Figure 2
Micelle size distribution for a solution of sodium dodecyl sulfate (SDS) at a concentration ten times its critical micelle concentration. Xg is the mole fraction of micelles with the aggregation number g. T = 25 ºC, P = 1 atm, and Nw = 3400000. The micelle size distribution converges to a Gaussian-like distribution after the optimization procedure.
Figure 3
Typical example of the Gibbs energy, G'/kT, as a function of the number of micelles with aggregation number g, Ng, and the number of surfactant molecules in the cylindrical part of the micelle, gcyl. We fixed the values of the length of the cylindrical part of the micelle, Lc, and the radius of the spherical ends of the micelles, Rs, to be equal to 2.89 nm and 1.23 nm, respectively.
Figure 4
Critical micelle concentration (CMC) for different surfactants in aqueous solutions obtained by the maximum term method (continuous lines), and the size distribution methodology (dashed lines). The squares are experimental data (Khan and Shah, 2008Khan, A. M. and Shah, S. S., Determination of Critical Micelle Concentration (CMC) of Sodium Dodecyl Sulfate (SDS) and the effect of low concentration of pyrene on its CMC using ORIGIN software. Journal of Chemical Society of Pakistan, 30(2), p. 186-191 (2008).; Neves et al., 2007Neves, A. C. S., Valente, A. J. M., Burrows, H. D., Ribeiro, A. C. F., Lobo, V. M. M., Effect of terbium(III) chloride on the micellization properties of sodium decyl and dodecyl-sulfate solutions. Journal of Colloid and Interface Science, 306, p. 166-74 (2007).; Evans, 1956Evans, H. C., Alkyl sulphates. Part I. Critical micelle concentrations of the sodium salts. Journal of Chemical Society, p. 579-586 (1956).; Zhao et al., 2012Zhao, M., Gao, Y. and Zheng, L., Micelle Formation by N-alkyl-N-methylpiperidinium bromide ionic liquids in aqueous solution. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 412, p. 90-95 (2012)., Velázquez and Lopez-Días, 2007Velázquez, M. M. and López-Díaz, D., Variation of the critical micelle concentration with surfactant structure: A simple method to analyze the role of attractive - repulsive forces on micellar association. The Chemical Educator, 12(5), p. 1-6 (2007).). (a) Sodium nc-alkyl sulfate, (b) nc-alkyl pyridinium bromide, (c) nc-alkyl trimethylammonium bromide, (d) nc-alkyl(dimethyl)phosphine.
Figure 5
Micelle size distributions for different surfactants obtained by the proposed methodology. Xg is the molar fraction of micelles with aggregation number g: (a) 16.34 mM SDS solution; (b) 81.7 mM C12TAB solution; (c) 32.68 mM C14TAB solution; (d) 32.68 mM C16TAB solution. We defined T = 25 ºC, P = 1 atm, and Nw = 3400000.
