Multimerization: closed or open association scenario?

We address the problem of classification of the type of association (multimerization) in solutions of identical unimers. Although the aggregation is still routinely characterized in terms of either "open association" or "closed association" models, neither of the two models can provide a fair description of many aggregation processes. We demonstrate that a realistic multimerization may show mixed basic features, i.e. simultaneously those typical of the classical open association and those typical of the classical closed association. In particular, we show that a living polymerization may seem to exhibit a critical micelle concentration (CMC), whereas the basic integral characteristics of a "closed" system with rather monodisperse micelles ((m(w)/m(n)(mic) = 1.02) may not imply a well-defined CMC. Therefore, a multimerization must be characterized by the detailed micelle size distribution that largely defines the equilibrium and dynamical properties of the system. To this end, we suggest a simple method of deriving the micelle size distribution c(m) (depending also on the total concentration of amphiphilic molecules) from the concentration dependence of just the mean aggregation number, m(w)(c). Our results thus invite a reconsideration of the basic methods used for interpretation of experimental data on micellization.