Thermodynamics of Hard Sphere and Spherocylinder Mixtures -- Scaled Particle Theory and Monte Carlo Simulations

TL;DR

This paper reviews scaled particle theory (SPT) and Monte Carlo simulations to analyze the thermodynamics of hard particle mixtures, including new results for ternary mixtures of spherocylinders and spheres, demonstrating SPT's accuracy.

Contribution

It extends scaled particle theory to multi-component mixtures and provides novel results for ternary systems with hard spherocylinders and spheres, validated by simulations.

Findings

SPT accurately predicts thermodynamic properties of hard particle mixtures.

New results for ternary mixtures of spherocylinders and spheres.

Good agreement between SPT and Monte Carlo simulations.

Abstract

We review the literature on scaled particle theory (SPT) and its extensions and discuss results applied to describe the thermodynamics of hard particle mixtures. After explaining the basic concepts of scaled particle theory to compute the free energy of immersing a particle into a mixture, examples are discussed for the simple case of a hard sphere dispersion and the free volume fraction of ghost spheres in a hard sphere dispersion. Next, the concept is applied to mixtures, and general expressions are shown that relate the free volume fraction in mixtures to the key thermodynamic properties, such as the chemical potential(s) and (osmotic) pressure. Subsequently, it is revealed how these concepts can be extended towards multi-component systems. It is shown that free volume fractions provide chemical potentials and total pressure of multi-component mixtures, and thereby yield the full equation of state. We present novel results for ternary particle dispersions composed of hard spherocylinders and two types of hard spheres differing in size. Throughout, we show the accuracy of SPT by comparing the results with those of Monte Carlo computer simulations.