Random systems of particles: An approach to polydisperse systems

Abstract

The concept of a random system of particles is introduced and a probabilistic description of these types of systems is given. In addition the relationship of random systems to polydisperse systems is explored. The random systems approach to polydisperse systems is a particle as opposed to a continuum type theory and yields a number of results concerning the particle structure of polydisperse systems as well as a statistical mechanical description of polydisperse systems. As an illustration, the thermodynamic properties of a polydisperse system of hard rods are obtained from first principles. Phase equilibrium in polydisperse systems is considered in the context of the random systems approach. A set of equilibrium conditions are derived and shown to be equivalent to conditions previously given.