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Critical Behavior of Non-Ideal Systems: Dmitry Yu. Ivanov

Critical Behavior of Non-Ideal Systems

Dmitry Yu. Ivanov

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Content

Part I The Statics of Critical Phenomena
1 Statics of Critical Phenomena in the Nearest Vicinity of the Critical Point: Experimental Manifestation
1.1 Short History of Critical Phenomena Research
1.2 Peculiarities of the Experiment in the Nearest Vicinity of the Critical Point
1.2.1 "Experimental" Critical Indices
1.2.2 Determination of Critical Parameters
1.2.3 Purity of Matter
1.2.4 Determination of Critical Density
1.2.5 Determination of Critical Temperature and Pressure
1.3 Experiments Near the Critical Point in the Presence of the Gravitational Field
1.3.1 The Gravitational Effect
1.3.2 The Coexistence Curve
1.3.3 Singularity of the Diameter of the Coexistence Curve
1.3.4 The Critical Isotherm
1.3.5 Isothermal Compressibility Along the Critical Isochore
1.3.6 (p ? T)-Dependence Along the Critical Isochore
2 Critical Indices and Amplitudes
2.1 Phenomenological Model of the Critical Behavior of Nonideal Systems
2.2 Critical Indices: External Field Effects
2.2.1 Critical Index ?
2.2.1.1 The Gravitational Effect
2.2.1.2 The Influence of Surface Forces
2.2.1.3 The Influence of Fields: Comparison with Magnetic Materials
2.2.1.4 Comparison with Metals
2.2.2 Critical Index ?
2.2.2.1 The Influence of Gravitation
2.2.2.2 The Influence of Coulomb Forces
2.2.3 Critical Index ?
2.2.3.1 The Influence of Gravitation
2.2.4 Critical Index ?
2.2.4.1 The Influence of Gravitation
2.2.5 Critical Index of the Correlation Radius ?
2.2.6 Micellar Systems
2.2.7 Influence of Boundaries: Finite-Size Effects
2.2.8 Results and Consequences
2.2.9 Some Unresolved Problems
2.3 Critical Indices and Amplitudes
2.3.1 Universal Relations Between Critical Indices
2.3.2 Universal Relations Between Critical Amplitudes
2.3.3 Correlation Between Critical Index and Critical Amplitude Values
3 Thermodynamics of the Metastable State
3.1 The "Pseudospinodal" Hypothesis
3.1.1 The History of the Occurrence of the "Pseudospinodal Hypthesis"
3.1.2 The Universal "Pseudospinodal"
3.2 The van der Waals Spinodal
3.2.1 First-Order Stability Conditions
3.2.2 Higher Order Stability Conditions
3.2.3 Approaching the Instability Points
3.2.4 The Instability Area
3.3 Thermodynamic Analysis of the "Pseudospinodal" Hypothesis
3.3.1 Physics and Geometry
3.3.2 Mathematical Foundation
3.3.3 Thermodynamic Consequences
3.4 Experimental Test of the "Pseudospinodal" Hypothesis
Part II The Dynamics of Critical Phenomena
4 Foundations of Critical Dynamics
4.1 Introduction
4.2 Critical Fluctuations: Light Scattering Intensity
4.3 Kinetics of Critical Fluctuations: Light Scattering Spectrum
4.4 Dynamic Critical Indices and Universal Amplitude
4.5 Scattering of Higher Orders
5 Critical Opalescence: Modeling
5.1 Introduction
5.2 Techniques and Experimental Methods
5.2.1 Experimental Setup
5.2.1.1 General Characteristics
5.2.1.2 The Optical System
5.2.1.3 Correlator
5.2.1.4 Time Correlation Function for High Scattering Multiplicities
5.2.1.5 Cumulants of the Correlation Function
5.2.1.6 Afterpulses
5.3 Physical Modeling
5.3.1 Model Systems
5.3.2 Dependence of the Spectrum Half-width of Multiple Scattering on the Physical Characteristics of the System and on the Scattering Multiplicity
5.3.2.1 Dependence on the Viscosity of the Fluid
5.3.2.2 Dependence on the Optical Thickness of the Scattering Medium
5.3.2.3 Angular Dependence
5.3.2.4 Dependence on the Polarization Mode
5.3.2.5 Dependence on the Concentration of the Scatterer
5.3.2.6 Dependence on the Dimensions of the Scattering Media
5.4 Mathematical Modeling
5.4.1 The Simplest Diffusion Model Approach
5.4.1.1 The First Approach
5.4.1.2 The Second Approach
5.4.2 Mathematical Model of Multiple Scattering
5.4.2.1 Basic Concepts of Radiation-Transport Theory
5.4.2.2 Multiple Scattering Spectra Determined via the Radiation-Transport Theory
5.4.2.3 Transition to High Multiplicity Scattering
5.4.2.4 Effect of the Shape of the Sample on the Mean Scattering Multiplicity
5.5 On the Nature of the Constant ?0
5.5.1 The Relation of ?0 to the Size of the Scatterers
5.5.2 The Relation of ?0 to the Depth of the Diffusion Source
6 Critical Opalescence: Theory and Experiment
6.1 Introduction
6.2 Theory of Critical Opalescence Spectra
6.2.1 Analysis of the Behavior of ?m Close to the Critical Point
6.2.1.1 Calculation of the Limiting Values of Key Quantities
6.2.1.2 Calculation of the Temperature Dependence
6.2.1.3 Analysis of the Obtained Results
6.3 Experiments Close to the Mixing Critical Point
6.3.1 Experimental Setup
6.3.2 Choice of the Object of Research
6.3.3 Binary Mixture Aniline–Cyclohexane
6.3.4 Experimental Results
6.4 Heating of the "Critical" Medium by Probe Radiation
7 Thermal Conductivity in the Vicinity of the Critical Point
7.1 Introduction
7.2 Thermal Conductivity of NH3 Near to the Critical Point
7.2.1 Experimental Setup for Determining Thermal Conductivity
7.2.2 Experimental Results: Background Thermal Conductivity
7.2.3 Extended Mode-Coupling (EMC) Theory
7.3 Static Light Scattering: The Extinction Coefficient
7.3.1 The Experimental Setup for Light Scattering
7.3.2 Results and Analysis of the Optical Experiment
7.3.3 Density Derivative of the Dielectric Constant
7.4 Determination of ? and ?0 Using Light Scattering
7.5 Critical Dynamics: Comparison of Theory and Experiment
7.5.1 Universal Dynamic Amplitude R
7.5.2 Thermal Conductivity Critical Index, ?
7.5.3 Checking the Feasibility of the Universal Relations Between the Critical Amplitudes for Ammonia
7.5.4 Thermal Conductivity of Ammonia in the Wide Neighborhood of the Critical Point
7.6 Conclusion
A Some Applications of the Photon Correlation Technique
A.1 Diffusing-Wave Spectroscopy
A.2 Method of Determination of the Mean Dimension and Concentration of Suspended Particles
A.3 Monitoring of Particle Motion in Drying Films
A.4 Dynamics of Particle Formation and Growth
A.4.1 Supercritical Fluids
A.4.2 Opaque Systems
A.4.3 Sol–Gel Process

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