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Triangular lattice models for pattern formation by hard-core soft-shellparticles at interfaces are introduced and studied in order to determine theeffect of the shell thickness and structure. In model I, we consider particleswith hard-cores covered by shells of cross-linked polymeric chains. In modelII, 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-neighborrepulsion following from overlapping shells is assumed. The capillary force isrepresented by the second- or the fifth neighbor attraction in model I or II,respectively. Ground states with fixed chemical potential $\mu$ or with fixedfraction of occupied sites c are thoroughly studied. For T > 0, the $\mu(c)$isotherms, compressibility and specific heat are calculated by Monte Carlosimulations. In model II, 6 ordered periodic patterns occur in addition to 4phases found in model I. These additional phases, however, are stable only atthe phase coexistence lines, i.e. in regions of zero measure at the $(\mu,T)$diagram which otherwise looks like the diagram of model I. In the canonicalensemble, these 6 phases and interfaces between them appear in model II forlarge intervals of c, and the number of possible patterns is much larger thanin model I. We calculated surface tensions for different interfaces and foundthat the favorable orientation of the interface corresponds to its smoothestshape in both models.

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