RG, Geometric Front Evolution, and Pore Formation in Polymer Electrolytes

The renormalization group (RG) approach has had success in the stability analysis of patterns which evolve on disparate length and time scales, in particular the semi-strong pulse interaction in chemical and optical systems. We turn this technique on a novel but fundamental application, the formation of pores in polymer electrolytes. These materials are comprised of a stiff hydrophobic polymer backbone, functionalized by short acidic sidechains. In the presence of a solvent they phase separate, forming a rich, nanoscale pore structure. We characterize the interfacial energy with a novel functional, and employ the RG approach to reduce a family of associated gradient flows to corresponding geometric front evolution, which has suprizingly good agreement with experiment.

Keith Promislow, Michigan State University

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