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16 Slow and fast dynamics The dynamics with characteristic time shorter than the alpha relaxation time is what we refer to as fast dynamics or equivalently high frequency dynamics. Measurements at a fixed frequency or fixed time scale naturally do not probe the time dependence of the dynamics. What they see is the dynamics on the time scale they are sensitive to. This means that a measurement with a timescale considerably shorter than the alpha relaxation time (or a frequency larger than the inverse alpha relaxation time) only probes the fast dynamics of the viscous liquid. The fast (linear) dynamics are, like any other property of the (viscous) liquid, dependent on the thermodynamic state determined by temperature and pressure. This means that properties characterizing fast dynamics, such as high frequency moduli, short time mean square displacement, etc. depend (sometimes strongly) on pressure and temperature. Fast dynamics are sometimes referred to as glassy dynamics because it is the dynamics at times faster than the structural relaxation, which governs the glass transition. However, fast dynamics measured in viscous liquids in their thermodynamic (metastable) equilibrium state are equilibrium properties. This means that they are not history nor path dependent, but uniquely determined by the thermodynamic state of the liquid. 2.5.2 Glassy dynamics The glassy state is, as described in section 2.1, a non-equilibrium state obtained when the alpha relaxation becomes so long that it is not possible to wait for the liquid to reach its thermodynamic equilibrium. All dynamical processes happening on the alpha relaxation time scale are consequently frozen in. However the particles keep moving in a solid-like manner, hence the fast dynamics stay active, and these remaining dynamical processes are what we refer to as glassy dynamics. The important distinction between the fast dynamics in the equilibrium liquid and the glassy dynamics is that the former is a well defined equilibrium quantity while the latter is a property of the non-equilibrium glassy state. The properties characterizing glassy dynamics are therefore in principle path and time dependent, as is characteristic for properties in non-equilibrium systems. It turns out that the path and time dependence of the glassy properties is only seen when the glass is subjected to quite extreme treatments such as very long waiting times, quenching or compression in the liquid and decompression in the glass. When the glass is cooled under “normal” isobaric conditions, not much happens under cooling. When the glass is formed the structure is frozen in, and this has the phenomenological consequence that most properties have very weak temperature
2.6. Fragility and other properties 17 dependence in the glass. This is also true for the glassy dynamics, which as we shall see in many cases just correspond to the fast dynamics in the liquid measured at T g . From the phenomenological point of view it is thus found that the major difference between glassy dynamics and fast dynamics in the liquid is that the former is virtually temperature independent while the latter can depend on temperature. Figure 2.3 illustrates how the glassy dynamics correspond to the fast dynamics. 2.5.3 Time scales - the actual phenomenology In the above we have considered dynamics happening at two different timescales. The actual phenomenology of glass-forming liquids is somewhat more complicated and also system dependent. The structural relaxation often bifurcates in two separate relaxations when the structural relaxation time is lower than approximately 10 −5 s. The process which appears in addition to the alpha process is faster and it has lower intensity as well as weaker temperature dependence. It is referred to as the slow beta-relaxation or the Johari Goldstein (JG) beta relaxation. The position of the bifurcation point differs by several decades from system to system (and from one experimental probe to another). Moreover, there are also numerous systems where this separation in two relaxations is not detectable. The JG-beta relaxation is faster than the alpha relaxation and it also stays active when the glass is formed. As such it is part of the fast as well as of the glassy dynamics. We shall deal a bit with the JG-process when discussing the interpretation of dielectric spectroscopy in chapter 5. However, the fast dynamics studied and discussed in this work occurs on a still faster time scale, namely in the pico-nanosecond range. 2.6 Fragility and other properties The fragility introduced in section 2.2 is the central point in our description of slow dynamics, and the main problem addressed here is to understand which properties (if any) relate to the fragility. The ultimate goal is to look for causal relations and to use them to understand what governs the viscous slowing down. We have already mentioned in section 2.3 that the fragility has been suggested to correlate to the departure from Debye relaxation. This correlation is just one among a large body of properties that have been suggested to correlate to the fragility. The excess in entropy of the liquid as compared to that of the glass has been found to decrease faster as a function of decreasing temperature in fragile liquids than
Page 1: THÈSE présentée par Kristine NIS
Page 5 and 6: Acknowledgement First of all I woul
Page 7 and 8: Contents Abstract iii Acknowledgeme
Page 9: CONTENTS ix 9 Summarizing discussio
Page 12 and 13: 2 Introduction fragility with other
Page 15: Résumé du chapitre 2 De manière
Page 18 and 19: 8 Slow and fast dynamics glass. The
Page 20 and 21: 10 Slow and fast dynamics energy in
Page 22 and 23: 12 Slow and fast dynamics increasin
Page 24 and 25: 14 Slow and fast dynamics (linear)
Page 28 and 29: 18 Slow and fast dynamics T > T 2
Page 30 and 31: 20 Slow and fast dynamics as theore
Page 32 and 33: 22 Slow and fast dynamics and sugge
Page 34 and 35: 24 Slow and fast dynamics The boson
Page 36 and 37: 26 Slow and fast dynamics modulus 3
Page 39 and 40: Chapter 3 What we learn from pressu
Page 41 and 42: 3.2. Empirical scaling law and some
