# Isotropic-Nematic Transition and Demixing Behaviour in Binary Mixtures of Hard Spheres and Hard Spherocylinders Confined in a Disordered Porous Medium: Scaled Particle Theory

## TL;DR

This paper develops a scaled particle theory to analyze the thermodynamics and phase behavior of a binary mixture of hard spheres and spherocylinders confined in a porous medium, predicting phase transitions and demixing phenomena.

## Contribution

The study introduces an improved scaled particle theory with corrections to describe isotropic-nematic transitions and demixing in confined binary mixtures of HS and HSC.

## Key findings

- Accurate phase diagrams for isotropic-nematic transition.
- Thermodynamic approach predicts demixing in phases.
- Porous medium influences phase transition behavior.

## Abstract

We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the analytical expressions of the free energy, the pressure and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equation for the orientation singlet distribution function and from the conditions of thermodynamic equilibrium. Both the approaches correctly predict the isotropic-nematic transition at low concentrations of hard spheres. However, the thermodynamic approach provides more accurate results and is able to describe the demixing phenomena in the isotropic and nematic phases. The effects of porous medium on the isotropic-nematic phase transition and demixing behaviour in a binary HS/HSC mixture are discussed.