Catalyst layer models theory

A timeline of major developments in porous electrode theory that led to the current approaches in catalyst layer modeling is depicted in Figure 3.3. 

FIGURE 3.3 A timeline of developments in porous electrode theory and catalyst layer modeling. 

FIGURE3.5 A general framework for structure-based catalyst layer modeling. The first step relates primary parameters of structure and composition to physicochemical properties, using the statistical theory of random composite media. The second step links these properties to performance. The performance model provides local functions as well as global performance... 

In nanoparticle electrocatalysis, the area that Michael entered just some time ago in Munich, he and his coworkers rationalized the sensitivity of electrocatalytic processes to the stmcture of nanoparticles and interfaces. Studies of catalytic effects of metal oxide support materials revealed intriguing electronic structure effects on thin films of Pt, metal oxides, and graphene. In the realm of nanoparticle dissolution and degradation modeling, Michael s group has developed a comprehensive theory of Pt mass balance in catalyst layers. This theory relates surface tension, surface oxidation state, and dissolution kinetics of Pt. 

XPS is among the most frequently used techniques in catalysis. It yields information on the elemental composition, the oxidation state of the elements and in favorable cases on the dispersion of one phase over another. When working with flat layered samples, depth-selective information is obtained by varying the angle between sample surface and the analyzer. Several excellent books on XPS are available [5,8,17-20], In this section we first describe briefly the theory behind XPS, then the instrumentation, and finally we illustrate the type of information that XPS offers about catalysts and model systems. 

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. 

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. 

The macrohomogeneous model was exploited in optimization studies of the catalyst layer composition. The theory of composifion-dependent performance reproduces experimental findings very well. - The value of the mass fraction of ionomer that gives the highest voltage efficiency for a CCL with uniform composition depends on the current density range. At intermediate current densities, 0.5 A cm < jo < 1.2 A cm , the best performance is obtained with 35 wt%. The effect of fhe Nation weight fraction on performance predicted by the model is consistent with the experimental trends observed by Passalacqua et al. ... 

Under certain approximations, using the concepts of percolation theory, the basic parameters can be related to the volume portions of the components of the layer. This offers a relationship between the structure of the porous composite catalyst layer and its performance. An optimum composition (in terms of volume fractions of electrolyte material, carbon and carbon-supported catalyst, and pore space) is a Holy Grail here. Albeit this goal can still be far away in view of the simplified character of the models used, these models give at least some rational scheme for... 

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. 

Even among the models that employ porous-electrode theory, there have been differences in how the various models choose to describe the electrode. For example, consider the catalyst layer in a state-of-the-art PEM fuel cell containing a supported-platinum-on-carbon (or platinum-alloy-on-carbon) catalyst, a polymeric membrane material, and, in some cases, a void volume. Whether this void volume is considered explicitly, or whether gas- and liquid-phase transport is simply described via permeability through the ionomer is one of the key differences between the various 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... 

In Refs. [18,19], the macrohomogeneous theory was extended to include concepts of percolation theory. The resulting structure-based model correlates the performance of the CCL with the volumetric amounts of Pt, C, ionomer, and pores. A detailed review of macroscopic catalyst layer theory can be found in Ref. [17]. A further extension of this theory in Ref. [25] explores the key role of the CCL for the fuel cell water balance. This function is closely linked to the pore size distribution. Major principles of these models will be reproduced here. The details can be found in the literature cited. 

As described in this chapter, the physieal theory and molecular modeling of catalyst layers provide various tools for relating the global performance metrics to local distributions of physical parameters and to structural details of the complex composite media at the hierarchy of scales from nanoscale to macroscale. The subsisting challenges and recent advances in the major areas of theoretical catalyst layer research include (i) structure and reactivity of catalyst nanoparticles, (ii) selforganization phenomena in catalyst layers at the mesoscopic scale, (iii) effectiveness of current conversion in agglomerates of carbon/Pt, and (iv) interplay of porous structure, liquid water formation, and performance at the macroscopic scale. 

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 addition to the equivalent circuit method, the impedance results can also be analyzed using mathematical models based on physicochemical theories. Guo and White developed a steady-state impedance model for the ORR at the PEM fuel cell cathode [15]. They assumed that the electrode consists of flooded ionomer-coated spherical agglomerates surrounded by gas pores. Stefan-Maxwell equations were used to describe the multiphase transport occurring in both the GDL and the catalyst layer. The model predicted a high-frequency loop due to the charge transfer process and a low-frequency loop due to the combined effect of the gas-phase transport resistance and the charge transfer resistance when the cathode is at high current densities. 

Going from planar to porous electrode introduces another length scale, the electrode thickness. In the case of a PEM fuel cell catalyst layer, the thickness lies in the range of IcL — 5-10 pm. The objective of porous electrode theory is to describe distributions of electrostatic potentials, concentrations of reactant and product species, and rates of electrochemical reactions at this scale. An accurate description of a potential distribution that accounts explicitly for the potential drop at the metal/electrolyte interface would require spatial resolution in the order of 1 A. This resolution is hardly feasible (and in most cases not necessary) in electrode modeling because of the huge disparity of length scales. The simplified description of a porous electrode as an effective medium with two continuous potential distributions for the metal and electrolyte phases appears to be a consistent and practicable option for modeling these stmctures. 

Simulations of physical properties of realistic Pt/support nanoparticle systems can provide interaction parameters that are used by molecular-level simulations of self-organization in CL inks. Coarse-grained MD studies presented in the section Mesoscale Model of Self-Organization in Catalyst Layer Inks provide vital insights on structure formation. Information on agglomerate formation, pore space morphology, ionomer structure and distribution, and wettability of pores serves as input for parameterizations of structure-dependent physical properties, discussed in the section Effective Catalyst Layer Properties From Percolation Theory. CGMD studies can be applied to study the impact of modifications in chemical properties of materials and ink composition on physical properties and stability of CLs. 

The most promising approach to the optimization of catalyst layers would be a concerted experimental-theoretical strategy. Since theory and modeling inevitably have to invoke simplifying assumptions, offering a pure theoretically driven optimization would be irresponsible. Ex situ diagnostics is needed to characterize structural details and explore their relations to effective properties. The availability of such experimental data defines the level of detail of structure-property relationships that a theory should be permitted to employ. 

Moving up the scale to the level of flooded nanoporous electrodes, Michael s group has developed the first theoretical model of ionomer-free ultrathin catalyst layers—a type of layer that promises drastic savings in catalyst loading. Based on the Poisson-Nernst-Planck theory, the model rationalized the impact of interfacial charging effects at pore walls and nanoporosity on electrochemical performance. In the end, this model links fundamental material properties, kinetic parameters, and transport properties with current generation in nanoporous electrodes. 

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