Hard sphere fluids at a soft repulsive wall: A comparative study using Monte Carlo and density functional methods

Abstract

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 σ) with a Weeks-Chandler-, with range σ w = σ/2. We vary the strength ǫ over a wide range and the case of simple hard walls is also treated for comparison. By the variation of ǫ one can change both the surface excess packing fraction and the wall-fluid (γ wf ) and wallcrystal (γ wc ) surface free energies. Several different methods to extract γ wf and γ 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.

Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei

“…Of course, for very small crystalline clusters (containing a few hundred particles only) a systematic effect on the contact angle is expected due to line tension effects, for the cluster sizes shown (where N * is several thousands) such effects are too small to be distinguished, given our statistical errors. Of course, in view of all the possible uncertainties whether or not γ f c depends on the interface orientation, and consequently Wall tension of the AO model plotted vs. bulk colloid packing fraction η b , as obtained from the "ensemble mixing method", as described in [64,70]. Two choices of WCA potential are included, and the resulting differences ∆γ = γ wf − γwc at the phase transition are quoted.…”

“…If we nevertheless accept this approximation, we can conclude from the work of Zykova-Timan et al, [40] that γ f c = (0.96 ± 0.05)k B T /σ 2 . For the estimation of the wall tensions γ wf and γ wc recently several fairly accurate methods were developed [64,70]. Fig.…”

“…3 are included, but choose an initial state that is similar to the bulk metastable fluid (without walls) as an initial condition, the system develops towards a metastable state where the density of colloids just show the familiar layering at both walls (cf. the analogous data for hard spheres at η < η f presented in [64]), but it would take an unacceptable long time in the simulation until a wall-attached solid cluster would be nucleated. This expectation actually is born out by the simulations (see next section).…”

“…We refer the interested reader to Refs. [64,70] for details on this method. Here, we only emphasize the two following facts: (i) for a homogeneous bulk system, the function p(η) found in the NVT ensemble precisely coincides with its counterpart in the NpT ensemble [70]: thus finite size effects due to the change of the statistical ensemble are negligibly small in our problem.…”

“…[40,64] for references) and nucleation (e.g. [12,13]) have been studied extensively; but since there is evidence [65] that hard spheres at hard walls (as well as on walls where a soft repulsion acts [64]) exhibit complete wetting when the freezing fraction η f (cf. Fig.…”