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74 Alpha Relaxation Measuring the capacitance. The capacitance is measured using a HP 4284A LCR-meter which covers the frequency range from 100Hz to 1MHz. The LCR-meter gives the complex capacitance directly as output. The measurement is based on a four point method. This means that the signal of the wires leading to the sample is eliminated. In order to exploit this advantage to its maximum it is important that the connection point of the wires is as close as possible to the dielectric cell, and it is therefore placed right outside the conical closing piece. The low frequency range from 100Hz to 1Hz is covered using a SR830 lockin. The lockin measures the amplitude and phase of output voltage with respect to an input voltage at a specified frequency. The sample capacitor is connected with a grounded known resistance. The frequency dependent capacitance of the sample is calculated based on the known characteristics of this network. The experiments Liquid m-toluidine was measured on one isotherm at 216.4 K. DBP was measured along 4 different isotherms: 205.5 K, 219.3 K, 236.3 K and 253.9 K, at pressures up to 4 kbar. DBP was moreover measured at different temperatures along two isobars: atmospheric pressure and 230 MPa. [Niss et al., 2007] (See appendix A for details on the samples). The pressure was continuously adjusted during the experiment along the 230 MPa isobar in order to compensate for the decrease of pressure which follows from the contraction of the sample due to decreasing temperature. It is of course always possible to reconstruct isobars based on experiments performed under isotherm conditions. However, such a procedure mostly involves interpolation of the data, which is avoided by performing a strictly isobaric measurement. For DBP we have obtained relaxation-time data at times shorter than 10 −6.5 s by using the high-frequency part of the spectrum and assuming time-temperature and time-pressure superposition (TTPS). Although TTPS is not followed to a high precision (see section 5.3.2), the discrepancies lead to no significant error on the determination of the relaxation time. This is verified by comparison to atmospheric-pressure data from the literature (see figure 5.2). Data were in all cases taken both by compression and decompression. By doing so we have verified that there was no hysteresis in the pressure dependence of the dynamics. This serves to confirm that the liquid has been kept at thermodynamical equilibrium at all stages.
5.2. Relaxation time 75 Data treatment The relaxation time is determined from a polynomial fit of the logarithm of the loss as function of the logarithm of the frequency. The fit is performed over less than a decade around the top. The further treatment, e.g. evaluation of the fragility and analysis of the spectra shape, is discussed in detail in the course of the chapter. 5.2 Relaxation time 5.2.1 Dibutyl phtalate The relaxation time of DBP at atmospheric pressure is shown in figure 5.2 along with literature results. T g (P atm ) = 177 K, when defined as the temperature where τ α = 100 s. We also present the data taken at P = 230 MPa in this figure. It is clearly seen that T g increases with pressure. An extrapolation of the data to τ α = 100 s gives T g = 200 K for P = 230 MPa, corresponding to dT g /dP = 0.1 K.MPa −1 . This corresponds well to the pressure dependence of T g (at τ α = 1 s) reported by Sekula et al. [2004], based on measurements taken at pressures higher than 600 MPa. It is however a stronger pressure dependence than dT g /dP = 0.06 K.MPa −1 reported by Fujimori et al. [1997] based on isothermal calorimetry. This indicates that the calorimetric and the dielectric relaxation may have somewhat different dependence of density. In figure 5.3 we illustrate the determination of T g and of the fragility m P for the atmospheric-pressure data, using the part of the atmospheric-pressure data of figure 5.2 where the relaxation time is longer than a millisecond. Along with the data we show the VTF fit (equation 2.2.2) from Sekula et al. [2004] extrapolated to low temperatures, which gives T g = 177.4 K and m P = 84. We have also performed a new VTF fit restricted to the data in the 10 −6 s−10 2 s region. The result of this fit yields T g = 176.6 K and m P = 82. Finally, we have made a simple linear estimate of log 10 τ α as a function of 1/T in the temperature range shown in the figure. This linear slope fits the data close to T g better than any of the VTF fits. The corresponding glass transition temperature and fragility are T g = 176 K and m P = 70. This illustrates that the determination of T g is rather robust while this is less so for the fragility. This latter depends on how it is obtained, and the use of extrapolated VTF fits can lead to an overestimation. (Of course, a VTF fit made over a very narrow range, e.g. 10 −2 s − 10 2 s, will agree with the linear fit, because the VTF becomes essentially linear over the relevant range.) The fragility of DBP
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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
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
Page 79: Résumé du chapitre 5 La relaxatio
Page 82 and 83: 72 Alpha Relaxation the dielectric
Page 86 and 87: 76 Alpha Relaxation 4 2 0 This work
Page 88 and 89: 78 Alpha Relaxation for the 1 s iso
Page 90 and 91: 80 Alpha Relaxation log10(τ α ) 2
Page 92 and 93: 82 Alpha Relaxation 2 1 0 216.4K th
Page 94 and 95: 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
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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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