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Theory of Liquids and Other Disordered Media: A Short Introduction 2015 ed. [Pehme köide]

  • Formaat: Paperback / softback, 167 pages, kõrgus x laius: 235x155 mm, kaal: 2876 g, 36 Illustrations, color; 19 Illustrations, black and white; XIV, 167 p. 55 illus., 36 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 887
  • Ilmumisaeg: 01-Sep-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319069497
  • ISBN-13: 9783319069494
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Theory of Liquids and Other Disordered Media: A Short Introduction 2015 ed.Suurem pilt
  • Formaat: Paperback / softback, 167 pages, kõrgus x laius: 235x155 mm, kaal: 2876 g, 36 Illustrations, color; 19 Illustrations, black and white; XIV, 167 p. 55 illus., 36 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 887
  • Ilmumisaeg: 01-Sep-2014
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319069497
  • ISBN-13: 9783319069494
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319069494.html
Märksõnad:
This set of lectures provides an introduction to the structure, thermodynamics and dynamics of liquids, binary solutions and polymers at a level that will enable graduate students and non-specialist researchers to understand more specialized literature and to possibly start their own work in this field.

Part I starts with the introduction of distribution functions, which describe the statistical arrangements of atoms or molecules in a simple liquid. The main concepts involve mean field theories like the Perkus-Yevick theory and the random phase approximation, which relate the forces to the distribution functions.

In order to provide a concise, self-contained text, an understanding of the general statistical mechanics of an interacting many-body system is assumed. The fact that in a classic liquid the static and dynamic aspects of such a system can be discussed separately forms the basis of the two-fold structure of this approach.

In order to allow polymer melts and solutions to be discussed, a short chapter acquaints readers with scaling concepts by discussing random walks and fractals.

