Abstract

Functionalized polymers play an essential role in almost every aspect of cellular biology and have recently found industrial use in polymer membrane fuel cells. Formed of hydrophobic backbones with short acid side chains, these complex materials phase separate in the presence of polar solvents, aka water, forming nanoscale pores filled with electrolyte and lined with acid groups. This fine structure lends these materials their exceptional ionic conductivity.

We present a model for the elastic deformation, ion conduction, and phase separation based upon the Lagrangian phase field approach introduced by Chun and Walkerton for elastic-fluid interactions. A key driving force is the solvent-polymer interfactial energy, based upon a balance between interfacial curvature and surface energy. Surprisingly the resulting fourth order variational derivative factors into an Allen-Cahn operator composed with its own linearization. We investigate a family of gradient flows associated to the interfacial energy, deriving formal geometric interface motion for both heteroclinic and homoclinic fronts.

TUESDAY, March 20, 2007
Time: 1:30 P.M.
Location: PPB 300