Phase field crystal simulations of the kinetics of Ostwald ripening in two dimensions

The kinetics of Ostwald ripening of solid domains in the liquid phase of one-component systems in two dimensions is investigated numerically via the phase field crystal model. The simulations, which are performed systematically as a function of volume fraction of the solid phase, show that dynamical scaling is reached during late times, and the growth law is in good agreement with the classical theory of Lifshitz, Slyozov, and Wagner (LSW), i.e., R[over ¯]∼t^{1/3}, an indication that domain growth is mediated by the long-range interdomain diffusion of atoms. In contrast to the LSW theory, however, the domain size distribution is symmetric, and can be fit with a Gaussian. The investigation of the topological domain structure, through the Voronoi tessellation of the domains' centers of mass shows that both the Lewis law and the Aboav-Weaire law of two-dimensional cellular patterns are satisfied, implying that the kinetics proceed such that the conformational entropy of the domain-containing Voronoi cells is maximized. These results are in very good agreement with an earlier experimental study of a phase-separating phospholipid-cholesterol Langmuir film.