Surfactant aggregate size distributions above and below the critical micelle concentration

Aggregate size distributions in an aqueous solution containing either charged or neutral surfactants are investigated using Raman multivariate curve resolution (Raman-MCR) spectroscopy and analyzed with the aid of a multi-aggregation chemical potential surface (MCPS) modeling strategy. Total least squares decompositions of the concentration-dependent Raman-MCR spectra are used to quantify the free and micelle surfactant populations, and the surfactant's C-H stretch frequency is used as a measure of its average aggregation state. MCPS predictions relate the experimental measurements to the underlying surfactant aggregate size distribution by fitting either the component concentrations or the average C-H frequency to MCPS predictions, and thus determine the critical micelle concentration (CMC) and estimate the corresponding micelle size and polydispersity. The Raman-MCR spectra of aqueous 1,2-hexanediol, sodium octanoate, and sodium dodecyl sulfate, measured both below and above CMC, provide critical tests of the assumed functional form of the MCPS and the presence of low-order premicellar aggregates. Our results indicate that the low-order aggregate population gradually emerges as the CMC is approached and then remains nearly concentration-independent after the appearance of micelles.