Critical Behavior of Non-ideal Systems

by Ivanov, Dmitry Yu.

• ISBN13: 9783527406586
• ISBN10: 3527406581
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-09-02
• Publisher: Wiley-VCH

Summary

This comprehensive systematic overview covers the static and dynamic critical phenomena of real, non-ideal fluids in the nearest vicinity of the critical point, offers new approaches and presents research results on the highest level. Including both theoretical and experimental researches, it also deals with the critical opalescence as phenomenon with continuously growing scattering multiplicity upon approaching the critical point.

Author Biography

Dmitry Yu. Ivanov is a professor at the Baltic State Technical University (St. Petersburg, Russia). His research focuses on thermodynamics, critical phenomena and phase transitions, theoretical and experimental investigations of multiple light scattering and correlation spectroscopy in application to Material Science and critical phenomena. His research activities included projects at the Nuclear Research Center in Dubna and Krichevsky Laboratory (Russia) and at the CNRS laboratories and Universities of Paris and Nice (France). He has authored about 70 scientific publications.

Table of Contents

Foreword to the Russian Edition	p. V
Foreword to the English Edition	p. VIII
Editor's Preface	p. XIII
Introduction	p. 1
The Statics of Critical Phenomena	p. 7
Statics of Critical Phenomena in the Nearest Vicinity of the Critical Point: Experimental Manifestation	p. 9
Short History of Critical Phenomena Research	p. 9
Peculiarities of the Experiment in the Nearest Vicinity of the Critical Point	p. 17
"Experimental" Critical Indices	p. 17
Determination of Critical Parameters	p. 19
Purity of Matter	p. 20
Determination of Critical Density	p. 21
Determination of Critical Temperature and Pressure	p. 23
Experiments Near the Critical Point in the Presence of the Gravitational Field	p. 24
The Gravitational Effect	p. 25
The Coexistence Curve	p. 26
Singularity of the Diameter of the Coexistence Curve	p. 32
The Critical Isotherm	p. 34
Isothermal Compressibility Along the Critical Isochore	p. 38
(p-T)-Dependence Along the Critical Isochore	p. 42
Critical Indices and Amplitudes	p. 45
Phenomenological Model of the Critical Behavior of Nonideal Systems	p. 45
Critical Indices: External Field Effects	p. 48
Critical Index [beta]	p. 48
The Gravitational Effect	p. 49
The Influence of Surface Forces	p. 50
The Influence of Fields: Comparison with Magnetic Materials	p. 51
Comparison with Metals	p. 53
Critical Index [delta]	p. 55
The Influence of Gravitation	p. 55
The Influence of Coulomb Forces	p. 56
Critical Index [gamma]	p. 57
The Influence of Gravitation	p. 57
Critical Index [alpha]	p. 61
The Influence of Gravitation	p. 61
Critical Index of the Correlation Radius [nu]	p. 63
Micellar Systems	p. 65
Influence of Boundaries: Finite-Size Effects	p. 66
Results and Consequences	p. 67
Some Unresolved Problems	p. 69
Critical Indices and Amplitudes	p. 76
Universal Relations Between Critical Indices	p. 76
Universal Relations Between Critical Amplitudes	p. 80
Correlation Between Critical Index and Critical Amplitude Values	p. 82
Thermodynamics of the Metastable State	p. 89
The "Pseudospinodal" Hypothesis	p. 89
The History of the Occurrence of the "Pseudospinodal Hypthesis"	p. 89
The Universal "Pseudospinodal"	p. 90
The van der Waals Spinodal	p. 91
First-Order Stability Conditions	p. 92
Higher Order Stability Conditions	p. 93
Approaching the Instability Points	p. 94
The Instability Area	p. 95
Thermodynamic Analysis of the "Pseudospinodal" Hypothesis	p. 96
Physics and Geometry	p. 96
Mathematical Foundation	p. 97
Thermodynamic Consequences	p. 98
Experimental Test of the "Pseudospinodal" Hypothesis	p. 100
The Dynamics of Critical Phenomena	p. 103
