Determination of Critical Micelle Concentration from the Diffusion-Driven Dilution of Micellar Aqueous Mixtures

Micellization is a phenomenon of central importance in surfactant solutions. Here, we demonstrate that the diffusion-based spreading of the free boundary between a micellar aqueous solution and pure water yields a one-dimensional spatial profile of surfactant concentration that can be used to identify the critical micelle concentration, here denoted as C*. This can be achieved because dilution of micelles into water leads to their dissociation at a well-defined position along the concentration profile and an abrupt increase in the diffusion coefficient. Rayleigh interferometry was successfully employed to determine C* values for three well-known surfactants in water at 25 °C: Triton X-100 (TX-100), sodium dodecyl sulfate (SDS), and poly(oxyethylene)(4)Lauryl Ether (Brij-30). The dependence of C* on salt concentration was also characterized for TX-100 in the presence of Na₂SO₄, NaCl, and NaSCN. Accurate values of C* can be directly identified by visual inspection of the corresponding concentration-gradient profiles. To apply the method of least squares to experimental concentration profiles, a mathematical expression was derived from Fick's law and the pseudophase separation model of micellization with the inclusion of appropriate modifications. While Rayleigh interferometry was employed in our experiments, this approach can be extended to any experimental technique that yields one-dimensional profiles of surfactant concentration. Moreover, diffusion-driven surfactant disaggregation is precise, noninvasive, requires single-sample preparation, and applies to both nonionic and ionic surfactants. Thus, this work provides the foundation of diffusion-driven dilution methods, thereby representing a valuable addition to existing techniques for the determination of C*.