  Using the notion of aggregation work, we construct a system of differential
equations for the aggregation number of micelles which is a function of the
parameters of micellization (parametric equations). There are explicit
solutions for two important models of spherical micelles. Based on these
solutions, we obtain an analytical expression for the equilibrium concentration
of surfactant monomers and consequently for the whole spectrum of equilibrium
concentrations of molecular aggregates in this framework. Accuracy of these
expressions is discussed, and they are applied on an example of micelles formed
by sodium dodecyl sulfate.
