Theory of spinodal decomposition assisted crystallization in binary mixtures

Abstract

We propose a general theory of crystallization of one component from an unstable mixture of two components by addressing the coupling between the spinodal decomposition associated with concentration fluctuations in the mixture and the nucleation kinetics for the crystallization. We propose that the domains created spontaneously by spinodal decomposition then present interfaces on which heterogeneous nucleation of the crystallizable component takes place with a much reduced nucleation barrier. Combining the theories of heterogeneous nucleation and spinodal decomposition kinetics, we present an analytic calculation of the nucleation rate as a function of the allowed duration of spinodal decomposition as well as the spinodal quench depth. In the present theory, shorter time evolution of spinodal decomposition or, equivalently, larger propensity of heterogeneous nucleation, results in faster crystallization. This is in contrast to the expectation of faster nucleation in more pure phases at later stages of spinodal decomposition. The analytic formula is found to correspond well with the recent experimental results on polymer mixtures for the late stage of spinodal decomposition kinetics. More detailed experiments are required to verify our prediction for the nucleation rate for early times and for different quench depths.