Electrochemical reactions, computational analysis

Figure 3.37. Computed velocity fields (m/s) for flows in adjacent interdigitated oxygen channels (with gas diffusion layer on the left side) of a PEM fuel cell (A inlet, C outlet, in x-y plane). In the middle (B), the flow from one gas channel through the gas diffusion layer to the adjacent gas channel is shown in the z-y plane, for the midpoint of the cell extension in the z-direction. The flows in A and C are for the midpoint value of z. (From S. Um and C. Wang (2004). Three-dimensional analysis of transport and electrochemical reactions in polymer electrolyte fuel cells. /. Power Sources 125, 40-51. Used with permission from Elsevier.)...

The application of atomic scale computational methods in the analysis of electrochemical reactions has now reached a level, where accurate prediction of electrocatalysts for the efficient conversion of excess sustainable electricity into synthetic fuels like hydrogen, ammonia, methane, and methanol, or in the design of new materials for the next generation in battery technologies. 

An electrochemical reaction may be a sequence of several steps involving one or more intermediates. If a particular step is rate-determining, the standard free energies AGf and AG2 can be computed. The method that is commonly employed is to assume quasi-equilibrium for all the preceding steps and thus to obtain the concentration of the intermediates as a function of potential (compare cases c and f in section 2 of this chapter). In an alternate derivation Parsons [17] treated the passage of the representative point of a system over a series of activation barriers. The state P immediately before the highest barrier and the state Q immediately after it have to be considered besides the initial and final states. This treatment [17-19] which is equivalent [18] to the quasiequilibrium analysis is discussed subsequently. 

It is probably the complexity of these theories that prohibited this particular aspect of electrode kinetics from being attractive for application in the study of homogeneous reaction kinetics per se. Yet it must be clear that the electrochemical techniques, together providing an extremely wide range of time scales, should be preeminently suited for investigations of both slow and (very) fast homogeneous reactions. This is the more true since, nowadays, the problem of the non-availability of a closed-form expression for the response—perturbation or response—time relation has been overcome by numerical analysis procedures conducted with the aid of computers. 

The input of the problem requires total analytically measured concentrations of the selected components. Total concentrations of elements (components) from chemical analysis such as ICP and atomic absorption are preferable to methods that only measure some fraction of the total such as selective colorimetric or electrochemical methods. The user defines how the activity coefficients are to be computed (Davis equation or the extended Debye-Huckel), the temperature of the system and whether pH, Eh and ionic strength are to be imposed or calculated. Once the total concentrations of the selected components are defined, all possible soluble complexes are automatically selected from the database. At this stage the thermodynamic equilibrium constants supplied with the model may be edited or certain species excluded from the calculation (e.g. species that have slow reaction kinetics). In addition, it is possible for the user to supply constants for specific reactions not included in the database, but care must be taken to make sure the formation equation for the newly defined species is written in such a way as to be compatible with the chemical components used by the rest of the program, e.g. if the species A1H2PC>4+ were to be added using the following reaction ... 

Most electrochemical studies carried out today make use of online computers for control of experiments and for data acquisition and analysis, including the techniques described earlier. Examples of the application of computer evaluation of experimental results include, for instance, pattern recognition [151] and the recording of current-time profiles of the form A(lni)/A(lnt) versus t for mechanistic classification [152] as well as nonlinear regression techniques [153-155]. Efforts have also been made to use knowledge-based systems for the elucidation of reaction mechanisms [156]. 

For a given pair of electrode reactions of known thermodynamic and kinetic characteristics, electrochemical engineering procedures must provide a reactor design in which these reactions can occur with high material and energy efficiencies. Simultaneously, appropriate provisions have to be made for the input of reactants and outflow of products and for the addition (or removal) of electric and thermal energy. The emphasis here is on the complete system and the inter-related surface reactions and transport processes. System analysis and design of electrochemical reactors require elaborate computer-implemented process simulation, synthesis, and optimization. 

Therefore, the analysis of the product distribution in the H2, HD, and D2 mixtures obtained during electrocatalytic hypophosphite oxidation on nickel electrode suggests that the hydride mechanism, assuming the release of hydride ion and instantaneous reaction with water, is unlikely due to HD content lower than the equilibrium values (hydride mechanism should lead to HD as a prevailing component [77]). Furthermore, this also puts to a question the electrochemical mechanism, according to which equilibrium H2, HD, and D2 mixtures must be formed due to the statistical recombination of H and D atoms for equally accessible electrode surface. To clarify this issue, computer simulations for the H2, HD, and D2 formed by the recombination of H and D atoms were performed. 

Linear sweep and cyclic voltammetry are among the most widely used electroana-lytical techniques for analysis of electron transfer related reactions. They are simple to apply, available in modem computer based electrochemical instmments and backed by extensive theoretical treatment. Besides classical applications in mechanistic analysis (see also Volume 8, Chapter 1), advances in data treatment, ultramicroelectrode use, and combination with other techniques allow the study of molecular electrochemical systems in great detail. 

Computational Structural Analysis - based codes. These are based on publicly or commercially available 3-dimensional structural analysis codes (e.g. ANSYS, Nastran, Abacus). Typically, these must be augmented to represent ionic conduction, fluid flow, and electrochemical and chemical reactions. While these codes do not provide as much insight... 

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