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

TL;DR

This paper uses two-dimensional Cahn-Hilliard simulations to study the coarsening kinetics of spinodal decomposition in binary mixtures, revealing composition-dependent growth exponents and proposing a comprehensive model for coarsening behavior.

Contribution

It provides new insights into the coarsening exponent variability and introduces a model capturing the full kinetics of phase separation in binary mixtures.

Findings

Coarsening rate is slower than t^{1/3} for off-critical mixtures.

The coarsening exponent depends on mixture composition and morphology.

A model describing the complete coarsening kinetics is proposed.

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 $L\sim C t^{\alpha}$. To understand the structure-property relationship, the knowledge of the coarsening exponent $\alpha$ 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 mobility term and show that the coarsening for off-critical mixtures is slower than the expected $t^{1/3}$-growth. Instead, we find $\alpha$ to be dependent on the mixture composition and thus from the morphology. Finally, we propose a model to describe the complete coarsening kinetics including the rate constant $C$.