A Concise Course on the Theory of Classical Liquids: Basics and Selected Topics

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Springer, May 13, 2016 - Science - 271 pages

This short primer offers non-specialist readers a concise, yet comprehensive introduction to the field of classical fluids – providing both fundamental information and a number of selected topics to bridge the gap between the basics and ongoing research.

In particular, hard-sphere systems represent a favorite playground in statistical mechanics, both in and out of equilibrium, as they represent the simplest models of many-body systems of interacting particles, and at higher temperature and densities they have proven to be very useful as reference systems for real fluids. Moreover, their usefulness in the realm of soft condensed matter has become increasingly recognized – for instance, the effective interaction among (sterically stabilized) colloidal particles can be tuned to almost perfectly match the hard-sphere model.

These lecture notes present a brief, self-contained overview of equilibrium statistical mechanics of classical fluids, with special applications to both the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere potential or closely related model potentials. In particular it addresses the exact statistical-mechanical properties of one-dimensional systems, the issue of thermodynamic (in)consistency among different routes in the context of several approximate theories, and the construction of analytical or semi-analytical approximations for the structural properties.

Written pedagogically at the graduate level, with many figures, tables, photographs, and guided end-of-chapter exercises, this introductory text benefits students and newcomers to the field alike.

 

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Contents

1 Summary of Thermodynamic Potentials
1
2 Summary of Equilibrium Statistical Ensembles
13
3 Density Expansion of the Equation of State
33
4 Spatial Correlation Functions and Thermodynamic Routes
97
Exact Solution for NearestNeighbor Interactions
125
6 Density Expansion of the Radial Distribution Function and Approximate Integral Equations
157
7 Exact Solution of the PercusYevick Approximation for Hard Spheres and Beyond
202
References
255
Index
267
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