, the sum of the transition enthalpies

of the main and the satellite peak was calculated. For the phase transition between

liquid crystalline and isotropic phase also the phase transition enthalpy of the main

peak is considered.

For both phase transitions, the transition enthalpies decrease linearly with decreas-

ing pore size. This implies a decrease of the amount of plastic crystalline as well as

liquid crystalline material with decreasing pore sizes. Because the amount of organic

molecules inside the pores is not reduced, this indicates that a part of the material does

67

6 Results and Discussion

not undergo the phase transition. As the surface curvature increases with decreasing

pore size, the ordered regions are subject to stronger elastic distortions and limited

in their volume.[65] This means that for a small enough pore size only disordered

amorphous volume is observed as reported for Py4CEH confined in nanoporous silica

(diameter d=8 nm).[105] The increase in the amount of amorphous material might

result in a more intensive glass transition (see Figure 6.11).

By extrapolating the linear decrease of ∆HP y4CEH one can estimate a critical pore

diameter dcri for both phase transitions. Here a value of ca. 19 nm is found for the

phase transition between liquid crystalline phase and isotropic phase. For the transi-

tion enthalpy of the main peak the corresponding value is estimated to ca. 20 nm. For

the phase transition between plastic crystalline and liquid crystalline phase ∆HP y4CEH

is ca. 23 nm (see Figure 6.15). This is in contrast to the value of 10 nm predicted in

an X-ray study on Py4CEH confined to AAO membranes [105] which might be due to

different surface properties of the membranes used in each case.

0.00 0.01 0.02 0.03 0.040.00

0.05

0.10

0.15

∆H

Sate

lit/∆

HA

ll

1/d [nm-1]

Figure 6.16: Relative transition enthalpy of the satellite peak for the phase transitionfrom the liquid crystalline to the isotropic phase versus inverse pore size.The dashed line denotes a linear regression to the data under the assump-tion that it goes through the point of origin.

Figure 6.16 gives the relative transition enthalpy of the satellite peaks for the phase

transition between liquid crystalline and isotropic phase. This ratio increases with de-

creasing pore size which supports the hypothesis of the both differently arranged phases

inside the pores. As discussed above the satellite peaks correspond to the homeotrop-

ically arranged material close to the pore walls. Here our findings suggest an increase

68

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

of this material with decreasing pore size with respect to the bulk-like phase in the

middle of the pore. By considering the difference in the phase transition enthalpies of

main and satellite peaks one can estimate the thickness of this ordered surface layer to

ca. 1 nm.

However in a different study with a different host system and sample preparation,

contrary results were obtained.[105] The extent or amount of the phase close to the

wall is related to the strength of the interaction of the molecules with the wall, and

it also depends on the elastic energy and/or the formation of topological defects, the

pore size and the thermal history (see reference [49]). This means that depending on

a combination of these factors its extent can increase or decrease.

69

6 Results and Discussion

0.004

0.008

0.012

200 250 300 350

0.000

0.002

0.004

ε''

(a)

plastic crystallinephase

(b)

ε''

T [K]

liquidcrystallinephase

Figure 6.17: Dielectric loss versus temperature for different frequencies: 1 kHz(squares), 677 kHz (circles), 1.33 MHz (triangles up) (a) for AAO mem-branes with a diameter of 80 nm filled with Py4CEH. Stars indicate thedielectric loss for the corresponding emtpy membrane at a frequeny of1 kHZ. Dashed lines denote polynomial fits: (b) for Py4CEH inside thepores where the contribution of the empty AAO membrane is substractedas described in the text.

6.1.4 Molecular Dynamics under Confinement

Dielectric Relaxation spectroscopy was employed to further study the dynamics of AAO

confined Py4CEH. The loss part of the complex dielectric function versus temperature

for different frequencies as indicated for Py4CEH confined to the pores with 80 nm

diameter is shown in Figure 6.17. For the confined material a peak is observed in the

same temperature range as for for the bulk material (see 6.1.2).[99] The dielectric in-

tensity of the peaks varies for the different frequencies because the different frequencies

correspond to maximum temperatures of the peak belonging to different phases (low

frequencies - plastic crystalline phase; higher frequencies - liquid crystalline phase).

When analyzing the experimental data of the dielectric measurements the dielectric

loss of the empty membranes cannot be ignored (see Figure 6.17a). The electrical field

70

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

3.5 4.0 4.5 5.01

2

3

4

5

6

7

3.5 4.0 4.5 5.0 5.5

-2

0

2

4

6

8

log(f

p [H

z])

1000 / T [K-1]

log(f

p [H

z])

1000 / T [K-1]

Figure 6.18: Relaxation map of Py4CEH in the bulk (open squares) and confined toAAO membranes with pore diameters of 180 nm (open circles) and 80nm (open triangles). Lines are guides to the eyes. Inset: relaxation mapof Py4CEH in the bulk (open squares) and confined to AAO membraneswith pore diameters 40 nm (hexagons) and 25 nm (open stars).

is oriented in parallel to the direction of the channels of AAO. Therefore this system

can be treated as a parallel circuit and the measured complex dielectric function is the

sum of the material confined to the pores and of the empty host membrane. First the

scaled contribution of the corresponding empty membrane for the complex dielectric

function of the confined Py4CEH was described by a polynomial and then subtracted

from the spectra of the filled membrane. A Gaussian fit of the data obtained by that

procedure (see Figure6.17b) delivers the maximum position of the peak in the temper-

ature domain. Figure 6.18 shows the temperature dependence of the relaxation rate

for bulk and confined Py4CEH. Similar to the bulk for temperatures above and below

the phase transition the temperature dependence of the relaxation rate for confined

Py4CEH can be described the Vogel-Fulcher-Tamman (VFT-) equation (4.3) but with

essential considerably different parameters in the different phases.

As can be seen in Figure 6.18 a more or less step-like change takes place in the

temperature dependence of the relaxation rates of confined Py4CEH. With decreasing

pore size the temperature dependence of the relaxation rates changes to a lesser extent.

Generally the temperature dependence of the relaxation rates for the confined material

should follow the VFT formula similar to the bulk. But here the temperature depen-

dence of the relaxation rates are approximated by an Arrhenius equation (4.8) due to

the limitation of data sets available for the confined samples. The pore size dependence

71

6 Results and Discussion

0.00 0.02 0.0470

80

90

100

110

0.00 0.01 0.02 0.03 0.04 0.05

45

50

55

60

65

70

75

80

EA

,Cry [kJ/m

ol]

1/d [nm-1]

EA

,LC [kJ/m

ol]

1/d [nm-1]

Figure 6.19: Apparent activation energy EA versus inverse pore size for the liquid crys-talline phase. Apparent activation energy EA versus inverse pore size forthe plastic crystalline phase. Lines are guides for the eyes.

of the apparent activation energies EA as calculated by (4.8) for both phases is shown

in Figure 6.19.

As expected the values for EA are smaller for the liquid crystalline phase than for

the plastic crystalline phase because the structure of the former is less complex than

for the latter. While for the liquid crystalline phase EA decrases with decreasing pore

size, the observed behavior for the plastic crystalline phase is slightly more complex:

there is an increase in EA,Cry with decreasing pore size until a maximum after which

a decrease follows with further decreasing pore size (see inset Figure 6.19). This de-

pendency might originate from a counterbalance of pore size and interaction effects.

For large pore sizes the interaction of the molecules with the pore walls impedes their

molecular mobility which leads to a higher activation energy. For smaller pore sizes

the confinement distorts the crystal structure releasing the molecular fluctuations of

the pyrene molecules. For the liquid crystalline phase the confinement effect wins over

the interaction for all pore sizes. Interestingly the pore size dependence of the activa-

tion energy and of the phase transition temperature are similar. Until now there is no

explanation for this fact and further experiments are required.

In Figure 6.20 f∞ versus EA is shown for both phases and all pore sizes. All data

points collapse into one correlation line. This is an expression of the well-known com-

pensation law.[106, 107] Although to date there is no generally accepted theoretical

interpretation of the compensation law, it seems obvious that the physical origin for

72

6.1 Py4CEH-a Pyrene-based Discotic Liquid Crystal

50 60 70 80 90 100 110

16

18

20

22

24

26

28

Liquid Crystalline

Phase

log

(f0

0 [H

z])

]

EA [kJ/mol]

Plastic Crystalline Phase

Figure 6.20: log f∞ versus EA for all pore sizes in the different phases: circles-liquidcrystalline phase; squares-plastic crystalline phase. The line is a linearregression to all data

such a law is directly linked to the cooperativity of the underlying processes.[106] For

the complex β-relaxation of liquid crystalline side group polymers a similar correlation

was found.[108, 109] In case of the liquid crystalline side group polymers this compen-

sation law was also interpreted by assuming a cooperative process for the rotational

fluctuations of the calamatic mesogen around its long axis.[108] See reference [99] and

6.1.2 for a detailed discussion on the cooperative character of the molecular dynamics

of bulk Py4CEH for the both phases. The observation of a compensation law for the

confined Py4CEH implies a cooparative nature of the molecular dynamics also under

confinement.

The midtemperature of the transition range can be used to define a dielectric relaxation

temperature (see Figure 6.21). Probably due to the essential lower effective heating

rate in the dielectric experiments, the absolute values of the dielectric phase transition

temperatures are lower than the corresponding phase. Furthermore it only weakly de-

pends on the pore size (see inset of Figure 6.21).

For large pore sizes it first decreases with decreasing pore size and then slightly in-

creases with further decreasing pore size.

It has to be kept in mind that the main dipole moment of Py4CEH is oriented par-

allely with respect to the pyrene core. Furthermore the pyrene molecules in the pore

center are planarly arranged. As a result changes ocurring here will be hardly de-

tected by dielectric spectroscopy. Therefore the phase transition observed by dielectric

73

6 Results and Discussion

0.00 0.01 0.02 0.03 0.04 0.05220

230

240

250

Ph

ase

Tra

nsitio

n T

em

pe

ratu

re [

K]

1/d [nm-1]

DSC

DRS

3.8 4.0 4.2 4.4

2

4

6

8

log (

f p [H

z])

1000/T [K-1]

Figure 6.21: Definition of the dielectric phase transition temperature for Py4CEH con-fined to AAO membranes with a pore diameter of 80 nm. Inset: Com-parison of phase transition temperatures between the plastic crystallineand the liquid crystalline phase versus inverse pore size as obtained bydielectric spectroscopy (solid circles) and DSC (open squares - main peak;open circles - satellite peak.The solid line is a linear regression to thecorresponding data where the dashed lines are guides for the eyes.

spectroscopy is ascribed to the homeotropically oriented molecules near the pore walls.

This is supported by the pore size dependence of the dielectric phase transition tem-

perature showing some similarities with the corresponding transition observed by DSC

(see inset of Figure 6.21).

74

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

150 200 250 300 350 400

-2

0

2

4

Heat flow

[W

/g]

T [K]

exo

180 190 200 210 220

0.10

0.11

0.12

0.13

Heat flow

[W

/g]

T [K]

Tg ?

Figure 6.22: DSC thermogram for HAT6 during cooling (blue line) and heating (redline). Inset: DSC thermogram for cooling in the range between 180 and220 K, the temperature where a glass transition is observed in reference[33].

6.2 Triphenylene-based Discotic Liquid

Crystals-Hexakis(n-alkyloxy)triphenylene (HATn)

6.2.1 Phase Transitions in the Bulk

Figure 6.22 gives the DSC thermograms for HAT6 for heating and cooling. The peaks

in the heat flow indicate the phase transition between the plastic crystalline and the

liquid crystalline phase (Tcry,colh) and between liquid crystalline and isotropic phase

(Tcolh,iso).

Similar to Py4CEH a hysteresis between heating and cooling is observed, which is larger

for the phase transition between the plastic crystalline and the liquid crystalline phase.

The inset of Figure 6.22 enlarges the heat flow in the temperature range from 180 K to

220 K, the temperature where a glass transition is found in reference [33]. A tiny step-

like change of the heat flow which might indicate a glass transition was detected during

cooling. In contrast to what was observed by Wübbenhorst et al. [33], here the step-

like change in the heat flow is much weaker and hard to discover. To investigate this

in more detail Temperature Modulated Differential Scanning Calorimetry was carried

out but nevertheless no evidence for a glass transition was found.

For all HATn under study corresponding DSC curves were obtained. All discotic

75

6 Results and Discussion

4 6 8 10 12

320

340

360

380

400

Tcry, colh

TP

hase

tra

ns [K

]

n

Tcolh, iso

4 6 8 10 120

20

40

60

80

∆T

me

so [K

]

n

Figure 6.23: Transition temperatures for the phase transitions between plastic crys-talline and liquid crystalline phase Tcry,colh and between liquid crystallineand isotropic phase Tcolh,iso of the HATn materials in dependence of thelength of the side chains n for heating (red circles) and cooling (blue downtriangles). Pentagons and stars indicate phase transition temperaturesgiven in the literature.[110] Inset: Temperature range of the liquid crys-talline mesophase ∆Tmeso in dependence on the length of the side chainsn.

liquid crystals under study show a hysteresis as demonstrated for HAT6. A step in

the heat flow is also observed for HAT5, HAT8 and HAT10 which might suggest that

this small change in the heat flow is a real effect. With increasing n the step height

decreases. During the heating scans no step-like change is detected for any material

under study.

Figure 6.23 shows the phase transition temperatures in dependence on the length of the

side chains n for cooling and the second heating. In reference [110] similar results were

published for several HATn (n=5, 6, 7, 8, 9, 10) with only slight differences for n=10

(HAT10; ∆Tcolh,iso=4 K). The phase transition temperature for the transition between

the liquid crystalline and the isotropic phase decreases with increasing n while the

phase transition temperature for the phase transition between the plastic crystalline

and the liquid crystalline phase exhibits almost no dependence on the length of the

aliphatic side chain. This leads to a narrowed temperature range ∆Tmeso of the liquid

crystalline mesophase with increasing n as shown in the inset of Figure 6.23. The

transition enthalpy in dependence on the chain length for both phase transitions is

given in Figure 6.24.

76

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

4 6 8 10 12

0

20

40

60

80

100

∆Η

Ph

ase

Tra

nsitio

n [J/g

]

n

Figure 6.24: Phase transition enthalpies for the transition from the plastic crystallineto the liquid crystalline phase (squares) and for the transition from theliquid crystalline to the isotropic phase (circles) in dependence on thelength n of the side chains during heating. Lines are guides for the eyes.The errors for the transition enthalpies for the phase transition from theliquid crystalline to the isotropic phase are smaller the size of the symbolswith regard to the scale of the y-axis.

For the phase transition between the plastic crystalline and the liquid crystalline phase,

the transition enthalpy first increases with n until a maximum enthalpy for n=8 is

reached. For higher volumes of n ∆H decreases again. For the phase transition between

the liquid crystalline and the isotropic phase the transition enthalpy decreases slightly

with n until a small increase for the longest side chain n=12 is observed.

6.2.2 Structure in the Different Phases

Figure 6.25 presents the X-ray diffractograms of HAT6 in the plastic crystalline phase.

It appears complex with numerous reflections in the whole q-range with the most promi-

nent peak at q = 3.5nm−1. Firstly, this suggests a more or less crystalline structure.

Secondly, HAT6 exhibits a kind of amorphous halo in the q-range from ca. 10 nm−1 to

20 nm−1. An amorphous halo is a characteristic of semi-crystalline polymers consisting

of amorphous and crystalline regions and corresponds to the amorphous parts of the

material.[111] Thus the existence of an amorphous halo implies the existence of some

disorder in the system also for this material in the plastic crystalline state.

The X-ray scattering pattern of HAT6 and semicrystalline polyethylene in the q-range

77

6 Results and Discussion

0 5 10 15 20 25

-2

-1

0

10 12 14 16 18 20 22 24

log(I

/Im

ax)

q [nm-1]

Amorphous Halo

(a)

q [nm-1]

Figure 6.25: X-ray spectra of HAT6 in the plastic crystalline phase at T=295 K. In-set: diffractogram of plastic crystalline HAT6 (dashed line) and semi-crystalline polyethylene (solid line) in the q-range between 10 nm−1 and25 nm−1.

between 10nm−1 and 25nm−1 (PE, degree of crystallization ca. 38 %) is shown in the

inset of Figure 6.25. The data for polyethylene are taken from reference [112]. Al-

though more detailed reflections are observed in the X-ray pattern for HAT6 than that

of PE, there are close similarities for both spectra, especially concerning the amor-

phous halo. Since the side chains of HATn consist of CH2 groups like PE this might

imply that the amorphous halo for HAT6 can be attributed to a disordered structure

of the methylene groups in the intercolumnar space. As discussed for liquid hydro-

carbons a disordered structure on a larger length scale does not exclude local short

range correlations.[113, 114] In a coherent neutron diffraction study on the compara-

ble amorphous polymer polybutadien a similar structure was verified, which is also in

accordance with detailed atomistic molecular simulations.[115]

Several efforts have been made to determine also the single crystal structure and the

lattice type of triphenylene derivatives in the plastic crystal state but met only with

limited success.[116] This might be explained by the low scattering lengths of the

C, H, O and N-atoms and the difficulty to prepare sufficiently large single crystals

for X-ray single crystal diffraction experiments. Furthermore the disordered amor-

phous structure indicated by the halo might prevent the identification for this material.

For triphenylene- HAT2 − NO2 and other triphenylene-based discotic molecules with

shorter side chains suitable samples to investigate the single crystal structure can be

prepared by sublimation or recrystallization of the ethylacetate.[117, 118]

78

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

5 6 7 8 9 10

0 5 10 15 20 25

-2

-1

0

2*(3)1/2

*qmax

q [nm-1]

qmax

(3)1/2

*qmax

log(I

/ I

ma

x)

q [nm-1]

Amorphous Halo

Disk-Disk

Distance

Figure 6.26: X-ray spectra of HAT6 in the liquid-crystalline phase (T=351 K). Inset:X-ray diffractogramm of liquid crystalline HAT6 between q = 5 nm−1 andq = 10 nm−1.

For several materials in the plastic crystalline phase the discotic cores organize into

columns with seperated side chains. Furthermore the aromatic cores and the aliphatic

side chains are incompatible. Hence here for the HAT6 in the plastic crystalline phase

also a selforganization of the cores into columns is assumed.

