General Surface Kinetics Formalism

We can compare the coverage of mobile surface species predicted by Eq. 11.99 with the coverage calculated for immobile species (Langmuir adsorption isotherm) derived in Section 11.5.3. To do this comparison, we take the low-pressure limit of Eq. 11.79, in which the denominator becomes unity. The ratio of the coverages in these two limiting cases is 

The numerator on the right-hand side of Eq. 11.100 is just the molecular partition function for the 2D gas (i.e., qxy), and the denominator is the product of the x-direction and y-direction partition functions for the bound motion in the potential well surrounding a surface site in the immobile-species case. 

In this section we introduce a very general mathematical formalism to describe mass-action kinetics of arbitrarily complex reaction mechanisms. It is analogous to the approach taken in Section 9.3.2 to describe gas-phase mass-action kinetics. 

Assume a surface reaction mechanism involving I (reversible or irreversible) surface reactions with K chemical species that can be represented in the general form 

The vki are integer stoichiometric coefficients and Xk is the chemical name of the fcth species. Normally an elementary reaction involves only three or four species (reactants plus products). Hence, as in the gas phase, the matrix is very sparse for a large set of reactions. 

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The Surface Chemkin formalism [73] was developed to provide a general, flexible framework for describing complex reactions between gas-phase, surface, and bulk phase species. The range of kinetic and transport processes that can take place at a reactive surface are shown schematically in Fig. 11.1. Heterogeneous reactions are fundamental in describing mass and energy balances that form boundary conditions in reacting flow calculations. 

In the Surface Chemkin formalism, surface processes are written as balanced chemical reactions governed by the law of mass-action kinetics. The framework was developed to provide a very general way to describe heterogeneous processes. In this section many of the standard surface rate expressions are introduced. The connection between these common forms and the explicit mass-action kinetics approach is shown in each case. 

We continue our study of chemical kinetics with a presentation of reaction mechanisms. As time permits, we complete this section of the course with a presentation of one or more of the topics Lindemann theory, free radical chain mechanism, enzyme kinetics, or surface chemistry. The study of chemical kinetics is unlike both thermodynamics and quantum mechanics in that the overarching goal is not to produce a formal mathematical structure. Instead, techniques are developed to help design, analyze, and interpret experiments and then to connect experimental results to the proposed mechanism. We devote the balance of the semester to a traditional treatment of classical thermodynamics. In Appendix 2 the reader will find a general outline of the course in place of further detailed descriptions. 

M.E. Coltrin, RJ. Kee, and F.M. Rupley. Surface Chemkin A Generalized Formalism and Interface for Analyzing Heterogeneous Chemical Kinetics at a Gas-Surface Interface. Int. J. Chem. Kinet., 23 1111-1128,1991. 

Lastly, non-elementary several-stage reactions are considered in Chapters 8 and 9. We start with the Lotka and Lotka-Volterra reactions as simple model systems. An existence of the undamped density oscillations is established here. The complementary reactions treated in Chapter 9 are catalytic surface oxidation of CO and NH3 formation. These reactions also reveal undamped concentration oscillations and kinetic phase transitions. Their adequate treatment need a generalization of the fluctuation-controlled theory for the discrete (lattice) systems in order to take correctly into account the geometry of both lattice and absorbed molecules. As another illustration of the formalism developed by the authors, the kinetics of reactions upon disorded surfaces is considered. 

Kemp elimination was used as a probe of catalytic efficiency in antibodies, in non-specific catalysis by other proteins, and in catalysis by enzymes. Several simple reactions were found to be catalyzed by the serum albumins with Michaelis-Menten kinetics and could be shown to involve substrate binding and catalysis by local functional groups (Kirby, 2000). Known binding sites on the protein surface were found to be involved. In fact, formal general base catalysis seems to contribute only modestly to the efficiency of both the antibody and the non-specific albumin system, whereas antibody catalysis seems to be boosted by a non-specific medium effect. 

Kinetics of reactions on more than one site are more complex. A general formalism for single-step surface reactions and rate control by the reaction, adsorption of a reactant, or desorption of a product has been developed by Hougen and Watson ... 

A general method to calculate dynamic surface tension is obtained from our formalism. In the diffusion-limited case, it coincides with previous results which used the equilibrium equation of state, but in the kinetically limited case it produces different expressions leading to novel conclusions. 

There is a rationale for studying these redox systems, one that originates largely from the work of McCreery and coworkers in recent years with glassy carbon electrodes [139-143]. Redox reactions are generally of two types. One type includes electrode reactions that proceed by simple diffusion of the analyte to the interfadal reaction zone with the electrode serving solely as a source or sink for electrons. In this case, the electrode reaction kinetics are relatively insensitive to factors such as the surface chemistry and microstructure, but very sensitive to the density of electronic states at the formal potential (so-called outer-sphere reaction). The other pathway includes reactions that occur via some specific... 

Note 1. From the formal point of view, the equations for the adsorption kinetics on a heterogeneous surface with a given adsorption-time distribution may be modified to have the same expression [Eq. (42)], as the desorption kinetics with the same desorption-time distribution (see, for instance. Refs. [35]). The forms (46) and (47), however, may be apphed only to thermally activated adsorption kinetics chemisorption usually runs in this situation, whereas physisorption is generally a nonactivated process. 

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