Effective forces in square well and square shoulder fluids

TL;DR

This paper derives an analytical expression for the effective force between macrospheres in a fluid with square well or shoulder interactions, extending previous hard-core models and validating results with simulations.

Contribution

It introduces a new analytical formula for effective forces in square well and shoulder fluids, expanding prior hard-core interaction models.

Findings

Analytical expression for effective force derived.

Force profiles validated against Monte Carlo simulations.

Qualitative phase diagram features analyzed.

Abstract

We derive an analytical expression for the effective force between a pair of macrospheres immersed in a sea of microspheres, in the case where the interaction between the two unlike species is assumed to be a square well or a square shoulder of given range and depth (or height). This formula extends a similar one developed in the case of hard core interactions only. Qualitative features of such effective force and the resulting phase diagram are then analyzed in the limit of no interaction between the small particles. Approximate force profiles are then obtained by means of integral equation theories (PY and HNC) combined with the superposition approximation and compared with exact ones from direct Monte Carlo simulations.