Micelle formation and CMC of gemini surfactants: a thermodynamic model

Gemini surfactants possess a structure resembling a pair of conventional single chain surfactants covalently connected by a spacer. The spacer can vary in length and chemical structure. In this paper, the aggregation behavior of gemini surfactants is examined on the basis of a free energy model developed by extending our theory for conventional surfactants. Free energy contributions beyond those considered for conventional surfactants arise because of the spacer. They originate from the fact that (a) the spacer shields the hydrophobic core of the aggregate from contact with water, (b) the spacer constrains the distance between the head groups, thus imposing non-uniformity in charge distribution at the aggregate surface, (c) the spacer prevents the two linked tails from having a packing conformation inside the micelle identical to that of analogous unlinked single chain surfactants, and (d) the spacer can be partially buried inside the micelle core provided its length and the molecular interactions allow it. Illustrative calculations for gemini surfactants with tail lengths of 5–16 carbon atoms and various spacers are discussed here. The spacers considered include the polymethylene chain and a combination of polymethylene chain with NCH3, O, S, and aromatic groups. The predicted critical micelle concentration (CMC), micelle aggregation number, sphere-to-rod transition parameter (K) and shape of aggregates are compared with available experimental data. A comparative analysis of the magnitude and shape dependence of the individual contributions to the free energy shows that the nonuniform charge distribution at the aggregate surface and the additional packing constraint on the tails, both originating from the short length of the spacer, play a central role in determining the equilibrium shape of the aggregates.