Modeling Framework for Predicting Phase Behavior and Transport in Oppositely Charged Polyelectrolyte Solutions

We develop a modeling framework for phase behavior and transport of oppositely charged polyelectrolytes (PE) in coacervates and Layer-by-Layer (LbL) assemblies that accounts for diffusion of both oppositely charged chains and their complexation. The core of the model is the development of a free energy model that includes free energies for ion pairing, counterion condensation, charge regulation, electrostatic free energy, as well as elastic energy of the network and Flory Huggins entropy and enthalpy. Combinatorial entropies for ion pairing, counterion condensation, and charge regulation are included along with reference state chemical potentials as adjustable parameters. A numerical approach is developed to carry out multi-component highly nonlinear flash calculations to determine phase behavior. We find a very strong influence of ion pairing and counterion condensation on phase behavior, and on the distribution of salt and polyelectrolyte species between the coacervate and supernatant phases. From this free energy model, and an extended Stefan-Maxwell flux law, diffusion of PE chains into a LbL film can be computed, providing a unified approach that connects phase behavior to transport in polyelectrolyte assemblies.