Mathematical models of ion transport through Nafion membranes in modified electrodes and fuel cells without electroneutrality.

摘要

Electrodes modified with polymer films have distinct permeability. Electroactive redox probes partition from solution into film and are electrolyzed at the electrode. This creates a flux of probe into the polymer film and a flux of electrolyzed probe out of the polymer film. Transport of the probe through the film is governed by diffusion and migration, mathematically described by the Nernst-Planck equation as Ji&parl0;x,t&parr0;=-Di6 Ci&parl0;x,t&parr0;6x- ziFRTDiCi &parl0;x,t&parr0;6F&parl0;x,t&parr0; 6x where x is the distance from the electrode, t is time, Ci(x, t) is the space and time dependent concentration of the probe i, zi is the charge of the probe i, F is Faraday's constant, R is the gas constant, T is absolute temperature, J i(x, t) is the flux of the probe i, Di is the diffusion constant of the probe i, and phi(x, t) is the space and time dependent potential.;In most natural systems, charge accumulation is not appreciable and a charged ion is neutralized by a counterion. Electroneutrality is mathematically represented by Laplace's condition on the potential, 62F&parl0;x,t&parr0; 6x2 = 0. In systems where counterions are insufficient to neutralize an ion, local electroneutrality is set by local charge and Poisson's equation replaces Laplace's condition as 62F6x 2=-F3 iziCi&parl0;x,t&parr0; where epsilon is the relative permittivity. The Nernst-Planck under Poisson's condition is not solved analytically. The extreme magnitude of F/epsilon yields a system that resists solution by standard techniques. The first system investigated determines the concentration and potential profiles over the polymer membrane of a fuel cell without the assumption of electroneutrality.;In the second system investigated, the probes physical motion is highly restricted. This gives a more generalized form of the Nernst-Planck equation with spatially varying diffusion coefficient results J=-D&parl0;x,t&parr0;6C&parl0;x,t&parr0; 6x-zFRTD&parl0; x,t&parr0;C&parl0;x,t&parr0;6F&parl0;x, t&parr0;6x. D(x, t) is the space and time dependent diffusion coefficient, which can include a physical displacement term and an electron hopping term. The second system this thesis investigates is a modified electrode system where electron hopping is responsible for a majority of the probe transport within the film.;Lastly, preliminary methods are presented to determine physical diffusion of a probe at a modified electrode by sweep voltammetry.