Polydisperse hard spheres at a hard wall

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.