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Variational models of network formation and ion transport: applications to polyelectrolyte membranes (FuncCahnHilliardPNP)
Start date: Sep 1, 2013, End date: Aug 31, 2017 PROJECT  FINISHED 

The functionalized Cahn-Hilliard energy is a phase-field characterization of an interfacial energy usedto describe dynamics of amphiphilic network formation. We havesuccessfully applied the functionalized Cahn-Hilliard energy to model the morphology of water nano-pore networks in ionomer membranes. The resulting morphology model was validated with experimental scattering data of Nafion, anionomer membrane which is a critical component in fuel cells.It is natural to use, as a basis, the successful morphology model to study the effect of morphologyon membrane performance, e.g., conductivity. The functionalized Cahn-Hilliard energy offers, however, only a phenomenological treatment of the electrostaticforces between the polymer and the water. Such a treatment effectively blocks important extensions of the model.The main goal of this proposal is the development, analysis, and simulation of continuum models which characterize amphiphilic network formation coupled to ion transport. Attaining this goal requires redeveloping key components of the functionalized Cahn-Hilliard model while operating on a wide range of scales, e.g., from the non-uniform water structure in a pore at the nanoscale to membrane conductivity at the macroscale.A key application of this proposal is to study conductivity and selectivity of ionomer membranes and their dependence upon morphology and ionic concentrations.The project is of clear interdisciplinary nature, merging problems, ideas and tools from Mathematics, material science, solution chemistry and soft matter physics. The design and performance of novel clean energy devices such as fuel cells, flow batteries, or organic solar cells critically depends on the optimized coupling between material nanostructure, electrostatics, charge transport and nanoflows. Any progress in the directions proposed above will open the way to robust phase-field models which can incorporate and couple these four effects.

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