Solid-phase chemical kinetics

Detailed evaluation of heat transfer rates from burning particles also is required. The interaction between heat, mass, gas, and solid-phase chemical kinetics requires further research. 

There are many chemically reacting flow situations in which a reactive stream flows interior to a channel or duct. Two such examples are illustrated in Figs. 1.4 and 1.6, which consider flow in a catalytic-combustion monolith [28,156,168,259,322] and in the channels of a solid-oxide fuel cell. Other examples include the catalytic converters in automobiles. Certainly there are many industrial chemical processes that involve reactive flow tubular reactors. Innovative new short-contact-time processes use flow in catalytic monoliths to convert raw hydrocarbons to higher-value chemical feedstocks [37,99,100,173,184,436, 447]. Certain types of chemical-vapor-deposition reactors use a channel to direct flow over a wafer where a thin film is grown or deposited [219]. Flow reactors used in the laboratory to study gas-phase chemical kinetics usually strive to achieve plug-flow conditions and to minimize wall-chemistry effects. Nevertheless, boundary-layer simulations can be used to verify the flow condition or to account for non-ideal behavior [147]. 

Solid-Phase Chemical Equilibrium. For the growth of multicomponent films, the solid film composition must be predicted from the gas-phase composition. In general, this prediction requires detailed information about transport rates and surface incorporation rates of individual species, but the necessary kinetics data are rarely available. On the other hand, the equilibrium analysis only requires thermodynamic data (e.g., phase equilibrium data), which often are available from liquid-phase-epitaxy studies, as discussed by Anderson in Chapter 3. 

There is a variety of fundamental physical and chemical principles lhat can control the deposition rate and quality of a film resulting from a CVD process. We briefly introduce them here, but refer the reader to Chapter 2 and other books on CVD for more detailed discussions. The basic processes underlying CVD can be subdivided into mass transport effects and chemical effects, each of which can occur in both the gas and solid phases. Chemical effects can be further subdivided into thermodynamic effects and kinetic effects. In some cases, a particular effect can be separated out as rate limiting, and a CVD process can be said to be mass-transport controlled or surface-kinetics controlled. In reality, transport and chemical reactions are closely coupled, with their relative importance varying with the details of the operating conditions. 

We wUl firstly deal with the theories and models currently used in plasma-ceramic technology thermodynamic and transport properties, heat and mass transfer between a solid and a plasma, gas phase chemical kinetics. Then we will present a short review of the plasma measurement techniques (mainly temperature and velocity). 

Kinetic investigations cover a wide range from various viewpoints. Chemical reactions occur in various phases such as the gas phase, in solution using various solvents, at gas-solid, and other interfaces in the liquid and solid states. Many techniques have been employed for studying the rates of these reaction types, and even for following fast reactions. Generally, chemical kinetics relates to tlie studies of the rates at which chemical processes occur, the factors on which these rates depend, and the molecular acts involved in reaction mechanisms. Table 1 shows the wide scope of chemical kinetics, and its relevance to many branches of sciences. 

The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. 

One of the cornerstones of combinatorial synthesis has been the development of solid-phase organic synthesis (SPOS) based on the original Merrifield method for peptide preparation [19]. Because transformations on insoluble polymer supports should enable chemical reactions to be driven to completion and enable simple product purification by filtration, combinatorial chemistry has been primarily performed by SPOS [19-23], Nonetheless, solid-phase synthesis has several shortcomings, because of the nature of heterogeneous reaction conditions. Nonlinear kinetic behavior, slow reaction, solvation problems, and degradation of the polymer support, because of the long reactions, are some of the problems typically experienced in SPOS. It is, therefore, not surprising that the first applications of microwave-assisted solid-phase synthesis were reported as early 1992 [24],... 

The main goal of this chapter is to review the most widely used modeling techniques to analyze sorption/desorption data generated for environmental systems. Since the definition of sorption/desorption (i.e., a mass-transfer mechanism) process requires the determination of the rate at which equilibrium is approached, some important aspects of chemical kinetics and modeling of sorption/desorption mechanisms for solid phase systems are discussed. In addition, the background theory and experimental techniques for the different sorption/ desorption processes are considered. Estimations of transport parameters for organic pollutants from laboratory studies are also presented and evaluated. 

The processes controlling transfer and/or removal of pollutants at the aqueous-solid phase interface occur as a result of interactions between chemically reactive groups present in the principal pollutant constituents and other chemical, physical and biological interaction sites on solid surfaces [1]. Studies of these processes have been investigated by various groups (e.g., [6-14]). Several workers indicate that the interactions between the organic pollutants/ SWM leachates at the aqueous-solid phase surfaces involve chemical, electrochemical, and physico-chemical forces, and that these can be studied in detail using both chemical reaction kinetics and electrochemical models [15-28]. 

It is important to differentiate between two terms that are widely used in the literature, namely chemical kinetics and kinetics . Chemical kinetics is defined as the investigation of chemical reaction rates and the molecular processes by which reactions occur where transport (e.g., in the solution phase, film diffusion, and particle diffusion) is not limiting. On the other hand, kinetics is the study of time-dependent processes. Because of the different particle sizes and porosities of soils and sediments, as well as the problem to reduce transport processes in these solid phase components, it is difficult to examine the chemical kinetics processes. Thus, when dealing with solid phase components, usually the kinetics of these reactions are studied. 

The main reasons for investigating the rates of solid phase sorption/desorption processes are to (1) determine how rapidly reactions attain equilibrium, and (2) infer information on sorption/desorption reaction mechanisms. One of the important aspects of chemical kinetics is the establishment of a rate law. By definition, a rate law is a differential equation [108] as shown in Eq. (32) ... 

Mechanistic rate laws assume that only chemical kinetics is operational and transport phenomena are not occurring. Consequently, it is difficult to determine mechanistic rate laws for most solid phase systems due to the heterogeneity of the solid phase system caused by different particle sizes, porosities, and types of retention sites. 

Transport with mechanistic rate laws describe simultaneous transport-con-trolled and chemical kinetics phenomena and explain accurately both the chemistry and the physics of the solid phase system. 

The Elovich model was originally developed to describe the kinetics of heterogeneous chemisorption of gases on solid surfaces [117]. It describes a number of reaction mechanisms including bulk and surface diffusion, as well as activation and deactivation of catalytic surfaces. In solid phase chemistry, the Elovich model has been used to describe the kinetics of sorption/desorption of various chemicals on solid phases [23]. It can be expressed as [118] ... 

Equation (57) is empirical, except for the case where v = 0.5, then Eq. (57) is similar to the parabolic diffusion model. Equation (57) and various modified forms have been used by a number of researchers to describe the kinetics of solid phase sorption/desorption and chemical transformation processes [25, 121-122]. 

Experimental determination of Ay for a reaction requires the rate constant k to be determined at different pressures, k is obtained as a fit parameter by the reproduction of the experimental kinetic data with a suitable model. The data are the concentration of the reactants or of the products, or any other coordinate representing their concentration, as a function of time. The choice of a kinetic model for a solid-state chemical reaction is not trivial because many steps, having comparable rates, may be involved in making the kinetic law the superposition of the kinetics of all the different, and often unknown, processes. The evolution of the reaction should be analyzed considering all the fundamental aspects of condensed phase reactions and, in particular, beside the strictly chemical transformations, also the diffusion (transport of matter to and from the reaction center) and the nucleation processes. 

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