Mechanistic approach to performance equations for cathodes in polymer electrolyte fuel cells

Performance equations that describe the dependence of cathode potential on current density for polymer electrolyte fuel cells (PEFCs) are developed based on a mechanistic approach. The equations take into account, in detail, potential losses caused by: (i) electric resistance and gas transport limitations in the gas diffuser; (ii) limitations of oxygen diffusion, proton migration and electron conduction in the catalyst layer; (iii) oxygen reduction within the catalyst layer. Derivation of the equations is initiated with the formulation of a one-dimensional model and followed by the incorporation of appropriate profiles for oxygen concentration, ionomer potential and catalyst potential. The final forms of the equations are obtained by lumping the oxygen reduction reaction at a reaction center of the catalyst layer. Since the equations are derived from a mechanistic model, all parameters appearing in the equations are endowed with a precise physical meaning. In addition, potential losses caused by various sources can be clearly quantified. Excellent agreement is found between the results obtained from the equations and from the one-dimensional model over an extensive range of the values of model parameters. This indicates that the present equations can be employed to replace the one-dimensional model as an efficient and convenient predictive tool for cathode performance with greatly reduced computational efforts while keeping the same level of accuracy.