A simple Maxwell-Wagner-Butler-Volmer approach to the impedance of the hydrogen electrode in a nafion fuel cell

A simple one-dimensional model of the impedance of a hydrogen/Nafion electrode is set up combining the usual Maxwell-Wagner approach for linear, homogeneous, and isotropic media with the linearized Butler-Volmer equation for the interfacial, electrochemical reaction. Only one relaxation semicircle is normally seen in the Nyquist diagram, but a low-frequency arc may appear at high overvoltages. The model is described by only two dimensionless parameters (in addition to the dimensionless frequency). These parameters are related to the double-layer capacitance and to the interfacial electrochemical reaction rate, respectively. With some adjustments, the model can be used to explain the observed equilibrium impedance from 40 to 70 degrees C of a symmetric cell of the type C/Pt/H(2)|Nafion 117/H(2)/Pt/C. The hydrogen electrodes in this cell were built up as a disperse multiphase region (carbon, platinum grains, Nafion 117, and hydrogen gas) as commonly done in solid polymer fuel cells.