The steady-state rate coefficient

A solution of eqn. (66) with l(r) given by eqn. (63) for exchange transfer in the steady-state limit, dp/dt = 0, where 

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To convert this to units of dm3 mol-1 s 1, eqn. (19) should be multiplied by 103iV where N is Avogadro s number. In the long time limit, the steady-state rate coefficient is found to be... 

The Smoluchowski theory of diffusion-limited (or controlled) reactions relies heavily on the appropriateness of the inital condition [eqn. (3)]. Though the initial condition does not determine the steady-state rate coefficient [eqn. (20)] because diffusion of B in towards the reactant A is from large separation distances (>10nm) in the steady-state, it does directly determine the magnitude of the transient component of the rate coefficient because this is due to an excess concentration of B present initially compared with that present in the steady-state. As a first approximation to the initial distribution, the random distribution is intuitively pleasing and there is little experimental evidence available to cast doubt upon its appropriateness. Section 6.6 and Chap. 8 Sect. 2.2 present further comments on this point. 

Obviously, the importance of diffusion on slow chemical reaction rates is small. It is only when the diffusion rate coefficient 4irRD is comparable with or less than the activation-limited rate coefficient that the effect of diffuse process becomes apparent. Noyes [5] pointed out that the steady-state rate coefficient of eqn. (26) is k(°°) and this can be written as... 

Of greatest importance is the steady-state rate coefficient which is the... 

On substituting eqn. (79) for the density distribution into eqn. (76), the steady-state rate coefficient may be shown to be... 

It is not unreasonable that the steady-state rate coefficient [eqn. (80)] and the time-independent component of Yokota and Tanimoto s [140] rate coefficient expression (83) do not agree very well. Perhaps the similarity might be described as surprising ... 

Using this potential energy in eqn. (44) gives the steady-state rate coefficient as approximately [260]... 

There exist many different approximations describing various aspects of diffusion-confrolled reversible reactions [57-64], When the concentration of monomers is high enough, fhe modified rafe-equation approach [58] describes poly-merizafion well. Wifhin fhe framework of fhis theory, for freely diffusing reagents, the steady-state rate coefficients in liquids take the form... 

Tq ) compared with the limiting value of the steady-state rate coefficient,... 

X 10 m s. Some departure from Forster kinetics might be expected leading to the steady-state rate coefficient of eqn. (80) contributing a little. The contribution would be observed as a small reduction in the decay time of the fluorescence in the presence of acceptors. 

The steady state rate coefficient k(st) does not depend on time, whereas the general rate coefficient k(t) does depend on time. This time dependence is typically quite important in laser chemistry, because steady state is often reached only after reaction has proceeded by 10 to 30%. If equation (128) holds, one has similarly for the steady state rate coefficient k/ st) defined in terms of the fluence dependent remaining fraction of reactant Fr in equation (137) ... 

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