Graded Density Ion Exchange Polymer Films on Electrodes: Impacts on Structure and Transport

The full expression of Fick’s second law includes a distance dependent diffusion coefficient, D(x). In one dimension, for distance x and time t, the concentration is expressed as shown in Equation 1.

Eyring models for transport as a function density and viscosity are predicated on an activation energy for short distance hopping of the diffusing species from one low energy site to an adjacent site of similar low energy. This results in a correlation between density and viscosity.

In turn, the Stokes Einstein relationship (Equation 2) specifies diffusion coefficient and viscosity η are inversely related. Equation is for a spherical diffusion species of radius r, k is the Boltzmann constant, T is temperature.  If viscosity varies in space as η(x), then D(x) varies in space proportional to 1/η.

Ficoll^® (GE Life Sciences) is a highly branched, water soluble, hydrophilic copolymer of sucrose and epichlorohydrin that is used to establish density gradients. On application of Ficoll films to electrodes, the density gradient is preserved. Cyclic voltammetry of outer sphere redox probes such as tetramethylphenylenediamine yields near steady state responses as scan rate slows. Modeling of the voltammetric responses establishes that the density gradient establishes a steady state flux of materials to the electrodes. Images of Ficoll films immersed in solution confirm a density gradient.

Here, Ficoll is used as a template to form a graded film of the ion exchange polymer, Nafion^® (DuPont). Films are formed on electrodes by cocasting Ficoll and Nafion. Alternatively, a cast film of Ficoll can serve as the template for the Nafion. Films are evaluated by imaging. When compared to a uniform Nafion film, cyclic voltammograms for outer sphere redox probes that pass through the ion exchange polymer are altered. Sigmoidal as well as Gaussian voltammograms are observed, dependent on conditions of film formation.  The structural morphology changes imprinted on formation of Ficoll Nafion layers alters flux through the ion exchange polymer layer.

References and Acknowledgments: Support of the National Science Foundation and the University of Iowa is gratefully acknowledged.  Thanks also to Dick Buck for his example as a thoughtful scientist and mentor.

[1] Krysti L. Knoche and Johna Leddy, manuscript in preparation.

[2] K. L. Knoche, P. D. Moberg, C. Hettige, and J. Leddy, "Simulation of Fick's Second Law for Spatially Variant Diffusion Coefficients," ECS Trans. (2013) 53 (15) 1-6.