Isotropic-nematic transition in a mixture of hard spheres and hard spherocylinders: scaled particle theory description

TL;DR

This paper develops a scaled particle theory to describe the thermodynamics of a mixture of hard spheres and spherocylinders, analyzing the isotropic-nematic transition and comparing results with simulations.

Contribution

It introduces analytical expressions for thermodynamic properties and formulates a nonlinear integral equation for the orientational distribution, advancing understanding of phase transitions in mixed particle systems.

Findings

The phase boundary shifts with sphere concentration.

The theory's predictions align with simulation data.

The total packing fraction at transition slightly increases.

Abstract

The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the minimization of free energy, a nonlinear integral equation for the orientational singlet distribution function is formulated. An isotropic-nematic phase transition in this mixture is investigated from the bifurcation analysis of this equation. It is shown that with an increase of concentration of hard spheres, the total packing fraction of a mixture on phase boundaries slightly increases. The obtained results are compared with computer simulations data.