Foundations of Critical Dynamics	p. 105
Introduction	p. 105
Critical Fluctuations: Light Scattering Intensity	p. 107
Kinetics of Critical Fluctuations: Light Scattering Spectrum	p. 111
Dynamic Critical Indices and Universal Amplitude	p. 115
Scattering of Higher Orders	p. 118
Critical Opalescence: Modeling	p. 121
Introduction	p. 121
Techniques and Experimental Methods	p. 122
Experimental Setup	p. 123
General Characteristics	p. 123
The Optical System	p. 124
Correlator	p. 125
Time Correlation Function for High Scattering Multiplicities	p. 126
Cumulants of the Correlation Function	p. 127
Afterpulses	p. 130
Physical Modeling	p. 132
Model Systems	p. 132
Dependence of the Spectrum Half-width of Multiple Scattering on the Physical Characteristics of the System and on the Scattering Multiplicity	p. 133
Dependence on the Viscosity of the Fluid	p. 133
Dependence on the Optical Thickness of the Scattering Medium	p. 136
Angular Dependence	p. 136
Dependence on the Polarization Mode	p. 138
Dependence on the Concentration of the Scatterer	p. 140
Dependence on the Dimensions of the Scattering Media	p. 144
Mathematical Modeling	p. 146
The Simplest Diffusion Model Approach	p. 147
The First Approach	p. 147
The Second Approach	p. 148
Mathematical Model of Multiple Scattering	p. 153
Basic Concepts of Radiation-Transport Theory	p. 153
Multiple Scattering Spectra Determined via the Radiation-Transport Theory	p. 154
Transition to High Multiplicity Scattering	p. 156
Effect of the Shape of the Sample on the Mean Scattering Multiplicity	p. 159
On the Nature of the Constant [Gamma subscript 0]	p. 162
The Relation of [Gamma subscript 0] to the Size of the Scatterers	p. 162
The Relation of [Gamma subscript 0] to the Depth of the Diffusion Source	p. 163
Critical Opalescence: Theory and Experiment	p. 165
Introduction	p. 165
Theory of Critical Opalescence Spectra	p. 166
Analysis of the Behavior of [Gamma subscript m] Close to the Critical Point	p. 166
Calculation of the Limiting Values of Key Quantities	p. 169
Calculation of the Temperature Dependence	p. 172
Analysis of the Obtained Results	p. 173
Experiments Close to the Mixing Critical Point	p. 177
Experimental Setup	p. 177
Choice of the Object of Research	p. 180
Binary Mixture Aniline-Cyclohexane	p. 180
Experimental Results	p. 183
Heating of the "Critical" Medium by Probe Radiation	p. 184
Thermal Conductivity in the Vicinity of the Critical Point	p. 191
Introduction	p. 191
Thermal Conductivity of NH[subscript 3] Near to the Critical Point	p. 194
Experimental Setup for Determining Thermal Conductivity	p. 195
Experimental Results: Background Thermal Conductivity	p. 198
Extended Mode-Coupling (EMC) Theory	p. 201
Static Light Scattering: The Extinction Coefficient	p. 204
The Experimental Setup for Light Scattering	p. 205
Results and Analysis of the Optical Experiment	p. 206
Density Derivative of the Dielectric Constant	p. 207
Determination of [nu] and [xi subscript 0] Using Light Scattering	p. 208
Critical Dynamics: Comparison of Theory and Experiment	p. 212
Universal Dynamic Amplitude R	p. 213
Thermal Conductivity Critical Index, [open phi]	p. 213
Checking the Feasibility of the Universal Relations Between the Critical Amplitudes for Ammonia	p. 214
Thermal Conductivity of Ammonia in the Wide Neighborhood of the Critical Point	p. 215
Conclusion	p. 216
Some Applications of the Photon Correlation Technique	p. 219
Diffusing-Wave Spectroscopy	p. 219
Method of Determination of the Mean Dimension and Concentration of Suspended Particles	p. 221
Monitoring of Particle Motion in Drying Films	p. 224
Dynamics of Particle Formation and Growth	p. 225
Supercritical Fluids	p. 225
Opaque Systems	p. 226
Sol-Gel Process	p. 226
References	p. 229
Index	p. 249
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