Field-Theoretic Simulation Method to Study the Liquid-Liquid Phase Separation of Polymers

Liquid-liquid phase separation (LLPS) is a process that results in the formation of a polymer-rich liquid phase coexisting with a polymer-depleted liquid phase. LLPS plays a critical role in the cell through the formation of membrane-less organelles, but it also has a number of biotechnical and biomedical applications such as drug confinement and its targeted delivery. In this chapter, we present a computational efficient methodology that uses field-theoretic simulations (FTS) with complex Langevin (CL) sampling to characterize polymer phase behavior and delineate the LLPS phase boundaries. This approach is a powerful complement to analytical and explicit-particle simulations, and it can serve to inform experimental LLPS studies. The strength of the method lies in its ability to properly sample a large ensemble of polymers in a saturated solution while including the effect of composition fluctuations on LLPS. We describe the approaches that can be used to accurately construct phase diagrams of a variety of molecularly designed polymers and illustrate the method by generating an approximation-free phase diagram for a classical symmetric diblock polyampholyte.