STATISTICAL MECHANICAL TREATMENT OF A COMPARTMENTALIZED MOLECULAR ENSEMBLE - APPLICATION TO ELECTRONIC-ENERGY TRANSFER IN MICELLAR SYSTEMS

A statistical mechanical treatment of the equilibrium properties of a compartmentalized molecular ensemble is presented by taking, as a typi cal example of such a system, an ensemble of probes solubilized in mic elles. The role of probe-probe interactions in influencing both the sp atial distribution of probes in a micelle and the intermicellar statis tical probe distribution is explored. Three cases are considered conce rning the distribution of probes among micelles, namely (i) the case o f a one-component one-phase system, or the system of identical probes dissolved exclusively in micelles, (ii) the case of a one-component tw o-phase system, where the probes are also dissolved in the bulk aqueou s phase, and (iii) the case of a binary one-phase system. The relation ship between the fluctuation of the number of probes in a micelle and the spatial correlation function is emphasized. An alternative kinetic approach to the problem is discussed. It is stressed that the equilib rium distribution is governed by thermodynamics only and is independen t of the details of intermicellar migration of probes. The problem of intermolecular electronic energy transfer in micellar systems is treat ed with special reference to the effect of interaction between the chr omophore molecules on the overall fluorescence decay kinetics. Followi ng the approach put forward recently [A.V. Barzykin, Chem. Phys. 155 ( 1991) 221] and developed in this work, one can determine the equilibri um spatial distribution of the chromophores knowing only two microscop ic potentials, namely the intermolecular interaction potential and the hydrophobic potential characterizing the interaction of the probe wit h the micelle interior. The energy transfer observables are directly r elated to the spatial distribution of donors and acceptors, and once t he latter is defined the fluorescence decay behavior can be predicted.