Bose–Einstein-like statistics of amphiphilic self-assembly

In the present paper, we formulate a statistical mechanical framework of amphiphilic self-assembly that allows a proper understanding of surfactant self-association processes on the basis of an occupation number formalism. In this model, amphiphilic molecules in solution can occupy different levels of well-defined energies corresponding to aggregates of different aggregation numbers. Due to its definition, the occupation number of a level can only take values which are proportional to the level aggregation number, thus giving rise to a modified version of Bose–Einstein statistics. In this new level-filling scheme an adequate statistical foundation of conventional micellization thermodynamics can be attained, the occupation of the different levels being controlled by the monomer chemical potential (μk0) in the conventional manner. The implications of the new statistics on fluctuations of the number of monomers in the different aggregation levels are analyzed. Particularly, an analogy is seen to exist between the cooperative process of micellization in self-assembling clusters and Bose–Einstein (BE) momentum condensation of molecules in the energetically most favored aggregation level. Finally, micellar growth is also a matter of study in the new formalism.