Figure 6.26 gives the X-ray spectrum corresponding to the hexagonally ordered liq-

uid crystalline mesophase. The Bragg reflection at qmax = 3.5 nm−1 corresponds to the

core-core distance of the triphenylene cores.[2] Higher order reflections at q values ∼ √3

evidence the hexagonal ordering as shown in the inset of Figure 6.26. The detected

broad amorphous halo is related to the disordered structure of the methylene groups of

the side chains in the intercolumnar space between the triphenylene cores. The amor-

phous halo is slightly shifted to lower q values than found for the plastic crystalline

phase. Moreover, the fact that it occurs in both phases indicates the disordered struc-

ture of the alkyl chains in the plastic crystalline phase. An additional peak at q = 17.5

nm−1 linked to the horizontal distance of the triphenylene cores within a column is

observed.[95, 2]

Even in the deeply “isotropic state” (see Figure 6.27) a column-like ordering is implied

by a a reflection at q = 3.65 nm−1 and in a q-range similar to the two other phases an

amorphous halo is observed. However the peak is essential broader when compared to

the liquid crystalline phase. This suggests a more disordered structure of the columns

with smaller column lengths. As a result the peak corresponding to the disc-disc dis-

79

6 Results and Discussion

0 5 10 15 20 25

-0.8

-0.6

-0.4

-0.2

0.0

log(I

/Im

ax)

q [nm-1]

Amorphous Halo

Column-like

Structures

Figure 6.27: X-ray spectra of HAT6 at T=423 K where the material is supposed to bein the isotropic phase.

tance might be also quite broad and overlaid by the amorphous halo.

For all HATn under study a similar behavior is observed in the different phases:

1. In the plastic crystalline phase there are many reflections whereas the most pro-

nounced peak in the lower q-range corresponds to the intercolumnar distance. An

amorphous halo due to the alkyl chains is found for all HATn under study. An

additional reflection occurs at a higher q-range indicating the horizontal distance

of the cores.

2. In the liquid crystalline phase the Bragg-reflection qmax indicating the core-core

distance as well as higher order reflections at ∼ √3qmax confirming the hexagonal

ordering are observed. The amorphous halo which is shifted to lower q-values

when compared to the plastic crystalline phase is linked to the disordered struc-

ture of the side chains in the intercolumnar space.

3. In the “isotropic phase” a broader peak in the lower q-range as well as the amor-

phous halo at higher q-values are detected for all HATn indicating a kind of order

to some extent even in this state.

The X-ray diffractograms for HAT5, HAT6, HAT8 and HAT10 in the columnar hexag-

onal mesophase are compared in Figure 6.28. (For n=12 the temperature range of the

mesophase is very narrow and due to the high heating rate, no data for the correspond-

ing phase could be obtained for n=12.) At scattering vectors smaller than 5 nm−1 a

pronounced reflection is observed for all materials. This peak position shifts to lower

80

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

5 10 15 20 25

n=10

n=8

n=6

log(I

/Im

ax)

q [nm-1]

n=5

Figure 6.28: X-ray diffractogram for the HATn materials at a temperature correspond-ing to the columnar hexagonal mesophase: T = 353 K for n = 5, T = 351 Kfor n=6 and 8, T = 341 K for n = 10. The curves are shifted on the y-scalefor sake of clearness.

q values with increasing n. The intercolumnar distance dcc is calculated by means of

equation (5.20).

Figure 6.29 shows the core-core distance dcc in dependence on the number of C-Atoms

in the side chains. As expected, the core-core distance increases more or less linearly

with increasing lengths of the side chain for both the hexagonal columnar liquid crys-

talline and the isotropic phase with a similar slope. The data of DLCs are compared

to the length of a single alkyl chain in all trans conformation in dependence on n in

the same plot to confirm this in more detail. Both the experimental data for the DLC

and the theoretical values for a single alkyl chain have a similar slope with regard to

n. This evidences that the lengths of the alkyl chains determine the distance between

the columns. As more side chains are involved the d values for the DLCs are larger

than for one alkyl chain in all trans conformation. In Figure 6.29 the obtained data for

HATn are also compared to Py4CEH (see section 6.1.2) to the size of alkyl group rich

nanodomains found in nanophase separated poly(n-alkylmetharylates).[119, 101] The

former fits well to the data of the HATn materials and also for the latter the distance

increases as well linearly with regard to n with a similar slope.

81

6 Results and Discussion

2 4 6 8 10 12 14

0.8

1.2

1.6

2.0

2.4

2.8

dcc [n

m]

n

all trans

Figure 6.29: Core-Core Distance versus number of C-Atoms in the side chain for HATn:red circles – the columnar hexagonal phase; blue squares – “isotropicphase”. Error bars were given for the distance in the liquid crystallinephase. In the isotropic state the error is similar. The dashed and dasheddotted lines are linear fits to the corresponding data. Data for trian-gles – Poly (n–alkyl metharylates) are taken from reference [119]. Thestraight line corresponds to data for a single alkyl chain in all transconformation.[119] Non integer numbers for the Poly (n-alkyl methary-lates) refer to mixtures of polymers with different lengths of the side chain.Star - Py4CEH

82

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

6.2.3 Influence of Confinement on the Phase Behavior

In order to study the effect of confinement on HATn materials similar to Py4CEH

HAT5, HAT6, HAT10 and HAT12 were embedded in self-ordererd membranes with

four different pore sizes (180nm, 80nm, 40 nm and 25 nm) and studied by differential

scanning calorimetry. At first, HAT6 is discussed in more detail. Figure 6.30 shows

DSC heating thermograms of HAT6 in the bulk state and in confinement for three dif-

ferent pore sizes as indicated. The values of the heat flow were recalculated according

to the actual mass of the material inside the pores.

Similar to the pyrene-based discotic liquid crystal Py4CEH three effects are ob-

200 300 400

Tg

Tcol

h,iso

40 nm

80 nm

Heat flow

[a.u

.]

T [K]

bulk

25 nm

Tcry,col

h

Tg

Figure 6.30: DSC thermograms of bulk HAT6 and HAT6 embedded inside the pores ofself-ordered AAO membranes with pore diameters as indicated (heatingrate 10 K/min, second heating scan). The dashed lines indicate the phasetransitions temperatures of the bulk. The data is shifted on the y-axis forsake of clearness. Taken from own publication.[120]

served:

1. Both phase transitions between plastic crystalline and liquid crystalline phase as

well as between liquid crystalline and isotropic phase are observed down to the

smallest pore size.

2. The transition temperatures decrease for both phase transitions with decreasing

pore size.

3. The transition enthalpies decrease with with decreasing pore size.

83

6 Results and Discussion

180 195 210 225 240

300 320 340 360 380 400

He

at

Flo

w [

a.u

.]

T [K]

Glass Transition ?

Surface

of the Pores

(Sattelite Peak)

He

at F

low

[a.u

.]

T [K]

TLC,Iso; Bulk

Center

of the Pores

(Main Peak)

Exo

Figure 6.31: Heat flow for HAT6 confined to AAO channels with a diameter of 25nm in the temperature range for the transition from hexagonal orderedliquid crystalline and to the isotropic phase during heating. The dashedline indicates the phase transition temperature of the bulk. Inset: Heatflow for HAT6 confined to pores with a pore diameter of 40 nm in thetemperature range between 180 K and 240 K.

4. Under confinement satellite peaks are detected. For the phase transition between

the hexagonal ordered liquid crystalline and the isotropic state besides the main

peak only one satellite peak is detected.

For the phase transition between the plastic crystalline and the hexagonal ordered

liquid crystalline phase the behavior becomes more complex with decreasing pore size

where more additional peaks appear for HAT6 more peaks are observed. The molecular

assignment of the satellite peaks is discussed in detail below. To demonstrate this more

clearly for the smallest pore size, Figure 6.31 enlarges the heat flow for HAT6 confined

to channels with a diameter of 25 nm in the temperature range for the phase transition

from hexagonal ordered liquid crystalline and to the isotropic state. Additionally in

the temperature range between 180 K and 240 K a small step-like change in heat flow

is observed which might imply a glass transition (see inset Figure 6.31). In the same

temperature range a glass transition is discussed for bulk HAT6 in the literature [33]

which is not clearly observed in the experiments carried out here. This discrepancy

requires more detailed investigations.

Figure 6.32 gives the phase transition temperatures for HAT6 for the phase transition

between plastic crystalline and liquid crystalline phase as well as between liquid crys-

talline and isotropic phase versus inverse pore size. For both phase transitions the peak

84

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.00 0.01 0.02 0.03 0.04

330

340

350

360

370

Ttr

an

s[K

]

1/d [nm-1]

Tcry,col

Tcol,iso

T=340 K

T=372 K

T=323 K

Figure 6.32: Phase transition temperatures for HAT6. Phase transition temperaturesbetween the plastic crystalline and the liquid crystalline phase - squares,satellite peaks for the phase transition between the plastic crystalline andthe liquid crystalline phase- upward triangles, phase transition temper-atures between liquid crystalline and isotropic phase - circles, satellitepeaks for the phase transition between liquid crystalline and isotropicphase- downward triangles. The solid line is a linear regression to thecorresponding data where the dashed line is a guide for the eyes.

of the phase transition of the bulk splits up into at least two single peaks: the main

peak whose pore size dependence can be described by means of the Gibbs-Thomson

formula (Equation (4.9)) and an additional satellite peak at a temperature which is

slightly higher than that of the more pronounced main peak. The satellite peak does

not depend on the pore size. Employing the Gibbs-Thomson formula the surface ten-

sion for the phase transition between liquid crystalline and isotropic phase for HAT6 is

estimated to 1.73 mJm−2. This value is slightly lower than the value found for the con-

fined pyrene-based DCL (Py4CEH) (see section 6.1.3).[99] Different interaction of the

two kinds of molecules with the pore wall might lead to this difference in the values of

the surface tension. Similar to what was discussed for Py4CEH (see section 6.1.3), the

two peaks are attributed to different layers of molecules with a different arrangement of

the molecules and different pore size dependence of the phase transition temperature.

The main peak is assigned to the more or less planarly oriented material in the pore

center and the satellite peaks to the molecules developing a liquid crystalline ordered

surface layer with a homeotropic-like arrangement closer to the pore walls.[105, 99, 120]

The pore size strongly influences the extent of the former phase, and therefore the de-

85

6 Results and Discussion

crease of the corresponding phase transition temperatures should approximately follow

the Gibbs/Thomson prediction.

As already described for Py4CEH the interaction of the molecules with the wall deter-

mine the homeotropic-like orientation of the material close to the wall.[121] As a result

the corresponding phase transition temperature corresponding to the liquid crystalline

surface layer should not or only weakly depend the pore size. Also for HAT6 the rela-

tive amount of the homeotropic phase close to the wall increases with decreasing pores

size similar to Py4CEH (see reference [120] and section 6.1.3).

Similar to the phase transition from the hexagonally ordered liquid crystalline to the

isotropic state, the phase transition from the plastic crystal to the liquid crystalline

phase the peak characteristic for the phase transition of the bulk splits up into a main

and a satellite component, which are assigned in a similar manner as discussed above

to a bulk-like phase in the center of the pores (main peak) and to a surface layer.

The observed pore size dependence obtained for the phase transition between plastic

crystalline and liquid crystalline phase corresponds to the one for the phase transi-

tion to the isotropic state. While the transition temperature for the satellite peak is

more or less independent of the pore size that for the main peak decreases linearly

with decreasing pore size. By using the Gibbs/Thomson equation (Equation (4.9)) for

HAT6 the surface tension is estimated to 7.83 mJm−2, which is much larger than the

surface tension for the phase transition from hexagonal ordered liquid crystalline to the

isotropic state. The reason for that needs further experimental investigations including

smaller pore sizes. An investigation on the pyrene-based system has shown that the

Gibbs/Thomson approach is no longer valid for small pore sizes and has to be replaced

by a Landau/de Gennes formulation.[77] This might imply that the estimated surface

tension by means of the Gordon/Thomson approaches is subjected to larger errors.

Figure 6.33 gives the phase transition enthalpy for HAT6 for the phase transition

(sum of main and satellite peak) between the liquid crystalline and the isotropic phase

Hcol,iso (sum of main and satellite peak) versus inverse pore size. As for Py4CEH the

transition enthalpy decreases with decreasing pore size whereas the amount of material

inside the host material does not change. This indicates that the amount of the ordered

phase (bulk-like and ordered surface layer) undergoing the phase transition decreases

with decreasing pore size. Therefore, it can be concluded, that a part of the confined

material does not undergo the phase transition and should be more or less amorphous

and disordered. This result is also in agreement with molecular dynamic simulations.

[122] With decreasing pore size the surface curvature of the pore increases. This results

in stronger elastic distortions of the ordered regions and preventing the molecules from

structure formation and limiting the volume of the ordered phase.

For HAT6 the linear extrapolation of ∆Hcol,iso (sum of main and satelite peak) versus

86

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.00 0.02 0.04 0.06

0

2

4

6

0.00 0.01 0.02 0.03 0.040.0

0.2

0.4

0.6

∆H

iso [J/g

]

1/d [nm-1]

∆H=0

∆H

Sa

tte

lite/∆

HM

ain

1/d [nm-1]

Figure 6.33: Phase transition enthalpy for the phase transition from the liquid crys-talline to the isotropic phase (sum of main and satellite peak) for HAT6-full circles, Phase transition enthalpy for the main peak of the phase tran-sition from the liquid crystalline to the isotropic phase for HAT6- emptycircles. Lines are linear regression to the data. Inset: Transition enthalpiesof the satellite peak relative to that of the main peak versus inverse porediameter. The dashed line is a fit of Equation (6.1) to the data.

inverse pore diameter to ∆H = 0 delivers a value for a critical diameter dcri of the liq-

uid crystalline (ordered) phase of approximately 17 nm which corresponds well to the

value found for Py4CEH. By using the law of error propagation the error of this critical

diameter is estimated to be ≈ 3.3 nm. For the transition enthalpy of the main peak a

value of ∼ 20 nm is obtained. For smaller pore sizes than dcri,main the phase transtion

of the bulk-like phase in the center of the pores is supressed and for diameters smaller

than dcri,ges structure formation is completely prevented. The observed difference in

the different critical diameter dcri for the main peak and the sum of main and satellite

peak can give information about the thickness of the ordered surface layer close to the

wall.

The inset of Figure 6.33 gives the ratio of the transition enthalpy of the satellite peak

and that of the main peak versus inverse pore size for HAT6. This ratio increases which

supports the hypothesis of an ordered surface layer and a bulk-like phase in the center

of the pores. Under the assumption of a similar density in the surface layer and in the

bulk-like phase, for cylindrical pores the following two phase model is suggested :

∆HSatellite

∆HMain

= mSurfaceLayer

mbulk−like

≈ VSurfaceLayer

Vbulk−like

= drS − r2S(d/2 − rS)2

(6.1)

87

6 Results and Discussion

where rS denotes the thickness of the surface, d the pore diameter, mi and Vi are the

mass and the volume of the surface layer/bulk-like phase. Equation (6.1) describes the

data given in the inset of Figure 6.33 quite well. A fit yields approximately 2.5 nm

for the thickness of the ordered surface layer. This value is smaller than the lateral

size of a single HAT6 molecule (see section 6.2.2 and reference [123]). Therefore this

value provides further evidence that the molecules within the ordered surface layer

have a homeotropic orientation. Alternatively the thickness of the surface layer can

be estimated from the difference in the critical diameter for the transition of the main

peak and the sum of main and satellit peak. Here a value of approximately 2.6 nm is

obtained.

Figure 6.34 gives the phase transition enthalpy (main and satellite peak) between

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

10

20

30

40

50

∆Hcry,col

H

= 0

(ca. 17 nm)

∆H

cry

, co

l H

[J/g

]

1/d [nm-1]

Figure 6.34: Phase transition enthalpies versus inverse pore diameter d for the transi-tion from the plastic crystalline to the liquid crystalline phase for HAT6.The line is a linear regression to the data.

plastic crystalline and liquid crystalline phase for HAT6: the phase transition enthalpy

decreases linearly with the inverse pore size as it is observed for the phase transition

from liquid crystalline to the isotropic state. The corresponding extrapolation to ∆H =0 gives a value of ca. 17 nm for the diameter of bulk-like phase in the center of the

pore as is also obtained for the phase transition from the liquid crystalline to isotropic

phase. Accordingly a similar structural model as discussed for liquid crystalline phase

can also be assumed for the plastic crystalline state.

For HAT6 besides the discussed peak for the phase transition between plastic crystalline

and liquid crystalline phase an additional peak at approximately 323 K indicating a

88

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.00 0.02 0.04

0.0

0.5

1.0

∆H

T=

32

3 K

/∆H

ma

in

1/d [nm-1]

Figure 6.35: Transition enthalpy of the phase transition at 323 K for HAT6 relative tothat of the main peak. The line is a fit of Equation (6.1) to the data.

further phase transition is observed. Figure 6.35 shows the transition enthalpy of that

phase transition relative to that of the main peak. As ∆HT=323K/∆Hmain increases with

decreasing pore size, it might be attributed to the liquid crystalline surface layer. The

two layer surface model introduced above can be employed to approximately describe

the data. The fit yields a value of 3.5 nm for the thickness of the liquid crystalline

surface layer. This seems to be in accordance with the value of 2.5 nm obtained from

the analysis of the phase transition enthalpies of the phase transition from the liquid

crystalline to the isotropic phase. However the detailed molecular assignment of this

additional peak at a low temperature is not completely understood yet and requires

further studies.

Figure 6.36 gives the phase transition temperatures for HAT5, HAT10 and HAT12 for

the phase transition between plastic crystalline and liquid crystalline phase as well as

between liquid crystalline and isotropic phase versus inverse pore size. As for Py4CEH

and HAT6 for all confined HATn under study for both phase transitions:

1. The peaks split up into one main and one satellite peak.

2. The main peak decreases in temperature with decreasing pore size.

3. The satellite peak remains independent of the pore size.

For the the two longest side chains (HAT10, HAT12) and for smaller pore sizes (40 nm,

25 nm), the main peaks of the phase transition between liquid crystalline and isotropic

phase seem to disappear and only the satellite peaks are detected. This indicates that

89

6 Results and Discussion

0.00 0.01 0.02 0.03 0.04

330

345

360

375

390

1/d [nm-1]

T=397 K

Tcol,iso

Ttr

an

s [K

]

Tcry, col

T=338 K

0.00 0.01 0.02 0.03 0.04

325

330

335

340

345

T=331 K

Tcol,iso

Ttr

an

s [K

]

1/d [nm-1]

Tcry,col

T=345 K

0.00 0.01 0.02 0.03 0.04

325

330

335

Ttr

an

s [K

]

Tcol,iso

Tcry,col

T=334 K

1/d [nm-1]

T=331 K

90

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

Figure 6.36: Phase transition temperatures for (a) HAT5, (b) HAT10, (c) HAT12 asindicated. Phase transition temperatures between the plastic crystallineand the liquid crystalline phase - squares, satellite peaks for the phasetransition between the plastic crystalline and the liquid crystalline phase-upward triangles, phase transition temperatures between liquid crystallineand isotropic phase - circles, satellite peaks for the phase transition be-tween liquid crystalline and isotropic phase- downward triangles. The solidline is a linear regression to the corresponding data where the dashed lineis a guide for the eyes.

the phase transition of the bulk-like layer in the center of the pores is supressed and

the corresponding material has become completely disordered. This will be discussed

in more detail when considering the phase transition enthalpies (see Figures 6.38, 6.39,

6.40).

