The Wilemski and Fixman theory of fluorescence quenching

Reactions between species which are present in comparable, and large, concentrations are complicated to analyse because any one species may react with one of several reactants. This competitive effect is one form of the many-body problem and these cannot be solved exactly. 

In this section, and much of the remainder of this chapter and also Chaps. 10 and 12, the approximate methods which have been used to analyse these competitive effects are introduced. These comments are not meant to be a comprehensive analysis of such work, but rather a means of introducing the concepts behind such approximations. 

The first reasonably successful theory of diffusion-limited chemical reactions which specifically endeavoured to develop a model that could described, in principle, the competitive effect was introduced by Wilemski and Fixman [51], They considered the fluorescence of a species A which can be quenched by natural decay (lifetime t) and by a quencher, Q, of concentration [Q] 

Their analysis is discussed in this section. For convenience, the natural decay of the excited state will be ignored, but it is easily incorporated into the analysis. 

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