Classification of ordering kinetics in three-phase systems - art. no. 031403

Though equations of motion containing transport coefficients are required t o quantitatively predict the phase-ordering dynamics of any given system, a great deal can be gleaned Just from the shape of the free-energy landscape . We demonstrate how to extract the most information concerning phase-order ing phenomenology from a knowledge of a system's free-energy function, or p hase diagram. Many putative pathways to equilibrium can be ruled out on the grounds of the second law of thermodynamics. In some parts of the phase di agram. these considerations are sufficient to completely determine the phas e-ordering process without ever having to calculate a transport coefficient . even when three phases are present. The results include a large number of regions of the phase diagram with distinct phase-ordering kinetics, and so me surprisingly elaborate routes to the equilibrium state. A process is fou nd whereby a crystalline condensation nucleus becomes coated with a shell o f gas, buffering it from a majority metastable liquid phase. Our results, b ased on thermodynamic arguments, are supported by numerical solution of mod el B. which describes diffusive phase-ordering kinetics. Some of our predic tions are tested against experimental observations of colloid-polymer mixtu res. described in more detail in the preceding paper [F. Renth. W.C.K. Poon , and R.M.L. Evans, Phys. Rev. E 64, 031402 (2001)]. A compact notation is developed to represent intricate phase-ordering pathways.