For all materials the surface tension σ for both phase transitions were calculated ac-

6 8 10 12

0

4

8

σ [m

Jm

-2]

n

Figure 6.37: Surface tension for the phase transition between plastic crystalline andliquid crystalline phase -black squares- and between liquid crystalline andisotropic phase - red circles in dependence on the chain length.

cording to the Gibbs-Thomson approach (Equation (4.9)). The values are summarized

in Table 6.2 and Figure 6.37. For the phase transition between plastic crystalline and

liquid crystalline phase the surface tension is much higher than for the phase transition

between liquid crystalline and isotropic phase. This result requires further investiga-

tions including smaller pore sizes. As already mentioned in section 4.4, for small pore

sizes a Landau/de Gennes formulation is more suitable. [77] For both phase transitions

σ decreases with increasing n.

91

6 Results and Discussion

HATn σcol,iso[mJm−2] σcry,col[mJm−2]HAT5 1.55 ± 0.29 9.94 ± 1.44HAT6 1.73 ± 0.18 7.83 ± 0.99HAT10 0.89 ± 0.05 7.7 ± 0.98HAT12 0.89 ± 0.05 5.97 ± 0.98

Table 6.2: Surface tension for HAT5, HAT6, HAT10, HAT12 for both phase transitions.

0.00 0.02 0.04 0.06

0

5

10

∆H=0

∆H

iso [J/g

]

1/d [nm-1]

Figure 6.38: Phase transition enthalpy for the phase transition from the liquid crys-talline to the isotropic phase for HAT5 (sum of main and satellite peak)- full squares. Phase transition enthalpy for the main peak of the phasetransition from the liquid crystalline to the isotropic phase for HAT5-empty squares. Lines are linear regression to the corresponding data.

The transition enthalpy for the phase transition between liquid crystalline and isotropic

phase is shown in Figures 6.38, 6.39, 6.40. For all materials one observes a decrease

in the transition enthalpy corresponding to the main peak as well as for the overall

enthalpy (sum of main and satellite peak). For HAT10 and HAT12 the linear regression

intersects with ∆H=0 for a pore size bigger than the smallest pore size.

The estimated critical pore diameters for the phase transition (of the sum of main and

satellite peak) and the main peak with in dependence on the number n of C-atoms in the

carbon chain are given in Figure 6.41. Both critical diameters increase with increasing

chain length dcri in both cases, whereas the critical diameter for the main peak is

higher. One might speculate that with decreasing pore size and longer chain lengths

the space between the columns is more and more limited. Therefore the organization

into ordered phases is hindered. At first, this might affect the planarly arranged bulk-

like layer in the pore center whose extension is also limited both by the pore diameter

92

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.00 0.01 0.02 0.03 0.04 0.05

0

1

2

3

4

∆H

iso [J/g

]

1/d [nm-1]

∆H=0

Figure 6.39: Phase transition enthalpy for the phase transition from the liquid crys-talline to the isotropic phase (sum of main and satellite peak) for HAT10-full triangles. Phase transition enthalpy for the main peak of the phasetransition from the liquid crystalline to the isotropic phase for HAT10-empty triangles. Lines are linear regression to the corresponding data.

0.00 0.01 0.02 0.03 0.04

0

4

8

12

16

∆H

iso

,ge

s [J/g

]

1/d [nm-1]

0.00 0.01 0.02 0.03 0.04

0

2

4

6

8

10

12

14

16

∆H

iso

,ma

in [J/g

]

1/d [nm-1]

Figure 6.40: Phase transition enthalpy for the phase transition from the liquid crys-talline to the isotropic phase for HAT12 (sum of main and satellite peak) -full stars. Inset: Phase transition enthalpy for the main peak of the phasetransition from the liquid crystalline to the isotropic phase for HAT12-empty stars. Lines are linear regression to the corresponding data.

93

6 Results and Discussion

4 6 8 10 12

15

20

25

30

35

40

45

6 8 10 12

2

4

6

dcri

,iso

[nm

]

n

dcri,g

es [nm

-1] -

dcri,m

ain

[nm

-1]

n

Figure 6.41: Critical pore size for the phase transition from the liquid crystalline tothe isotropic phase dcri,iso for the main peak - circles and the overall phasetransition - squares in dependence on the chain length. Inset: Differencein the critical diameter dcri,ges − dcri,main for the phase transition of thesum (main and satellite peak) and the phase transition of the main peakfor the transition between liquid crystalline and isotropic phase.

and the homeotropically arranged crystalline surface layer. Unfortunately an analysis

of the thickness of the surface layer employing the two phase model similar to HAT6

above is not possible for the other HATn under study, because too few data points

could be obtained for the ratio of surface-layer and the bulk-like phase. As already

done for HAT6 from calculating the difference between the critical diamater for the

phase transition of the main peak and for the phase transition of the sum of main and

satellite peak, one can estimate the thickness of the surface layer (see the inset of 6.41).

The thickness of the surface layer appears to be more or less independent of the chain

length within the margin of error and an average value of 3.6 nm is obtained.

Figure 6.42 gives the phase transition enthalpy (main and satellite peak) between

plastic crystalline and liquid crystalline phase for HAT5, HAT6, HAT10 and HAT12.

In contrast to HAT6 for all other HATn under study (HAT5, HAT10, HAT12) the

transition enthalpy is more or less independent of the pore size until it sharply decreases

for a pore size of 25 nm. The reason for this is not fully understood yet and needs

further investigations. However, in Figure 6.42 it is assumed that the peaks are due to

the different phase structures within the pore and similar to what is observed for HAT6

for the same phase transition and for the phase transition between liquid crystalline

and isotropic phase for all HATn under study. This is supported by the fact that for

94

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.00 0.01 0.02 0.03 0.04

30

40

50

60

70

0.00 0.01 0.02 0.03 0.04

30

40

50

60

70

∆Η

me

so

[J/g

]

1/d [nm-1]

∆Η

meso [J

/g]

1/d [nm-1]

Figure 6.42: Phase transition enthalpies versus inverse pore diameter d for the transi-tion from the plastic crystalline to the liquid crystalline phase. The dashedline is a linear regression to the data: open squares - HAT5, open circles- HAT6 Inset: Phase transition enthalpies versus inverse pore diameterd for the transition from the plastic crystalline to the liquid crystallinephase: open triangles - HAT 10, open stars - HAT 12.

HAT6 besides the discussed peak an additional peak at approximately 323 K indicating

a further phase transition is observed. Such a peak was not found for Py4CEH as

well. One might speculate that for the triphenylene-based systems the phase transition

temperature of this particular phase is masked by the main peak of these materials as

these are in the same temperature range as the peak at 323 K observed for HAT6.

95

6 Results and Discussion

0

2

4

6

200

250

300350

400

-3

-2

-1

0

T [K]

log ε

''

log (f [H

z])Cry

Colh

I

conductivity

α

β

Figure 6.43: Dielectric spectra of HAT6 in dependence on frequency and temperaturein a 3D representation while cooling.

6.2.4 Molecular Dynamics in Dependence of the Chain Length

Figure 6.43 presents the dielectric loss of HAT6 in dependence on frequency and tem-

perature while cooling: two relaxation processes, a β-relaxation at low and an α-

relaxation at higher temperatures, are found in the temperature range of the plastic

crystalline phase. Furthermore a conductivity contribution is detected in the temper-

ature range of the liquid crystalline and the isotropic phase.

Similar to the analysis of the dielectric data for Py4CEH, for α and β-relaxation, the

empirical Havriliak-Negami equation (5.10) is fitted to the obtained curves for ǫ′′. In

the case of the conductivity the peak observed in the imaginary part of the dielectric

Modulus M′′

is also analysed by the HN-equation (5.10). As an example Figure 6.44

gives the dielectric loss ǫ′′

of HAT6 in dependence on frequency at different temper-

atures in the temperature range of the α-relaxation. The dashed lines in Figure 6.44

denote the corresponding fits of the HN-equation (5.10) to the data.

Figure 6.45 shows the obtained relaxation rates in dependence on 1/T.

The relaxation rate of the β-process exhibits an Arrhenius-type temperature depen-

dence (Equation (4.8)). By means of equation (4.8) the activation energy EA,β is

calculated to 20.6 kJ mol−1. This value is higher than for Py4CEH and is probably due

to differences in the chemical structure. In the case of HAT6, the β-relaxation might

be assigned to local conformation transitions as known for Polyethylene.[33, 124]

The dielectric strength ∆ǫβ of the β-relaxation of HAT6 versus temperature is plotted

96

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

-2 0 2 4 6

-4

-3

-2

log ε

''

log(f [Hz])

Figure 6.44: Dielectric loss ǫ′′ versus frequency for the α-relaxation of HAT6 at differenttemperatures: blue stars T=234 K, green triangles T=219 K, red circlesT=204 K, black squares T=183 K. Lines denote fits of equation (5.10) tothe data.

3 4 5 6 7

0

2

4

6

8

log

(f m

ax[H

z])

1000/T [K-1]

β

α

Figure 6.45: Relaxation map of HAT6: red stars - dielectric β - relaxation, red cir-cles - dielectric α-relaxation, red squares - conductivity, black squares -α-relaxation as observed in reference [33]. Straight lines are a linear re-gression to the data in the corresponding temperature range. Dashed linesdenote a guide to the eyes.

97

6 Results and Discussion

0 50 100 150 200 250 300

1

2

3

4

5

6

7

d lo

g (

f ma

x,α

[H

z])

/dT

-1/2

T[K]

T0

Figure 6.46: (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of HAT6.Straight lines denote a linear regression to the data. The arrow denotesthe Vogel-Temperature T0. Dashed lines are guides to the eyes.

in the inset of Figure 6.47. In contrast to Py4CEH (see section 6.1.2) for HAT6 ∆ǫβ

weakly increases at low temperatures followed by a more pronounced increase in the

temperature range of the step in the heat flow observed by DSC (see section 6.2.1).

According to Equation (5.15) an increase in the dielectic strength implies an increase

in the number density of dipoles involved. Due to the onset of the α-relaxation the

structure becomes softer and allows so for more localized fluctuations. At T>240 K a

further crossover takes place in ∆ǫβ. This will be discussed in more detail below.

One would expect that the relaxation rate of the α-relaxation is curved versus 1/Tand follows a Vogel-Fulcher-Tammann temperature dependence similar to what was

suggested by Wübbenhorst.[33] However, this does not apply to the relaxation rate of

HAT6 obtained in this study. Instead for HAT6 fmax,α the temperature dependence

appears to be more complicated, which can neither be described by the Arrhenius

equation (4.8) nor by the VFT-equation (4.3). Moreover a change in the slope oc-

curs around 1000/(T=200 K) which is in the same temperature range where a step

is observed in the DSC experiments (see section 6.2.1). This is investigated in more

detail by means of the derivative technique which was already applied for Py4CEH (see

section 6.1.2). For an Arrhenius behaviour it holds:

(d log fmax

dT)−1/2 = (ln 10EA/R)−1/2 ⋅ T (6.2)

98

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

175 200 225 250 275 300

0.01

0.02

0.03

0.04

0.05

150 200 250

0.04

0.08

0.12

∆ε α

T [K]

∆ε β

T [K]

Figure 6.47: Dielectric strength ∆ǫα in dependence on temperature for the α-relaxationof HAT6. Inset: Dielectric strength ∆ǫβ in dependence on temperaturefor the β-relaxation of HAT6. The dashed and straight lines are guidesfor the eyes.

This means a dependence according to the Arrhenius equation (4.8) should appear as

a straight line which goes through the point of origin. A VFT-dependence also shows

up as a straight line but it intersects with the x-axis at a temperature T0>0. Figure

6.46 gives (d log fmax

dT)−1/2

versus temperature for the α-relaxation. Here three different

temperature regimes which can be described by three straight lines are observed. In

the very low temperature range below T=210 K a linear dependence is observed which

goes through the point of origin. At very high temperatures there is also a linear

dependence which goes through the point of origin but with a different slope. This

indicates an Arrhenius behaviour in the both temperature regimes but with different

activation energies. The corresponding activation energies are calculated to EA= 89 kJ

mol−1 for the low temperature range and EA= 46.4 kJ mol−1 for the high temperature

range. The difference in the activation energies might be due to a higher mobility

at higher temperatures. For the middle temperature range (between T=210 K and

T=240 K) the data might follow the VFT-equation whereas a T0 = 171 K is estimated.

As the Vogel-Temperature T0 is 30-40 K below the glass transition temperature, this

result corresponds well to the step at around T=205 K observed by DSC (see 6.2.1).

Accordingly, in this temperature range, the relaxation rates exhibit a VFT-behaviour

which is supposed to indicate glassy dynamics. Taking a closer look at the data given

by Wübbenhorst (see Figure 6.45) it seems possible to also describe their data by two

Arrhenius equations in two different temperature regimes with a crossover region. A

99

6 Results and Discussion

transition from VFT to Arrhenius behaviour is characteristic for molecular dynamics

under nanoscale confinement.[6, 102, 125, 126] The α-relaxation is assigned to seg-

mental motions of the alkyl chains in the intercolumnar space. Keeping in mind the

structure of DLCs (see section 6.2.2) the alkyl chains can be regarded as confined in

between the columns (“self-organized confinement”). Then considering the cooperativ-

ity approach to glassy dynamics a Cooperatively Rearranging Region (CRR) can be

introduced. A CRR is small at high temperatures and its size increases with decreasing

temperature. In the middle temperature range the size of the CRR is smaller than the

intercolumnar distance enabling glassy dynamics and a VFT temperature dependence

of the relaxation rate. With decreasing temperature it becomes larger until a further

increase is limited by the columns resulting in a transition to an Arrhenius behaviour.

At very high temperatures T>240 K the size of a CRR might be too small to allow for

glassy dynamics and therefore an Arrhenius temperature dependence of the relaxation

rate is also observed here. A transition between Arrhenius and VFT-behavior is also

found for low molecular weight and polymeric glass formers.[6]

The three different temperature regimes are reflected also in the temperature depen-

dence of the dielectric strength of the α-relaxation for HAT6 (see Figure 6.47). ∆ǫα

increases in the temperature range of the step in the heat flow at around 210 K imply-

ing an increase in the mobility in accordance with Equation (5.15). Above T=240 K a

crossover takes place where ∆ǫα seems to be more or less constant. To summarize, the

three different temperature regimes are observed in the temperature dependence of

1. the relaxation rate of the α-relaxation fmax,α

2. the dielectric strength of the α-relaxation ∆ǫα

3. the dielectric strength of the β-relaxation ∆ǫβ

The temperature dependence of the relaxation rate of the conductivity in the isotropic

phase can be described by means of the Arrhenius equation (4.8). The activation en-

ergy is calculated to 75.8 kJ mol−1 which is slightly higher than found for Py4CEH in

the same phase.

Figure 6.48 shows the relaxation rates in dependence on temperature for HAT5,

HAT6, HAT8, HAT10 and HAT12. All HATn under study exhibit an α - as well as a

β-relaxation in the temperature range of the plastic crystalline phase. However, with

increasing n the dielectric loss ǫ′′

decreases in intensity resulting in a larger scattering

of the available data for longer side chains.

The behaviour of the α-relaxation changes with varying n. For n=5, 8 the relaxation

rates for the α-relaxation decrease more or less linearly with increasing 1/T and do not

follow the VFT-equation, but can be described by means of the Arrhenius equation.

100

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

2.8 3.5 4.2 4.9 5.6 6.3 7.0 7.7

-2

-1

0

1

2

3

4

5

6

7

8

9

log

(f m

ax[H

z])

1000/T [K-1]

β

α

Figure 6.48: Activation Plot for HATn for the α-and the β-relaxation: squares - HAT5,red circles - HAT6, green triangles - HAT8, blue pentagons - HAT10, pinkstars - HAT12. Solid lines are fits of the Arrhenius equation to the dataof the β-relaxation. Dashed lines denote relaxation rates of PE to thecorresponding process taken from reference [35].

0 50 100 150 200 250 300

0

2

4

6

d lo

g (

f ma

x[H

z])

/dT

-1/2

T [K]

Figure 6.49: (d log fmax

dT)−1/2

versus temperature for HAT5 - black squares and HAT8 -

green triangles. Lines are a linear regression to the data.

101

6 Results and Discussion

This supported by means of the derivative technique (see Figure 6.49) where for both

materials (d log fmax

dT)−1/2

can be described by straight lines which intersect at the point

of origin but with different slopes and therefore different activation energies for HAT5

and HAT8. For HAT5 EA,α=51.5 kJ mol−1 which is slightly higher than for HAT6 but

of the same order of magnitude in the high temperature range. For HAT8 a value of

178.7 kJ mol−1

is obtained which is significantly higher.

The relaxation rates of HAT10 and HAT12 appear to be curved versus 1/T and might

be described by the VFT-equation. However a confirmation of this hypothesis by means

of the derivative technique is not possible due to the scattered data. Also the values

of the relaxation rate are almost in the same range as those obtained for Polyethylene.

