Local reaction conditions, concept

In this chapter, connections will be established between electrocatalytic surface phenomena and porous media concepts. The underlying logics appear simple, at least at first sight. Externally provided thermodynamic conditions, operating parameters, and transport processes in porous composite electrodes determine spatial distributions of reaction conditions in the medium, specifically, reactant and potential distributions. Local reaction conditions in turn determine the rates of surface processes at the catalyst. This results in an effective reactant conversion rate of the catalytic medium for a given electrode potential. 

Combination of the macrohomogeneous approach for porous electrodes with a statistical description of effective properties of random composite media rests upon concepts of percolation theory (Broadbent and Hammersley, 1957 Isichenko, 1992 Stauffer and Aharony, 1994). Involving these concepts significantly enhanced capabilities of CL models in view of a systematic optimization of thickness, composition, and porous structure (Eikerling and Komyshev, 1998 Eikerling et al., 2004). The resulting stmcture-based model correlates the performance of the CCL with volumetric amounts of Pt, C, ionomer, and pores. The basis for the percolation approach is that a catalyst particle can take part in reaction only if it is connected simultaneously to percolating clusters of carbon/Pt, electrolyte phase, and pore space. Initially, the electrolyte phase was assumed to consist of ionomer only. However, in order to properly describe local reaction conditions and reaction rate distributions, it is necessary to account for water-filled pores and ionomer-phase domains as media for proton transport. 

This section emphasizes the importance of local reaction conditions in nanopores of CLs. In this case, spatially varying charge distributions ions exert a major impact on electrochemical processes at internal pore surfaces. Such charge distributions, occurring in the region of the electrochemical double layer, invalidate the assumption of electroneutrality. In fact, the double layer concept itself becomes meaningless when the nominal thickness of the double layer, that is, the Debye length, is of the same order as the pore radius. 

For applications in the field of micro reaction engineering, the conclusion may be drawn that the Navier-Stokes equation and other continuum models are valid in many cases, as Knudsen numbers greater than 10 are rarely obtained. However, it might be necessary to use slip boimdaty conditions. The first theoretical investigations on slip flow of gases were carried out in the 19th century by Maxwell and von Smoluchowski. The basic concept relies on a so-called slip length L, which relates the local shear strain to the relative flow velocity at the wall ... 

The subject of kinetics is often subdivided into two parts a) transport, b) reaction. Placing transport in the first place is understandable in view of its simpler concepts. Matter is transported through space without a change in its chemical identity. The formal theory of transport is based on a simple mathematical concept and expressed in the linear flux equations. In its simplest version, a linear partial differential equation (Pick s second law) is obtained for the irreversible process, Under steady state conditions, it is identical to the Laplace equation in potential theory, which encompasses the idea of a field at a given location in space which acts upon matter only locally Le, by its immediate surroundings. This, however, does not mean that the mathematical solutions to the differential equations with any given boundary conditions are simple. On the contrary, analytical solutions are rather the, exception for real systems [J. Crank (1970)]. 

The phenomenology of localized corrosion helps to define certain requirements for localized corrosion that can be expressed in terms of the concepts already discussed in Chapter 2. In order for localized corrosion to occur, there must be a spatial variation in the electrochemical or metallurgical conditions. The occurrence of discrete sites of attack demonstrates that passivity must be able to coexist on the same surface with active regions. In fact, this is one of the scientifically interesting aspects of localized corrosion. Under normal circumstances, one would expect that a surface would either be completely passive or completely active, not a mixture of the two. Finally, there is a physical separation of the anodic and cathodic reaction sites during localized corrosion. In order to understand localized corrosion and thus how to test for resistance to localized corrosion, we must understand each of these aspects and their interrelations. 

Over the past 10-15 years a new trend has been developed in theoretical electrochemistry the electrochemistry of solvated electrons. In this review theoretical concepts of the electrochemical properties of solvated electrons and the results of experimental studies are considered from a unified position. Also discussed are energy levels of localized (solvated) and delocalized electrons in solutions and methods for their determination conditions of electrochemical formation of solvated electrons and properties of these solutions equilibrium on an electron electrode . The kinetics and mechanisms of cathodic generation of solvated electrons and of their anodic oxidation are discussed in detail. In the last sections participation of solvated electrons in ordinary electrode reactions is discussed, and the possibilities of cathodic electrosyntheses utilizing solvated electrons are considered. 

The modem theory of chemical reaction is based on the concept of the potential energy surface, which assumes that the Born-Oppenheimer adiabatic approximation [16] is obeyed. However, in systems subjected to the Jahn-Teller effect, adiabatic potentials have the physical meaning of the potential energy of nuclei only under the condition that non-adiabatic corrections are small [28]. In the vicinity of the locally symmetric intermediate, these corrections will be very large. The complete description of nuclear motion, i.e. of the mechanism of the chemical reaction, can be obtained only from Schroedinger s equation without applying the Born-Oppenheimer approximation in the vicinity of the locally... 

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