Conductive Polymer Electrolytes: Phase Separation and Ion Transport

Michigan State University, East Lansing MI

Investigators

Abstract

Promislow 0708804 The investigator analyses the mathematical underpinnings of a novel Conductive Polymer Electrolyte (CPE) model for phase separation and ion transport in polymer electrolyte solutions. An exothermic acid-solvent reaction leads to an interfacial energy that decreases with increasing surface area but grows with the curvature of the interface. The family of gradient flows associated to the interfacial energy are compelling fourth and sixth order extensions of the familiar Allen-Cahn and Cahn-Hilliard operators with rich new structure. The investigator rigorously derives sharp interface limits for the gradient flows associated with pore formation. The exclusion potential that separates the protonic defects from the anions generates a novel equilibrium charge distribution within the phase separated membrane, modifying the classic Gouy-Chapmann diffusive double layer. A multiscale analysis of the elliptic equations governing the charge distribution quantifies the impact of the exclusion potential on the structure of the electrostatic double layer, and the impact of the electrostatic pressure upon the phase separation. The solvent pore network within the polymer electrolyte is a novel high-contrast conductive composite media. For local minimizers of the phase separation arising from interfacial and electrostatic energies, the investigator exploits the high contrast afforded by the permittivity and exclusion potential to derive the effective conductivity of polymer network. This entails asymptotic analysis of the saddle point structure of charge distribution at channel junctions and development of a variational characterization of the effective protonic conductivity. Polymer electrolytes are comprised of long hydrophobic polymers (essentially Teflon) with short acidic side-chains attached, like a single pole ladder. They form a rich structure that phase separates in the presence of water, forming intricate nanoscale geometries lined with pendant acid groups and filled with charged fluid. Such structures are the workhorses of ion transport, generating the selectivity of ion channels in cell membranes, the complex biochemical processes that occur within the pores of lipid membranes, and the motivation of this project: the transport of charge within polymer electrolyte membranes of fuel cells. This project analyzes the mathematical underpinnings of a novel Conductive Polymer Electrolyte (CPE) model for phase separation and ion transport in polymer electrolyte solutions. The fundamental understanding of pore formation and ion conduction in these materials is essential to the development of high-temperature membranes for fuel cell vehicles. High temperature membranes are a key step in the transition to a hydrogen economy, as higher fuel cell operating temperatures will greatly reduce costs associated with platinum catalyst loading and radiative cooling of the engine.