Furthermore a step in the temperature dependence of the relaxation rate occurs at ∼T=250 K. In contrast to reference [110], in this study in this temperature range a small

peak is observed in the heat flow for both materials which might imply a phase tran-

sition. When considering only the data from the temperature range below the change

in fmax,α and estimating an activation energy by means of the Arrhenius equation for

HAT10 149.8 kJ mol−1 and for HAT12 131.8 kJ mol−1 are obtained. To summarize,

for longer side chains there seems to be a decrease in the activation energies as seen

in Figure 6.50. Similar to Polyethylene (PE), the side arms of the triphenylene deriva-

tives consist of a sequence of CH2 groups. Hence, a comparison to PE is drawn. With

increasing chain length the intercolumnar distance increases (see section 6.2.2) and

also the structure becomes more and more PE-like. The alkyl chains can be regarded

as stiffly organized and “confined” in between the rigid columns. With increasing n,

therefore increasing distance between the columns, this so-called self-organized con-

finement is weakened and released. As a result the temperature dependence of the

relaxation rates might change from an Arrhenius to a VFT behaviour. For HAT10 and

HAT12 fmax,α almost converges with the relaxation rate observed for the glass tran-

sition for PE (see Figure 6.48). Therefore it is concluded that the α-relaxation might

be attributed to restricted glassy dynamics of the nanophase separated alkyl chains in

the intercolummnar space.[33] This hypothesis is further supported by the occurence

of a Boson Peak (BP) for HATn (n=5, 6, 10, 12) and the dependence of its behavior on

n. It shifts to lower frequencies which reflects the decrease of the estimated activation

energies for the α-relaxation. For HAT10 and HAT12 the BP becomes narrower and

gains in intensity (see section 6.2.5).

The β-relaxation follows an Arrhenius-type temperature dependence for all HATn un-

der study. Employing equation (4.8) the activation energies are calculated for each

discotic liquid crystal and given in Figure 6.51 and Table 6.3. At first the activation

energies decrease with increasing n until a minimum followed by an increase. The for-

mer is due to an increase in the core-core distance: With longer intercolumnar distance

102

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

8 10 12

120

130

140

150

160

170

180

Activation energy α-Relaxation PE

EA

,α [kJ m

ol-1

]

n

Figure 6.50: Activation energy EA,αfor the α-relaxation in dependence on the chainlength for HAT8, HAT10 and HAT12. The line is a guide for the eyes.

HATn E,α EA,β EA,cond,col EA,cond,iso[kJmol−1] [kJmol−1] [kJmol−1] [kJmol−1]HAT5 51.5 25.4 89.2 69.3HAT6 20.6 - 75.8HAT8 178.7 23.8 126.0 55.3HAT10 149.8 28.0 74.6 63.2HAT12 131.8 28.6 - 67.0

Table 6.3: Activation energy for the α, the β-relaxation and the conductivity processin the different temperature ranges as indicated.

this already mentioned “self-organized confinement” is released leading to lower acti-

vation energies. Due to the similarity to PE in the structure, especially for longer side

chains, the exhibited behaviour starts to converge with the one found for PE. Therefore

an increase in the activation energies is observed.

The characteristic rates of the conductivity process fmax,con are given in Figure 6.52

for all HATn. fmax,con increases with temperature whereas for each material its slope

and therefore its activation energy changes in the vicinity of its specific transition tem-

perature from the hexagonal columnar liquid crystalline to the isotropic liquid phase.

The corresponding activation energies have been estimated by means of the Arrhenius

equation (4.8) and are given in Table 6.3. The activation energy of the conductivity in

the temperature range of the isotropic phase is more or less independent off the chain

length.

103

6 Results and Discussion

6 8 10 12

15

18

21

24

27

30

36

39

EA

,β [kJ/m

ol]

n

Activation energy β-Relaxation PE

Figure 6.51: Activation energy for the β-relaxation for all HATn in dependence on thechain length. The dashed line denotes the activation energy of the β-relaxation of PE taken from reference [35]. The line is a guide to theeyes.

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1

-1

0

1

2

log

(f m

ax[H

z])

1000/T [K-1]

Figure 6.52: Activation Plot for HATn for the conductivity process: squares - HAT5,red circles - HAT6, green triangles - HAT8, blue pentagons - HAT10, pinkstars - HAT12. Solid lines denote fits of the Arrhenius equation to thedata.

104

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 5 10 15 20

0.00

0.04

0.08

0.12

0.16

0.20

0.0 2.5 5.0 7.5 10.00.0

0.2

0.4

0.6

0.8

g(ω

) /

ω2 [10

3 p

s3]

ω [ps-1]

g(ω

) /

ω2 [10

3 p

s3]

ω [ps-1]

Increasing

Order

Figure 6.53: Vibrational density of states (VDOS) of HAT5 measured at T=80 K atIN6. Inset: Vibrational density of states for HAT5 - red circles, the ne-matic mixture E7 - blue stars [47] and for polymeric glass poly (methylphenyl siloxane) (PMPS) [45] - upward green triangles. Measurementswere carried out at T=80 K. The data for the different materials were notnormalized.

6.2.5 Vibrational Density of States (VDOS) in Dependence on the

Chain Length

Figure 6.53 gives the vibrational density of states (VDOS) for HAT5 in the plastic

crystalline state in the frequency range of the Boson peak. The VDOS is normalized to

the VDOS expected from the Debye theory of sound waves which gives g(ω) ∼ ω2. The

same procedure is applied for all VDOS under discussion in the course of this study.

As can be seen in the Figure this disoctic liquid crystal shows a Boson Peak (BP).

The BP which seems to be characteristic for a glassy behavior. This indicates that the

DLC under study here exhibits features of a glass, although in the DSC measurements

(see section 6.2.1) only a weak step-like change in the heat flow indicating a thermal

glass transition is observed.

The scattering used to calculate the VDOS results from the hydrogen atoms in the

alkyl chains in the intercolumnar space which have a more or less disordered structure

(see section 6.2.2). Therefore it can be reasoned that the observed glassy features are

linked to these regions. A comparison of the VDOS of HAT5 to the one reported for

“amorphous” polyethylene (PE) by Kanaya et al. [127] is made in Figure 6.54. Please

note that the “amorphous” VDOS used here was estimated for the amorphous regions

105

6 Results and Discussion

0.0 2.5 5.0 7.5 10.0

0.08

0.12

0.16

0.20

0.24

g(ω

) /

ω2 [ 1

03 p

s3]

ω [ps-1]

Figure 6.54: Vibrational density of states of HAT5 (empty red circles) and of “amor-phous” polyethylene (PE) (filled circles) given by Kanaya et al. in refer-ence [127]. The data for PE are scaled to collapse at the high frequencyside with the HAT5 data.

of semicrystalline polyethylene under constraint by or within the crystalline regions.

The data for PE were scaled to collapse at the high frequency side with the HAT5

data because no absolute values for g(ω)/ω2 are given in reference [127]. The Boson

peak of HAT5 is similar with regard to both its position and its shape with the data

estimated for PE. One can conclude that the VDOS of HAT5 where the alkyl groups

in the intercolumnar regions are monitored, coincides well to that for the CH2 groups

in the constraint amorphous regions of semicrystalline polyethylene.

The inset of Figure 6.53 compares the BP for HAT5 with the Boson Peak for the

amorphous polymeric glass former poly(methyl phenyl siloxane) (PMPS) and the ne-

matic glass of the liquid crystalline mixture E7. Firstly, the Boson peak for HAT5

appears to be comparatively weak with regard to PMPS and E7 while for PMPS it

is strongest. Secondly, an increase in the degree of molecular order takes place from

PMPS over E7 to HAT5 (amorphous glass, nematic glass, plastic crystal). Hence, it

can be concluded that the intensity of the Boson peak of a material is related to the

amount of order involved in the material, where with an increase of molecular order

the BP shifts to higher frequencies in position and decreases in intensity. The fact

that the position of the BP shifts to higher frequencies with increasing order of the

material under study might be explained by that the material becomes stiffer with an

increasingly better ordered structure.[128, 41]

Figure 6.55 presents the reduced density of states g(ω)/ω2 for HATn (n=5, 10, 12)

106

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0.0 2.5 5.0 7.5 10.00.08

0.12

0.16

0.20

0.24

0 5 10 15 20

0.0

0.1

0.2

0.3

HAT6

g(ω

) /

ω2 [10

3 p

s3]

ω [ps-1]

HAT5

HAT12

HAT10

g(ω

) /

ω2 [10

3 p

s3]

ω [ps-1]

HAT5

Figure 6.55: VDOS at T= 80 K for HAT. for different lengths of the alkyl chains: HAT5-circles, HAT10 -stars, HAT12 - diamonds. Inset: Boson Peak for HAT5- circles and HAT6 - squares. Lines are guides for the eyes. Taken fromown publication.[123]

in the frequency range of the BP. All HATn considered till here exhibit a weak but

well developed Boson peak (for HAT6 see the corresponding inset). The “hard” (stiff)

ordered columns formed by the triphenylene cores can be pictured to confine the “soft”

and flexible alkyl chains in between. Therefore one could compare this case from a phe-

nomenological point of view with the often investigated case of molecules embedded in

hard confining matrices. For hard confinement with decreasing pore size, the BP shifts

to higher frequencies and loses in its intensity particularly at its low frequency side

(see section 4.3). However, the contrary is observed for the HATn under study here:

the BP is shifted to lower frequencies and gains in intensity with increasing number

of side chain carbons. As the intercolumnar distance increases with n this can be dis-

cussed as a partial release of the self-organized confinement built up by the columns

onto methylene groups in between those columns: More precisely, the columns gener-

ate a self-organized confinement with regard to the intercolumnar space and therefore

also the akyl side chains. As a result the side chains are organized in between these

columns. The intercolumnar distance increases with n which resulting in a release and

weakening of the confinement whereas the systems transform from a stiff system to a

softer one.

This is depicted in more detail in 6.56 where the maximum frequency of the Boson

Peak ωBP shifts to lower frequencies with increasing n. The model of the release of

the self-organized confinement corresponds well to what is stated in references [41] and

107

6 Results and Discussion

4 5 6 7 8 9 10 11 12 13

1.0

1.5

2.0

2.5

3.0

ωB

P [ps

-1]

Number C-Atoms

rigid soft

Figure 6.56: Frequency of the Boson peak ωBP versus the number of carbon atom inthe side chains. Taken from own publication.[120]

[128]. The fact that for n=10, 12 the peaks are are much narrower than for n=5, 6

might further support this line of argument. Moreover one might consider the Schirma-

cher model [41]: the broad Boson Peak of HAT5 and HAT6 where the alkyl chains are

dominated by the rigid columns corresponds to an uncorrelated disorder. In the case

of HAT10 and HAT12 the alkyl chains are more free to organize themselves, occupy a

larger space and interact more with their neighbors. Therefore their elastic constants

are possibly stronger correlated compared to the shorter ones of HAT5 and HAT6. To

summarize, this means that the behavior for HAT10 and HAT12 corresponds to a cor-

related disorder while the data measured for HAT5 and HAT6 implies an uncorrelated

disorder. This line of argument is in accordance with the self-organized confinement

model considered above.

In contrast to the other materials HAT8 unexpectedly does not show a Boson Peak as

observed in Figure 6.57 which compares the VDOS reduced by ω2 for HAT8 with those

of HAT5 and HAT12. A clear explanation for this observation has not been found yet

and requires further studies by other techniques. In the line of the arguments of the

transition from an uncorrelated to a correlated disorder (with increasing n) one might

speculate that n=8 corresponds to transitional state between the two kinds of disor-

der. As mentioned in reference [41] for a critical value of the disorder parameter for the

uncorrelated state the calculations become unstable. This might possibly explain the

absence of a Boson Peak in HAT8. Moreover in the high frequency range the data for

HAT8 coincides with those of HAT5 and HAT6 which further affirms this argument.

108

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 5 10 15 20

0.0

0.1

0.2

0.3HAT8

HAT5

g(ω

)/ω

2 [10

3 p

s3]

ω [ps-1]

HAT12

Figure 6.57: VDOS of HATn with different lengths of the side chains: diamonds -HAT12, triangles - HAT8, circles - HAT5.

109

6 Results and Discussion

0.00 0.01 0.02 0.03 0.041.5

2.0

2.5

3.0

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

soft

ωB

P [

ps

-1]

1/d [nm-1]

rigid

g(ω

)/ω

2 [10

-3 p

s3]

ω [ps-1]

ωBP

Figure 6.58: Vibrational density of states of HAT6 in the bulk (black squares) andconfined to self-ordered AAO membranes with pore sizes 80 nm (greencircles), 40 nm (red stars) and 25 nm (blue diamonds). The lines areguides to the eyes. Inset: frequency of the Boson peak ωBP versus inversepore size.

6.2.6 Vibrational Density of States (VDOS) under Confinement

Figure 6.58 depicts the VDOS for HAT 6 in the bulk and in the confined state in the

frequency range of the Boson Peak normalized to the VDOS expected from the Debye

theory of sound waves which gives g(ω) ∼ ω2. Also for the confined HAT6 a Boson Peak

is found for all pore sizes under study. Consequently in consideration of the relevance of

the Boson Peak for glassy dynamics similar to the bulk the confined material exhibits

features of glasses down to the smallest pore size investigated here. In contrast to what

is observed for conventional glass forming systems under hard confinement (see 4.3),

for HAT6 the Boson Peak increases in intensity, becomes narrower and shifts to lower

frequencies with decreasing pore diameter. Therefore unlike stated for glasses under

confinement in reference [44] here the behavior of the Boson Peak in dependence on

the confinement size cannot be explained by a cut-off of sound waves. The inset of

Figure 6.58 gives the frequency of the maximum of the Boson Peak ωP versus inverse

pore diameter. As can be seen already from the VDOS for the different pore sizes,

the BP moves to lower frequencies until for small pore sizes a plateau value is reached.

Commonly this indicates a transformation from a more stiff and rigid system to a

softer one which in this case is a result of the confinement. As indicated by the results

from differential scanning calorimetry (see section 6.2.3), with decreasing pore size an

110

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

increasing amount of material has to be regarded as more or less disordered as indicated

by the pore size dependence of the phase transition enthalpies in the DSC experiments.

This means that for the confined material the elastic properties should be softer than

for the plastic crystalline state of the bulk material. Accordingly the modification of

the Boson Peak can be a result of a modification in the degree of order. The plateau

value found for pore sizes 40 nm and 25 nm implies that the elastic properties as well as

the degree of order of the confined systems are comparable at a lower pore size. A more

detailed analysis of the data requires the sound velocity for plastic crystalline HAT6

which unfortunately seems not to be available in the literature. As concluded from

the thermal data there is a liquid crystalline surface layer where the (homeotropic)

orientation of the molecules is different from the bulk-like planarly arranged molecules

in the pore center. Therefore one might regard the VDOS under the consideration of a

two phase model. According to reference [44] the VDOS gd(ω) observed for cylindrical

pores of a diameter d should be an average of the bulk VDOS gbulk and that of the

surface gsurf

gD(ω) = Vsurf

Vpore

gsurf(ω) + (1 − Vsurf

Vpore

) gbulk(ω) (6.3)

weighed by the respective volume fractions. In this case the ratio

gbulk(ω) − gd(ω)gbulk(ω) − g25nm(ω) ∼ Vsurf

Vpore

= dr2S(d/2)2

(6.4)

is expected to be independent of ω and proportional to the surface fraction Vsurf/Vpore

where rS is the thickness of the surface layer. The following procedure was carried out

to calculate the ratio: In order to obtain equidistant points and to slightly average the

experimental data, the points in the frequency range from 0.8 ps−1 to 1.8 ps−1 were

interpolated. Then the ratio defined by Equation (6.4) was calculated point by point

(inset Figure 6.59). In spite of the considerable scattering of the data it is obvious that

in the frequency range examined here the ratio predominantly does not depend on the

frequency.

Figure 6.59 plots the average ratio (arithmetic average using all points) versus inverse

pore diameter. At first glance the two phase model seems appropriate to describe the

data. However, a fit to these results delivers a value of 12.5 nm for the thickness of the

surface layer which corresponds to the pore radius of the smallest pore size. Firstly,

this value is much larger than that obtained from the analysis of the DSC data (see

section (6.2.3)). Secondly, the DSC data also demonstrate that a bulk-like phase which

is not part of an ordered surface layer remains down to a pore size of 25 nm. As a

result the simple two layer model is not in agreement with the results obtained by DSC

and cannot be applied to characterize the effect of hard confinement on HAT6.

111

6 Results and Discussion

0.8 1.0 1.2 1.4 1.6 1.8

0.4

0.8

1.2

0.00 0.01 0.02 0.03 0.04

0.0

0.4

0.8

1.2

(gB

ulk-g

d)

/ (g

Bulk-g

25

nm)

ω [ps-1]

(gB

ulk-g

d)

/ (g

Bu

lk-g

25

nm)

1/d [nm-1]

Figure 6.59: Ratios of the VDOS according to Equation (6.4). The main graph showsthe averages of the data in the frequency range ω = 0.8...1.8 ps−1. Theerror bars indicate the standard deviation of the average given in theinset. The dashed line is a fit to the data according to Equation (6.4).The inset gives the underlying values in dependence on ω: open squares -80 nm; grey circles - 40 nm. The lines indicate the averages.

Figure 6.60: Scheme of orientation of the pore axis with respect to the momentumtransfer vector q (scattering vector). ki and kf are the wave vectors of theincident and detected neutron beam in a neutron scattering measurement.

The orientation of the pore axis with respect to the q vector of the incident beam can

112

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 20 40 60 80 1000.0

0.1

0.2

0 5 10 15 20

0.0

0.1

0.2

0.3

0.4

<u

2>

[2]

T [K]

g(ω

)/ω

2 [10

-3 p

s3]

ω [ps-1]

Figure 6.61: Vibrational density of states of HAT6 confined to self-ordered AAO mem-branes with a pore sizes of 25 nm with parallel (open squares) and per-pendicular orientation (grey circles) of the pore axis with respect to theq vector of the incident beam at T=80 K. Lines are guides to the eyes.Inset: Temperature dependence of the mean-square displacement ⟨u2⟩ re-calculated from the vibrational densities of states according to equation(6.5): solid line - pore axis perpendicular to the q vector of the incidentbeam, dashed line - pore axis parallel to the q vector of the incident beam.The dashed-dotted line indicate ⟨u2⟩ at 80 K.

have an impact on the Boson Peak. Therefore HAT6 confined to pores with a diameter

of 25 nm was measured in two orientations of the pore axis parallel and perpendicular

to the q vector of the incident beam as can be seen in Figure 6.60. Compared to

a perpendicular orientation for the pore axis with respect to the incident beam the

reduced VDOS g(ω)/ω2 is slightly decreased for the pore axis parallel to the q vector

of the incident beam. To elucidate if this results barely from steric restriction of the

amplitudes caused by the confinement, the mean-square displacement ⟨u2⟩ due to the

vibrations was calculated from g(ω) according to reference [129]:

⟨u2⟩ = h

m∫ ωmax

0

g(ω)ω

coth( hω

2kBT)dω (6.5)

where ωmax is defined by the energy transfer limit of the TOF spectrometer which

suffices to encompass the complete vibrational spectrum. The result is given in the

inset of Figure 6.61. As the mean square displacement is significantly smaller than the

pore size (⟨u2⟩1/2 ≤ 0.06 nm), the lower values of the VDOS g(ω)/ω2 in parallel when

compared to the perpendicular orientation are probably not an effect of the pore size.

