Physical Modeling of Fuel Cells and their Components
Authors: Eikerling Michael , Kornyshev Alexei A. , Kulikovsky Andrei A. 
Published: December 2007

This chapter presents an overview of the status of physical modeling of polymer‐electrolyte fuel cells (PEFCs), the understanding gained from modeling and its impact on optimization of the operation regime and new cell design.

It begins with the physical theory of proton transport in polymer‐electrolyte membranes (PEMs). This comprises microscopic aspects of the elementary act of proton transfer in aqueous environments, their realization in a single water‐filled pore and the statistical geometry of the pore network. Based on these fundamental properties, electroosmosis and different models of water backflow under fuel cell operation conditions are discussed. The resulting water‐content profiles and current–voltage performance are compared with experimental data. The diffusion model of water backflow perceives the membrane as a solution of water in a polymer host, while the hydraulic permeation model rests on the idea of a swelling porous structure, inside of which the proton and water transport take place. An important result is the critical current density, at which water content near the anode drops below the percolation threshold for water network proton conductance.

Next, theories of performance and structure of composite catalyst layers are presented, mainly focusing on the cathode as an eminent example. They account for the transport of feed gas, protons and electrons, as well as for the reaction at the membrane/catalyst interface, and result in a “phase diagram”, which suggests an optimum thickness of the layer, subject to the basic parameters and the target current density. The relation between the structure and performance, rationalized using the concepts of the percolation theory, paves the way for an optimum composition of the layer. A similar theory of the complex impedance connects the composite structure and ac response. This gives a tool for determining the catalyst layer parameters.

With this background we move toward 3D effects in the cell. The approach rests on a quasi‐three‐dimensional (Q3D) model of the stack element. The fuel cell stack is a two‐scale system. The small and large scales are determined, respectively, by membrane‐electrode assembly (MEA) thickness and by the length of the feed channel. The fully 3D model of the stack element is split into a 2D model of a cell cross section (internal model) and a 1D model of the feed flow along the channel (channel model). The two models are coupled via the local current density along the channel and the overall solution is obtained by iterations. The model is designed to investigate the interplay of small‐ and large‐scale processes in PEFC/DMFC. It results in distributions of gas concentrations, proton and electron currents, and reaction rates in a cell cross section, perpendicular to a long meander‐like channel, that is, it gives a functional “map of a cell”. Model equations and numerical procedures are discussed. The results of simulations are shown for the stack modules of the gas‐feed DMFC and hydrogen–oxygen PEFC. A simplified theory of “along‐the‐channel” feed gas consumption, important for understanding the cell starvation effect is surveyed and compared with simulations and experiments.

The message of the model results is summarized and discussed in the sequence of the rising potential for improving PEFC/DMFC design and operation.