Conductive Polymer Electrolytes: Phase Separation and Ion Transport

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Promislow0708804The investigator analyses the mathematical underpinnings of anovel Conductive Polymer Electrolyte (CPE) model for phaseseparation and ion transport in polymer electrolyte solutions. An exothermic acid-solvent reaction leads to an interfacialenergy that decreases with increasing surface area but grows withthe curvature of the interface. The family of gradient flowsassociated to the interfacial energy are compelling fourth andsixth order extensions of the familiar Allen-Cahn andCahn-Hilliard operators with rich new structure. Theinvestigator rigorously derives sharp interface limits for thegradient flows associated with pore formation. The exclusionpotential that separates the protonic defects from the anionsgenerates a novel equilibrium charge distribution within thephase separated membrane, modifying the classic Gouy-Chapmanndiffusive double layer. A multiscale analysis of the ellipticequations governing the charge distribution quantifies the impactof the exclusion potential on the structure of the electrostaticdouble layer, and the impact of the electrostatic pressure uponthe phase separation. The solvent pore network within thepolymer electrolyte is a novel high-contrast conductive compositemedia. For local minimizers of the phase separation arising frominterfacial and electrostatic energies, the investigator exploitsthe high contrast afforded by the permittivity and exclusionpotential to derive the effective conductivity of polymernetwork. This entails asymptotic analysis of the saddle pointstructure of charge distribution at channel junctions anddevelopment of a variational characterization of the effectiveprotonic conductivity. Polymer electrolytes are comprised of long hydrophobic polymers(essentially Teflon) with short acidic side-chains attached, likea single pole ladder. They form a rich structure that phaseseparates in the presence of water, forming intricate nanoscalegeometries lined with pendant acid groups and filled with chargedfluid. Such structures are the workhorses of ion transport,generating the selectivity of ion channels in cell membranes, thecomplex biochemical processes that occur within the pores oflipid membranes, and the motivation of this project: thetransport of charge within polymer electrolyte membranes of fuelcells. This project analyzes the mathematical underpinnings of anovel Conductive Polymer Electrolyte (CPE) model for phaseseparation and ion transport in polymer electrolyte solutions. The fundamental understanding of pore formation and ionconduction in these materials is essential to the development ofhigh-temperature membranes for fuel cell vehicles. Hightemperature membranes are a key step in the transition to ahydrogen economy, as higher fuel cell operating temperatures willgreatly reduce costs associated with platinum catalyst loadingand radiative cooling of the engine.