Density profiles and pair correlation functions of hard spheres in narrow slits

TL;DR

This study uses a weighted density functional theory to analyze the behavior of hard sphere fluids confined in narrow slits, providing detailed profiles and forces, and extending results to sphere interactions.

Contribution

It applies a specific density functional theory to quantitatively analyze confined hard sphere fluids, including density profiles and solvation forces, with validation against rigorous results.

Findings

Density profile remains finite and large as slit width approaches sphere diameter.

Quantitative agreement with rigorous results for density profiles.

Derived solvation force between large spheres in small sphere fluid.

Abstract

A hard sphere fluid confined by hard, structureless, and parallel walls is investigated using a certain version of weighted density functional theory. The density profile, the excess coverage, the finite size contribution to the free energy, the solvation force, and the total correlation function are determined as function of the slit width $L$ for various bulk number densities $\rho_b$. In quantitative agreement with rigorous results the present version of density functional theory yields a constant and large but finite number density profile for the limiting case that $L$ is reduced to the diameter of the hard spheres. Within the Derjaguin approximation the results for the slit geometry allows us to obtain the solvation force between two large hard spheres immersed into a fluid of much smaller hard spheres.