Higher order curvature driven flows: pore formation in polymer electrolytes

Energy conversion, particularly conversion of chemical and photonic energy to useful voltage, requires the selective conduction of charged ions. Polymer electrolytes are hydrophobic polymers functionalized with acid-tipped side-chains. In the presence of solvent they form nanoscale pore networks which are lined with the dissociated acid groups which serve as primative ion channels, conducting ions of one charge only.

We describe the dynamic formation of the pore network as the gradient flow of a novel classes of ''functionalized'' energies. In particular we derive sharp interface evolution laws for pores which couple the evolution of the background state, a higher order curvature flow, and the pore width.