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Math Colloquium
Keith Promislow
Michigan State University
Title: Network formation and ion conduction in ionomer membranes: searching for solvation in an energetic world

Abstract: Many important processes in the physical world can be described as a gradient (overdamped) flow of a variational energy. We present a broad formalism for the generation of new classes of variational energies with physically motivated structure. In particular we reformulate the Cahn-Hilliard energy, which is well know to describe the surface area of mixtures, into a higher-order model of interfacial energy for mixtures of charged polymers (ionomers) with solvent. These materials are important as selectively conductive membrane separators in a wide variety of energy conversion devices, including polymer electrolyte membrane fuel cells, Lithium ion batteries, and dye-sensitized solar cells. We reformulated energy, called the Functionalized Cahn-Hilliard (FCH) energy, captures elastrostatic interactions between the charged groups and the complex entropic effects generated by solvent-ion interactions, and allows us to unfold the bilayer and pore networks formed by the solvent phase imbibed into the polymer matrix. We discuss sharp interface reductions of the FCH energy, its gradient flows, and extensions to models that couple ionic transport and multiphase casting processes.

Date: Friday, January 20, 2012
Time: 4:30 pm
Location: Wean Hall 7500
Submitted by:  Leoni