Catalyst layer operation modeling

The factors 4 and 4 accormt for the heterogeneity of the interface. The interfacial flux conditions. Equations (6.56) and (6.57), can be straightforwardly applied at plain interfaces of the PEM with adjacent homogeneous phases of water (either vapor or liquid). However, in PEFCs with ionomer-impregnated catalyst layers, the ionomer interfaces with vapor and liquid water are randomly dispersed inside the porous composite media. This leads to a highly distributed heterogeneous interface. An attempt to incorporate vaporization exchange into models of catalyst layer operation has been made and will be described in Section 6.9.4. 

This section provides a comprehensive overview of recent efforts in physical theory, molecular modeling, and performance modeling of CLs in PEFCs. Our major focus will be on state-of-the-art CLs that contain Pt nanoparticle electrocatalysts, a porous carbonaceous substrate, and an embedded network of interconnected ionomer domains as the main constituents. The section starts with a general discussion of structure and processes in catalyst layers and how they transpire in the evaluation of performance. Thereafter, aspects related to self-organization phenomena in catalyst layer inks during fabrication will be discussed. These phenomena determine the effective properties for transport and electrocatalytic activity. Finally, physical models of catalyst layer operation will be reviewed that relate structure, processes, and operating conditions to performance. 

At macroscopic level, the overall relations between structure and performance are strongly affected by the formation of liquid water. Solution of such a model that accounts for these effects provides full relations among structure, properties, and performance, which in turn allow predicting architectures of materials and operating conditions that optimize fuel cell operation. For stationary operation at the macroscopic device level, one can establish material balance equations on the basis of fundamental conservation laws. The general ingredients of a so-called "macrohomogeneous model" of catalyst layer operation include ... 

B. Andreaus and M. Eikerling. Catalyst layer operation in PEM fuel cells From structural pictures to tractable models. In Device and materials modeling in PEM fuel cells, ed. K. Promislow and S. Paddison, Topics in applied physics 113, 41-90. New York Springer, 2009. 

Catalyst Layer Operation in PEM Fuel Cells From Structural Pictures to Tractable Models... 

How are we going to disentangle this mess The strategy of the modeling approaches reviewed in this contribution is to start from appropriate structural elements, identify relevant processes, and develop model descriptions that capture major aspects of catalyst layer operation. In the first instance, this program requires theoretical tools to relate structure and composition to relevant mass transport coefficients and effective reactivities. The theory of random... 

Figure 8.1. Outline of the general framework for structure-based modeling of catalyst layer operation in polymer electrolyte fuel cells [51], (Reprinted from Elecfrochimica Acta 53.13, Liu J, Eikerling M. Model of cathode catalyst layers for polymer electrolyte fuel cells The role of porous structure and water accumulation, 4435-46, 320 08, with permission from Elsevier.)...

The modeling of structure and operation of CLs is a multiscale problem. The challenges for the theory and modeling of catalyst layer operation are, however, markedly reduced if we realize that the main structural effects occur at well-separated scales, viz. at catalyst nanoparticles (a few nm), at agglomerates of carbon/Pt ( 100 nm), and at the macroscopic device level. 

In the section Structure Eormation in Catalyst Layers and Effective Properties aspects related to the self-organization phenomena in CL inks will be discussed. These phenomena determine the effective properties for transport and electrocatalytic activity. Thereafter, catalyst layer performance models that involve parameters related to structure, processes, and operating conditions will be presented. 

The two-step strategy in the physical modeling of catalyst layer operation is depicted in Figure 3.5. The first step relates structure to the physical properties of the layer, considered as an effective medium. The second step relates these effective properties to electrochemical performance. Relations between structure and performance are complicated by the formation of liquid water, affecting effective properties and performance. Solutions for such a model provide relations between structure, properties, and performance. These relations allow predictions of architectures of materials and operating conditions that optimize catalyst layer and fuel cell operation to be made. 

This chapter is devoted entirely to performance models of conventional catalyst layers (type I electrodes), which rely on reactant supply by gas diffusion. It introduces the general modeling framework and employs it to discuss the basic principles of catalyst layer operation. Structure-based models of CCL rationalize distinct regimes of performance, which are discernible in polarization curves. If provided with basic input data on structure and properties, catalyst layer models reproduce PEFC polarization curves. Consistency between model predictions and experimental data will be evaluated. Beyond polarization curves, performance models provide detailed maps or shapes of reaction rate distributions. In this way, the model-based analysis allows vital conclusions about an optimal design of catalyst layers with maximal catalyst utilization and minimal transport losses to be drawn. 

This chapter gives an overview of the state of affairs in physical theory and molecular modeling of materials for PEECs. The scope encompasses systems suitable for operation at T < 100°C that contain aqueous-based, proton-conducting polymer membranes and catalyst layers based on nanoparticles of Pt. 

The previous discussion asserts that design, fabrication, and implementation of stable and inexpensive materials for membranes and catalyst layers are the most important technological challenges for PEFC developers. A profound insight based on theory and modeling of the pertinent materials will advise us how fuel cell components with optimal specifications can be made and how they can be integrated into operating cells. 

Within the last five years, many fuel-cell models have come out of the Research Center in Julich, Germany. These models have different degrees of complexity and seek to identify the limiting factors in fuel-cell operation. The model of Kulikovsky et al. examined a 2-D structure of rib and channel on the cathode side of the fuel cell, and is similar to that of Springer et al. Other models by Kulikovsky included examination of depletion along long feed channels and effects in the catalyst layers.The most recent model by Kulikovsky relaxed the assumption of constant water content in the membrane and examined quasi 3-D profiles of it. Also at the research center, Eikerling et developed many... 

Accurate modeling of the temperature distribution in a PEFC requires accurate information in four areas heat source, thermal properties of various components, thermal boundary conditions, and experimental temperature-distribution data for model validation. The primary mechanism of heat removal from the catalyst layers is through lateral heat conduction along the in-plane direction to the current collecting land (like a heat sink). Heat removed by gas convection inside the gas channel accounts for less than 5% under typical PEFC operating conditions. 

An appropriate model of CCL operation should account for the interdiffusion of oxygen, nitrogen, and water vapor, migration of protons and electrons, and kinetics of the electrochemical reaction. The pertinent theory was developed in Refs. 8, 9, 15. A model similar to that was more recently studied analytically [17, 107, 108], and we will dwell on these transparent closed form results. We will see that having such solutions at hand helps in revealing the reserves for optimization of the structure and function of the catalyst layers. 

The apparent transfer coefficient of the cathodic reaction, ac, is a measure of the sensitivity of the transition state to the drop in electrostatic potential between electrolyte and metal [109,112]. According to Ref. 113, it is ac = 0.75 for the O2 reduction on Pt in aqueous acid electrolytes. In Ref. Ill the value ac = 1.0 was reported instead. Since the cathodic reaction is a complex multistep process, it might follow several reaction pathways, and the competition between them is affected by the operation conditions (rj, p, T). Therefore, different values of ac have been reported in different regimes of operation. Although in the simple reactions the transfer coefficient is a microscopic characteristic of the elementary act [112], for complex multistage reactions in fuel cell electrodes it is rather an empirical parameter of the model. The dependence of effective a for methanol oxidation on the catalyst layer preparation was recently studied [114]. 

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