Two-dimensional Cahn–Hilliard simulations for coarsening kinetics of spinodal decomposition in binary mixtures

Abstract

The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale L ∼ Ct^α. To understand the structure–property relationship, the knowledge of the coarsening exponent α and the coarsening rate constant C is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn–Hilliard equation. We restrict ourselves to binary mixtures using a symmetric Flory–Huggins free energy and a constant composition-independent mobility term and show that the coarsening for off-critical mixtures is slower than the expected t^1/3-growth. Instead, we find α to be dependent on the mixture composition and associate this with the observed morphologies. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant C.