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Dielectric properties of molecular glass formers [Elektronische Ressource] : from the liquid state to the tunneling regime / von Catalin P. Gainaru

De
168 pages
Dielectric Properties of Molecular Glass Formers; from the Liquid State to the Tunneling Regime Der Universität Bayreuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) vorgelegte Abhandlung von Catalin P. GAINARU geboren am 27. Mai 1977 in Botosani, Rumänien 1. Gutachter: Prof. Dr. E.A. Rössler 2. Gutachter: Prof. Dr. R. Böhmer “Make everything as simple as possible, but not simpler.” Albert Einstein Contents I. Introduction 1 I.1. The glass transition 1 I.2. Relaxation processes in molecular glass forming systems 2 I.3. Scope and structure of the present study 4 II. Dielectric spectroscopy: theory, experiment and phenomenological description of the dielectric response 7 II.1. Theoretical background 7 II.2. Experimental details 13 II.2.1. Frequency domain measurements 14 .2. Time 16 II.2.3. Low temperature 17 II.3. Phenomenological description of the dielectric response 17 II.3.1. The Debye function 17 .2. Cole-Davidson function 19 II.3.3. The Kohlrausch 19 .4 Distributions of relaxation times 20 III. The evolution of the dynamic susceptibility of simple glass formers from the liquid state to the tunneling regime; overview 23 III.1.
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Dielectric Properties of Molecular
Glass Formers; from the Liquid
State to the Tunneling Regime





Der Universität Bayreuth
zur Erlangung des Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
vorgelegte Abhandlung


von
Catalin P. GAINARU
geboren am 27. Mai 1977 in Botosani, Rumänien

1. Gutachter: Prof. Dr. E.A. Rössler
2. Gutachter: Prof. Dr. R. Böhmer








































“Make everything as simple
as possible, but not simpler.”


Albert Einstein Contents

I. Introduction 1
I.1. The glass transition 1
I.2. Relaxation processes in molecular glass forming systems 2
I.3. Scope and structure of the present study 4

II. Dielectric spectroscopy: theory, experiment and
phenomenological description of the dielectric response 7

II.1. Theoretical background 7
II.2. Experimental details 13
II.2.1. Frequency domain measurements 14 .2. Time 16
II.2.3. Low temperature 17
II.3. Phenomenological description of the dielectric response 17
II.3.1. The Debye function 17 .2. Cole-Davidson function 19
II.3.3. The Kohlrausch 19 .4 Distributions of relaxation times 20

III. The evolution of the dynamic susceptibility of simple glass
formers from the liquid state to the tunneling regime;
overview 23

III.1. The high temperature regime (T >> T) 23 g
III.2. The intermediate temperature range (T > T > T) 24 x g
III.2.1. Glass formers with excess wing 25
III.2.2. Glass formers with β-process 27
III.3. The glassy state (T < T) 29 g
III.3.1. The secondary relaxation processes 29
III.3.2. The asymmetric double well potential dynamics 31

IV. Results; Relaxation properties of molecular glass formers
at T ≥ T 41 g

IV.1. Experimental results 42 IV.2. Spectra analysis using approach I 43
A critical assessment 48
IV.3. Spectra analysis using approach II 53
IV.3.1. Analysis of type A systems 53
IV.3.2. Analysis of type B systems 63
IV.3.3. The excess wing at T > T 67 g
IV.4. Consequences of approach II 68
IV.4.1. Unperturbed type A characteristics 68
IV.4.2. The nearly constant loss 71
IV.4.3. The influence of the molecular dipole moment on the
amplitude of secondary processes 73
IV.5 Conclusions 77

V. Results; Low temperature relaxations in molecular
glasses (T << T) 79 g

V.1. Experimental results and discussion 80
V.1.1. Systems with weak β-contribution (type A) 80
V.1.2. Systems with strong β-contribution 87
V.2. The tunneling regime (T < 10 K) 89
V.3. The thermally activated Asymmetric Double Well Potential
dynamics (10 K < T < T) 95 CL
V.3.1. Systems with weak β-contribution 95
V.3.2. Systems with strong β 101
V.4. Conclusions 105

VI. Results; A joint study of glycerol by dielectric
spectroscopy, field cycling NMR and light scattering 107

VI.1. Theoretical background – dispersion of spin-lattice relaxation 108
VI.2. Experimental results 110
VI.2.1. Dielectric spectroscopy
1 VI.2.2. H field cycling nuclear magnetic resonance 111
VI.2.3. Light scattering 112
VI.3. Discussion 113 VI.3.1. T > T 113 g
VI.3.2. T < T 120 g
VI.4. Conclusions 123

