Density functional theory for Baxter's sticky hard spheres in confinement

TL;DR

This paper develops a new density functional theory for Baxter's sticky hard spheres under confinement, improving accuracy over previous models and applicable to adhesive hard sphere glasses.

Contribution

It introduces a regularized free energy functional combining weighted densities, enhancing accuracy for confined sticky hard spheres beyond Percus-Yevick approximations.

Findings

The new theory matches simulation data better than PY-based models.

It provides an exact zero-dimensional limit.

The free energy is applicable to adhesive hard sphere glasses.

Abstract

It has recently been shown that a free energy for Baxter's sticky hard sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard sphere fluid, provided that it obeys scaled-particle theory and the Percus-Yevick (PY) result for the direct correlation function [Hansen-Goos and Wettlaufer, J. Chem. Phys. {\bf 134}, 014506 (2011)]. Here, combining weighted densities from common versions of FMT with a new vectorial weighted density, we derive a regularization of the divergences of the associated strongly confined limit. Moreover, the simple free energy that emerges is exact in the zero-dimensional limit, leaves the underlying equation of state unaffected, and yields a direct correlation function distinct from the PY expression. Comparison with simulation data for both the bulk pair correlation function and the density profiles in confinement shows that the new theory is significantly more accurate than the PY-based results. Finally, the resulting free energy is applicable to a glass of adhesive hard spheres.