Explaining the growth behavior of surfactant micelles

The growth behavior of surfactant micelles has been investigated from a theoretical point of view. It is demonstrated that predictions deduced from the spherocylindrical micelle model, which considers micelles that are only able to grow in the length direction, are inconsistent with experimental measurements. Accordingly, the rise in aggregation numbers above a certain concentration, roughly corresponding to the second critical micelle concentration, appears to be much stronger than predicted by the spherocylindrical micelle model. On the other hand, predictions deduced from the general micelle model, which considers micelles that are able to grow with respect to both width and length, show excellent agreement with experimental observations. The latter theory is based on bending elasticity and it is demonstrated that the associated three parameters spontaneous curvature, bending rigidity and saddle-splay constant may all be determined for a micellar system from experimental measurements of the aggregation number as a function of surfactant concentration. The three parameters turn out to influence the appearance of a micellar growth curve rather differently. In accordance, the location of the second cmc is mainly determined by the saddle-splay constant and the bending rigidity. The shape of the growth curve, when going from the region of weakly growing micelles at low surfactant concentrations to strongly growing micelles above the second cmc, is mainly influenced by the bending rigidity.