Page 47 and 48: 3.3. Correlations with fragility 37
Page 49 and 50: 3.4. Temperature dependences 39 mea
Page 51: 3.5. Summary 41 assumption that the
Page 55 and 56: Chapter 4 Experimental techniques a
Page 57 and 58: 4.2. Dielectric spectroscopy 47 4.1
Page 59 and 60: 4.2. Dielectric spectroscopy 49 fie
Page 61 and 62: 4.3. Inelastic Scattering Experimen
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4.3. Inelastic Scattering Experimen
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Résumé du chapitre 5 La relaxatio
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72 Alpha Relaxation the dielectric
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74 Alpha Relaxation Measuring the c
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76 Alpha Relaxation 4 2 0 This work
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78 Alpha Relaxation for the 1 s iso
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80 Alpha Relaxation log10(τ α ) 2
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82 Alpha Relaxation 2 1 0 216.4K th
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84 Alpha Relaxation function has a
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86 Alpha Relaxation 2.5 2.5 2 2 log
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88 Alpha Relaxation 0.4 log 10 Im(
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90 Alpha Relaxation keeping the rel
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92 Alpha Relaxation correlation bet
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Chapter 6 High Q collective modes I
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6.1. Inelastic X-ray scattering 97
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6.2. Sound speed and attenuation 99
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6.3. Nonergodicity factor 105 where
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6.3. Nonergodicity factor 107 1 0.9
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6.3. Nonergodicity factor 109 high
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6.4. Nonergodicity factor and fragi
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6.5. Summary 117 d log (e(ρ))/ d l
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Résumé du chapitre 7 Dans ce chap
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122 Mean squared displacement colle
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124 Mean squared displacement 1.5 I
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126 Mean squared displacement 1.4 1
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128 Mean squared displacement a cen
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130 Mean squared displacement cumen
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132 Mean squared displacement / a
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134 Mean squared displacement I P i
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136 Mean squared displacement as be
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Résumé du chapitre 8 Le pic de bo
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142 Boson Peak The FEC-model sugges
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144 Boson Peak the Qout Q in factor
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146 Boson Peak We are mainly intere
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148 Boson Peak 1.5 x 10−3 ω [meV
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150 Boson Peak comparison of the ev
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152 Boson Peak In figure 8.6 we sho
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154 Boson Peak Predictions/explanat
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156 Boson Peak meaning that the Deb
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158 Boson Peak g(ω)/ω 2 [arb. uni
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160 Boson Peak are equivalent becau
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162 Boson Peak m P /m ρ 2 1.8 1.6
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164 Boson Peak S(ω) [arb.unit] S(
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166 Boson Peak 3 2.5 S(ω) [arb. un
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168 Boson Peak perature effect on t
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Chapter 9 Summarizing discussion Wh
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173 temperature in the harmonic app
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Chapter 10 Perspectives In this wor
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178 BIBLIOGRAPHY Angell, C. A. [199
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180 BIBLIOGRAPHY Casalini, R. and R
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182 BIBLIOGRAPHY Farago, B., Arbe,
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184 BIBLIOGRAPHY Inamura, Y., Arai,
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186 BIBLIOGRAPHY Monaco, A., Chumak
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188 BIBLIOGRAPHY Patkowski, A., Gap
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190 BIBLIOGRAPHY Sekula, M., Pawlus
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Appendix A Details on the samples T
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A.1. Cumene 195 the value found fro
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A.2. PIB 197 The temperature depend
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A.4. DBP 199 peak differently at di
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A.6. Other samples 201 NH 2 tempera
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Appendix B Data compilations B.1 Da
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B.1. Data compilation 205 DHIQ = De
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B.1. Data compilation 207 Triphenyl
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Appendix C Dielectric setup Figure
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Abstract The degree of departure fr
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