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 typical example of such a system, an ensemble of probes solubilized in micelles. The role of probe-probe interactions in influencing both the spatial distribution of probes in a micelle and the intermicellar statistical probe distribution is explored. Three cases are considered concerning the distribution of probes among micelles, namely (i) the case of a one-component one-phase system, or the system of identical probes dissolved exclusively in micelles, (ii) the case of a one-component two-phase system, where the probes are also dissolved in the bulk aqueous phase, and (iii) the case of a binary one-phase system. The relationship 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 equilibrium distribution is governed by thermodynamics only and is independent of the details of intermicellar migration of probes. The problem of intermolecular electronic energy transfer in micellar systems is treated with special reference to the effect of interaction between the chromophore molecules on the overall fluorescence decay kinetics. Following the approach put forward recently [A.V. Barzykin, Chem. Phys. 155 (1991) 221] and developed in this work, one can determine the equilibrium spatial distribution of the chromophores knowing only two microscopic potentials, namely the intermolecular interaction potential and the hydrophobic potential characterizing the interaction of the probe with the micelle interior. The energy transfer observables are directly related to the spatial distribution of donors and acceptors, and once the latter is defined the fluorescence decay behavior can be predicted.