The critical micelle condition revisited.

Several simple alternatives have been examined as a possible basis for micellar size distributions which are internally consistent with the experimentally required concept of a threshold concentration, the critical micelle condition. Among these are the two-state system, monomer in equilibrium with a single high polymer, indefinite self-association, and continuous self-association with an arbitrary upper limit beyond which all further association is absolutely prohibited. Of these, only the last is a possible choice, although lacking experimental support. This report considers in deeper detail a thermodynamic model for micelle distributions, the so-called shell model of the present author, which is in basic agreement with an earlier statistic-mechanical study [Hoeve CA & Benson GC (1957), Colloid Polym Sci, 252, 56] in predicting the possibility of broad distributions of micellar species. A self-consistent distribution model which predicts a critical micelle condition must also predict a location with respect to degree of polymerization having a minimum concentration. Thus, the molar distribution function for the shell model satisfies this requirement, whereas the equivalent concentration distribution function fails to do so, as would the statistical models for multiple ligand binding. Moreover, the position of this minimum is predicted to change with concentration.