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Abstract
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A coarse-grained effective solvent model of two-patch particles is
extended to study the self-assembly of three- and four-patch particles to two-
dimensional honeycomb and square lattices, respectively. Employing this model, grand
canonical ensemble simulations are done to calculate vapor−liquid equilibria and the
critical temperatures for patchy particles of various patch widths. The range of stability
of the liquid, although very limited compared to isotropic particles, which interact
through a longer-range potential, depends on the patch width and on the number of
patches. Biased sampling and unbiased simulations are also done to investigate the
mechanism of nucleation and crystal growth for honeycomb and square lattices, self-assembled from three- and four-patch particles, respectively. A two-step mechanism governs the nucleation of both lattices. In the first step, the particles form a dense amorphous network, and in the second step, the particles inside the amorphous network reorient to form crystalline nuclei. Barrier heights for the nucleation of honeycomb and square lattices are 7.8 k B T and 7.4 k B T, which are close to the reported values for the nucleation of the kagome lattice. In agreement with confocal microscopy experiments, the self-assembly in a honeycomb lattice involves the formation of 5- to 7-membered rings. The 5- and 7-membered rings hamper the nucleation of the honeycomb lattice, through defect formation and rotation of the symmetry planes of crystals that form at their surfaces. With the progress of self-assembly, a substantial amount of restructuring of the defects and crystals in their vicinity is needed to heal the defects.
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