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.

Abstract. We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystal-liquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.

Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which is based on expanding the crystal partition function in terms of the number n of free particles while the remaining particles are frozen at their ideal lattice positions. The free energies of fcc/hcp and one branch of bcc agree well with Stillinger's approach truncated at n = 2. A second branch of bcc solutions features rather spreadout density distributions around lattice sites and large equilibrium vacancy concentrations and is presumably linked to the shear instability of the bcc phase. Within fundamental measure theory and the Stillinger approach (n = 2), hcp is more stable than fcc by a free energy per particle of about 0.001 k B T . In previous simulation work, the reverse situation has been found which can be rationalized in terms of effects due to a correlated motion of at least 5 particles in the Stillinger picture.