Phase behavior and transport in solutions of oppositely charged polyelectrolytes

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 phase behavior 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. We quantify 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, and find consistency of predictions with experimental data. From this free energy model, and an extended Stefan-Maxwell flux law based on the Doi-Onuki Rayleighian approach, the transport of PE chains, salts, and waters through polyelectrolyte LbL films are modeled, including the effects of chemical and electrostatic potentials, as well as mechanic stresses. The result is a unified approach that connects phase behavior to transport in polyelectrolyte assemblies, and may eventually allow rates of Layer-by-Layer assembly to be inferred from measurements of phase behavior and rheology.