Patchy sticky hard spheres: analytical study and Monte Carlo simulations

TL;DR

This study combines analytical theory and Monte Carlo simulations to explore how patchy sticky hard spheres behave, revealing how surface coverage and patch distribution influence fluid transitions and percolation.

Contribution

It provides an almost fully analytical approach to understanding patchy sphere interactions and validates findings with Monte Carlo simulations, advancing modeling of anisotropic colloidal particles.

Findings

Fluid-fluid transition and percolation lines depend on patch coverage and distribution.

Analytical treatment captures qualitative critical behavior.

Monte Carlo simulations support the theoretical predictions.

Abstract

We consider a fluid of hard spheres bearing one or two uniform circular adhesive patches, distributed so as not to overlap. Two spheres interact via a ``sticky'' Baxter potential if the line joining the centers of the two spheres intersects a patch on each sphere, and via a hard sphere potential otherwise. We analyze the location of the fluid-fluid transition and of the percolation line as a function of the size of the patch (the fractional coverage of the sphere's surface) and of the number of patches within a virial expansion up to third order and within the first two terms (C0 and C1) of a class of closures Cn hinging on a density expansion of the direct correlation function. We find that the locations of the two lines depend sensitively on both the total adhesive coverage and its distribution. The treatment is almost fully analytical within the chosen approximate theory. We test our findings by means of specialized Monte Carlo (MC) simulations and find the main qualitative features of the critical behaviour to be well captured in spite of the low density perturbative nature of the closure. The introduction of anisotropic attractions into a model suspension of spherical particles is a first step towards a more realistic description of globular proteins in solution.