Chemical Reaction and Phase Transformation Kinetics in Solids

CHEMICAL REACTION AND PHASE TRANSFORMATION KINETICS IN SOLIDS 

At thermodynamic equilibrium, the forward and reverse rates are equal and no net reaction occurs. 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A] [B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus 

If the reaction in Eq. 2.32 is elementary, the following condition holds at equilibrium  

the product of the concentrations of the reaction products divided by the product of the concentrations of the starting materials (each raised to a power given by the coefficients in the chemical equation) equals a certain numerical value, Kc, characteristic of the reaction. For Eq. 2.32 this gives 

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Another class of equations subsumes kinetic and phase transformations of all involved reactants. Such equations describe how the reactants molecules are transformed and distributed in the reactor depending on time and other environmental parameters. Depending on the kind of chemical processes under consideration, both classes of equations are of varying importance for modelling. E.g. for catalytic packed-bed reactors the chemicals reaction rates heavily depend on local physical conditions at the (solid) catalyst material. The precise modelling of the local physical conditions and the mixture of chemicals flowing is important and complex in this case. In contrast, for classic stirred-tank reactors kinetic and phase transformations are comparatively easy to model. 

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],... 

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. 

Due to the fact that industrial composites are made up of combinations of metals, polymers, and ceramics, the kinetic processes involved in the formation, transformation, and degradation of composites are often the same as those of the individual components. Most of the processes we have described to this point have involved condensed phases—liquids or solids—but there are two gas-phase processes, widely utilized for composite formation, that require some individualized attention. Chemical vapor deposition (CVD) and chemical vapor infiltration (CVI) involve the reaction of gas phase species with a solid substrate to form a heterogeneous, solid-phase composite. Because this discussion must necessarily involve some of the concepts of transport phenomena, namely diffusion, you may wish to refresh your memory from your transport course, or refer to the specific topics in Chapter 4 as they come up in the course of this description. 

The thermodynamics of formation and transformation of a solid phase into another are characterized by two aspects, both of them explaining the difficulty to produce solids of homogeneous composition. The more important of these is nucleation The other is the tendency of certain components of the solid to diffuse to, or away from, surfaces. These aspects, however, cannot be considered in isolation. Chemical reactions involve the breaking of bonds and formation of new ones. This involves kinetically limited processes. In many cases, diffusion brings about additional kinetic limitations. The final result is the combination of the effects of all these processes. 

We need to understand what controls the rate of a phase transformation. We can monitor both chemical and structural changes to address the sometimes subtle question— which change (chemistry or structure) occurs first The answer depends on why the phase change itself occurs. The experimental techniques we use are those given in Chapter 10, so we just give some specific illustrations here. The classical approach used to study the kinetics of solid-state reactions between two ceramic oxides is to react a bulk diffusion couple in much the same way as, for example, when studying the Kirkendall effect in metals. 

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