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Journal of The Electrochemical Society, 156 �2 � B225-B233 �2009� 0013-4651/2008/156�2�/B225/9/$23.00 © The Electrochemical Society Diffuse Charge Effects in Fuel Cell Membranes

By P. Maarten Biesheuvel, Z Alej, Ro A. Franco and Martin Z. Bazant D


It is commonly assumed that electrolyte membranes in fuel cells are electrically neutral, except in unsteady situations, when the double-layer capacitance is heuristically included in equivalent circuit calculations. Indeed, the standard model for electron transfer kinetics at the membrane/electrode interface is the Butler–Volmer equation, where the interfacial overpotential is based on the total potential difference between the electrode and bulk electrolyte. Here, we develop an analytical theory for a solid-state proton-conducting membrane that accounts for diffuse charge in the electrostatic polarization layers and illustrate its use for a steady-state hydrogen concentration cell. The theory predicts that the total membrane charge is nonzero, except at a certain hydrogen pressure, which is a thermodynamic constant of the fuel cell membrane. Diffuse layer polarization introduces the Frumkin correction for reaction rates, where the overpotential is based on the potential difference across only the compact �Stern� part of the polarization layer. In the Helmholtz limit of a relatively thin diffuse layer, we recover well-known results for a neutral membrane; otherwise, we predict significant effects of diffuse charge on the electron-transfer rate. Our analysis also takes int

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