Ph.D. thesis (pdf) - dirac

More documents

Recommendations

Info

$Guide to Imfufa LaTeX - dirac$

36 What we learn from pressure experiments 3.3 Correlations with fragility As described in section 2.6 there is a flourishing variety of correlations between fragility and other properties of the liquids or its corresponding glass. These correlations hold a lot of empirical information which should be useful as guidelines and tests in the development of models and theories of the dynamics in viscous liquids. However in order for this to be possible, it is important to clarify if the correlations result from, and consequently unveil information on, the effect of density on the relaxation time, the intrinsic effect of temperature on the relaxation time, (or a balanced combination of the two). In the following we provide a framework for analyzing correlations between fragility and other properties of the liquid or glass by disentangling temperature and density effects [Niss and Alba-Simionesco, 2006; Niss et al., 2007]. The arguments presented in this section are not relevant for correlations between fragility and the temperature dependence in the liquid of some other property. These types of correlations are specifically considered in section 3.4 3.3.1 Pressure and isobaric fragility The correlations between fragility and other properties that have been suggested in literature all refer to the standard isobaric fragility. They are obtained empirically by plotting the property in question as a function of fragility (measured at T g , τ ≈ 100 s -1000 s). The plots obtained in this way are mostly very scattered, which is to be expected, because specific characteristics of the system can affect either the fragility or the property which is suggested to correlate with fragility. Assuming that there is nothing special about atmospheric pressure (from the point of view of the liquid), then a strict correlation to m P should follow this pressure dependence, where the property correlating to m P is to be evaluated at the same pressure. Consequently, the simplest way in which pressure can be used to test this type of correlation is to view pressure as a smooth way to change the isobaric fragility without changing the chemistry of the system. The correlation between isobaric fragility and some chosen property can then be scrutinized by measuring both quantities as a function of pressure. If the property in question has a pressure dependence which is consistent with the correlation then the situation would be the one illustrated in figure 3.2. This type of agreement would suggest that the property in question is sensitive to the same factors as the isobaric fragility, m P .
3.3. Correlations with fragility 37 Property increasing P Fragility Figure 3.2: An illustration of how a correlation between a property and isobaric fragility could be most simply tested with pressure experiments (section 3.3.1). 3.3.2 Isochoric fragility The existence of a correlation with fragility is always interpreted as indicating that the property in question is related to the effect of temperature on the structural relaxation. Moreover, computer simulations and theoretical attempts to understand these correlations, and viscous slowing down in general, mainly consider isochoric conditions, hence taking into account only the effect of temperature, see e.g. [Parisi et al., 2004; Bordat et al., 2004; Srivastava and Das, 2001; Ruocco et al., 2004]. However, when a liquid is cooled isobarically the thermal energy decreases and the density increases at the same time and the isobaric fragility contains, as we have seen, information on both these effects. According to the discussion in section 3.2.2, a property which is related to the pure effect of temperature should be correlated to the isochoric fragility. From equation 3.2.8 it can be seen that m P contains m ρ , and it has consistently been found by including a large amount of fragile and intermediate systems that m ρ correlates to the ambient pressure m P [Casalini and Roland, 2005 a]. It is therefore very possible that the correlations which have been proposed as correlations to the conventional isobaric fragility are in fact reminiscences of a more fundamental correlation to m ρ . The scaling described equation 3.2.1 must be taken as an empirical result and despite the variety of systems for which it has been shown to hold, there is no guarantee that it is universal. However, the scaling gives a rationalized picture of the pressure and temperature dependence of the relaxation time in the data obtained so far on polymers and molecular liquids. The emerging picture is that m ρ is intrinsic to the system in the sense that it is density independent. A quantity correlating to the
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 26 and 27: 16 Slow and fast dynamics The dynam
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 43 and 44: 3.2. Empirical scaling law and some
Page 45: 3.2. Empirical scaling law and some
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 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 111 and 112:
Page 113 and 114:
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 123 and 124:
Page 125 and 126:
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
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,
Page 196 and 197:
186 BIBLIOGRAPHY Monaco, A., Chumak
Page 198 and 199:
188 BIBLIOGRAPHY Patkowski, A., Gap
Page 200 and 201:
190 BIBLIOGRAPHY Sekula, M., Pawlus
Page 203 and 204:
Appendix A Details on the samples T
Page 205 and 206:
A.1. Cumene 195 the value found fro
Page 207 and 208:
A.2. PIB 197 The temperature depend
Page 209 and 210:
A.4. DBP 199 peak differently at di
Page 211 and 212:
A.6. Other samples 201 NH 2 tempera
Page 213 and 214:
Appendix B Data compilations B.1 Da
Page 215 and 216:
B.1. Data compilation 205 DHIQ = De
Page 217 and 218:
B.1. Data compilation 207 Triphenyl
Page 219 and 220:
Appendix C Dielectric setup Figure
Page 222:
Abstract The degree of departure fr
show all

Ph.D. thesis (pdf) - dirac

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?