Derivation of size distributions of surfactant micelles taking into account shape, composition, and chain packing density fluctuations

The size distributions of spherical, rod-shaped, and disk-shaped surfactant micelles are derived by means of extending the conventional multiple-equilibrium approach to account for the number of water molecules adjacent to the hydrocarbon core of the micelle and, for mixed micelles, the number of aggregated cosurfactant monomers. Similarly to what we have previously obtained for spherical vesicles, these size distribution functions are products of a statistical-mechanical factor, which accounts for fluctuations in composition, chain packing density, and shape and an exponential Boltzmann factor. For rod-shaped and disk-shaped micelles, the former is a monotonously increasing function while the latter decreases rather slowly with the size of the aggregate, resulting in distinct maxima of the size distributions which are located at much higher aggregation numbers than the corresponding free energy minima. For ordinary spherical micelles, however, the preexponential, statistical-mechanical factor is a constant and, hence, it affects neither the position nor the width but merely the magnitude of the size distribution peak. In particular, as to the Boltzmann factor for polydisperse rod-shaped micelles, it is formally, in essence, the same as for bilayer vesicles. Nevertheless, because of fluctuations, the relative width of the size distribution peak is generally larger, σ(L)/[removed] = 0.816 (rods), to be compared with σ(R)/[removed] = 0.266 (vesicles).