Variational Models of Pore Networks in Ionomer Membranes: The Role of Electrostatics

We present a self-consistent, dynamic model for the morphology of the pore networks which form in Nafion and other ionomer membranes when they imbibe solvent. The model incorporates the interactions of the tethered ionic groups with the solvent and the entropic energy of the counter ions. Numerical simulations are presented which display hysteresis, and the development of pearled pore structures. A framework for extensions of the model that couple the electrostatic double layer at the interface of the pore wall and the transport equations for the counter-ions is presented. The framework derives the ionic transport and generalized Poisson equation from an action whose gradient flows dissipate a related free energy, in agreement with the second law of thermodynamics.