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This short primer offers non-specialist readers a concise, yetcomprehensive introduction to the field of classical fluids - providing bothfundamental information and a number of selected topics to bridge the gapbetween the basics and ongoing research.
In particular, hard-sphere systems represent a favorite playground instatistical mechanics, both in and out of equilibrium, as they represent thesimplest models of many-body systems of interacting particles, and at highertemperature and densities they have proven to be very useful as referencesystems for real fluids. Moreover, their usefulness in the realm of softcondensed matter has become increasingly recognized - for instance, theeffective interaction among (sterically stabilized) colloidal particles can betuned to almost perfectly match the hard-sphere model.
These lecture notes present a brief, self-contained overview ofequilibriumstatistical mechanics of classical fluids, with specialapplications to both the structural and thermodynamic properties of systemsmade of particles interacting via the hard-sphere potential or closely relatedmodel potentials. In particular it addresses the exact statistical-mechanicalproperties of one-dimensional systems, the issue of thermodynamic(in)consistency among different routes in the context of several approximatetheories, and the construction of analytical or semi-analytical approximationsfor the structural properties.
Written pedagogically at the graduate level, with many figures, tables,photographs, and guided end-of-chapter exercises, this introductory textbenefits students and newcomers to the field alike.
List of contents
Foreword.- Preface.- Summary of Thermodynamic Potentials.- Summary of Equilibrium Statistical Ensembles.- Density Expansion of the Equation of State.- Spatial Correlation Functions and Thermodynamic Routes.- One-Dimensional Systems. Exact Solution for Nearest-Neighbor Interactions.- Density Expansion of the Radial Distribution Function. Approximate Integral Equations.- Exact Solution of the Percus-Yevick Approximation for Hard Spheres ... and Beyond.- Index.- References.
Summary
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
equilibriumstatistical 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.
