Poisson statistics behavior

Calculations of micelle sizes and aggregation numbers have been made from static and time-resolved quenching experiments in which deviations from the behavior in homogeneous solutions due to compartmentalization of the reactants in micelles (cage effect) were quantitatively exploited (cf. Section IV). It is assumed that the number of quenchers per micelle follows Poisson statistics, and it must be guaranteed that the time which donors and acceptors spend in a micelle is long compared to fluorescence lifetimes of donors and that quenching by the acceptors is the main deactivation process of the donors. 

The limitations imposed on DDL theory as a molecular model by these four basic assumptions have been discussed frequently and remain the subject of current research.In Secs. 1.4 and 3.4 it is shown that DDL theory provides a useful framework in which to interpret negative adsorption and electrokinetic experiments on soil clay particles. This fact suggests that the several differences between DDL theory and an exact statistical mechanical description of the behavior of ion swarms near soil particle surfaces must compensate one another in some way, at least in certain applications. Evidence supporting this conclusion is considered at the end of the present section, whose principal objective is to trace out the broad implications of Eq. 5.1 as a theory of the interfacial region. The approach taken serves to develop an appreciation of the limitations of DDL theory that emerge from the mathematical structure of the Poisson-Boltzmann equation and from the requirement that its solutions be self-consistent in their physical interpretation. TTie limitations of DDL theory presented in this way lead naturally to the concept of surface complexation. 

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