Selected topics in the statistical mechanics of fluids.

The phase behaviour and thermodynamic properties of simple model mixtures
are examined using the statistical associating fluid theory as extended to chain
molecules interacting with potentials of variable range (SAFT-VR), and by computer
simulation. The SAFT-VR approach is based on an accurate and compact
representation of the free energy of chain molecules. We present the SA FT -VR
methodology as applied to mixtures of non-conformal molecules. A series of mixing
rules are presented, beginning with the van der Waals one-fluid prescription
and including more complex treatments. The vapour-liquid equilibria of a mixture
consisting of hard spheres and square-well monomers is examined with the
SAFT-VR equation of state, together with the liquid-liquid equilibria of a symmetrical
square-well mixture with no unlike interactions. Additionally, we examine
the vapour-liquid equilibria of a square-well monomer-dimer mixture, composed of
equal-sized segments, both with the SAFT-VR approach and by Gibbs ensemble
Monte Carlo simulation. The simulation data are used to determine the vapourliquid
critical line of the mixture. An extension of the SAFT-VR approach to
describe the phase behaviour of chain molecules interacting with a soft repulsive
potential and an attractive well of variable range is presented. We focus on the
vapour-liquid properties of Lennard-Jones chains using a simple recipe for the evaluation
of the chain free energy. We also perform a case study for a specific class
of phase equilibria exhibited by binary mixtures, where systems are seen to posses
a region of closed-loop immiscibility in their phase diagrams. We examine the
nature of this type of pl1ase behaviour using the SA FT· VR equation of state and
Gibbs ensemble simulation for a simple model system with an anisotropic bonding
site, which is seen to be the governing factor in the appearance of the region
of low-temperature miscibility for this system. The model is chosen in order to
mimic the physical features of real systems which exhibit this type of re-entrant
phase behaviour. The critical regions of this model are examined using a finite-size
scaling analysis performed in the semigrand canonical ensemble.