March 4 Math Colloquium

Keith Promislow, Michigan State University

Network Formation in Amphiphilic Polymer Membranes

Polymer chains are typically hydrophobic, the addition of functional groups to the backbone adds regions of hydrophilicity. The amphiphilic material (both hydrophobic and hydrophilic) has a strong affinity for solvent, imbibing it to self assemble charge-lined networks which serve as charge-selective ion conductors in a host of energy conversion applications. We present a continuum model for the free energy of an amphiphilic mixture. The associated gradient flows admit dynamic competition between network morphologies of distinct co-dimension.  We present the competitive geometric evolution for co-dimension 1 bilayers and co-dimension two pore morphologies, present an analysis of the associated spectral problems, and describe rigorous existence results

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