Role of metastable states in phase ordering dynamicsR

{ We show that the rate of separation of two phases of diierent densities (e.g. gas and solid) can be radically altered by the presence of a metastable intermediate phase (e.g. liquid). Within a Cahn-Hilliard theory we study the growth in one dimension of a solid droplet from a supersaturated gas. A moving interface between solid and gas phases (say) can, for suucient (transient) supersaturation, unbind into two interfaces separated by a slab of metastable liquid phase. We investigate the criteria for unbinding, and show that it may strongly impede the growth of the solid phase. The innuence of metastable states on the dynamics of phase transformations is an important issue in materials physics. Their role has long been acknowledged in metallurgy, where the rate of phase transformation is often limited by conduction of (latent) heat 1, 2]. Indeed, Ostwald's empiricaìrule of stages' 3] asserts that the transformation from one stable phase to another proceeds via all metastable intermediates in turn. In complex uid systems such as colloidal suspensions, particle diiusion, not heat diiusion, is often rate-limiting 4]. Here too, a strong innuence of metastable phases on ordering dynamics has been suggested, e.g. in the phase ordering kinetics of polymer liquid crystals 5], random-coil polymers 6], proteins 7] and colloid-polymer mixtures 8, 9]. In this Letter, we propose a simple model to account for the role of metastable states in phase ordering limited by particle diiusion (described by a conserved order parameter; for the nonconserved case, e.g. nematic order, see refs. 10]). To establish ideas, consider rst a homogeneous uid of a simple substance which is quenched to a temperature below its triple point. It will separate into two coexisting phases, the gas and the solid, whose densities are given by the construction in g. 1. However, in this temperature range, the low density ((uid) branch of the free energy has an additional minimum, representing the metastable liquid phase, whose presence can interfere with the phase separation process. Free energy curves of precisely this form can be realized in several complex uid systems, notably mixtures of spherical colloids and much smaller polymers 11]. Experiments 8] show that, when such a mixture is prepared with a composition at which a metastable minimum is present 11] it does not separate quickly into dilute colloidal uid and dense colloidal crystal (the predicted equilibrium phases). Instead, after an initial latency Typeset using EURO-L A …