Influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures

TL;DR

This study uses Monte Carlo simulations to explore how polydispersity affects the critical parameters of an effective potential model for asymmetric hard sphere mixtures, revealing shifts in critical points and implications for phase separation.

Contribution

It generalizes the depletion potential to include explicit size dispersity and analyzes its impact on critical parameters in asymmetric mixtures.

Findings

Polydispersity shifts the critical point to lower small particle volume fractions.

Inclusion of polydispersity moves the critical point into the percolating regime.

Results agree with generalized corresponding states predictions.

Abstract

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential (R. Roth {\em et al}, Phys. Rev. E{\bf 62} 5360 (2000)) designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: $q\equiv\sigma_s/\bar\sigma_b=0.1$ and $q=0.05$. We find that inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.