Ph.D. thesis (pdf) - dirac

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90 Alpha Relaxation keeping the relaxation time constant. If this finding is indeed general then it suggests that the spectral shape of the alpha relaxation has the same intrinsic character as the isochoric fragility, namely that it stays constant along an isochrone (chapter 3). The isobaric fragility on the other hand will in general change when pressure changes. Hence, the pressure dependence of the isobaric fragility and spectral shape is in disagreement with the behavior expected from the correlation between the two. This leads us to suggest that the stretching might/or better correlate to the isochoric fragility than to the isobaric fragility. 200 150 m P 100 50 0 0.2 0.4 0.6 0.8 1 β KWW Figure 5.17: Isobaric fragility as a function of the stretching parameter. Circles represent polymers, diamonds represent molecular liquids. See the table in appendix B for numerical values and references. To test this hypo<strong>thesis</strong> we have collected data from literature reporting isobaric fragility and stretching of the relaxation at T g . We consider here the description of the shape of the relaxation function in terms of the KWW stretching parameter β KWW . This choice is made because it is convenient to use a description with only one parameter for the shape and because β KWW is the most reported of the liquids where m ρ is also available (see section 5.3.1). The compilation of this data is shown in figures 5.17 and 5.18 where both the isochoric (figure 5.18) and isobaric fragility at atmospheric pressure (figure 5.17) are plotted against the stretching parameter. There is a great deal of scatter in both figures. There is however an observable trend, the fragilities decrease with the stretching. The relative effect on the slowing down of the relaxation is characterized d log e(ρ) by the term α P T g d log ρ = m P /m ρ −1. In figure 5.19 we show the ratio m P /m ρ as a function of β KWW . It is clear that no correlation is found between this ratio and the stretching. This indicates that there is no relation between the effect of density on the correlation time and the spectral shape (see chapter 3). Based on the pressure dependence and the clear lack of correlation between stretching and the relative effect of density (seen in figure 5.19) we suggest that a possible
5.3. Spectral shape 91 200 150 m ρ 100 50 0 0.2 0.4 0.6 0.8 1 β KWW Figure 5.18: Isochoric fragility m ρ the stretching parameter β KWW . Circles represent polymers, diamonds represent molecular liquids. See the table in appendix A for numerical values and references. 3 2.5 m P /m ρ 2 1.5 1 0.2 0.4 0.6 0.8 1 β KWW Figure 5.19: The ratio between isochoric and isobaric fragility as a function of the stretching parameter β KWW . Circles represent polymers, diamonds represent molecular liquids. See the table in appendix A for numerical values and references.
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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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Page 45 and 46:
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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 84 and 85: 74 Alpha Relaxation Measuring the c
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 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 146 and 147: 136 Mean squared displacement as be
Page 149: 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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