Network formation and curvature driven flow of structured interfaces
Keith Promislow, Michigan State University

We present a novel interfacial energy which unfolds the Canham-Helfrich energy. Combining elementary differential geometry with dynamical systems  techniques, we construct critical points by balancing structural  energy against negative surface area terms. In R^3 we show that a universal unfolding leads to formation of bilayer, radial pore, and spherical micellular (pearled pore) networks. We derive a thin-interface limit of bilayer structures we reduces  an associated gradient flow to a Kuramoto-Sivashinsky type  curvature driven flow coupled to the interfacial structure. We  present applications to pore formation and ion conduction in polymer electrolytes, in particular a fitting of SAXS data, and discuss the use of Temperature Accelearted MD to calibrate the models to subscale simulations.