Triangular lattice models for pattern formation by core-shell particles with different shell thicknesses.

Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with hard-cores covered by shells of cross-linked polymeric chains. In model II, such inner shell is covered by a much softer outer shell. In both models, the hard cores can occupy sites of the triangular lattice, and nearest-neighbor repulsion following from overlapping shells is assumed. The capillary force is represented by the second or the fifth neighbor attraction in model I or II, respectively. Ground states with fixed chemical potential µ or with fixed fraction of occupied sites c are thoroughly studied. For T > 0, the µ(c) isotherms, compressibility and specific heat are calculated by Monte Carlo simulations. In model II, 6 ordered periodic patterns occur in addition to 4 phases found in model I. These additional phases, however, are stable only at the phase coexistence lines at the (µ, T) diagram, which otherwise looks like the diagram of model I. In the canonical ensemble, these 6 phases and interfaces between them appear in model II for large intervals of c and the number of possible patterns is much larger than in model I. We calculated line tensions for different interfaces, and found that the favorable orientation of the interface corresponds to its smoothest shape in both models.

Thermodynamics and diffusion of a lattice gas on a simple cubic lattice.

A lattice gas model with nearest neighbor attractive interactions on a simple cubic lattice is considered. The method of nonequilibrium statistical ensembles due to Zubarev is used to derive expressions for jump and chemical diffusion coefficients. For thermally activated hopping dynamics in the hydrodynamical (low frequency, long wavelength) limit, and neglecting specific memory effects, these expressions are represented in a simple form in terms of the zero concentration limit of the chemical diffusion coefficient and equilibrium characteristics, i.e., the chemical potential, and the probability for two nearest neighbor sites to be vacant. These equilibrium characteristics are calculated by means of the self-consistent diagram approximation. The equilibrium characteristics and diffusion coefficients are in a good agreement with extensive Monte Carlo simulation results.