Hard sphere fluids confined between soft repulsive walls: A comparative study using Monte Carlo and density functional methods

Hard-sphere fluids confined between parallel plates a distance $D$ apart are studied for a wide range of packing fractions, including also the onset of crystallization, applying Monte Carlo simulation techniques and density functional theory. The walls repel the hard spheres (of diameter $\sigma$) with a Weeks-Chandler-Andersen (WCA) potential $V_{WCA}(z) = 4 \epsilon [(\sigma_w/z)^{12}-(\sigma_w/z)^6 + 1/4]$, with range $\sigma_w = \sigma/2$. We vary the strength $\epsilon$ over a wide range and the case of simple hard walls is also treated for comparison. By the variation of $\epsilon$ one can change both the surface excess packing fraction and the wall-fluid $(\gamma_{wf})$ and wall-crystal $(\gamma_{wc})$ surface free energies. Several different methods to extract $\gamma_{wf}$ and $\gamma_{wc}$ from Monte Carlo (MC) simulations are implemented, and their accuracy and efficiency is comparatively discussed. The density functional theory (DFT) using Fundamental Measure functionals is found to be quantitatively accurate over a wide range of packing fractions; small deviations between DFT and MC near the fluid to crystal transition need to be studied further. Our results on density profiles near soft walls could be useful to interpret corresponding experiments with suitable colloidal dispersions.