Does confining the hard-sphere fluid between hard walls change its average properties?

TL;DR

This study investigates how confining a hard-sphere fluid between smooth hard walls affects its average thermodynamic and kinetic properties, revealing insensitivity under many conditions but notable deviations when the confinement is very tight and dense.

Contribution

The paper demonstrates that confinement has minimal impact on average properties of the hard-sphere fluid except in dense, narrow gaps, and provides an analytical relation linking confined and bulk densities.

Findings

Inhomogeneous structuring has negligible effect on average properties over broad conditions.

A simple analytical equation relates confined and bulk fluid densities.

Significant deviations occur only in dense, narrow confinements below three particle diameters.

Abstract

We use grand canonical transition-matrix Monte Carlo and discontinuous molecular dynamics simulations to generate precise thermodynamic and kinetic data for the equilibrium hard-sphere fluid confined between smooth hard walls. These simulations show that the pronounced inhomogeneous structuring of the fluid normal to the confining walls, often the primary focus of density functional theory studies, has a negligible effect on many of its average properties over a surprisingly broad range of conditions. We present one consequence of this insensitivity to confinement: a simple analytical equation relating the average density of the confined fluid to that of the bulk fluid with equal activity. Nontrivial implications of confinement for average fluid properties do emerge in this system, but only when the fluid is both (i) dense and (ii) confined to a gap smaller than approximately three particle diameters. For this limited set of conditions, we find that "in-phase" oscillatory deviations in excess entropy and self-diffusivity (relative to the behavior of the bulk fluid at the same average density) occur as a function of gap size. These paired thermodynamic/kinetic deviations from bulk behavior appear to reflect the geometric packing frustration that arises when the confined space cannot naturally accommodate an integer number of particle layers.