Heterogeneous systems kinetic models

It is the purpose of this paper to describe some of the major mechanisms that control arsenic in aquatic systems. Particularly, this paper addresses the problem of arsenic speciation and compartmentalization in sediments. To this end, results obtained from speciation, compartmentalization, kinetic, and adsorption studies using both field and laboratory samples will be interfaced in a descriptive model for arsenic in heterogeneous systems. The model has particular significance... 

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

Analysis of the simplest non-linear kinetic models (in particular, of kinetic models for heterogeneous catalysis). The aim is to select the simplest non-linear kinetic models to carry out the most complete investigation of their steady-state and relaxation characteristics. The obtained systems of typical relationships facilitates the interpretation of complex reactions, including simpler "typical units. 

Different data interpretation models have been applied simple dissociation constants (Langford and Khan, 1975), discrete multi-component models (Lavigne et al., 1987 Plankey and Patterson, 1987 Sojo and de Haan, 1991 Langford and Gutzman, 1992), discrete kinetic spectra (Cabaniss, 1990), continuous kinetic spectra (Olson and Shuman, 1983 Nederlof et al., 1994) and log normal distribution (Rate et al., 1992 1993). It should be noted that for heterogeneous systems, analysis of rate constant distributions is a mathematically ill-posed problem and slight perturbations in the input experimental data can yield artefactual information (Stanley et al., 1994). 

This review is a discussion of the kinetic modelling of the photoelectrochemistry of colloidal semiconductor systems. This area is currently attracting significant attention from the scientific community due to the applications of colloidal semiconductors within two rapidly advancing research fronts heterogeneous photocatalysis and nanocrystalline particle technology. 

For colloidal semiconductor systems, Albery et al. observed good agreement between the value of the radial dispersion obtained from dynamic light scattering and the value found from application of the above kinetic analysis to flash photolysis experiments [144], It should be remembered that this disperse kinetics model can only be applied to the decay of heterogeneous species under unimolecular or pseudo-first order conditions and that for colloidal semiconductors it may only be applied to dispersions whose particle radii conform to equation (37), i.e., a log normal distribution. However, other authors [145] have recently refined the model so that assumptions about the particle size distribution may be avoided in the kinetic data analysis. 

In heterogeneous catalysis these models are generally referred to as the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The term Michaelis-Menten kinetics is often used in homogeneous catalysis, enzyme reactions and reactions of microbial systems. 

Heterogeneously catalyzed reactions are usually studied under steady-state conditions. There are some disadvantages to this method. Kinetic equations found in steady-state experiments may be inappropriate for a quantitative description of the dynamic reactor behavior with a characteristic time of the order of or lower than the chemical response time (l/kA for a first-order reaction). For rapid transient processes the relationship between the concentrations in the fluid and solid phases is different from those in the steady-state, due to the finite rate of the adsorption-desorption processes. A second disadvantage is that these experiments do not provide information on adsorption-desorption processes and on the formation of intermediates on the surface, which is needed for the validation of kinetic models. For complex reaction systems, where a large number of rival reaction models and potential model candidates exist, this give rise to difficulties in model discrimination. 

Several key questions must be answered initially in a study of reaction chemistry. First, is the reaction sufficiently fast and reversible so that it can be regarded as chemical-equilibrium controlled Second, is the reaction homogeneous (occurring wholly within a gas or liquid phase) or heterogeneous (involving reactants or products in a gas and a liquid, or liquid and a solid phase) Slow reversible, irreversible, and heterogeneous (often slow) reactions are those most likely to require interpretation using kinetic models. Third, is there a useful volume of the water-rock system in which chemical equilibrium can be assumed to have been attained for many possible reactions This may be called the local equilibrium assumption. 

The present review, however, is confined to kinetics of local, momentary ion-exchange phenomena. After a brief overview of kinetic models commonly used to interpret ionic reactions on soil constituents (essentially based on kinetic theory of homogeneous systems), current kinetic models of heterogeneous systems will be examined in order to identify the limitations of their application to inorganic soil constituents. 

With respect to ion-exchange kinetics, the great complexity of soils has resulted in a penchant for the easy approximations of homogeneous models, even where the premise of a quasi-continuum of liquid and solid is hard to accept. The theory of heterogeneous systems offers the Nernst-Planck equations, but these also can provide no more than an approximation for migration of ions in soil constituents. 

Further development of kinetic models for the OCM process followed the path of addition of a limited number of heterogeneous steps (first of all— initiation or generation of primary methyl radicals) to homogeneous schemes of methane oxidation (Aparicio et al, 1991 Hatano et al, 1990 McCarty et al, 1990 Shi et al, 1992 Vedeneev et al, 1995 Zanthoff and Baerns, 1990). There was certain logic in such an approach since the most efficient OCM catalysts are almost exclusively oxides with no transition metal ions (some Mn-contain-ing oxide systems are the only exception), any reactions in adsorbed layers at such temperatures can be neglected. In the framework of such models some substantial features of the process could be described. For instance, they predicted the limit in the C2-hydrocarbon yield close to that reliably observed experimentally over the most efficient catalysts (20-25%). 

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