Further estimates of the rate coefficient

In the previous chapter, the theory developed by Wilemski and Fixman [51] is discussed in some detail (see Chap. 9, Sect. 4). While there are a number of reservations about this approach to describing diffusion-limited reaction rates (see Chap. 9, Sect. 4.3), it is very useful analysis because it is capable of further refinement. A most interesting case in point is the variation analysis by Doi [485]. This section discusses his analysis in more detail. 

The general approach of Wilemski and Fixman [51] was followed by Doi [485], but the possibility of interactions between reactants was also included. Hence, the spatial diffusion and drift operator becomes 

By integrating eqn. (272) similarly and noting that there is no particle current at the outer boundary (nor any across the reaction surface) then 

By taking Laplace transforms and using the approximate expression for 0, developed by Wilemski and Fixman [see eqn. (220)] 

To force eqn. (274) to have the same long-time (or small s) character as this means that, at the pole where s = — fe i, so too must 

---