VII. Results; Dielectric properties of 1,4 Polybutadiene 125

VIII. Summary 133

Zusammenfassung 135
Appendix 139
A. Systems investigated in this work 139
B. Dielectric response of 2-methyl tetrahydrofuran 141
C. The spectra analysis using approach I; scaling relations 143
D. Aging experiment on 4-tertbutyl pyridine (4-TBP) 147
Bibliography 149
List of publications 157
Danksagung - Acknowledgement 159

I. Introduction

I. Introduction

I.1 The glass transition

The glass transition phenomenon has been recognized since a long time as one of
the major topics in condensed matter physics. In spite of its considerable scientific
impact there still exists a fairly widespread lack of understanding the nature of the
glass transition.
A glass can be defined as a solid with irregular microscopic structure or, equivalently,
as a liquid with infinite viscosity. The simplest way to produce a glass is by
supercooling a liquid. Presumably, any liquid can be transformed into a glass if
cooled fast enough to avoid crystallization. Supercooling a liquid results in a
continuous slowing down of the structural relaxation process or, equivalently, a
continuous increase of viscosity. This process, called glass transition, is purely kinetic
in nature, as no thermodynamic phase transition is involved.
12The temperature associated with the liquid surpassing a viscosity value of η ≈ 10
•Pa s or with an increase of the time constant of the liquid structural relaxation beyond
100 seconds gives the conventional definition for the glass transition temperature T . g
Another criterion for T may be given by the temperature at which a step is recorded g
in the specific heat while heating the sample at 10 K/min. This is called the
calorimetric glass transition temperature. All the experiments probing structural
relaxation, viscosity or specific heat yield similar values for T . g
The glass is produced by the inability of the liquid structure to equilibrate on the
experimental time scale at low temperatures. Since in the liquid, well above the
melting point, the structural relaxation takes place on the time scale of picoseconds
and on the time scale of hundreds of seconds around T , the structural relaxation g
time constant (or viscosity) changes by many decades upon supercooling. One of the
most interesting features of supercooled liquids is that this change occurs in a rather
small temperature range, as shown in Fig. I.1. Here the time constants of the glass
former SiO obeys a thermally activated behavior (straight line in Fig. I.1), i.e. their 2
Eatemperature dependence is given by an Arrhenius law: ln η ∝ ln τ ∝ , with an
RT
activation energy E = constant. However, as the most glass formers, glycerol and o-a
terphenyl (OTP) show deviations from the Arrhenius behavior and a curvature in the
“Arrhenius plot” is observed. Close to T, this non-Arrhenius temperature g
1 I. Introduction

dependence can be phenomenologically described by the Vogel-Fulcher-Tammann
(VFT) equation [19,20]:
D
(I.1) η(T ) ∝ τ (T ) = τ exp( )0 T −T0



Fig. I.1 The Arrhenius plot for the
viscosity for two supercooled liquids:
SiO and glycerol. In addition, time 2
constants from dielectric measurements
for o-terphenyl (OTP) are plotted as open
circles. Figure from [18].





The good interpolation of the data with the VFT function can be interpreted as
pointing to the existence of a non-zero temperature T < T at which the relaxation 0 g
time of the supercooled liquid may diverge, i.e. a phase transition is expected here.
However, since the relaxation time τ becomes inaccessibly large at such
temperatures, it is impossible to actually verify this scenario.
Based on the temperature dependence of the viscosity, a classification of glass
formers was introduced [21,22]: systems showing a weak change of viscosity at T in g
the above representation, lg η vs. T /T, are called “strong” (e.g. SiO ) while the others g 2
with a strong change are called “fragile” (e.g. OTP).

I.2 Relaxation processes in molecular glass forming systems

Dielectric spectroscopy (DS) is a powerful tool to investigate the extremely broad
dynamic range involved in the glass transition (cf. Fig. I.1). Though dielectric
measurements covering more than 18 decades in frequency were already performed,
a conclusive picture of the evolution of molecular dynamics upon supercooling is still
missing. This is due to the fact that there are not so many glass formers investigated
in this full relevant relaxation time range. As most of commercially available dielectric
spectrometers operate below some GHz, there are actually only two molecular liquids
2

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