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136 Mean squared displacement as being due to the softening of the harmonic potential. The break in 〈u 2 〉 around T g is in this frame understood as being due the change in temperature dependence of the high frequency elastic constants (sound speeds) at T g (see sections 2.5 and 6.2). The arguments behind the elastic model ignore/disregard any possible contributions to 〈u 2 〉 from non-harmonic and relaxational movements. In order to test the elastic model it is necessary to assume that there is no extra relaxational motion contributing to 〈u 2 〉 around T g . However, it is not likely that this assumption is fulfilled. We know from the time of flight spectra that DHIQ has strong quasi-elastic scattering already at T g (section 8.3.3). The time of flight has a broader resolution function, so this quasi-elastic scattering correspond to relaxation at even shorter times than the 〈u 2 〉 we probe with backscattering. If the relaxational contribution is larger for more fragile liquids, then it might explain that the prediction of the elastic model appears to hold better for stronger systems. The alpha relaxation itself also enters the experimental window at some time, maybe already when τ α ≈ 1µs. This happens intrinsically faster for fragile liquids than for strong liquids. The fragility dependent difference in the temperature dependence of 〈u 2 〉 seen in figure 7.13 is difficult to anticipate very close to T g but becomes significant only above 1.1T g . This explains why differences that are apparent to the naked eye in figure 7.13 correspond to relatively small differences in figure 7.14. The liquids are already quite far from the glass transition at 1.1T g and the actual alpha relaxation time depends intrinsically and strongly on the fragility of the liquid. In figure 7.15 we show the mean square displacement of the least fragile of the systems we study, glycerol, and of the most fragile liquid, DHIQ. The mean square displacement is scaled with its values at T g as a function of temperature scaled with T g (hence, it is the same type of plot as the one depicted in figure 7.13, just with a different scale). Glycerol has τ α ≈ 0.01 s while the very fragile DHIQ has an alpha relaxation time of only τ α ∼ 1µs, meaning that their alpha relaxation time differ by four orders of magnitude when compared at T = 1.1T g . The alpha relaxation time of glycerol only becomes as fast as τ α ∼ 1µ s at a much higher temperature, namely around T = 1.3T g , where the mean square displacement of glycerol also increases rapidly. 7.7 Summary The mean square displacement at the nanosecond timescale has been studied as a function of temperature in a set of molecular liquids which covers a large range of fragilities.
7.7. Summary 137 The isobaric temperature dependence of the mean square displacement above T g was found to correlate with the isobaric fragility when comparing systems at atmospheric pressure in agreement with earlier results in literature. However, no systematics were found regarding the value of the mean square displacement at T g . We have found that the pressure dependent Lindemann criterion holds for the liquids studied. This suggests that there is an intimate relation between the amplitudes of vibrations and the transition from glass to liquid, in agreement with the elastic model [Dyre, 2006]. Moreover, we find that the order of magnitude of the temperature dependence of 〈u 2 〉 above T g agrees with the prediction of the elastic model. However, contributions from relaxational processes makes 〈u 2 〉 measured on the nanosecond timescale inadequate for precise quantitative test of the elastic model. The relaxational processes appear to have larger amplitude the more fragile the liquid is (see also section 8.3.3).
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THÈSE présentée par Kristine NIS
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Acknowledgement First of all I woul
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Contents Abstract iii Acknowledgeme
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CONTENTS ix 9 Summarizing discussio
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2 Introduction fragility with other
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Résumé du chapitre 2 De manière
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8 Slow and fast dynamics glass. The
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10 Slow and fast dynamics energy in
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12 Slow and fast dynamics increasin
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14 Slow and fast dynamics (linear)
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16 Slow and fast dynamics The dynam
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18 Slow and fast dynamics T > T 2
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20 Slow and fast dynamics as theore
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22 Slow and fast dynamics and sugge
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24 Slow and fast dynamics The boson
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26 Slow and fast dynamics modulus 3
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Chapter 3 What we learn from pressu
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3.2. Empirical scaling law and some
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3.3. Correlations with fragility 37
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3.4. Temperature dependences 39 mea
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3.5. Summary 41 assumption that the
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Chapter 4 Experimental techniques a
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4.2. Dielectric spectroscopy 47 4.1
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4.2. Dielectric spectroscopy 49 fie
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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
Page 96 and 97: 86 Alpha Relaxation 2.5 2.5 2 2 log
Page 98 and 99: 88 Alpha Relaxation 0.4 log 10 Im(
Page 100 and 101: 90 Alpha Relaxation keeping the rel
Page 102 and 103: 92 Alpha Relaxation correlation bet
Page 105 and 106: Chapter 6 High Q collective modes I
Page 107 and 108: 6.1. Inelastic X-ray scattering 97
Page 109 and 110: 6.2. Sound speed and attenuation 99
Page 115 and 116: 6.3. Nonergodicity factor 105 where
Page 117 and 118: 6.3. Nonergodicity factor 107 1 0.9
Page 119 and 120: 6.3. Nonergodicity factor 109 high
Page 121 and 122: 6.4. Nonergodicity factor and fragi
Page 127 and 128: 6.5. Summary 117 d log (e(ρ))/ d l
Page 129: Résumé du chapitre 7 Dans ce chap
Page 132 and 133: 122 Mean squared displacement colle
Page 134 and 135: 124 Mean squared displacement 1.5 I
Page 136 and 137: 126 Mean squared displacement 1.4 1
Page 138 and 139: 128 Mean squared displacement a cen
Page 140 and 141: 130 Mean squared displacement cumen
Page 142 and 143: 132 Mean squared displacement / a
Page 144 and 145: 134 Mean squared displacement I P i
Page 149: Résumé du chapitre 8 Le pic de bo
Page 152 and 153: 142 Boson Peak The FEC-model sugges
Page 154 and 155: 144 Boson Peak the Qout Q in factor
Page 156 and 157: 146 Boson Peak We are mainly intere
Page 158 and 159: 148 Boson Peak 1.5 x 10−3 ω [meV
Page 160 and 161: 150 Boson Peak comparison of the ev
Page 162 and 163: 152 Boson Peak In figure 8.6 we sho
Page 164 and 165: 154 Boson Peak Predictions/explanat
Page 166 and 167: 156 Boson Peak meaning that the Deb
Page 168 and 169: 158 Boson Peak g(ω)/ω 2 [arb. uni
Page 170 and 171: 160 Boson Peak are equivalent becau
Page 172 and 173: 162 Boson Peak m P /m ρ 2 1.8 1.6
Page 174 and 175: 164 Boson Peak S(ω) [arb.unit] S(
Page 176 and 177: 166 Boson Peak 3 2.5 S(ω) [arb. un
Page 178 and 179: 168 Boson Peak perature effect on t
Page 181 and 182: Chapter 9 Summarizing discussion Wh
Page 183 and 184: 173 temperature in the harmonic app
Page 185: Chapter 10 Perspectives In this wor
Page 188 and 189: 178 BIBLIOGRAPHY Angell, C. A. [199
Page 190 and 191: 180 BIBLIOGRAPHY Casalini, R. and R
Page 192 and 193: 182 BIBLIOGRAPHY Farago, B., Arbe,
Page 194 and 195: 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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