Theories of gas-diffusion electrodes

The theory of gas-diffusion electrodes has a long history [11, 12, 105, 106]. Specifically, catalyst utilization and specific effective surface area in composite electrodes were always in the focus of attention (see, e.g., Ref. 13 and the articles quoted therein). A comprehensive review of the theory and models of ionic-into-electronic current transformation in two-and three-phase distributed electrodes can be found in Ref. 14. 

The importance of structural effects in gas diffusion electrodes was realized long before the development of the current generation of CLs for PEFCs. The basic theory of gas diffusion electrodes, including the interplay of reactant transport through porous networks and electrochemical processes at highly dispersed electrode I electrolyte interfaces, dates back to the 1940s and 50s [13, 14]. Later work realized the importance of surface area and utilization of electrocatalysts in porous electrodes [15]. A series of seminal contributions by R. De Levie opened... 

Porous-electrode theory has been used to describe a variety of electrochemical devices including fuel cells, batteries, separation devices, and electrochemical capacitors. In many of these systems, the electrode contains a single solid phase and a single fluid phase. Newman and Tiedemann reviewed the behavior of these flooded porous electrodes [23]. Many fuel-cell electrodes, however, contain more than one fluid phase, which introduces additional complications. Typical fuel cell catalyst layers, for example, contain both an electrolytic phase and a gas phase in addition to the solid electronically conducting phase. An earher review of gas-diffusion electrodes for fuel cells is provided by Bockris and Srinivasan [24]. 

The beginning of modeling of polymer-electrolyte fuel cells can actually be traced back to phosphoric-acid fuel cells. These systems are very similar in terms of their porous-electrode nature, with only the electrolyte being different, namely, a liquid. Giner and Hunter and Cutlip and co-workers proposed the first such models. These models account for diffusion and reaction in the gas-diffusion electrodes. These processes were also examined later with porous-electrode theory. While the phosphoric-acid fuel-cell models became more refined, polymer-electrolyte-membrane fuel cells began getting much more attention, especially experimentally. 

Srinivasan D, Hurwitz HD. Theory of a thin film model of porous gas-diffusion electrodes. Electrochim Acta 1967 12(5) 495-512. 

Permeability Measurement. The general theory of gas transport in polymers and detailed discussion of the method of measurement and calculation of the permeability, diffusion coefficients have been published elswhere In this study, two kinds of permeability measurement were made. One experimental method was an adaptation of the high vacuum gas transmission technique described by Stannett and co-workers. The other experimental method for permeation of oxygen dissolved in water was an adaptation of the oxygen electrode as follows.5... 

The reactant gas species transport to reaction sites through the porous electrodes based on the concept of gas diffusion in porous media. In porous media, the diffusion mechanism can be of three different types ordinary diffusion, Knudsen diffusion, and surface diffusion. If the pores are much larger than the mean free path length, then the molecules collide with each other more frequently than with the pore walls, and ordinary diffusion is assumed to be the dominant diffusion mechanism. Knudsen diffusion is encoimtered in smaller pores or at lower pressure or density. In this case, molecules collide more frequently with the walls than with other gas molecules. The Knudsen diffusion coefficient given is based on kinetic theory as... 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

While an understanding of the molecular processes at the fuel cell electrodes requires a quantum mechanical description, the flows through the inlet channels, the gas diffusion layer and across the electrolyte can be described by classical physical theories such as fluid mechanics and diffusion theory. The equivalent of Newton s equations for continuous media is an Eulerian transport equation of the form... 

Chebotin s scientific interests were characterized by a variety of topics and covered nearly all aspects of solid electrolytes electrochemistry. He made a significant contribution to the theory of electron conductivity of ionic crystals in equilibrium with a gas phase and solved a number of important problems related to the statistical-thermodynamic description of defect formation in solid electrolytes and mixed ionic-electronic conductors. Vital results were obtained in the theory of ion transport in solid electrolytes (chemical diffusion and interdiffusion, correlation effects, thermo-EMF of ionic crystals, and others). Chebotin paid great attention to the solution of actual electrochemical problem—first of all to the theory of the double layer and issues related to the nature of the polarization at the interface of the solid electrol34e and gas electrode. 

The convective diffusion theory was developed by V.G. Levich to solve specific problems in electrochemistry encountered with the rotating disc electrode. Later, he applied the classical concept of the boundary layer to a variety of practical tasks and challenges, such as particle-liquid hydrodynamics and liquid-gas interfacial problems. The conceptual transfer of the hydrodynamic boundary layer is applicable to the hydrodynamics of dissolving particles if the Peclet number (Pe) is greater than unity (Pe > 1) (9). The dimensionless Peclet number describes the relationship between convection and diffusion-driven mass transfer ... 

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

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