Phase Behaviour of Binary Hard-Sphere Mixtures: Free Volume Theory Including Reservoir Hard-Core Interactions

TL;DR

This paper extends the free volume theory to better predict phase behavior in binary hard-sphere mixtures by explicitly including reservoir interactions, resulting in improved agreement with computer simulations.

Contribution

The authors develop an extended free volume theory that incorporates reservoir hard-core interactions, enhancing predictive accuracy for phase diagrams of binary colloidal mixtures.

Findings

Accurately predicts phase diagrams matching simulations

Improves understanding of size ratio effects on phase behavior

Demonstrates qualitative differences at specific size ratios

Abstract

Comprehensive calculations were performed to predict the phase behaviour of large spherical colloids mixed with small spherical colloids that act as depletant. To this end, the free volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] is used as a basis and is extended to explicitly include the hard-sphere character of colloidal depletants into the expression for the free volume fraction. Taking the excluded volume of the depletants into account in both the system and the reservoir provides a relation between the depletant concentration in the reservoir and in the system that accurately matches with computer simulation results of Dijkstra et al. [Phys. Rev. E 59 (1999) 5744]. Moreover, the phase diagrams for highly asymmetric mixtures with size ratios q . 0:2 obtained by using this new approach corroborates simulation results significantly better than earlier FVT applications to binary hard-sphere mixtures. The phase diagram of a binary hard-sphere mixture with a size ratio of q = 0:4, where a binary interstitial solid solution is formed at high densities, is investigated using a numerical free volume approach. At this size ratio, the obtained phase diagram is qualitatively different from previous FVT approaches for hard-sphere and penetrable depletants, but again compares well with simulation predictions.