113

6 Results and Discussion

Even tough it was discussed above that a two layer model cannot be applied here, it

is hypothesized that the observed orientation dependence of the reduced VDOS is a

result of a boundary layer close to the pore walls. This is further supported by DSC

data which indicates the existence of an ordered surface layer and a layer of more or

less disordered molecules. Accordingly the effect of the orientation of the pore axis with

respect to the q-vector on the VDOS might possibly be attributed to these layers.

114

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 50 100 150 200 250 300

0.0

0.4

0.8

1.2

0 100 200 300 400

0

4

8

12

16Molecular mobility

in the plastic crystal phase

Onset of

Methyl group rotations

Vibrations

<u

2>

eff [

2]

T [K]

TCol,Iso

TCry,Col

<u

2>

eff [

2]

T[K]

Figure 6.62: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for HAT6. The dotted lines denote the phase transition tempera-tures obtained by DSC. The inset enlarges the temperature dependence of⟨u2⟩eff in the low temperature range up to a temperature of 300 K. Taken

from own publication.

6.2.7 Mean Squared Displacement in Dependence on the Chain

Length

The effective mean squared displacement ⟨u2⟩eff (T ) is extracted by a fractal model fit

[130] from the scattered intensities:

Iel(T )I0

= exp [−q2 ⟨u2⟩eff

(T )/3] (6.6)

The temperature dependence of the effective mean squared displacement ⟨u2⟩eff for

HAT6 is shown in Figure 6.62. Both phase transitions between the plastic crystalline

and the liquid crystalline as well as between the liquid crystalline and the isotropic

phase are also detected by neutron scattering. They appear as changes in the temper-

ature dependence ⟨u2⟩eff . The values for the phase transition temperatures estimated

from ⟨u2⟩eff (T ) here coincide well to the data obtained by DSC. (see section 6.2.1)

The temperature dependence of ⟨u2⟩eff in the low temperature range is depicted in

more detail in the inset of Figure 6.62. Changes in ⟨u2⟩eff (T ) indicate different dy-

namical processes: at low temperatures ⟨u2⟩eff is attributed to vibrations. The step in

⟨u2⟩eff at ∼ 100 K corresponds to the onset of methyl group rotations.[131] A further

change in the slope of ⟨u2⟩eff at T = 220 K implies larger scale motions due to the

115

6 Results and Discussion

0 100 200 300

0.0

0.4

0.8

1.2

180 210 240

0.2

0.4

0.6

<u

2>

eff [

2]

T [K]

<u

2>

eff [

2]

T [K]

Figure 6.63: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for open squares - HAT5, open circles - HAT6, open pentagons- HAT10 and open stars - HAT12 at lower temperatures in the plasticcrystalline phase. The inset enlarges the temperature range between 150K and 250 K.

CH2-groups within the plastic crystalline phase.

Figure 6.63 compares ⟨u2⟩eff for HAT5, HAT6, HAT10 and HAT12 for low temper-

atures. In this temperature range ⟨u2⟩eff is much smaller than the core-core distance

d: (⟨u2⟩eff)1/2 ≪ d (see Figure 6.29). Therefore ⟨u2⟩eff exhibits a more or less simi-

lar dependence for all HATn whereas above the characteristic temperature for methyl

group rotation the mean squared displacement slightly decreases with increasing side

chain lengths n (see the inset of Figure 6.63). This is due to the fact that the relative

amount of methyl groups increases with increasing n.

At higher temperatures in the liquid crystalline phase (see Figure 6.64) ⟨u2⟩eff is in

the order of magnitude of the core-core distance of the columns ((⟨u2⟩eff)1/2 <∼ d),

see inset of Figure 6.29). As already discussed in more detail for the VDOS of HATn

(see section 6.2.5), the methylene groups in the intercolumnar space can be regarded

as confined by the rigid stiff columns and are therefore constrained in their diffusion.

With increasing n, the core-core distance and the distance between the columns in-

creases. Therefore the alkyl chains can explore a wider space by diffusion. This can be

regarded as a release of a “self-organized” confinement generated by the columns with

regard do the alkyl chains. As a result the effective mean squared displacement ⟨u2⟩eff

increases with increasing n.

This is illustrated in more detail in the inset of Figure 6.64 which compares the mean

116

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

250 300 350 400 450

0

10

20

30

40

50

2.1 2.4 2.7 3.0

0.25

0.30

0.35

0.40

<u

2>

eff [

2]

T [K]

<u

2>

eff

1/2 [nm

]

Core-Core Distance dCC

[nm]

T=TCry, LC

+ 10 K

Figure 6.64: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for open squares - HAT5, open circles - HAT6 and open trian-gles - HAT8 at higher temperatures in the hexagonal ordered liquid crys-talline phase. Inset: Effective mean squared displacement ⟨u2⟩eff versus

the core-core distance in the liquid crystalline phase.

squared displacement ⟨u2⟩eff in dependence on the core-core distance: With increasing

n and therefore increasing core-core distance ⟨u2⟩eff increases until a plateau value is

reached.

117

6 Results and Discussion

0 80 160 240 320 400 480

0.0

0.3

0.6

0.9

1.2

Ela

stic Inte

nsity/E

lastic Inte

nsity

T=

30

K

T [K]

Vibrations

Methyl Group

Rotations

Phase Transitions

Dynamics

Tcry,col,bulk T

col,iso,bulk

Figure 6.65: Temperature dependence of the scattered elastic intensity for HAT6 in thebulk-red circles and in the confined state (40 nm - green triangles, 25 nm- blue stars) normalized to the elastic intensity at T=30 K. Open blackpentagons correspond to the empty membranes with a pore size of 40 nm.The dotted lines denote the bulk phase transition temperatures obtainedby DSC.

6.2.8 Mean Squared Displacement in the Bulk and in the

Confined State

In order to study how the underlying microscopic dynamics are effected by the con-

finement, HAT6 was embedded to self-ordered alumina membranes with different pore

sizes (80 nm, 40 nm and 25 nm). Figure 6.65 gives the elastic scattered intensity in

the q-range q = 1.15...1.85 versus temperature for HAT6 in the bulk as well as confined

to pore sizes 40 nm and 25 nm. Please note, that the scattered intensity has been

normalized to Iel = 1 for temperatures T < 30 K. Changes in the temperature depen-

dence of the mean squared displacement ⟨u2⟩eff correspond to phase transitions and

the onset of different microscopic dynamics. These are observed in the bulk as well as

under confinement. However at first glance the phase transitions between plastic and

liquid crystalline as well as between liquid crystalline and isotropic phase appear to be

smeared out under confinement.

This is investigated in more detail by considering the mean squared displacement

⟨u2⟩eff for HAT6 in the bulk and confined to pore sizes of 80 nm and 40 nm as shown

in Figure 6.66.

For a pore size of 80 nm the phase transitions are also detected under confinement,

118

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 100 200 300 400

0

4

8

12

16

<u

2>

eff [

2]

T[K]

Figure 6.66: Temperature dependence of the effective mean square displacement ⟨u2⟩eff

for HAT6 in the bulk-red circles and in the confined state (80 nm - greentriangles, 40 nm - blue stars). The dotted lines denote the bulk phasetransition temperatures obtained by DSC.

whereas for a smaller pore sizes of 40 nm it appears to be more smeared out.[132] Fur-

thermore ⟨u2⟩eff is reduced with respect to the bulk. As a result of the confinement

the diffusion of the methylene groups is more and more surpressed.

⟨μ2⟩eff for HAT6 in the bulk and confined to the pores with a size of 40 nm in the

lower temperature range corresponding to the plastic crystalline phase is depicted in

Figure 6.67. Here ⟨u2⟩eff is increased under confinement which is attributed to the

existence of a surface layer as supported by results obtained by DSC. While in the

pore center the molecules are more or less planarly arranged and more close to the

wall homeotropically, an additional more or less disordered amorphous surface layer

is observed near the pore walls. The relative amount of this boundary layer increases

with decreasing pore size. This is dissussed in more detail in section 6.2.3 and 6.2.6.

When approaching higher temperatures in the liquid crystalline and in the isotropic

phase (see Figure 6.68) ⟨u2⟩eff is reduced. In order to evidence the effect of the pore

orientation with respect to the q-vector of the incident beam, HAT6 confined to pores

with a diameter of 40 nm was measured in two different orientations of the pore axsis

parallel and perpendicular to the q-vector. As can be seen in Figure 6.69, for a per-

pendicular orientation with respect to the incident beam ⟨u2⟩eff is reduced after the

phase transition between plastic crystalline and liquid crystalline phase. This is not

an effect of the pore size itself because ⟨u2⟩eff is much smaller than the pore diameter.

However it might be an effect of the boundary layer.

119

6 Results and Discussion

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

1.0

1.2

<u

2>

eff [

2]

T [K]

Figure 6.67: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for HAT6 red circles - in the bulk and blue stars - confined tothe pores with a pore size of 40 nm in the low temperature range until300K.

250 300 350 400 450

0

4

8

12

16

Tcol,iso

<u

2>

eff [

Å2]

T[K]

Tcry,col

Figure 6.68: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for HAT6 red circles - in the bulk and blue stars - confined tothe pores with a pore size of 40 nm in the temperature range between 250K and 400 K.

120

6.2 Triphenylene-based Discotic Liquid Crystals-Hexakis(n-alkyloxy)triphenylene

(HATn)

0 100 200 300 400

0

4

8

12

16

<u

2>

eff [

2]

T[K]

Figure 6.69: Temperature dependence of the effective mean squared displacement⟨μ2⟩eff for HAT6 confined to the pores with a pore size of 40 nm withparallel orientation of the pore axis with respect to the incident beam -green stars, with perpendicular orientation of the pore axis with respectto the incident beam - red diamonds

121

6 Results and Discussion

6.3 Triphenylenebased Discotic Liquid

Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

6.3.1 Structure and Phase Transistions in the bulk

Figure 6.70 gives the DSC thermogram for HOT6 during heating and cooling. Like

Py4CEH and all HATn materials under study a hysteresis between heating and cooling

is observed. During the heating cycle two peaks are observed which correspond to

the phase transition between plastic and liquid crystalline phase (T=382 K) and to the

phase transtion between liquid crystalline and isotropic phase (T=391 K). Furthermore

there is an additional peak at 288 K.

This becomes more obvious in Figure 6.71 which gives the phase transition temper-

200 300 400

-1.0

-0.5

0.0

0.5

Heat flow

[W

/g]

T (K)

Tg?

Figure 6.70: DSC thermogram for HOT 6 in dependence on heating -red line and cool-ing -blue line.

atures for all phase transitions in dependence on the chain length. While for HOT6

only two peaks are found, the number of observed phase transitions increases with the

chain length.

In accordance with references [110, 133], where for similar alkanoyloxy triphenylene

derivatives besides several plastic crystalline phases different liquid crystalline colum-

nar phases with a different 2D organization of the cores/columns are reported, the first

peak is attributed to a phase transition between different plastic crystalline phases,

122

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

6 8 10 12

330

360

390

Ttr

ans [K

]

n

Figure 6.71: Phase transition temperatures in dependence on the number n of C-Atomsin the alkyl chain during heating: red circles- transition betweeen differentplastic crystalline phases, black squares-transition between plastic crys-talline and liquid crystalline phases, blue triangles- transition betweendifferent liquid crystalline phases, green pentagons between liquid crys-talline and isotropic phases.

the peaks in the middle temperature range to the phase transition between plastic and

liquid crystallline phase as well as between different columnar phases. The highest

temperature corresponds to the phase transition to the isotropic phase and remains

more or less independent of the chain length. The phase transistion temperatures be-

tween the plastic crystalline phase first decrease and then increase again with n.

The phase transition enthalpies for both phase transitions during heating and cool-

ing are shown in Figures 6.73 and 6.74. Similar to the HATn DLC series (see section

6.2.1), the phase transition enthalpies for the phase transition between the liquid crys-

talline and the isotropic phase (see Figure 6.74) is lower than between the plastic

crystalline and the liquid crystalline phase. For the phase transition between the liq-

uid crystalline and the isotropic phase the transistion enthalpies first increase until a

maximum is reached for n=8 after which they decrease again. As the phase transitions

between the plastic crystalline and the liquid crystalline phase as well as between the

different liquid crystalline phases are very complicated, only the sum of the transition

enthalpies is considered in Figure 6.73. With increasing chain length n an increase in

the transition enthalpies is observed. This might be due to the increasing number of

phase transitions with increasing n as can be deduced from Figure 6.71.

123

6 Results and Discussion

6 8 10 12

280

320

360

400

Ttr

an

s [K

]

n

Figure 6.72: Phase transition temperatures in dependence on the number n of C-Atomsin the alkyl chain during cooling: black squares - phase transition betweenplastic crystalline and liquid crystalline phase, green pentagons- phasetransition between liquid crystalline and isotropic phase.

6 8 10 12

10

20

30

40

50

60

70

∆H

me

so[J

/g]

n

Figure 6.73: Sum of the phase transition enthalpies of the phase transition betweenplastic crystalline and liquid crystalline and for the phase transition be-tween different liquid crystalline phases in dependence on the number nof C-Atoms in the alkyl chain: Red circles - heating, open blue pentagons- cooling.

124

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

6 9 12

1.6

2.0

2.4

∆H

iso [J/g

]

n

Figure 6.74: Phase transition enthalpies for the phase transition between liquid crys-talline and isotropic phase in dependence on the number n of C-Atoms inthe alkyl chain: Red circles - heating, open blue pentagons - cooling.

125

6 Results and Discussion

0 5 10 15 20 25 30 35

log (

I/I m

ax)

q [nm-1]

Figure 6.75: X-ray diffractogramm for HOT6 in the different phases: black line-plasticcrystalline phase (T=299 K), red line - liquid crystalline phase (T=385K) and blue line - isotropic phase (T=423 K)

6.3.2 Structure in the Different phases

The structure of the Hexakis(n-alkanoyloxy)triphenylene HOTn DLCs was investigated

by means of X-ray Scattering. Figure 6.75 gives as an example the X-ray diffrac-

togramm for HOT6 in the plastic crystalline, one of the liquid crystalline phases and

the isotropic phase. Similar to the HATn materials the spectra for the plastic crys-

talline exhibits many reflections in the whole q-range and and the most pronounced

peak at q = 4.42 nm−1. Also an amorphous halo in the q-range between 10 nm−1 and 25

nm−1 is observed which is attributed to a certain amount of disorder within the system

like for the HATn discotic liquid crystals (see section 6.2.2). Due to the similarities for

the HOTn materials it is also assumed that the cores organize into columns whereas

the distance in between those columns increases with increasing n.

The X-ray spectrum corresponding to the liquid crystalline mesophase exhibits a re-

flection at qmax=3.44 nm−1 corresponding to the core-core distance of the triphenylene

cores.[2] Higher order reflections occur but not at q values ∼ √3qmax. Therefore no

hexagonal ordering is assumed in the case of HOT6. The broad amorphous halo cor-

responding to the disordered structure of the alkyl chains in the intercolumnar space

is slightly shifted to lower q values than found for the plastic crystalline phase. A

reflection at q =2.8 nm−1 which is broad when compared to the liquid crystalline phase

and an amorphous halo indicate a column-like ordering also in the isotropic phase. An

analogous behaviour is found for all HOTn under study.

126

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

0 5 10 15 20 25 30 35

log (

I/I 0

)

q [nm-1]

Figure 6.76: X-ray diffractogram for the HOTn materials at a temperature correspond-ing to the columnar hexagonal mesophase: black line - n=6 (T=385 K),red line - for n=8 (T=333 K), green line - n=10 (T=345 K), blue line n=12(T=354 K). The curves are shifted on the y-scale for sake of clearness.

The diffractogram corresponding to the liquid crystalline mesophases for all HOTn

2 4 6 8 10 12 14

1.0

1.5

2.0

2.5

3.0

3.5

dC

C [n

m]

n

all trans

Figure 6.77: Distance versus number of C-Atoms for HOTn -blue circles and HATn -green triangles. The star corresponds to the value found for Py4CEH.The straight line corresponds to data for a single alkyl chain in all transconformation.[119]

127

6 Results and Discussion

under study is shown in Figure 6.76. In the q-range below 5 nm−1 a prominent reflec-

tion is detected for each material. With increasing chain length this peak moves to

lower q-values and larger distances.

Figure 6.77 gives the values for the intercolumnar distance calculated from equation

(5.20) for the HOTn materials in the liquid crystalline phase and compares them to

those obtained for the HATn materials. Similar values are obtained for both series of

triphenylene-based discotic liquid crystals.

128

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

6.3.3 Molecular Dynamics in Dependence on the Chain Length

-2

0

2

4

6

-2

-1

0

1

2

200

250

300

log ε

''

T [K]log (f[Hz])

α

β

Figure 6.78: Dielectric loss ǫ′′

in dependence on frequency and temperature in a 3Drepresentation while heating.

Figure 6.78 shows the dielectric loss ǫ′′

for HOT6 in dependence on frequeny and tem-

perature. Like for the HATn materials, for HOT6 three processes were observed, an

α-relaxation, a β-relaxation as well as a conductivity process.

A similar analysis as for Py4CEH is carried out: the HN equation (5.10) is fitted to

the dielectric loss ǫ′′

for α- and β-relaxation. Figure 6.79 compares the relaxation rates

obtained for HOT6 to those for HAT6.

The β-relaxation also follows an Arrhenius-type temperature dependence and is shifted

to higher temperatures with respect to HAT6. By means of equation (4.8) the acti-

vation energy is calculated to 33.4 kJ mol−1 which is higher than obtained for HAT6.

This difference might be a result of the differences in the structure: for HOT6 the alkyl

chains are linked through an ester group to the triphenylene core and therefore more

confined in between the columns.

The dielectric strength ∆ǫβ for the β-relaxation is given in the inset of Figure 6.80. At

first ∆ǫβ increases until reaching a maximum at T=200 K where a step is observed in

the heat flow in the DSC experiments (see section 6.3.1). This is followed by a decrease

which might be due to an increasing order with increasing temperature. In the vicinity

of the assumed glass transition temperature there seems to be a kink in ∆ǫβ.

