The Mie ( λr, λa) intermolecular pair potential has been suggested as an alternative
to the traditional (12,6) Lennard-Jones potential for modelling real system both via
simulations and theory. Its implementation as a molecular-based equation of state
for the fluid phase has led to accurate derivative thermophysical properties, which
cannot be obtained when potentials of fixed exponents are considered. In this work,
the effect the attractive and repulsive exponents have on the solid-liquid-vapour phase
behaviour of this class of potentials is studied. A novel simulation technique, involving
use of a direct interfacial methodology, is presented and is used to obtain the solid-fluid
phase boundaries of monomer and chain systems of Mie potentials. The methodology
is used in conjunction with simulation techniques for vapour-liquid and solid-vapour
coexistence to determine the global phase behaviour of a number of potentials of this
family. The application of the principle of corresponding states is discussed, with the
focus of obtaining a unified view of the thermodynamic equilibrium properties of the
Mie potential. A three parameter corresponding states model is presented, where a
third parameter α, which corresponds to the mean-field integrated energy is proposed.
A unique relationship between the stable fluid range and α is presented, which can be
used to predict exponent parameters of the Mie models that can be used to treat real
systems. An equation of state (EOS) for the solid phase of Mie spheres and chains is
presented by extending Wertheim's thermodynamic perturbation theory (TPT1) to the
solid phase. The SAFT-VR framework (on which TPT1 is based) is used in conjunction
with the perturbation theory of Kang et al. for treatment of simple spherical solids to
develop the SAFT-VR Mie solid EOS. This EOS is used with the recently presented
SAFT-VR Mie fluid EOS of Lafitte et al., to solve for coexistence and determine the
global phase behaviour of a host of Mie potentials of varying range of attraction. The
accuracy of the theory is validated against the simulation results of this work and
following this, the limiting behaviour of Mie chain systems is determined using the
theory.