Classification of ordering kinetics in three-phase systems

Though equations of motion containing transport coefficients are required to 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-ordering phenomenology from a knowledge of a system's free-energy function, or phase 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 diagram, these considerations are sufficient to completely determine the phase-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 some surprisingly elaborate routes to the equilibrium state. A process is found whereby a crystalline condensation nucleus becomes coated with a shell of gas, buffering it from a majority metastable liquid phase. Our results, based on thermodynamic arguments, are supported by numerical solution of model B, which describes diffusive phase-ordering kinetics. Some of our predictions are tested against experimental observations of colloid-polymer mixtures, 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.