The α-relaxation of HOT6 occurs in the same temperature and frequency range as

for HOT6, however the shape is slightly different. In contrast to HAT6 it appears

more curved versus 1/T . This is investigated in more detail by means of the derivative

129

6 Results and Discussion

2 3 4 5 6 7

-2

0

2

4

6

8

2 3 4 5 6 7

-2

0

2

4

6

8

log

(f m

ax[H

z])

1000/T [K-1]

β

α

1000/T [K-1]

Figure 6.79: Relaxation map of HOT6 in comparison to HAT6: red pentagons - α-relaxation of HAT6, red stars - β-relaxation of HAT6, red downward tri-angles - conductivity of HAT6, black circles - α-relaxation of HAT6, blackupward triangles - β-relaxation of HOT6, black squares - conductivity ofHOT6.

technique as already applied for Py4CEH and HATn materials (see sections 6.1.2 and

6.2.4).

Figure 6.81 gives (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of

HOT6. For HOT6 two different temperature regimes can be identified by two straight

lines. For temperatures above T=220 K the line intersects with the point of origin.

Therefore it is concluded that in this temperature range fmax,α follows an Arrhenius-

type temperature dependence. For temperatures below T=220 K the plot follows a

straight line and intersects on the x-axis at the Vogel-Temperature T0=140 K. As a

result, in this temperature range the temperature dependence α-relaxation might be

described by the VFT-equation which is characteristic for glassy dynamics. Similar

to HATn the α-relaxation is assigned to segmental motions of the alkyl chains in the

intercolumnar space. A transition from Arrhenius to VFT behavior is characteristic

for molecular dynamics under nanoscale confinement. Analogously to HAT6 in the low

temperature range the size of a Cooperatively Rearranging Region (CRR) is smaller

than the intercolumnar distance leading to glassy dynamics whereas at higher temper-

atures the CRR has become to small to enable glassy dynamics.

Similar to ∆ǫβ the dielectric strength ∆ǫα for the α-relaxation first increases until a

maximum at T=250 K followed by a decrease. The decrease is more pronounced than

predicted by equation (5.15) which in addition to the VFT behavior of fmax,α is also

130

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

150 200 250 300

0.3

0.6

0.9

1.2

1.5

∆ε α

T [K]

150 200 250

0.0

0.7

1.4

∆ε β

T [K]

Figure 6.80: Dielectric strength ∆ǫα for the α-relaxation of HOT6 in dependence ontemperature. Inset: Dielectric strength ∆ǫβ for the β-relaxation of HOT6in dependence on temperature.

0 50 100 150 200 250 300

0

1

2

3

4

5

6

d lo

g (

f Ma

x,α [H

z])

/ d

T [K

]-1

/2

T [K]

T0=144 K

Figure 6.81: (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of HOT6.Straight lines denote a linear regression to the data. The arrow denotesthe Vogel-Temperature T0.

typical for glassy dynamics.

Figure 6.82 gives the relaxation map of all HOTn materials under study. An α-

relaxation is observed only for HOT6. All discotic liquid crystals exhibit at least a

131

6 Results and Discussion

2 4 6

0

4

8

log

(f m

ax [H

z])

1000/T [K-1]

Figure 6.82: Temperature dependence of the relaxation rates in dependence on 1000/T:red circles - HOT6, green triangles - HOT8, violet pentagons - HOT10,blue stars - HOT12

β-relaxtion in the low temperature range of the plastic crystalline phase. For HOT8

and HOT 10, two β-relaxations are observed, for HOT12 only one β-process is found.

The β-relaxation follows an Arrhenius-like temperature dependence and the activation

energies as calculated by means of Equation (4.8) are given in Table 6.4. Figure 6.83

compares the activation energies of the HATn and the HOTn materials. Like for the

HATn DLCs for the process located at lower temperatures EA,β first decreases unil

a minimum followed by an increase. This is attributed in a similar manner to the

counterbalance between the release of the self-organized confinement of the columns

(shorter chain lengths) and the convergence to a Polyethylene-like behavior (longer

chain lengths). For the second β-relaxation at higher temperatures for HOT8 44.04 kJ

mol−1 and for HOT10 37.07 kJ mol−1 are obtained.

The conductivity process in the high temperature range is detected for all HOTn ma-

terials. It is analysed by fitting the HN-function to the peak observed in the imaginary

part of the complex Modulus M′′. The relaxation rates fmax,con follow an Arrhenius-

like temperature dependence with different activation energies in the different phases

similar to HATn and Py4CEH as shown in table 6.4.

132

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

6 8 10 12

20

30

40

EA

,β [kJ m

ol-1

]

n

Figure 6.83: Activation energies for the β - relaxation for HOTn in dependence on thechain length: red circles - HOTn, red triangles - second β-relaxation ofHOTn, blue squares - HATn.

HOTn EA,β EA,cond,meso1 EA,cond,meso2 EA,cond,iso

kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1

HOT6 33.4 92.6 174.5 53.6HOT8 24.7 97.5 102.4 57.6HOT10 20.6 90.4 72.3 52.7HOT12 29.9 117.2 59.4 9.6

Table 6.4: Activation energy for the β-relaxation and the conductivity process in thedifferent temperature ranges as indicated.

133

6 Results and Discussion

0 5 10 15 20

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

g(ω

) /

ω2 [ps

-3

]

ω [ps-1]

0 5 10 15 20

g(ω

) /

ω2 [ps

-3

]

ω [ps-1]

Figure 6.84: Vibrational density of states (VDOS) of HOT6. Arrows are guides to theeyes. Inset: Vibrational density of states for HOT6 - red circles, HAT6 -open stars. The data for the different materials were normalized to themaximum of the y-value of the Boson Peak.

6.3.4 Vibrational density (VDOS) in Dependence on the Chain

Length

The vibrational density of states (VDOS) normalized to the VDOS expected from the

Debye theory of sound waves (g(ω) ∼ ω2) in the frequency range of the Boson peak for

HOT6 as measured by neutron scattering is presented in Figure 6.84. As the HATn

materials in the plastic crystalline phase this discotic liquid crystal shows a Boson peak

(BP) which seems to imply glassy dynamics. Accordingly, it can be reasoned that in the

plastic crystalline phase HOT6 exhibits features which resemble a glass. These features

are linked to the intercolumnar space as neutron scattering detects the dynamics of the

hydrogen atoms in the alkyl chains which are located in the intercolumnar space and

more or less disordered (see results obtained by X-ray scattering). In order to compare

the Boson Peak of the two different series of triphenylene-based discotic liquid crystals,

the VDOS of HOT6 and HAT6 are plotted in the inset of Figure 6.84. Whereas for

both materials a Boson Peak (BP) is observed, the BP for HOT6 is broader and shows

kind of a double peak/fine structure. One peak is located at the same position as

the one found for HAT6 and the second peak is broader and positioned at slightly

higher frequencies. Such behavior has been reported in the literature for gylcerol [134]

as well as other glassformers [135, 136, 137] and requires further investigations. One

might speculate, that this difference might be due to a difference in the microstructure.

134

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

0 5 10 15 20

1.0x10-4

2.0x10-4

3.0x10-4

0 5 10 15 20

7.0x10-5

1.4x10-4

2.1x10-4

2.8x10-4

g(ω

) /

ω2 [ps

-3

]

ω [ps-1]

g(ω

) /

ω2 [ps

-3

]

ω [ps-1]

Figure 6.85: Vibrational density of states (VDOS) of HOT6 - red circles, HOT8 - bluesquares. Inset VDOS for HOT10 -green pentagons and HOT12 -blue stars

In contrast to the HATn materials for the HOTn liquid crystals the alkyl chains are

linked through an ester group to the triphenylene group. This might provide the alkyl

chains with a higher mobility resulting in different lateral extent of the vibrations and

therefore additional contributions to the VDOS. Figure 6.85 gives the VDOS for HOT6,

HOT8 and HOT10. At first glance the behaviour of the HOTn materials seems to more

or less coincide with the one found for the HATn materials. For all HOTn under study

a Boson peak is observed, whereas similar to HOT6 a double peak structure is found.

From n=6 to n=8 the contribution of the Boson Peak at lower frequencies shifts to

even lower frequencies and higher intensities. Analogously to the HATn liquid crystals,

this can be explained by a release of the “self-organized confinement” imposed by the

stiff and rigid triphenylene cores unto the alkyl chains. However for n=10 and n=12

only the contribution of the second peak at higher frequencies can be identified where

no clear dependence on n is observed.

135

6 Results and Discussion

0 100 200 300 400

0

5

10

15

20

0 100 200 300 400

0

4

8

12

16

TCol, Iso

<u

2>

eff [

2]

T [K]

TCry, Col

Molecular mobility

in the plastic

crystal phaseOnset of

Methyl group rotationsVibrations

<u

2>

eff [

2]

TCol,Iso

TCry,Col

T[K]

Figure 6.86: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for HOT6. The dotted lines denote the phase transition temper-atures obtained by DSC. Inset: Temperature dependence of the effectivemean squared displacement ⟨u2⟩eff for HAT6.

6.3.5 Mean Squared Displacement in Dependence on the Chain

Length

Figure 6.86 shows the the effective mean squared displacement ⟨u2⟩eff for HOT6 which

follows a similar dependence as obtained for the HATn materials. As an example the

effective mean squared displacement of HAT6 is given in the inset for comparison. The

phase transitions of HOT6 can be detected in ⟨u2⟩eff as well as the different regimes of

molecular mobility: e.g. the vibrations at very low temperatures, the onset of methyl

group rotations at 150 K and larger scale motions within the plastic crystalline phase

at ∼ 220 K. In addition a step at 300 K is observed which resembles features of a ther-

mal glass transition. This corresponds well to the fact, that a Boson Peak indicating a

glass transition is observed for this material. For the phase transition between plastic

and liquid crystalline phase ⟨u2⟩eff increases but the increase is less pronounced than

for HAT6. For the transition to the isotropic phase the step is more pronounced.

Figure 6.87 gives the elastic scans for all HOTn under study. Above the characteristic

temperature for methyl group rotation as a result of the decreasing relative amount

of methyl groups ⟨u2⟩eff decreases with increasing chain length but more pronounced

than for the HATn materials.

Like for the HATn DLCs, in the liquid crystalline phase, ⟨u2⟩eff increases with increas-

ing n due to a release of this “self-organized” confinement with increasing chain length

136

6.3 Triphenylenebased Discotic Liquid Crystals-Hexakis(n-alkanoyloxy)triphenylene

(HOTn)

0 100 200 300 400

0

30

0 90 180 270

0

1

2

3

TCry1, Cry2

TColh, Iso

TCry2, Colh

<u

2>

[2]

T [K]

<u

2>

[2]

T [K]

Figure 6.87: Temperature dependence of the effective mean squared displacement⟨u2⟩eff for all HOTn under study in the high temperature range betweenT=250 K and T=410 K: red circles - HOT6, green triangles - HOT8, vio-let pentagons - HOT10, blue stars - HOT12. The dotted lines denote thephase transition temperatures for HOT6 obtained by DSC. Inset: Tem-perature dependence of the effective mean square displacement ⟨u2⟩eff forall HOTn under study in the low temperature range up to T=300 K: redcircles - HOT6, green triangles - HOT8, violet pentagons - HOT10, bluestars - HOT12.

1.8 2.1 2.4 2.7 3.0 3.3

0.15

0.20

0.25

0.30

0.35

0.40

0.45

<u

2>

eff

1/2 [n

m]

Core-Core Distance d [nm]

T=TCry, LC

+ 10 K

Figure 6.88: Effective mean squared displacement ⟨u2⟩eff versus the core-core distancein the liquid crystalline phase: Square- HATn; Circles - HOTn. Dashedlines are guides for the eyes.

137

6 Results and Discussion

and core-core distance. Figure 6.88 compares the mean squared displacement ⟨u2⟩eff in

dependence on the core-core distance for the HATn and HOTn materials in the liquid

crystalline phase: For both series of triphenylene-based discotic liquid crystals ⟨u2⟩eff

increases with the core-core distance until a plateau value is reached.

138

7 Summary

In the course of this work, the structure and dynamics of several discotic liquid crys-

tals (DLCs) were investigated in detail. Different techniques (Differential Scanning

Calorimetry, X-ray Scattering, Dielectric Relaxation Spectroscopy, Specific Heat Spec-

troscopy, Neutron Scattering) were applied whereas each technique is sensitive to a

different probe. For selected DLCs the impact of nanoscale confinement on the phase

transitions and dynamics for two DLCs as an example was studied.

This thesis focusses on the structure as well as the dynamics of two series of triphenylene-

based discotic liquid crystals (Hexakis(n-alkyloxy)triphenylene (HATn materials) and

Hexakis(n-alkanoyloxy) triphenylene (HOTn materials) and one pyrene-based discotic

liquid crystal (Py4CEH).

An α-relaxation was observed for Py4CEH by dielectric relaxation spectroscopy. Two

different VFT dependencies with different Vogel temperatures and fragilities were found

for the plastic and the liquid crystalline phase in the dielectric data. The glassy dynam-

ics were evidenced by specific heat spectroscopy. Two different Vogel-Fulcher-Tammann

(VFT)-dependencies were obtained by the two different techniques as a result of the

different restrictions of the molecular fluctuations close to the columns (dielectric spec-

troscopy) and the groups located more in the intercolumnar space (specific heat spec-

troscopy). From the specific heat capacity data a correlation length for glassy dynamics

is calculated which correlates well with structural data.

For charge transport in the high temperature range different activation energies are

observed in the liquid crystalline and the isotropic phases.

When confined to anodic aluminum membranes with four different pore diameters d (d

= 25, 40, 80, 180 nm) for both phase transitions of Py4CEH the peak of the bulk tran-

sition splits up into two peaks. This indicates different phase structures in the pore

center and close to the wall. A decrease in the phase transition temperatures with

decreasing pores size was found for the phase in the pore center which was described

by means of the Gibbs-Thomson equation. The phase transition temperatures of the

phase close to the wall remains independent of the pore size. Furthermore, a decrease

in the transition enthalpies with decreasing pore sizes was found for both phase transi-

tions which implies an increase of confined disordered material which does not undergo

139

7 Summary

the phase transitions. A critical pore size for which the whole material inside the pores

is completely disordered was estimated to ca. 20 nm for both phase transitions.

In the dielectric measurements a peak is observed which corresponds to the α-relaxation

as also found for the bulk material. At the phase transition the temperature depen-

dence of the relaxation rates changes allowing to define and estimate a dielectric phase

transition temperature.

The structure and phase behavior of the HATn materials (n=5, 6, 8, 10, 12) in the

bulk state is studied by means of X-ray Scattering, Differential Scanning Calorimetry

(DSC). In the liquid crystalline phase, the scattering pattern for all materials shows

a sharp Bragg-reflection corresponding to the intercolumnar distance in the lower q-

range. In the higher q-range, a reflection corresponding to the stacking of the cores

within one column and a broad amorphous halo linked to the disordered structure of

the methylene groups in the side chains are observed. In the plastic crystalline phase

a similar structural arrangement is assumed, these alkyl chains form a nanophase sep-

arated state between the columns.

DSC measurements were carried out on HATn materials (n=5, 6, 10, 12) confined to

self-ordered alumina oxide membranes with different pore sizes. The influence of chain

length and confinement on the phase transitions is discussed in more detail: In con-

finement the two phase transitions between plastic crystalline and hexagonal ordered

phase at lower and from the latter to an isotropic state at higher temperatures are

also observed. Different phase structures close to the wall and in the pore center are

evidenced by additional peaks in the heat flow. The temperature of the former peaks

is independent of the pore size. However, the depression of the phase transition tem-

peratures of the latter ones can be described by the Gibbs-Thomson-equation for the

phase transition between the liquid crystalline phase for all HATn under study. With

decreasing pore size for both phase transitions the transition enthalpies decrease. This

implies an increase in the amount of disordered amorphous material inside the pore

which does not undergo the phase transition. The critical pore size dcri estimated for

phase transformation for the liquid crystalline to the isotropic phase from the pore

size dependence of the transition enthalpies for each material increases with increasing

chain length. By considering the difference in the dcri of the bulk-like phase in the

center of the pores and the dcri considering the complete amount of material undergo-

ing the phase transition, the thickness of the surface layer can be estimated. For the

thickness of the surface layer comparable values are obtained for all n under study.

The molecular dynamics of the bulk materials have been studied by means of dielectric

relaxation spectroscopy and neutron scattering.

All HATn under study exhibit a β-relaxation at low temperatures which is followed

by α-relaxation and a conductivity contribution in the high temperature range. The

140

relaxation rates of the β-relaxation are described by means of the Arrhenius equa-

tion. A self-organized confinement model, where the confinement is generated by the

columns to the intercolumnar space, where with increasing n the confinement is weak-

ened, was developed to describe the different processes. The chain length dependence

of the estimated activation energies is explained by a counterbalance between a release

of self-organized confinement and polyethylene-like behavior. The temperature depen-

dence of the α-relaxation rates changes with increasing n from an almost linear to a

VFT-like temperature dependence approaching the behavior observed for poylethylene.

In the case of the relaxation rate of HAT6 thhe temperature dependence is more com-

plicated and changes with increasing temperature from an Arrhenius-type temperature

dependence to a VFT-dependence to an Arrhenius-type temperature dependence.

For the HATn materials a Boson Peak (BP) is observed for n=5, 6, 10, 12. The BP

shifts to lower frequencies and gains in intensity with increasing lengths n of the side

chains. This is discussed employing the model of a self-organized confinement. The

peaks for n=10, 12 are much narrower than for n=5, 6 which might imply the transfor-

mation from a rigid system to a softer one with increasing chain length. In agreement

with the model of the self-organized confinement, the results can be also discussed in

the framework of a transition from uncorrelated to a correlated disorder with increasing

n where n=8 might be speculatively considered as a transitional state.

For HAT6 confined to the pores with three different pore diameters (d=25, 40, 80 nm)

a Boson Peak is observed under confinement. The BP which shifts to lower tempera-

tures and gains in intensity with decreasing pore size. This is explained by a decrease

of order in the material in the pores.

The structure and dynamics of HOTn materials (n=6, 8, 10, 12) is similar to the

HATn materials in some aspects and differs in others. A similar structure is obtained

by means of X-ray scattering and the intercolumnar distance increases linearly with

increasing n. However the data obtained by differential scanning calorimetry reveals

several plastic crystalline as well as liquid crystalline phases indicated by additional

peaks in the heat flow.

Conductivity and β-relaxation are observed for all HOTn under study, an α-relaxation

only for HOT6. The former are described by means of the Arrhenius equation yielding

similar results to HATn. For the α-relaxation of HOT6 the temperature dependence

of fmax,α changes from an Arrhenius to a VFT-behavior with decreasing temperature.

