Preexponential factor, defining equation

Equation (2.1.84) predicts more slow decay as compared with the chemical kinetics (kinetic stage - (2.1.9)) unless d 2. That is, marginal dimension do = 2 occurs. The distinctive feature of (2.1.84) defining the range of its applicability is cofactor Sn2. Taking into account that (2.1.83) is valid as (d U where l = n(0) /d, the exponential kinetics (2.1.84) becomes essential as lD / n/(, l n = 8n ]/d. In another extreme case the preexponential factor predominates resulting in the asymptotics n (t) oc t d/4, as is observed for equal concentrations. That is, the crossover takes place (transition from power asymptotics to the exponential). Note that Schnorer, Sokolov and B lumen [48] have obtained these results employing the combination theory. 

For describing the elementary processes the transition state model (TSM) [20-23,57] is usually used. The TSM gives a clearly defined dependence of the preexponential factor on the type of the energy redistribution over the internal degrees of freedom of the reagents in the activated state. The reaction rate constant yields the following equation [20-23,57] ... 

Figure 8.8 displays the three reactions in the WGS model with the largest normalized sensitivity coefficients. These were computed using Equation (8.35), except that f. is the preexponential factor of reaction j, This is similar to the degree of rate control defined in Equation (8.34) except that the overall conversion is used rather than the reaction rate. Important insights from this plot are that the sensitivity (kinetic relevance) of a reaction depends on reaction conditions, for example, temperature, and that there is not always a single rate-determining step rather, multiple reactions can be simultaneously kinetically important. 

The Arrhenius plots in Fig. 8 are also characterized by the preexponential current densities and parameters analogous to the preexponential factor in the Arrhenius equation. These preexponential current densities are defined from Eqs. (54), when the limiting condition T = 0 is introduced ... 

This equation can be solved self-consistently for a given set of parameters, and flie dissipation-corrected pre-exponential factor 4, defined in Eqs (20) and (25) can be found. Calculations for the influence of flie interaction frequency (Dj on the preexponential term A show that in flic region of weak interactions A is equal to the value without fiiction When cOj- becomes greater, the value of A decreases abruptly by about 10-fold for all curves [44, 45]. This means that the dissociation... 

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