Entropic Forces in Binary Hard Sphere Mixtures: Theory and Simulation

TL;DR

This study combines Monte Carlo simulations and theoretical analysis to investigate entropic forces in binary hard-sphere mixtures, validating some classical theories and providing new insights into force behaviors at various densities.

Contribution

The paper offers a comprehensive simulation and theoretical comparison of entropic forces in binary mixtures, extending understanding beyond low-density limits.

Findings

Good agreement with HNC-based theoretical predictions.

Validation of the Derjaguin approximation for convex bodies.

Limitations of the Asakura-Oosawa theory at higher densities.

Abstract

We perform extensive Monte Carlo simulations of binary hard-sphere mixtures (with diameter ratios of 5 and 10), to determine the entropic force between (1) a macrosphere and a hard wall, and (2) a pair of macrospheres. The microsphere background fluid (at volume fractions ranging from 0.1 to 0.34) induces an entropic force on the macrosphere(s); the latter component is at infinite dilution. We find good overall agreement, in both cases, with the predictions of an HNC-based theory for the entropic force. Our results also argue for the validity of the Derjaguin approximation relating the force between convex bodies to that between planar surfaces. The earlier Asakura-Oosawa theory, based on a simple geometric argument, is only accurate in the low-density limit.