This result is explained under consideration of the structure of the DLC as well as the

Cooperativity approach to glassy dynamics.

All HOTn materials(n=6,8,10,12) exhibit a Boson Peak but with an additional contri-

bution at higher frequencies. The former seems to increase in intensity and shift to

lower frequencies whereas the latter shows no clear dependence on the chain length.

141

7 Summary

Elastic scans were carried out for all HATn and HOTn materials under study in the

bulk as well as for HAT6 confined to three different pore sizes to monitor the molecular

dynamics on a time scale of nanoseconds.

142

8 Publications

8.1 List of Peer-Reviewed Publications

1. C. Krause, H. Yin, C. Cerclier, D. Morineau, A. Wurm, C. Schick, F. Emmerling

and A. Schönhals, Molecular Dynamics of a Discotic Liquid Crystal Investigated

by a Combination of Dielectric Relaxation and Specific Heat Spectroscopy, Soft

Matter, 2012, 8, 11115-11122

2. C. Krause and A. Schönhals, Phase Transitions and Molecular Mobility of a

Discotic Liquid Crystal under Nanoscale Confinement, The Journal of Physical

Chemistry C, 2013, 117, 19712-19720

3. C. Krause, R. Zorn, F. Emmerling, B. Frick, P. Huber, J. Falkenhagen, and A.

Schönhals, Vibrational Density of States of Triphenylene Based Discotic Liquid

Crystals: Dependence on the Length of the Alkyl Chain, Physical Chemistry

Chemical Physics, 2014, 16, 7324-7333

4. C. Krause, R. Zorn, B. Frick and A. Schönhals, Thermal Properties and Vibra-

tional Density of States of a Nanoconfined Discotic Liquid Crystal, Colloid and

Polymer Science, 2014, 292, 1949-1960

5. C. Krause, R. Zorn, B. Frick and A. Schönhals, Quasi-elastic and Inelastic Scat-

tering to Investigate the Molecular Dynamics of Discotic Molecules in the Bulk,

QENSWINS2014 proceedings, accepted

6. A. V. Kityk, M. Busch, D. Rau, S. Calus, C. V. Cerclier, R. Lefort, D. Morineau,

E. Grelet, C. Krause, A. Schönhals, B. Frick and P. Huber, Thermotropic Orienta-

tional Order of Discotic Liquid Crystals in Nanochannels: an optical Polarimetry

Study and a Landau-de Gennes Analysis, Soft Matter, 2014, 10, 4522-4534

143

8 Publications

8.2 List of Talks

1. C. Krause, H. Yin, A. Wurm, C. Schick and A. Schönhals, Molecular Dynamics

of a Discotic Liquid Crystal Studied by Dielectric Relaxation and Specific Heat

Spectroscopy, DPG-Frühjahrstagung der Sektion Kondensierte Materie (SKM),

Regensburg, March 2013

2. C. Krause, H. Yin, A. Wurm, C. Schick and A. Schönhals, Glassy-Like Dynamics

in a Discotic Liquid Crystal Revealed by Broadband Dielectric and Specific Heat

Spectroscopy, 7th. Int. Discussion Meeting on Relaxations in Complex Systems,

Barcelona, Spain, July 2013

8.3 List of Posters

1. C. Krause, H. Yin and Andreas Schönhals, Investigation of Discotic Liquid Crys-

tals, DPG Frühjahrstagung der Sektion AMOP (SAMOP) und der Sektion Kon-

densierte Materie (SKM), Dresden, March 2011

2. C. Krause, B. Frick, R. Zorn and A. Schönhals, Neutron Scattering on Discotic

Liquid Crystals in the Bulk and in the Nanoconfined State, DPG-Frühjahrstagung

der Sektion Kondensierte Materie (SKM), Berlin, March 2012

3. Christina Krause, Huajie Yin and Andreas Schönhals, Glassy dynamics in Pyrene-

1,3,6,8-tetracarboxylic tetra(2-ethylhexyl)esther studied by Differential Alternat-

ing Current Chip Calorimetry and Dielectric Relaxation spectroscopy, DPG-

Frühjahrstagung der Sektion Kondensierte Materie (SKM), Berlin, March 2012

4. C. Krause, F. Emmerling and A. Schönhals, Triphenylene-Based Discotic Liquid

Crystals, 7th BDS/IDS Conference, Leipzig, September 2012

5. C. Krause, H. Yin, A. Wurm, C. Schick and A. Schönhals, Molecular Dynamics

of a Discotic Liquid Crystal, 7th BDS/IDS Conference, Leipzig, September 2012

6. Christina Krause, Huajie Yin and Andreas Schönhals, Vibrational Density of

States and Molecular Dynamics of Discotic Liquid Crystals in the Bulk and in the

Nanoconfined State Investigated by Neutron Scattering, DPG-Frühjahrstagung

der Sektion Kondensierte Materie (SKM), Regensburg, March 2013

144

9 List of Abbreviations, Symbols and

Constants

List of Abbreviations

Al AluminumCC Cole/Cole functionCD Cole/Davidson functionCRR Cooperatively Rearranging RegionDLC Discotic Liquid CrystalDRS Dielectric Relaxation SpectroscopyDSC Differential Scanning CalorimetryHATn Hexakis(n-alkyloxy)triphenyleneHN Havriliak-Negami EquationHOTn Hexakis(n-alkanoyloxy)triphenyleneKWW Kohlrausch-Williams-Watts EquationLC Liquid CrystalNS Neutron ScatteringMW Molecular WeightPy4CEH Pyrene-1,3,6,8-tetracarboxylictetra(2-ethylhexyl)esterSHS Specific Heat SpectroscopyTGA Thermogravimetric AnalysisVDOS Vibrational Density of StatesVFT Vogel-Fulcher-Tammann Equation

145

9 List of Abbreviations, Symbols and Constants

List of Symbols

cp Specific Heat Capacityd Pore diameterdCC Core-Core DistanceEA Activation EnergyC CapacitanceE Electric Field∆E Energy Transfer∆ǫ Dielectric Strengthǫ∗ Complex Dielectric Functionǫ′; ǫ′′

Real and Imaginary Part of the Complex Dielectric Functionf Frequencyfmax,α; fmax,β; fmax, Relaxation rates for α-relaxation, β-relaxation and conductivityIel; I0 Elastically Scattered Intensity and Low Temperature Limit of

the Elastically Scattered Intensityki; lf Incident and Final Wave Vectors of the Neutron Beam⟨u2⟩eff Mean Squared Displacement

λ wavelengthM Complex ModulusM

′; M

′′Real and Imaginary Part of the Complex Modulus

P Polarizationq Scattering Transfer VectorS Scattering Functionσ Scattering Cross SectionTg Glass Transition TemperatureTg Vogel Temperatureτ Relaxation TimeΩ Space Angle of Detectionω Angular Frequencyη Viscosityζ Cooperative Length of a CRR

List of Constants

kB Boltzmann ConstantR Ideal Gas Constant (R=8.314 Jmol−1K)ǫ0 Dielectric Permittivity Constant in Vacuum (ǫ0 = 8.854 ∗ 10−12AsV−1K)NA Avogadro Number (NA = 6.022 ∗ 1023mol−1)

146

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155

List of Figures

List of Figures

4.1 Different Phases of liquid crystals . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Discotic liquid crystals in the columnar phase . . . . . . . . . . . . . . . . 16

4.3 Overview on the dynamics ocurring at the glass transition. a) Dielectric

loss ǫ′′

versus frequencies for two different temperatures T1 and T2 b) Re-

laxation map (maximum frequency versus inverse temperature) for the

different processes c) specific heat capacity cp versus inverse temperature

(thermal glass transition). Adapted from [6]. . . . . . . . . . . . . . . . . 21

4.4 Vibrational density of states of poly(methylphenylsiloxane) (PMPS) in

the bulk and confined to Sol/Gel-Glasses with different pore sizes as

indicated taken at T=80 K at IN6. Taken from [48]. . . . . . . . . . . . 26

4.5 Vibrational density of states of the nematic liquid crystal E7 in the bulk

and confined to a molecular sieve (MCM) with a pore size of 2.5 nm.

Taken from [47]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1 Chemical structure of Py4CEH . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Chemical structure of Hexakis(n-alkyloxy)triphenylene HATn. The length

n of the side chains is varied: n=5, 6, 8, 10, 12. . . . . . . . . . . . . . . . 30

5.3 Chemical structure of Hexakis(n-alkanoyloxy)triphenylene HOTn. The

length n of the side chains is varied: n=6, 8, 10, 12. . . . . . . . . . . . . 30

5.4 MALDI-TOF spectrum of HAT6 (C54H84O6). The spectra were col-

lected employing a Bruker Autoflex III (Bruker Daltonik GmbH, Bre-

men, Germany) spectrometer equipped with a SmartbeamT M laser (356

nm, frequency 200 Hz). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.5 Electron microscopy (REM) pictures (Zeiss Gemini Supra 40 courtesy

to BAM 6.4) of Smart Membranes with a pore size of (a) 25 nm, (b) 180

nm (c) 180 nm breaking edge. . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.6 TG-curve of a) HAT6 in the bulk state b) Anopore Membrane (pore size

100 nm) filled with HAT6 (filling time of 24 hours at 393 K) . . . . . . . 33

5.7 Final weight loss in dependence on filling time for Anopore Membranes

(filling temperature 393 K, filling material HAT6) with different pore

sizes as indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

156

List of Figures

5.8 Electron microscopy (REM) pictures (Zeiss Gemini Supra 40 courtesy

to BAM 6.4) of a Smart Membrane with a pore size of 180 nm filled

with HAT6 breaking edge. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.9 Measurement techniques applied in the frequency range from 10−6 Hz to

1015 Hz. Taken from [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.10 Real ǫ′ and imaginary part ǫ′′ of the complex dielectric function ǫ∗ in

dependence on frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.11 Scheme of the scattering process due to interaction of radiation with the

sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.12 The Time of Flight spectrometer IN6, picture taken from [97] . . . . . . 47

5.13 IN6 spectra of HAT6 in the bulk normalized to the height of the elastic

peak (averaged over the detector range 54...108, corresponding to a q

range of 1.1...2.0 A−1 for elastic scattering): open squares - HAT6 in

the bulk at T=80 K; open circles correspond to a measurement at 2K

representing the instrumental resolution. . . . . . . . . . . . . . . . . . . . 47

5.14 The Neutron Backscattering spectrometer IN10, picture taken from [97] 48

6.1 DSC thermogram of Py4CEH during cooling (dashed line) and heating

(solid line) with a cooling/heating rate of 10 K/min. The inset enlarges

the temperature range between 120 K and 210 K. . . . . . . . . . . . . . 51

6.2 Dielectric loss of Py4CEH in dependence on frequency and temperature

during cooling. Taken from own publication [99]. . . . . . . . . . . . . . . 53

6.3 Dielectric loss in dependence on frequency at different temperatures

(T=331 K (downward triangles), 303 K (pentagrams), 255 K squares),

233 K (circles), 221 K (upward triangles), 207 K (stars), 185 K (right tri-

angles)). Lines denote fits by the Havriliak-Negami equation to the cor-

responding data. Inset: Imaginary Part of the complex modulus M′′

at

different temperatures (353 K (squares), 357 K(circles), 361 K (upward

triangles), 365 K (downward triangles), 369 K (stars), 373 K(pentagons)) 54

6.4 Relaxation map of Py4CEH: stars (dielectric β-relaxation), circles (di-

electric α-relaxation), squares (conductivity). The dashed-dotted line

represents the α-relaxation of Polyethylene ([35]). The figure is taken

from own publication.[99] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

157

List of Figures

6.5 (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of Py4CEH

in the crystalline as well as the columnar hexagonal liquid crystalline

phase - circles. The solid and the dashed lines are linear regressions to

the corresponding dielectric data in the different regions. T0 (arrows)

denote the estimated Vogel-temperatures. The dotted vertical line indi-

cates the phase transition temperature taken from DSC measurements

with a cooling rate of 10 K min−1. Taken from own publication.[99] . . 56

6.6 Temperature dependence of the dielectric strength ∆ǫα for heating (open

circles) and cooling (open triangles) for the α-relaxation. The dashed

lines are guides for the eyes. The dashed-dotted vertical lines indicate

the phase transition temperatures measured for heating and cooling by

DSC. The inset: dielectric strength ∆ǫβ for the β-relaxation. The line

is a guide for the eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.7 Real part C′p (open squares) and corrected phase angle dcorr (open cir-

cles) of the complex heat capacity versus temperature at f = 1.499×10−2

Hz of a TMDSC measurement. The solid line is a fit of a Gaussian to

the data of the phase angle to estimate its maximum position. The

width of the glass transition is taken from the variance of the Gaus-

sian. Inset: Normalized amplitude of the complex differential voltage

ofPy4CEH for heating at different frequencies: open stars=720 Hz, open

diamonds=560 Hz, open squares=360 Hz. Dashed-dotted vertical lines

denote the corresponding dynamic glass transition temperatures (half-

step height). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.8 Temperature dependence of the α-relaxation, obtained by dielectric re-

laxation spectroscopy (circles) and by specific heat spectroscopy (trian-

gles). Dashed lines are fits of the VFT-equation (4.3) to the different

branches of the dielectric α-relaxation and to the specific heat spec-

troscopy data. The dashed-dotted line denotes data of the dielectric

α-relaxation of polyethylene (PE) taken from reference [35]. . . . . . . . 59

158

List of Figures

6.9 (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation presented

in Figure 6.8 of Py4CEH in the crystalline as well as the columnar hexag-

onal liquid crystalline phase: circles - dielectric data; triangles - thermal

data. The solid and the dashed lines are linear regressions to the cor-

responding dielectric data in the different regions. The dashed dotted

line corresponds to the derivative of the dielectric relaxation rate of

polyethylene taken from reference [35]. T0 -arrows denote the estimated

Vogel-temperatures. The dotted vertical line indicates the phase transi-

tion temperature taken from DSC measurements with a cooling rate of

10 K min−1. Please note that the effective cooling rate for the dielectric

measurements is ca. two decades lower. . . . . . . . . . . . . . . . . . . . 60

6.10 X-ray diffractogram in the small angle range (SAXS) of Py4CEH at

T=303 K. Taken from own publication [99]. . . . . . . . . . . . . . . . . . 62

6.11 DSC Thermograms of bulk Py4CEH and Py4CEH located inside self-

ordered AAO membranes with different pore diameters as indicated

(Heating rate 10 K/min, second heating scan). The dashed lines in-

dicate the phase transitions of the bulk. . . . . . . . . . . . . . . . . . . . 64

6.12 Phase transition temperatures between the plastic crystalline and the

liquid crystalline phase versus inverse pore size as obtained by DSC

(Solid squares - main peak; Solid circles - satellite peak. The solid line

is a linear regression to the corresponding data where the line is a guide

for the eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.13 Phase transition temperatures between liquid crystalline and isotropic

phase as obtained by DSC versus inverse pore size. Solid squares - main

peak; Solid circles - satellite peak. The solid line is a linear regression

to the data of the main peak. The dashed line is a guide for the eyes for

the satellite peak. The open data points corresponds to literature data

of Py4CEH in AAO membranes with a pore diameter of 50 nm: star -

DSC; triangle - X-ray; diamond - SANS. Taken from own publication [99] 65

6.14 Schematic representation of the possible organization of Py4CEH inside

the pores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.15 Transition enthalpies at the transition from the liquid crystalline to the

isotropic phase versus inverse pore diameter: full circles - sum of main

and satellite peak, empty circles -main peak. The lines are a linear

regression to the data. Inset: Transition enthalpies from the plastic

crystalline to the liquid crystalline phase versus inverse pore diameter.

The line is a linear regression to the data. . . . . . . . . . . . . . . . . . . 67

159

List of Figures

6.16 Relative transition enthalpy of the satellite peak for the phase transition

from the liquid crystalline to the isotropic phase versus inverse pore

size. The dashed line denotes a linear regression to the data under the

assumption that it goes through the point of origin. . . . . . . . . . . . . 68

6.17 Dielectric loss versus temperature for different frequencies: 1 kHz (squares),

677 kHz (circles), 1.33 MHz (triangles up) (a) for AAO membranes with

a diameter of 80 nm filled with Py4CEH. Stars indicate the dielectric

loss for the corresponding emtpy membrane at a frequeny of 1 kHZ.

Dashed lines denote polynomial fits: (b) for Py4CEH inside the pores

where the contribution of the empty AAO membrane is substracted as

described in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.18 Relaxation map of Py4CEH in the bulk (open squares) and confined to

AAO membranes with pore diameters of 180 nm (open circles) and 80

nm (open triangles). Lines are guides to the eyes. Inset: relaxation map

of Py4CEH in the bulk (open squares) and confined to AAO membranes

with pore diameters 40 nm (hexagons) and 25 nm (open stars). . . . . . 71

6.19 Apparent activation energy EA versus inverse pore size for the liquid

crystalline phase. Apparent activation energy EA versus inverse pore

size for the plastic crystalline phase. Lines are guides for the eyes. . . . 72

6.20 log f∞ versus EA for all pore sizes in the different phases: circles-liquid

crystalline phase; squares-plastic crystalline phase. The line is a linear

regression to all data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.21 Definition of the dielectric phase transition temperature for Py4CEH

confined to AAO membranes with a pore diameter of 80 nm. Inset:

Comparison of phase transition temperatures between the plastic crys-

talline and the liquid crystalline phase versus inverse pore size as ob-

tained by dielectric spectroscopy (solid circles) and DSC (open squares

- main peak; open circles - satellite peak.The solid line is a linear regres-

sion to the corresponding data where the dashed lines are guides for the

eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.22 DSC thermogram for HAT6 during cooling (blue line) and heating (red

line). Inset: DSC thermogram for cooling in the range between 180 and

220 K, the temperature where a glass transition is observed in reference

[33]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

160

List of Figures

6.23 Transition temperatures for the phase transitions between plastic crys-

talline and liquid crystalline phase Tcry,colh and between liquid crystalline

and isotropic phase Tcolh,iso of the HATn materials in dependence of the

length of the side chains n for heating (red circles) and cooling (blue

down triangles). Pentagons and stars indicate phase transition temper-

atures given in the literature.[110] Inset: Temperature range of the liquid

crystalline mesophase ∆Tmeso in dependence on the length of the side

chains n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.24 Phase transition enthalpies for the transition from the plastic crystalline

to the liquid crystalline phase (squares) and for the transition from the

liquid crystalline to the isotropic phase (circles) in dependence on the

length n of the side chains during heating. Lines are guides for the eyes.

