Designing morphology of separated phases in multicomponent liquid mixtures

Morphology of multiphase membraneless organelles formed via intracellular phase separation plays an important role for their functionality. Yet, very little is known how intermolecular interactions can be tuned to achieve target microstructures of separated phases. To address this, we systematically investigate morphologies of coexisting phases obtained via phase separation in Flory-Huggins liquid mixtures with 4 or more components. We demonstrate that the topology of separated phases is completely determined by their surface tensions, while their volume fractions dictate the geometry of microstructure (e.g. droplets, percolated structure). We developed a novel method based on graphs that enabled us to enumerate all topologically distinct morphologies of separated phases. Each graph is associated with a set of inequalities for surface tensions and this enabled us to reverse engineered intermolecular interaction parameters to realize all topologically distinct morphologies for 4 coexisting phases. The developed approach is general and can be applied to design morphologies with an arbitrary number of coexisting phases.