Statistical thermodynamics of micellar solutions

In order to study the behavior of surfactant solutions near their critical micelle concentrations (CMC’s), the osmotic pressure and monomer concentration functions have been examined in the complex plane of total surfactant concentration y. By considering some simple models in detail it has been established that a locus of branch-point singularities for both functions intersects the positive real y axis at the CMC’s. The proximity of the closest branch-point pair straddling the real axis is related on the one hand to mean micelle size, and on the other hand to the sharpness of the critical micelle phenomenon. A perturbation procedure has been constructed which can help to locate the physically important branch points near the positive real axis for the general ideal solution case.