We analyze small-angle neutron scattering (SANS) data of sodium dodecyl sulfate (SDS) and sodium bis(2-ethylhexyl) sulfosuccinate (AOT) ionic micellar solutions taking into account the effect of size polydispersity on the particle form factor. The intermicellar structure factor is computed by a generalized one-component macroion theory (GOCM) assuming a constant fractional charge. The model fittings to SANS data for different concentrations allow us to extract the free energy parameters of micelle formation and growth, the size distribution function of micelles, and the minimum micelle size which is consistent with the fully stretched hydrocarbon tail lengths of the surfactant molecules. The critical micellar concentration (cmc) is predicted from the free energy parameters correctly. Combining the free energy of micelle formation with the double-layer free energy around the averaged micellar surface calculated by the nonlinear Poisson-Boltzmann equation, we obtain the hydrophobic free energy of micellization which is in quantitative agreement with the literature value. These analyses confirm the applicability of the ladder model of micellar growth in salt free ionic micellar solutions at moderate concentrations. The degree of polydispersity in size is about 11% for 2% SDS solution at 40 °C and 17% for 1% AOT at 22.6 °C.

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