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Micelles as compartmentalized systems
Experimental and theoretical studies of the manner in which molecules are distributed amongst micelles are described. Micelles are spherical, when separated "compartments" in aqueous solution that have the ability to solubilize water insoluble molecules. Much work and speculation have appeared over the years concerning the number distribution of these solublizates. In this work, the technique of electron spin resonance has been employed to test the dogma that uncharged molecules distribute randomly i.e. according to the Poisson distribution. Unlike most experimental techniques, this technique offers the tremendous advantage of being able to separate the contributions due to singly, doubly, triply, etc. occupied compartments. We have proved that the experimental results are inconsistent with a random distribution, and that particle-particle interactions must be taken into account. These interactions were studied theoretically in the framework of the grand canonical ensemble and also in the framework of a new phenomenology which models the flow of particles into compartments under the influence of an impedance to entry. The number distributions are shown to be identical in both frameworks, allowing two physical views of the process and allowing calculations to be carried out by either technique. In addition to a formal repulsion between particles that might be expected, an attractive pairing potential for singly occupied micelles was necessary to explain the results. Both the attractive and repulsive parts of the potential are found to be the same for two different solubilizates.