Surface Reaction Kinetics-Based Models

Surface Reaction Kinetics-Based Models. The basic consideration in reaction kinetics models is that the reaction rate is determined by the lattice strueture on the surface. The difference in the lattice structures of various crystal planes gives rise to differences in surface bond density, electron density, surface free energy, and so on, which then determine the dissolution rate of the surface silicon atoms. All etching 

FIGURE 7.39. Schematic illustration of the bonding condition of (100) and (111) Si surface. 

The difference in etch rate between (111) and (100) surfaces was related to the bond densities on the two surfaces in the early surface kinetics models. According to Hesketh et the etch rate difference between (100) and (111) planes is due to the difference in the surface free energy of the crystal planes which is proportional to the number of bonds on the surface. The (111) plane, which has the lowest surface free energy measured in vacuum, has the lowest bond density and thus has the lowest etch rate. They postulated that the etch rate of crystal planes is a function of the total number of bonds at the surface, that is, the sum of the in-plane, lateral bonds between atoms in the plane of the surface, and surface bonds, dangling bonds. It was recognized however, that this effect alone will not cause etch rate differences of more than a factor of two. °  

Jakob and Chabal reasoned that the silicon atoms, such as those at the steps and kink sites, that are most physically accessible are preferentially attacked. The reactants and the dissolved complex have certain physical dimension and orientation so that certain pathways may be forbidden due to steric constraints. While this argument is intuitively sound, its verification requires information on the solvation structure of the involved species and their interaction with the surface atomic structures. 

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This section briefly discusses some aspects of catalytic combustion mechanisms, i.e., surface reaction kinetics and heterogeneous-homogeneous reactions. Based on this discussion and the previous section, the extreme demands on combustion catalysts are presented. Finally, the role of mathematical modeling of this complex catalytic system is examined. 

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

The authors applied this model to the situation of dissolving and deposited interfaces, involving chemically interacting species, and included rate kinetics to model mass transfer as a result of chemical reactions [60]. The use of a stochastic weighting function, based on solutions of differential equations for particle motion, may be a useful method to model stochastic processes at solid-liquid interfaces, especially where chemical interactions between the surface and the liquid are involved. 

Specific research subjects have emerged with respect to improved descriptions of specific phenomena. Some time ago, it was speculated that gas-solid interactions and turbulence effects on reaction kinetics would be important areas of advance in the modeling art. Gas-solid interactions include both chemical formation of aerosols and reactions on surfaces of pre-existing suspended particulate matter. Because of differing effects of a material in the gas phase and in some condensed phase, it will be important to characterize transformation processes. The achex (Aerosol Characterization hYperiment) program recently carried out under the direction of Hidy will provide an extensive data base with which to test new ways of treating the gas-solid interaction problem. 

For CFD modeling a detailed chemical mechanism for the relevant gas phase and surface reaction steps is necessary. Due to the difficulty involved in determining kinetic and thermodynamic parameters for the elementary steps, these are often based on empiricism and even guessing. Here, theoretical first-principles methods can be very helpful. 

Liquid phase hydrogenation catalyzed by Pd/C is a heterogeneous reaction occurring at the interface between the solid catalyst and the liquid. In our one-pot process, the hydrogenation was initiated after aldehyde A and the Schiff s base reached equilibrium conditions (A B). There are three catalytic reactions A => D, B => C, and C => E, that occur simultaneously on the catalyst surface. Selectivity and catalytic activity are influenced by the ability to transfer reactants to the active sites and the optimum hydrogen-to-reactant surface coverage. The Langmuir-Hinshelwood kinetic approach is coupled with the quasi-equilibrium and the two-step cycle concepts to model the reaction scheme (1,2,3). Both A and B are adsorbed initially on the surface of the catalyst. Expressions for the elementary surface reactions may be written as follows ... 

Recently, Praharso et al also developed a Langmuir-Hinshelwood type of kinetic model for the SR kinetics of i-Cg over a Ni-based catalyst. In their model, it was assumed that both the hydrocarbon and steam dissociatively chemisorb on two different dual sites on the catalyst surface. The bimolecular surface reaction between dissociated adsorbed species was proposed as the ratedetermining step. The following generalized rate expression was proposed ... 

When a simple, fast and robust model with global kinetics is the aim, the reaction kinetics able to predict correctly the rate of CO, H2 and hydrocarbons oxidation under most conditions met in the DOC consist of semi-empirical, pseudo-steady state kinetic expressions based on Langmuir-Hinshelwood surface reaction mechanism (cf., e.g., Froment and Bischoff, 1990). Such rate laws were proposed for CO and C3H6 oxidation in Pt/y-Al203 catalytic mufflers in the presence of NO already by Voltz et al. (1973) and since then this type of kinetics has been successfully employed in many models of oxidation and three-way catalytic monolith converters... 

To have a quantitative idea of the higher unit surface area activity of the Monolith catalyst, rate constants based on surface area were considered essential to know. To accomplish this, the global reaction kinetics of desulfurization and denitrogen-ation were determined. For the desulfurization the following three kinetic models, as suggested in the literature, were tested to determine which best represented the data of this study. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Due to the formation of an intermediate complex, this type of reaction mechanism was described as being analogous to Michaelis-Menten kinetics [39]. A common error made when examining the behaviour of systems of this type is to use the Koutecky-Levich equation to analyse the rotation speed-dependence of the current. This is incorrect because the Koutecky-Levich analysis is only applicable to surface reactions obeying strictly first-order kinetics. Applying the Koutecky-Levich analysis to situations where the surface kinetics are non-linear, as in this case, leads to erroneous values for the rate constants. Below, we present the correct treatment for this problem based on an extension of a model originally developed by Albery et al. [42]... 

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