The errors for the transition enthalpies for the phase transition from

the liquid crystalline to the isotropic phase are smaller the size of the

symbols with regard to the scale of the y-axis. . . . . . . . . . . . . . . . 77

6.25 X-ray spectra of HAT6 in the plastic crystalline phase at T=295 K.

Inset: diffractogram of plastic crystalline HAT6 (dashed line) and semi-

crystalline polyethylene (solid line) in the q-range between 10 nm−1 and

25 nm−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.26 X-ray spectra of HAT6 in the liquid-crystalline phase (T=351 K). Inset:

X-ray diffractogramm of liquid crystalline HAT6 between q = 5 nm−1

and q = 10 nm−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.27 X-ray spectra of HAT6 at T=423 K where the material is supposed to

be in the isotropic phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.28 X-ray diffractogram for the HATn materials at a temperature corre-

sponding to the columnar hexagonal mesophase: T = 353 K for n = 5,

T = 351 K for n=6 and 8, T = 341 K for n = 10. The curves are shifted

on the y-scale for sake of clearness. . . . . . . . . . . . . . . . . . . . . . . 81

6.29 Core-Core Distance versus number of C-Atoms in the side chain for

HATn: red circles – the columnar hexagonal phase; blue squares –

“isotropic phase”. Error bars were given for the distance in the liq-

uid crystalline phase. In the isotropic state the error is similar. The

dashed and dashed dotted lines are linear fits to the corresponding data.

Data for triangles – Poly (n–alkyl metharylates) are taken from reference

[119]. The straight line corresponds to data for a single alkyl chain in

all trans conformation.[119] Non integer numbers for the Poly (n-alkyl

metharylates) refer to mixtures of polymers with different lengths of the

side chain. Star - Py4CEH . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

161

List of Figures

6.30 DSC thermograms of bulk HAT6 and HAT6 embedded inside the pores

of self-ordered AAO membranes with pore diameters as indicated (heat-

ing rate 10 K/min, second heating scan). The dashed lines indicate the

phase transitions temperatures of the bulk. The data is shifted on the

y-axis for sake of clearness. Taken from own publication.[120] . . . . . . 83

6.31 Heat flow for HAT6 confined to AAO channels with a diameter of 25

nm in the temperature range for the transition from hexagonal ordered

liquid crystalline and to the isotropic phase during heating. The dashed

line indicates the phase transition temperature of the bulk. Inset: Heat

flow for HAT6 confined to pores with a pore diameter of 40 nm in the

temperature range between 180 K and 240 K. . . . . . . . . . . . . . . . 84

6.32 Phase transition temperatures for HAT6. Phase transition temperatures

between the plastic crystalline and the liquid crystalline phase - squares,

satellite peaks for the phase transition between the plastic crystalline and

the liquid crystalline phase- upward triangles, phase transition temper-

atures between liquid crystalline and isotropic phase - circles, satellite

peaks for the phase transition between liquid crystalline and isotropic

phase- downward triangles. The solid line is a linear regression to the

corresponding data where the dashed line is a guide for the eyes. . . . . 85

6.33 Phase transition enthalpy for the phase transition from the liquid crys-

talline to the isotropic phase (sum of main and satellite peak) for HAT6-

full circles, Phase transition enthalpy for the main peak of the phase

transition from the liquid crystalline to the isotropic phase for HAT6-

empty circles. Lines are linear regression to the data. Inset: Transition

enthalpies of the satellite peak relative to that of the main peak versus

inverse pore diameter. The dashed line is a fit of Equation (6.1) to the

data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.34 Phase transition enthalpies versus inverse pore diameter d for the transi-

tion from the plastic crystalline to the liquid crystalline phase for HAT6.

The line is a linear regression to the data. . . . . . . . . . . . . . . . . . . 88

6.35 Transition enthalpy of the phase transition at 323 K for HAT6 relative

to that of the main peak. The line is a fit of Equation (6.1) to the data. 89

162

List of Figures

6.36 Phase transition temperatures for (a) HAT5, (b) HAT10, (c) HAT12

as indicated. Phase transition temperatures between the plastic crys-

talline and the liquid crystalline phase - squares, satellite peaks for the

phase transition between the plastic crystalline and the liquid crystalline

phase- upward triangles, phase transition temperatures between liquid

crystalline and isotropic phase - circles, satellite peaks for the phase

transition between liquid crystalline and isotropic phase- downward tri-

angles. The solid line is a linear regression to the corresponding data

where the dashed line is a guide for the eyes. . . . . . . . . . . . . . . . . 91

6.37 Surface tension for the phase transition between plastic crystalline and

liquid crystalline phase -black squares- and between liquid crystalline

and isotropic phase - red circles in dependence on the chain length. . . 91

6.38 Phase transition enthalpy for the phase transition from the liquid crys-

talline to the isotropic phase for HAT5 (sum of main and satellite peak)

- full squares. Phase transition enthalpy for the main peak of the phase

transition from the liquid crystalline to the isotropic phase for HAT5-

empty squares. Lines are linear regression to the corresponding data. . 92

6.39 Phase transition enthalpy for the phase transition from the liquid crys-

talline to the isotropic phase (sum of main and satellite peak) for HAT10-

full triangles. Phase transition enthalpy for the main peak of the phase

transition from the liquid crystalline to the isotropic phase for HAT10-

empty triangles. Lines are linear regression to the corresponding data. . 93

6.40 Phase transition enthalpy for the phase transition from the liquid crys-

talline to the isotropic phase for HAT12 (sum of main and satellite peak)

- full stars. Inset: Phase transition enthalpy for the main peak of the

phase transition from the liquid crystalline to the isotropic phase for

HAT12- empty stars. Lines are linear regression to the corresponding

data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.41 Critical pore size for the phase transition from the liquid crystalline to

the isotropic phase dcri,iso for the main peak - circles and the overall phase

transition - squares in dependence on the chain length. Inset: Difference

in the critical diameter dcri,ges − dcri,main for the phase transition of the

sum (main and satellite peak) and the phase transition of the main peak

for the transition between liquid crystalline and isotropic phase. . . . . 94

163

List of Figures

6.42 Phase transition enthalpies versus inverse pore diameter d for the tran-

sition from the plastic crystalline to the liquid crystalline phase. The

dashed line is a linear regression to the data: open squares - HAT5,

open circles - HAT6 Inset: Phase transition enthalpies versus inverse

pore diameter d for the transition from the plastic crystalline to the

liquid crystalline phase: open triangles - HAT 10, open stars - HAT 12. 95

6.43 Dielectric spectra of HAT6 in dependence on frequency and temperature

in a 3D representation while cooling. . . . . . . . . . . . . . . . . . . . . . 96

6.44 Dielectric loss ǫ′′ versus frequency for the α-relaxation of HAT6 at dif-

ferent temperatures: blue stars T=234 K, green triangles T=219 K, red

circles T=204 K, black squares T=183 K. Lines denote fits of equation

(5.10) to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.45 Relaxation map of HAT6: red stars - dielectric β - relaxation, red cir-

cles - dielectric α-relaxation, red squares - conductivity, black squares

- α-relaxation as observed in reference [33]. Straight lines are a linear

regression to the data in the corresponding temperature range. Dashed

lines denote a guide to the eyes. . . . . . . . . . . . . . . . . . . . . . . . . 97

6.46 (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of HAT6.

Straight lines denote a linear regression to the data. The arrow denotes

the Vogel-Temperature T0. Dashed lines are guides to the eyes. . . . . . 98

6.47 Dielectric strength ∆ǫα in dependence on temperature for the α-relaxation

of HAT6. Inset: Dielectric strength ∆ǫβ in dependence on temperature

for the β-relaxation of HAT6. The dashed and straight lines are guides

for the eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.48 Activation Plot for HATn for the α-and the β-relaxation: squares -

HAT5, red circles - HAT6, green triangles - HAT8, blue pentagons -

HAT10, pink stars - HAT12. Solid lines are fits of the Arrhenius equa-

tion to the data of the β-relaxation. Dashed lines denote relaxation rates

of PE to the corresponding process taken from reference [35]. . . . . . . 101

6.49 (d log fmax

dT)−1/2

versus temperature for HAT5 - black squares and HAT8 -

green triangles. Lines are a linear regression to the data. . . . . . . . . . 101

6.50 Activation energy EA,αfor the α-relaxation in dependence on the chain

length for HAT8, HAT10 and HAT12. The line is a guide for the eyes. 103

6.51 Activation energy for the β-relaxation for all HATn in dependence on

the chain length. The dashed line denotes the activation energy of the

β-relaxation of PE taken from reference [35]. The line is a guide to the

eyes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

164

List of Figures

6.52 Activation Plot for HATn for the conductivity process: squares - HAT5,

red circles - HAT6, green triangles - HAT8, blue pentagons - HAT10,

pink stars - HAT12. Solid lines denote fits of the Arrhenius equation to

the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.53 Vibrational density of states (VDOS) of HAT5 measured at T=80 K

at IN6. Inset: Vibrational density of states for HAT5 - red circles, the

nematic mixture E7 - blue stars [47] and for polymeric glass poly (methyl

phenyl siloxane) (PMPS) [45] - upward green triangles. Measurements

were carried out at T=80 K. The data for the different materials were

not normalized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.54 Vibrational density of states of HAT5 (empty red circles) and of “amor-

phous” polyethylene (PE) (filled circles) given by Kanaya et al. in refer-

ence [127]. The data for PE are scaled to collapse at the high frequency

side with the HAT5 data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.55 VDOS at T= 80 K for HAT. for different lengths of the alkyl chains:

HAT5 -circles, HAT10 -stars, HAT12 - diamonds. Inset: Boson Peak

for HAT5 - circles and HAT6 - squares. Lines are guides for the eyes.

Taken from own publication.[123] . . . . . . . . . . . . . . . . . . . . . . . 107

6.56 Frequency of the Boson peak ωBP versus the number of carbon atom in

the side chains. Taken from own publication.[120] . . . . . . . . . . . . . 108

6.57 VDOS of HATn with different lengths of the side chains: diamonds -

HAT12, triangles - HAT8, circles - HAT5. . . . . . . . . . . . . . . . . . . 109

6.58 Vibrational density of states of HAT6 in the bulk (black squares) and

confined to self-ordered AAO membranes with pore sizes 80 nm (green

circles), 40 nm (red stars) and 25 nm (blue diamonds). The lines are

guides to the eyes. Inset: frequency of the Boson peak ωBP versus inverse

pore size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.59 Ratios of the VDOS according to Equation (6.4). The main graph shows

the averages of the data in the frequency range ω = 0.8...1.8 ps−1. The

error bars indicate the standard deviation of the average given in the

inset. The dashed line is a fit to the data according to Equation (6.4).

The inset gives the underlying values in dependence on ω: open squares

- 80 nm; grey circles - 40 nm. The lines indicate the averages. . . . . . . 112

6.60 Scheme of orientation of the pore axis with respect to the momentum

transfer vector q (scattering vector). ki and kf are the wave vectors of the

incident and detected neutron beam in a neutron scattering measurement.112

165

List of Figures

6.61 Vibrational density of states of HAT6 confined to self-ordered AAO

membranes with a pore sizes of 25 nm with parallel (open squares) and

perpendicular orientation (grey circles) of the pore axis with respect to

the q vector of the incident beam at T=80 K. Lines are guides to the

eyes. Inset: Temperature dependence of the mean-square displacement

⟨u2⟩ recalculated from the vibrational densities of states according to

equation (6.5): solid line - pore axis perpendicular to the q vector of

the incident beam, dashed line - pore axis parallel to the q vector of the

incident beam. The dashed-dotted line indicate ⟨u2⟩ at 80 K. . . . . . . 113

6.62 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for HAT6. The dotted lines denote the phase transition temper-

atures obtained by DSC. The inset enlarges the temperature dependence

of ⟨u2⟩eff in the low temperature range up to a temperature of 300 K.

Taken from own publication. . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.63 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for open squares - HAT5, open circles - HAT6, open pentagons

- HAT10 and open stars - HAT12 at lower temperatures in the plastic

crystalline phase. The inset enlarges the temperature range between 150

K and 250 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.64 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for open squares - HAT5, open circles - HAT6 and open triangles -

HAT8 at higher temperatures in the hexagonal ordered liquid crystalline

phase. Inset: Effective mean squared displacement ⟨u2⟩eff versus the

core-core distance in the liquid crystalline phase. . . . . . . . . . . . . . . 117

6.65 Temperature dependence of the scattered elastic intensity for HAT6 in

the bulk-red circles and in the confined state (40 nm - green triangles,

25 nm - blue stars) normalized to the elastic intensity at T=30 K. Open

black pentagons correspond to the empty membranes with a pore size of

40 nm. The dotted lines denote the bulk phase transition temperatures

obtained by DSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.66 Temperature dependence of the effective mean square displacement ⟨u2⟩eff

for HAT6 in the bulk-red circles and in the confined state (80 nm - green

triangles, 40 nm - blue stars). The dotted lines denote the bulk phase

transition temperatures obtained by DSC. . . . . . . . . . . . . . . . . . . 119

6.67 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for HAT6 red circles - in the bulk and blue stars - confined to

the pores with a pore size of 40 nm in the low temperature range until

300K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

166

List of Figures

6.68 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for HAT6 red circles - in the bulk and blue stars - confined to

the pores with a pore size of 40 nm in the temperature range between

250 K and 400 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.69 Temperature dependence of the effective mean squared displacement

⟨μ2⟩eff for HAT6 confined to the pores with a pore size of 40 nm with

parallel orientation of the pore axis with respect to the incident beam -

green stars, with perpendicular orientation of the pore axis with respect

to the incident beam - red diamonds . . . . . . . . . . . . . . . . . . . . . 121

6.70 DSC thermogram for HOT 6 in dependence on heating -red line and

cooling -blue line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.71 Phase transition temperatures in dependence on the number n of C-

Atoms in the alkyl chain during heating: red circles- transition be-

tweeen different plastic crystalline phases, black squares-transition be-

tween plastic crystalline and liquid crystalline phases, blue triangles-

transition between different liquid crystalline phases, green pentagons

between liquid crystalline and isotropic phases. . . . . . . . . . . . . . . . 123

6.72 Phase transition temperatures in dependence on the number n of C-

Atoms in the alkyl chain during cooling: black squares - phase transition

between plastic crystalline and liquid crystalline phase, green pentagons-

phase transition between liquid crystalline and isotropic phase. . . . . . 124

6.73 Sum of the phase transition enthalpies of the phase transition between

plastic crystalline and liquid crystalline and for the phase transition be-

tween different liquid crystalline phases in dependence on the number n

of C-Atoms in the alkyl chain: Red circles - heating, open blue pentagons

- cooling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.74 Phase transition enthalpies for the phase transition between liquid crys-

talline and isotropic phase in dependence on the number n of C-Atoms

in the alkyl chain: Red circles - heating, open blue pentagons - cooling. 125

6.75 X-ray diffractogramm for HOT6 in the different phases: black line-

plastic crystalline phase (T=299 K), red line - liquid crystalline phase

(T=385 K) and blue line - isotropic phase (T=423 K) . . . . . . . . . . . 126

6.76 X-ray diffractogram for the HOTn materials at a temperature corre-

sponding to the columnar hexagonal mesophase: black line - n=6 (T=385

K), red line - for n=8 (T=333 K), green line - n=10 (T=345 K), blue

line n=12 (T=354 K). The curves are shifted on the y-scale for sake of

clearness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

167

List of Figures

6.77 Distance versus number of C-Atoms for HOTn -blue circles and HATn

- green triangles. The star corresponds to the value found for Py4CEH.

The straight line corresponds to data for a single alkyl chain in all trans

conformation.[119] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.78 Dielectric loss ǫ′′

in dependence on frequency and temperature in a 3D

representation while heating. . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.79 Relaxation map of HOT6 in comparison to HAT6: red pentagons - α-

relaxation of HAT6, red stars - β-relaxation of HAT6, red downward

triangles - conductivity of HAT6, black circles - α-relaxation of HAT6,

black upward triangles - β-relaxation of HOT6, black squares - conduc-

tivity of HOT6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.80 Dielectric strength ∆ǫα for the α-relaxation of HOT6 in dependence

on temperature. Inset: Dielectric strength ∆ǫβ for the β-relaxation of

HOT6 in dependence on temperature. . . . . . . . . . . . . . . . . . . . . 131

6.81 (d log fmax

dT)−1/2

vs. temperature for the data of the α-relaxation of HOT6.

Straight lines denote a linear regression to the data. The arrow denotes

the Vogel-Temperature T0. . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.82 Temperature dependence of the relaxation rates in dependence on 1000/T:

red circles - HOT6, green triangles - HOT8, violet pentagons - HOT10,

blue stars - HOT12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.83 Activation energies for the β - relaxation for HOTn in dependence on

the chain length: red circles - HOTn, red triangles - second β-relaxation

of HOTn, blue squares - HATn. . . . . . . . . . . . . . . . . . . . . . . . . 133

6.84 Vibrational density of states (VDOS) of HOT6. Arrows are guides to the

eyes. Inset: Vibrational density of states for HOT6 - red circles, HAT6 -

open stars. The data for the different materials were normalized to the

maximum of the y-value of the Boson Peak. . . . . . . . . . . . . . . . . . 134

6.85 Vibrational density of states (VDOS) of HOT6 - red circles, HOT8 - blue

squares. Inset VDOS for HOT10 -green pentagons and HOT12 -blue stars135

6.86 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for HOT6. The dotted lines denote the phase transition temper-

atures obtained by DSC. Inset: Temperature dependence of the effective

mean squared displacement ⟨u2⟩eff for HAT6. . . . . . . . . . . . . . . . 136

168

List of Figures

6.87 Temperature dependence of the effective mean squared displacement

⟨u2⟩eff for all HOTn under study in the high temperature range between

T=250 K and T=410 K: red circles - HOT6, green triangles - HOT8, vio-

let pentagons - HOT10, blue stars - HOT12. The dotted lines denote the

phase transition temperatures for HOT6 obtained by DSC. Inset: Tem-

perature dependence of the effective mean square displacement ⟨u2⟩eff

for all HOTn under study in the low temperature range up to T=300 K:

red circles - HOT6, green triangles - HOT8, violet pentagons - HOT10,

blue stars - HOT12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.88 Effective mean squared displacement ⟨u2⟩eff versus the core-core dis-

tance in the liquid crystalline phase: Square- HATn; Circles - HOTn.

Dashed lines are guides for the eyes. . . . . . . . . . . . . . . . . . . . . . 137

169