Some topics in statistical physics
Date
1974
Authors
White, Lee Raymond
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Abstract
The thesis is in two parts.
In Part One, the role of the angle-averaged potential
in the theory of non-simple liquids is investigated. Analytic
expressions for the angle-averaged potential are obtained and
their asymptotic approximations are derived and compared with
the exact expressions. The additivity of the angle-averaged
potential is discussed. The angle-averaged potential is shown
to provide a basis for the expression of the thermodynamic
properties of an angle-dependent system. The free energy for
such a system is derived as the sum of the free energy of the
simple system where the pair interaction is the angle-averaged
potential and a set of three body, four body etc. terms
involving the triplet and higher correlation functions for the
simple system. Some work on the two-dimensional coplanar point
dipole system is discussed. A first order perturbation theory
is derived where the reference potential is the angle-averaged
potential. This theory is compared with the first order
perturbation theory of Gubbins and Gray and the Mean
Spherical Model of Wertheim for the hard sphere plus imbedded
dipole system. The present theory is found to be in best
agreement with Monte Carlo studies of the exact dipole system. In Part Two the statistical mechanics of a model
adsorbed polymer is developed. The polymer is considered as a
string of non-interacting beads connected by freely rotating
bonds with an arbitrary bond length distribution. The beads
(Monomer units) are free to interact with the flat impenetrable
substrate via a one-body potential. Rigorous statistical formulae are derived for the expectation values of the number
of beads on the substrate, the spread of the polymer on the
substrate, the density of beads off the substrate and the
centre of mass of the polymer in terms of an adsorption energy
parameter W. These conformational properties are shown to
undergo a phase transition at a critical value of W=Wc , where
Wc is a functional of the bond length distribution function
only. For W>Wc the polymer is adsorbed on the wall and for
W<Wc the polymer moves into the bulk solvent and away from
the substrate. Some numerical calculations were carried out
with real polymer/solvent/substrate systems to discover whether
dispersion forces could yield values of W/Wc which could
span the complete range of behaviour of the adsorbed polymer.
The possibility of temperature and solvent-induced adsorption/
description phase transitions is exhibited.
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