Part II of the lecture series is essentially devoted to the presentation of the dynamics of simple and complex liquids in terms of the generalized hydrodynamics concept, such as that introduced by Mori and Zwanzig. A special topic is a comprehensive introduction of the liquid-glass transition and its discussion in terms of a mode-coupling theory.
1 Introduction
1(4)
References
2(3)
Part I Structure and Thermodynamics
2 Structure of Liquids
5(18)
2.1 Molecular Distribution Functions
5(2)
2.2 Scattering Theory
7(2)
2.3 Thermodynamic Relations
9(1)
2.4 Direct Correlation Function
10(1)
2.5 Density Response Function
11(1)
2.6 Mean Field Potential and Random Phase Approximation
12(1)
2.7 Integral Equation Theories for g(r)
12(1)
2.8 PY Solution for Hard Spheres
13(1)
2.9 Hard-Sphere Reference System
14(1)
2.10 Mean-Spherical Approximation
15(1)
2.11 Hard-Sphere Scaling of Liquid Metals
15(1)
2.12 Perturbative RPA for the Compressibility of Liquids
16(3)
2.13 Relation to the van-der-Waals Equation of State
19(1)
2.14 The Resistivity of Liquid Metals
20(3)
References
22(1)
3 Structure and Thermodynamics of Binary Mixtures (Solutions)
23(22)
3.1 General Definitions
23(1)
3.2 Cross-Sections and Partial Correlation Functions
24(2)
3.3 Number and Concentration Fluctuations
26(1)
3.4 Entropy of Mixing
27(1)
3.5 Partial Structure Factors of Ideal Solutions
28(1)
3.6 Direct Correlation Functions
28(1)
3.7 Perturbative RPA for Q = 0 and Regular Solution Model
29(2)
3.8 Activities and Activity Coefficients
31(1)
3.9 Partial Vapor Pressures Above a Regular Solution
32(1)
3.10 Phase Separation in Regular Solutions
32(2)
3.11 Phase Separation in Metal-Salt Solutions
34(1)
3.12 Integral Equation Theories for gij(r)
35(5)
3.12.1 The Liquid Alloy Li4Pb
37(2)
3.12.2 Critical Scattering in Mixtures with Demixing Transition
39(1)
3.13 Solutions of Polymers
40(5)
References
43(2)
4 Random Walk and Diffusion
45(16)
4.1 Einstein's Theory of Brownian Motion
45(2)
4.2 Diffusion Equation and Mean-Square Displacement
47(2)
4.3 Random Walk on a Lattice
49(3)
4.3.1 Master Equation
51(1)
4.4 Disordered Lattice and the Coherent-Potential Approximation (CPA)
52(9)
4.4.1 Percolating Lattice
55(1)
4.4.2 Continuum Limit: Activated Diffusion with Disorder
56(3)
References
59(2)
5 Fractals
61(14)
5.1 Fractal Dimension
61(3)
5.2 Percolation
64(1)
5.3 Random Walk on a Fractal
65(3)
5.3.1 Vibrations on a Fractal and Spectral Dimension
66(1)
5.3.2 The Vibrational Spectrum of Percolation Networks
67(1)
5.4 The ac Conductivity of a Fractal
68(2)
5.5 ac Conductivity of Porous Silicon
70(1)
5.6 The Fractal Dimension of a Self-avoiding Walk
71(2)
5.7 Diffusion-Limited Aggregation
73(2)
References
74(1)
6 Structure of Polymers
75(24)
6.1 Single Ideal Polymer Chain
75(4)
6.2 Swollen Polymer Chains
79(2)
6.3 Polymer Melts
81(1)
6.4 Polymer Solutions in Good Solvents
82(3)
6.5 Poor Solvents and Segregation
85(1)
6.6 Polymer Mixtures
86(2)
6.7 Diblock Copolymers
88(1)
6.8 Solid Polymers
89(1)
6.9 Gelation
90(3)
6.10 Elasticity of a Gel
93(6)
References
95(4)
Part II Dynamics
7 Time-Dependent Correlation and Response Functions
99(12)
7.1 Correlation Functions
99(3)
7.2 Linear Response and Fluctuation-Dissipation Theorem
102(2)
7.3 Kubo's Relaxation Function
104(1)
7.4 Moment Sum Rules and Continued-Fraction Expansions
105(2)
7.5 Projection Formalism of Mori and Zwanzig
107(4)
References
110(1)
8 Collective Excitations in Simple Liquids
111(10)
8.1 Linear Hydrodynamics
111(4)
8.2 Generalized Hydrodynamics
115(1)
8.3 Mode-Coupling Theory (MCT)
116(2)
8.4 Calculation of S(q,t) for Simple Liquids with MCT
118(3)
References
120(1)
9 Diffusive Motion in Simple Liquids
121(6)
9.1 Inelastic Neutron Scattering with a Mixture of Isotopes
121(1)
9.2 Individual-Particle Motion
122(1)
9.3 Jump Diffusion
123(1)
9.4 The Diffusivity of Interacting Colloidal Particles
124(3)
References
126(1)
10 Polymer Dynamics
127(12)
10.1 Dynamics of a Single Polymer: Rouse Model
127(3)
10.2 Rouse Dynamics with a Distribution of Interaction Constants
130(4)
10.3 Incoherent Relaxation Dynamics
134(1)
10.4 Hydrodynamic Interaction
135(1)
10.5 Zimm Model
136(1)
10.6 Diffusivity of a Single Polymer Chain in Solution
136(3)
References
137(2)
11 Glass Transition and Glass Dynamics
139(18)
11.1 Non-ergodicity and Glass Transition Phenomenology
139(4)
11.2 Idealized Glass Transition as Described by Mode-Coupling Theory
143(1)
11.3 Phenomenological Mode-Coupling Theory and Schematic Model
144(7)
11.3.1 Phenomenological Mode-Coupling Theory
144(1)
11.3.2 Schematic Model
145(4)
11.3.3 Summary of Anomalous Features Predicted by MCT
149(2)
11.4 Harmonic Vibrational Dynamics in Glasses
151(6)
11.4.1 Disordered Cubic Lattice and the Boson Peak
151(1)
11.4.2 Continuum CPA and Self-consistent Born Approximation, SCBA
152(4)
References
156(1)
12 Conclusions: Take-Home Messages
157(4)
12.1 The Structure of Simple Liquids Is Essentially Determined by the Hard Core of the Potential
157(1)
12.2 The Long-Wavelength Limit of the Structure Factors S(0) Gives a Relation to the Thermal Properties of Soft Materials
157(1)
12.3 The Perturbative Random-Phase Approximation (RPA) Describes Well the Deviations from the Hard-Sphere Structure
157(1)
12.4 In Binary Mixtures the Perturbative RPA Forms the Basis of the Regular-Solution Theory
158(1)
12.5 A Random Walk Is a Path of a Walker in Which the Direction Is Changed at Every Time Step Randomly and Is Described by the Diffusion Equation
158(1)
12.6 Fractals Have Non-integer Dimensionality
158(1)
12.7 A Random Walk Is a Fractal with Fractal Dimension 2
159(1)
12.8 The Thermodynamics of Polymers Are Governed by Their Fractal Scaling Properties
159(1)
12.9 The Dynamical Properties of Liquids Can Be Conventionally Described by Time Correlation Functions
159(1)
12.10 The Collective Excitations of a Simple Liquid Can Be Well Described by Mode-Coupling Theory
159(1)
12.11 Incoherent Liquid Dynamics Is Governed by Diffusion
160(1)
12.12 The Basic Polymer Dynamics Is Described by the Rouse Model, But a More Realistic Description Involves Disorder and Interaction
160(1)
12.13 The Liquid-to-Glass Transition Is a Transition from an Ergodic to a Nonergodic State
160(1)
12.14 Inside the Glassy State the High-Frequency Vibrations Show Irregularities Produced by the Quenched Disorder
160(1)
A Fourier Transforms 161(2)
B Laplace Transforms 163(2)
C Velocity Autocorrelation, Diffusivity and Mean-Square Displacement 165