Critical Micelle Concentration . A Transition Point for Micellar Size Distribution

A critical concentration is defined which separates two kinds of behavior of the size distribution of micellar aggregates of surfactant molecules. Below this concentration, the size distribution is a monotonic decreasing function of size; above this concentration, the size distribution is a function exhibiting two extrema and the contribution of larger aggregates becomes important. Quantitative results are obtained from the condition of thermodynamic equilibrium, decomposing the standard chemical potential per amphiphile of various aggregates into size-dependent and size-independent terms, and using for these terms the empirical expressions given by Tanford.