Steady-state kinetics basic theory

So far in this chapter, the chemical biology reader has been introduced to examples of biocatalysts, kinetics assays, steady state kinetic analysis as a means to probe basic mechanisms and pre-steady-state kinetic analysis as a means to measure rates of on-catalyst events. In order to complete this survey of biocatalysis, we now need to consider those factors that make biocatalysis possible. In other words, how do biocatalysts achieve the catalytic rate enhancements that they do This is a simple question but in reality needs to be answered in many different ways according to the biocatalyst concerned. For certain, there are general principles that underpin the operation of all biocatalysts, but there again other principles are employed more selectively. Several classical theories of catalysis have been developed over time, which include the concepts of intramolecular catalysis, orbital steering , general acid-base catalysis, electrophilic catalysis and nucleophilic catalysis. Such classical theories are useful starting points in our quest to understand how biocatalysts are able to effect biocatalysis with such efficiency. 

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

The research of Roy Jackson combines theory and experiment in a distinctive fashion. First, the theory incorporates, in a simple manner, inertial collisions through relations based on kinetic theory, contact friction via the classical treatment of Coulomb, and, in some cases, momentum exchange with the gas. The critical feature is a conservation equation for the pseudo-thermal temperature, the microscopic variable characterizing the state of the particle phase. Second, each of the basic flows relevant to processes or laboratory tests, such as plane shear, chutes, standpipes, hoppers, and transport lines, is addressed and the flow regimes and multiple steady states arising from the nonlinearities (Fig. 6) are explored in detail. Third, the experiments are scaled to explore appropriate ranges of parameter space and observe the multiple steady states (Fig. 7). One of the more striking results is the... 

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