Phase behavior and morphology of multicomponent mixtures

Multicomponent systems are ubiquitous in nature and industry. While the physics of binary and ternary liquid mixtures is well-understood, the thermodynamic and kinetic properties of N-component mixtures (N>3) have remained relatively unexplored. Inspired by recent examples of intracellular phase separation, we investigate equilibrium phase behavior and morphology of N-component mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm to construct complete phase diagrams, based on numerical convexification of the discretized free energy. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with N=4 and 5. We report on both the coarsening behavior of such systems and the resulting morphologies in 3D. The number of coexisting phases and their compositions can also be extracted with Principal Component Analysis (PCA) and K-Means algorithms. Finally, we discuss how to reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested "Russian dolls" and encapsulated Janus droplets.