A definition of the degree of ionization of a micelle based on its aggregation number

The "degree of ionization" of a micelle or the "apparent degree of counteri on dissociation", alpha, is defined by asserting that the aggregation numbe r, N, is dependent only on the concentration, C-aq, of counterions in the a queous pseudophase. Using different combinations of surfactant and added sa lt concentrations yielding the same value of C-aq leads to a straightforwar d definition of alpha. Any experimental method able to precisely distinguis h values of N may be used and should give the same values of alpha. The val ue of N is not needed in the method; the experiment needs only ensure that the value of N is the same for two samples. For systems in which N is a kno wn function of C-aq, alpha may be determined as a function of N. The method is demonstrated with sodium dodecyl sulfate (SDS) using an electron parama gnetic resonance method. For SDS, the method yields a constant value of alp ha = 0.272 +/- 0.017 for values of the aggregation number less than about N approximate to 110, which corresponds to combinations of surfactant and sa lt concentrations from [SDS] = 600 mM and [NaCl] = 0 to [SDS] = 25 mM and [ NaCl] = 155 mM. This value of cc is in excellent agreement with literature values based on activity measurements, micelle mobility measurements, and r adioisotope mobility measurements of the Na+ ion but in poor agreement with measurements employing light scattering. The constancy of alpha is in acco rd with theoretical arguments based on the Poisson-Boltzmann equation.