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 counterion dissociation”, α, is defined by asserting that the aggregation number, N, is dependent only on the concentration, C aq, of counterions in the aqueous pseudophase. Using different combinations of surfactant and added salt concentrations yielding the same value of C aq leads to a straightforward definition of α. Any experimental method able to precisely distinguish values of N may be used and should give the same values of α. The value 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 known function of C aq, α may be determined as a function of N . The method is demonstrated with sodium dodecyl sulfate (SDS) using an electron paramagnetic resonance method. For SDS, the method yields a constant value of α = 0.272 ± 0.017 for values of the aggregation number less than about N ≈ 110, which corresponds to combinations of surfactant and salt concentrations from [SDS] = 600 mM and [NaCl] = 0 to [SDS] = 25 mM and [NaCl] = 155 mM. This value of α is in excellent agreement with literature values based on activity measurements, micelle mobility measurements, and radioisotope mobility measurements of the Na + ion but in poor agreement with measurements employing light scattering. The constancy of α is in accord with theoretical arguments based on the Poisson−Boltzmann equation.