Physical Modeling of Fuel Cells and their Components

Abstract

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.

Role of water states on water uptake and proton transport in Nafion using molecular simulations and bimodal network

“…The calculated Debye length is the hard sphere diameter, d H 2 O = 0.3 nm, meaning that the effective interaction length is one layer of adsorbed water. This length is also consistent with the predictions using the Pekar-Marcus relation [39] and the mean field Poisson-Boltzmann theory [40]. Using 1.5 adsorbed-water layer and the two confining domain surfaces, a 1 nm nanogap (domain size) is set as the small domain size.…”

A Simple and Accurate Method for High‐Temperature PEM Fuel Cell Characterisation

“…In both cases the non-uniformity of ORR distribution across the CCL manifests itself as the doubling of apparent Tafel slope [6,17] and this seems to be the most probable explanation of the deviations of theory and experiment in Figures 2 and 3. In Figure 3 the experimental curves decay faster, than the model curves; this fact works in favour of the conjecture above.…”

“…In the first case the peak of the ORR rate is located close to the GDL/CCL interface, where the oxygen concentration is maximal. In the second case this peak is located at the membrane/CCL interface, where protons are 'cheaper' [6].…”

“…The hydrogen diffusivity and the rate of oxidation are very fast [6]; thus, the voltage loss on the anode side of HT-PEMFC can be safely ignored. Cell voltage V cell is then…”

Mechanistic Insights into the Oxygen Reduction Reaction on Metal–N–C Electrocatalysts under Fuel Cell Conditions

“…[34,35] Eikerlinga nd Kornyshev have derived analytical expressions correlating the cathode catalystlayer structure/composition with the AC impedance response of PEFCs. [36] Among the special cases described in this model,t here is the proton transport resistance signature in the EIS spectrum,w hich appears as a4 5 8 straight line in the highfrequency domain, as clearly observed in the inset of Figure S2 (dashedline) and indirectly in Figure 2. Eikerling and Kornyshev also pointed out that the developedm odel can be approximated by using af inite transmission line equivalentc ircuit; therefore, experimental data can be readily fitted with this element and the proton transport resistance in the catalystl ayer obtained, as suitably carriedo ut in the presentw ork (for further details refer to the Experimental Section and the Supporting Information S2.2).…”