The Characteristic Thickness of Polymer Electrolyte Membrane and the Efficiency of Fuel Cell

A simplified thermodynamic analysis is applied to elucidate the basic feature of fuel cells operation, i.e., the transformation of chemical energy into electricity. To be able to handle this problem analytically we propose a simple model of the chemical reaction kinetics at the electrodes and diffusion in the polymer electrolyte membrane (PEM). The description is based on a set of two mass balance equations involving water and proton transport through the membrane coupled with two reaction equations describing the electrochemical reactions at the electrodes. The transport parameters (water diffusivity, proton conductivity, electro-osmotic drag) involved in the equations for the water and proton flux densities are shown to comply with Onsager reciprocity relations. The resulting form of the transport equations is suitable for a quantitative analysis from the point of view of linear irreversible thermodynamics. In terms of our simplified model, a relation for the characteristic thickness of the PEM is derived that theoretically assures a stable fuel cell operation, and the maximum efficiency of a fuel cell is evaluated, both as functions of the transport properties of the membrane material.