Title: Pore formation in Polymer Electrolytes

Abstract: Much of our quality of life in the 21st century will depend
upon how efficiently we use our energy resources. The efficient
conversion of energy from one form to another, particularly solar,
chemical or thermal to electric, requires detailed nano-structured
morphology.  The polymer electrolytes in Polymer Electrolyte Membrane
(PEM) fuel cells conduct protons while forming a barrier for electrons
and molecular gases. We provide experimental evidence that they
dynamically form a complex nanostructured pore network when exposed to
liquid water, and provide a novel mathematical model for the
solvent-polymer interaction which incorporates the functionalization
of the polymer sidechains. We show that our model resides within a
mathematical class of energies, which we call functionalized
Lagrangians, which have a rich structure, preserving the critical
points of the old Lagrangian, while generating new critical points
(here the pore network) in a controllable, if hysteric, manner.