Kinetic parameter distribution applications

All the work just mentioned is rather empirical and there is no general theory of chemical reactions under plasma conditions. The reason for this is, quite obviously, that the ordinary theoretical tools of the chemist, — chemical thermodynamics and Arrhenius-type kinetics - are only applicable to systems near thermodynamic and thermal equilibrium respectively. However, the plasma is far away from thermodynamic equilibrium, and the energy distribution is quite different from the Boltzmann distribution. As a consequence, the chemical reactions can be theoretically considered only as a multichannel transport process between various energy levels of educts and products with a nonequilibrium population20,21. Such a treatment is extremely complicated and - because of the lack of data on the rate constants of elementary processes — is only very rarely feasible at all. Recent calculations of discharge parameters of molecular gas lasers may be recalled as an illustration of the theoretical and the experimental labor required in such a treatment22,23. ... 

Almost all physical models use simple pore geometries. Practical pore systems are, however, very complicated and contain parameters which are difficult to measure or which have a wide distribution of their characteristic parameters. The applicability of a rigorous treatment and of very refined models and physical expressions is therefore doubtful. The treatment in this chapter will make use mainly of phenomenological equations which allow description of data, data reduction and some extrapolation and which rely on experimentally determined parameter values. Gas kinetic theory and expressions based on the microscopic (atomic) level will be used only to estimate some parameter values and to predict trends. 

The GITT is one of frequent methods to investigate steady-state or equilibrium electrode potentials and diffusion coefficients as function of lithium content in a lithium intercalation electrode. The detailed experimental procedures to determine these thermodynamic and kinetic parameters have been well documented in previous studies [45]. From repeated coulombic titration processes of lithium in the electrode, by application of a constant current with a low value and sufficient time interval to reach equilibrium (i.e., to obtain uniform distribution of the lithium ions throughout the electrode), it is possible to obtain the electrode potentials at various lithium contents, as depicted in Figure 5.2. 

Same guidelines as those given in section 3.2.2 are applicable for the experimental determination of kinetic parameters of inhibition. Desirably no less than eight substrate concentrations and five initial inhibitor concentrations (including zero) should be considered, data points should be evenly distributed and the range of... 

The application of these comprehensive models to the prediction of the emulsion polymer molecular weight distribution requires a fundamental understanding of the very conaplex reaction mechanisms and knowledge of various kinetic parameters (e.g., the rate coefficients for the absorption of free radicals by the latex particles, the desorption of radicals out of the particles, and the bimolecular termination reaction). However, these mathematical models in combination with the polymer molecular weight distribution data may serve as a useful tool for estimating the values of the kinetic parameters involved in emulsion polymerization. 

Clearly, the procedure outlined above is complex. It requires solution of the flow fleld, in conjunction with the determination of the distribution of the electrostatic potential and of all species concentrations within the cell. In addition to the mathematical complexity, the transport properties (diffusivities, mobility) for all species must be given. This is further complicated by the fact that most practical electrolytes are concentrated and hence transport interactions between the species must be accounted for, requiring the application of the more complex concentrated electrolyte theory. Additionally, the electrode kinetics parameters must be known. However, as discussed below, simplifications are often possible, since most operating cells are typically controlled by either the electric potential distribution or by the concentration distribution (in conjunction with the electrode kinetics), and only a few systems are influenced about equally by both. 

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