Ideal surface reactions kinetic equation

Chapter 8 provides a unified view of the different kinetic problems in condensed phases on the basis of the lattice-gas model. This approach extends the famous Eyring s theory of absolute reaction rates to a wide range of elementary stages including adsorption, desorption, catalytic reactions, diffusion, surface and bulk reconstruction, etc., taking into consideration the non-ideal behavior of the medium. The Master equation is used to generate the kinetic equations for local concentrations and pair correlation functions. The many-particle problem and closing procedure for kinetic equations are discussed. Application to various surface and gas-solid interface processes is also considered. 

In an early paper on the subject Szepe and Levenspiel [refe 10) introduced the notion of separability. The equations (1), (2) and (3), In which the deactivation function is a variable factor multiplying the initial rate of a reaction, correspond to their definition of separability. It may be useful to remind here that any kinetic treatment assuming ideal surfaces or accepting an average activity for the catalytic sites is bound to lead to such a form, provided, of course, there is no shift in rate determining steps. The question whether the deactivation is separable or not reduces to the question generally encountered in kinetic studies is it necessary to account explicitly for non uniform activity of the catalytic sites ... 

Reaction kinetics represented by the general form of Equation 1 have been employed in a number of quantitative chemical models of natural systems. Under ideal conditions, the four parameters, total mass transfer, kinetic rate constants, time, and the reactive surface area can be determined independently, permitting the unique definition of the model. In most cases, at least one of the variables, most often surface area, is treated as a dependent term. This nonuniqueness arises when the reactive surface area of a natural system cannot be estimated, or because such estimates made either from geometric or BET measurements do not produce reasonable fits to the other parameters. Most often the calculated total mass transfer significantly exceeds the observed transfer based on measured aqueous concentrations. 

Equations (11) and (12) enable the generation of the total isotopic transient responses of a product species given (a) the transient response that characterises hypothesized catalyst-surface behaviour and (b) an inert-tracer transient response that characterises the gas-phase behaviour of the reactor system. Use of the linear-convolution relationships has been suggested as an iterative means to verify a model of the catalyst surface reaction pathway and kinetics. I This is attractive since the direct determination of the catalyst-surface transient response is especially problematic for non-ideal PFRs, since a method of complete gas-phase behaviour correction to obtain the catalyst-surface transient response is presently unavailable for such reactor systems.1 1 Unfortunately, there are also no corresponding analytical relationships to Eqs. (11) and (12) which permit explicit determination of the catalyst-surface transient response from the measured isotopic and inert-tracer transient responses, and hence, a model has to be assumed and tested. The better the model of the surface reaction pathway, the better the fit of the generated transient to the measured transient. 

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

In 1940, Frumkin explored the relationships among the double-layer structure on mercury electrodes, the capacitance measured by use of a Wheatstone bridge, and the surface tension, following the theoretical underpinnings of the Lippmann equation. Grahame ° expanded this treatment of the mercury electrode, providing a fundamental understanding of the structure of the electrical double layer. Dolin and Ershler applied the concept of an equivalent circuit to electrochemical kinetics for which the circuit elements were independent of frequency. Randles developed an equivalent circuit for an ideally polarized mercury electrode that accounted for the kinetics of adsorption reactions. ... 

In this chapter, the Navier-Stokes equations have been solved in the actual 3D geometry of the reactor, thereby exploiting the full potential of the new approach, and detailed surface kinetics (Visconti et al., 2013) was implemented in the model with two main implications. On a more fundamental level, it demonstrates the power of the CAT-PP approach proposed here, which allows us to perform simulations of complex catalytic reactors characterized by nonideal flow fields, in which multistep reactions take place. On a more applied level, it allows us to assess the extent of the nonidealities of the simulated operando FTIR reaction cell, which is commercially available and is used by many research groups worldwide. This is extremely relevant especially for researchers who ivant to use the cell to collect quantitative information, since it will allow the verification of whether the cell is an ideal reactor or not. This latter hypothesis has been exploited, for example, by Visconti et al. (2013) to develop the first comprehensive and physically consistent spectrokinetic model for NOx storage... 

Dispersion due to surface adsorption/diffusion processes, or the so-called kinetic dispersion effect, is related to slow, i.e., kineticaUy limited, adsorption of ions or neutral molecules (often impurities) at the electrode surface. It has also been observed for surface reconstmction and changes in the adsorption layer where sharp deviations from ideal behavior and drop of the CPE exponent appeared. It has been found that in very clean solutions at monociystalline electrodes the CPE parameter (p is very close to unity, e.g., at Au(l 11) in 0.1 M HCIO4 it is 0.997 [367], which indicates a practically ideal capacitive behavior. However, in the presence of specifically adsorbed anions, this value is always smaller. This behavior could be explained by assuming diffusion-kinetics-controlled ionic adsorption [367-375] and is described by the Frumkin and Melik-Gaykazyan model [376, 377]. The rate of an ionic adsorption reaction, v, is described by the following equation [367] ... 

The two most important things to notice in Eq. (1.6) are (i) that the limiting current density is independent of potential, and (ii) that it depends linearly on the bulk concentration. A less obvious, but equally important, consequence of this equation is that Jl is independent of the kinetics of the reaction (i.e., of the nature of the surface and its catalytic activity). These characteristics make it an ideal tool for probing the concentration of species in solution. This is why most electroanalytical methods... 

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