Values of the degree of counterion dissociation, R, for sodium n-alkyl sulfate micelles, denoted by SN c S, where N c is the number of carbon atoms in the alkyl chain, are defined by asserting that the aggregation number, N, is dependent only on the concentration, C aq , of counterions in the aqueous pseudophase. By using different combinations of surfactant and added salt concentrations to yield the same value of N, R can be determined, independent of the experimental method. Electron paramagnetic resonance measurements of the hyperfine spacings of two nitroxide spin probes, 16-and 5-doxylstearic acid methyl ester (16DSE and 5DSE, respectively), are employed to determine whether micelles from two samples have the same value of N to high precision. The EPR spectra are different for the two spin probes, but the values of R are the same, within experimental error, as they must be. In agreement with recent work on S12S and with prevailing thought in the literature, values of R are constant as a function of N. This implies that the value of R is constant whether the surfactant or added electrolyte concentrations are varied. Interestingly, R varies with chain length as follows: However, the theory also predicts that, for a given value of N c , R decreases as N increases. Moreover, this decrease is predicted to be different if N is increased by adding salt or by increasing the surfactant concentration. A modification to the theory in which dissociated counterions contribute to the ionic strength while added co-ions (Cl -) do not, brings theory and experiment into closer accord. Assuming R to be constant versus N permits a direct application of the aggregation number-based definition of R using time-resolved fluorescence quenching to measure values of N as well as other experimental parameters that vary monotonically with N, such as the microviscosity measured with spin probes and the quenching rate constant. For S13S micelles at 40°C, R ) 0.20 ( 0.02 is derived from N; R ) 0.21 ( 0.02 from the microvisicosity, and R ) 0.21 ( 0.02 from the quenching rate constants, in agreement with the hyperfine spacing results. The aggregation numbers for S13S are well described by the power law N ) N°(C aq /cmc 0 ) γ , where cmc 0 is the critical micelle concentration in the absence of added salt, N°) 67, and γ ) 0.26.
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