Polydisperse hard spheres at a hard wall

TL;DR

This study combines Monte Carlo simulations and density functional theory to analyze how polydisperse hard spheres distribute near a hard wall, revealing size segregation, depletion effects, and local polydispersity variations.

Contribution

It provides a detailed comparison of DFT and simulation results for polydisperse spheres near a wall, highlighting the impact of polydispersity shape and degree on structural properties.

Findings

Excellent agreement between DFT and simulations at lower volume fraction.

Oscillatory size segregation effects depend on polydispersity shape.

Large particles are enhanced near the wall due to depletion interactions.

Abstract

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focussed on the local density distribution $\rho(\sigma,z)$, measuring the number density of particles of diameter $\sigma$ at a distance $z$ from the wall. The form of $\rho(\sigma,z)$ is obtained for bulk volume fractions $\eta_b=0.2$ and $\eta_b=0.4$ for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity $\delta=11.5%$ and $\delta=40.4%$, and a truncated Schulz form having $\delta=40.7%$. Excellent overall agreement is found between the DFT and simulation results, particularly at $\eta_b=0.2$. A detailed analysis of $\rho(\sigma,z)$ confirms the presence of oscillatory size segregation effects observed in a previous DFT study (Pagonabarraga {\em et al.}, Phys. Rev. Lett. {\bf 84}, 911 (2000)). For large $\delta$, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive $\sigma$-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity $\delta(z)$ is suppressed in this region, while further from the wall it exhibits oscillations.