Self assembling pore networks: high order curvature driven flows

Energy conversion devices, such as fuel cells, lithium ion batteries,
and photocatalytic devices operate by selective conduction of charged ions
through a membrane.  The membranes are created by emerging polymer
electrolytes in a solvent in which the polymers spontaneously form
nanoscale pore networks which serve as primitive ion channels.

I this talk, I present a novel model for the self-assembly of the nanoscale
pore network as a gradient ן¬ ow along classes of competing interfacial and
bending energies.  I present a sharp interface analysis of the model, and
show that the evolution laws for the pores are given by high-order
Ricci-curvature flows, coupled to interfacial dynamics.

We use our model, in conjunction with experimental scattering data, to
study the morphology of Nafion, the industry standard polymer electrolyte
membrane used in Fuel Cells.

This is a joint work with Keith Promislow.