Hybrid Field Theory and Particle Simulation Model of Polyelectrolyte-Surfactant Coacervation

Solutions of oppositely-charged polyelectrolytes and surfactants have been widely studied for a variety of applications; they play an important role in the formulation of personal care products, can be used as an effective strategy for drug encapsulation, and serve as analogues to biological systems such as biomolecular condensates. Surfactant molecules self-assemble into micellar macroions that are known to form complexes with oppositely-charged polyelectrolytes, and can undergo a bulk liquid-liquid phase separation known as complex coacervation. This process results in a `coacervate' phase that is rich in macroions, and a `supernatant' phase that is dilute in macroions. It is challenging to model this phase separation process, due to the disparate length scales and strong Coulombic interactions in these mixed macroion systems. In this work, we present a hybrid simulation and field theory model to describe polyelectrolytes/surfactants solutions, where the surfactant species has self-assembled into worm-like micelle structures. We use self-consistent field theory (SCFT) to model the polyelectrolytes in the solution which interact with the surfactant micelles. The surfactant micelle structures are determined by performing Monte Carlo (MC) simulations, which are used to determine applied external fields in the SCFT portion of the model. We use these calculations to determine the system free energy and map the phase diagrams for polyelectrolyte-surfactant coacervates, and subsequently consider the effect of a number of molecular parameters such as polyelectrolyte chain length, the volume of the interacting micelle surface-sites, and the electrostatic binding energy between the polyelectrolyte and micelle surface. Our model shows that local charge-charge correlations are critical for phase separation to occur. Additionally, we evaluate the statistics of micelle bridging by the polyelectrolyte, and the relationship between bridging and the densities of the macroions and salt ions. This hybrid SCFT/MC model can be generalized to study a variety of mixed macroion systems, and make predictions for phase behavior and molecular structure.