Transport reactions, involving solids

In Section 9.3, we focus more on the intrinsic rates for reactions involving solids, since there are some modem processes in which mass transport rates play a relatively small role. Examples in materials engineering are chemical vapor deposition (CVD) and etching operations. We describe some mechanisms associated with such heterogeneous reactions and the intrinsic rate laws that arise. 

In Chapter 7 we considered catalytic reactions on solid surfaces and foimd that transport steps are essential in describing these reactions because mass transfer of reactants and products between phases must accompany reaction. In this chapter we consider the reactions of solids in which the solid enters the stoichiometry of the reaction as a reactant or product or both. We remark that the texts of Levenspiel give excellent and thorough descriptions of the reactions of solids, and we will only summarize some of the features of reactions involving solids here. 

Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [111] has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. 

Models of atmospheric phenomena are similar to those of combustion and involve the coupling of exceedingly complex chemistry and physics with three-dimensional hydrodynamics. The distribution and transport of chemicals introduced into groundwater also involve a coupling of chemical reactions and transports through porous solid media. The development of groundwater models is critical to understanding the effects of land disposal of toxic waste (see Chapter 7). 

Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

Decomposition reactions are solid-gas reactions which do not involve diffusional transport through the solid. Their reaction rates are determined by surface kinetics and possibly pore diffusion. The assumption of local equilibrium is not valid. The course of an isothermal decomposition is schematically illustrated in Figure 15-15. There is often an induction period followed by a rapid increase in relative yield until, after the inflection point, the reaction eventually ceases (the yield will not always be 100%). Since atomic transport in crystals is normally not involved in these decomposition reactions, we shall restrict ourselves to a few comments only. 

Subject areas for the Series include solutions of electrolytes, liquid mixtures, chemical equilibria in solution, acid-base equilibria, vapour-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, equilibria in analytical chemistry, dissolution of gases in liquids, dissolution and precipitation, solubility in cryogenic solvents, molten salt systems, solubility measurement techniques, solid solutions, reactions within the solid phase, ion transport reactions away from the interface (i.e. in homogeneous, bulk systems), liquid crystalline systems, solutions of macrocyclic compounds (including macrocyclic electrolytes), polymer systems, molecular dynamic simulations, structural chemistry of liquids and solutions, predictive techniques for properties of solutions, complex and multi-component solutions applications, of solution chemistry to materials and metallurgy (oxide solutions, alloys, mattes etc.), medical aspects of solubility, and environmental issues involving solution phenomena and homogeneous component phenomena. 

In addition to the chemical steps, which are the only steps involved in stoichiometric or in homogeneous catalysis reactions, heterogeneous catalysis reactions involve also physical steps, i.e. transport (transfer) of organic molecules (and heat) from the reaction mixture to the active sites of the solid catalyst and vice versa.113-151 Another difference deals with the chemical steps, which do not occur in the fluid phase, but for part of them involve both fluid and solid phases (chemisorption and desorption), the other part occurring at the surface of the catalyst.113-151... 

Subsurface solute transport is affected by hydrodynamic dispersion and by chemical reactions with soil and rocks. The effects of hydrodynamic dispersion have been extensively studied 2y 3, ). Chemical reactions involving the solid phase affect subsurface solute transport in a way that depends on the reaction rates relative to the water flux. If the reaction rate is fast and the flow rate slow, then the local equilibrium assumption may be applicable. If the reaction rate is slow and the flux relatively high, then reaction kinetics controls the chemistry and one cannot assume local equilibrium. Theoretical treatments for transport of many kinds of reactive solutes are available for both situations (5-10). 

The high-temperature fuel cell to which most attention is paid at present is the solid electrqlyte cell. Solid oxide fuel cells (SOFC) use zirconia compounds as the electrolyte layer to conduct oxygen ions formed at the positive electrode. The electrode reactions involve oxygen ion transport (in contrast to the hydrogen ion transport in the basic scheme given by (3.15) and (3.16)), whence the appearance of "oxygen" in the cell name. 

Mechanism and kinetics in biochemical systems describe the cellular reactions that occur in living cells. Biochemical reactions involve two or three phases. For example, aerobic fermentation involves gas (air), liquid (water and dissolved nutrients), and solid (cells), as described in the Biocatalysis subsection above. Bioreactions convert feeds called substrates into more cells or biomass (cell growth), proteins, and metabolic products. Any of these can be the desired product in a commercial fermentation. For instance, methane is converted to biomass in a commercial process to supply fish meal to the fish farming industry. Ethanol, a metabolic product used in transportation fuels, is obtained by fermentation of corn-based or sugar-cane-based sugars. There is a substantial effort to develop genetically modified biocatalysts that produce a desired metabolite at high yield. 

Diffusion processes participate in, and may even control the rates of many types of chemical reactions involving sohds. For example, (i) in decompositions of solids the rate may be controlled by the diffusive escape of a volatile product, and (ii) in reactions between solids a solid product may be formed between the reactants [5], so that progress is maintained by transport across the barrier layer (Figure 3.3.). 

Soil reactions are generally classified according to the nature of the main chemical process involved adsorption, ion exchange, dissolution, etc. However, in order to assess the kinetics one should consider the nature and the rate of the transport processes associated with the chemical reaction flow and diffusion in the soil solution, transport across the solid-liquid interface, diffusion in liquid-filled pores and micropores, and surface diffusion penetration into the solid. An expression for the kinetics of soil reactions can be devised by assigning rate equations to transport and chemical processes and combining these equations. The expression finally obtained has to be validated by comparison to experimental results. 

Solid-state electrochemistry is an important and rapidly developing scientific field that integrates many aspects of classical electrochemical science and engineering, materials science, solid-state chemistry and physics, heterogeneous catalysis, and other areas of physical chemistry. This field comprises - but is not limited to - the electrochemistry of solid materials, the thermodynamics and kinetics of electrochemical reactions involving at least one solid phase, and also the transport of ions and electrons in solids and interactions between solid, liquid and/or gaseous phases, whenever these processes are essentially determined by the properties of solids and are relevant to the electrochemical reactions. The range of applications includes many types of batteries and fuel cells, a variety of sensors and analytical appliances, electrochemical pumps and compressors, ceramic membranes with ionic or mixed ionic-electronic conductivity, solid-state electrolyzers and electrocatalytic reactors, the synthesis of new materials with improved properties and corrosion protection, supercapacitors, and electrochromic and memory devices. 

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