Bending energetics of tablet-shaped micelles: a novel approach to rationalize micellar systems

A novel approach to rationalize micellar systems is expounded in which the structural behavior of tablet-shaped micelles is theoretically investigated as a function of the three bending elasticity constants: spontaneous curvature (H0), bending rigidity (k(c)), and saddle-splay constant (k(c)). As a result, experimentally accessible micellar properties, such as aggregation number, length-to-width ratio, and polydispersity, may be related to the different bending elasticity constants. It is demonstrated that discrete micelles or connected cylinders form when H0 > 1/4xi, where xi is the thickness of a surfactant monolayer, whereas various bilayer structures are expected to predominate when H0 < 1/4xi. Our theory predicts, in agreement with experiments, a transition from discrete globular (tablet-shaped) micelles to a phase of ordered, or disordered, connected cylinders above a critical surfactant concentration. Moreover, a novel explanation for the mechanism of growth, from small globular to long rodlike or wormlike micelles, follows as a consequence from the theory. In accordance, polydisperse elongated micelles (large length-to-width ratio) form as the bending rigidity is lowered, approaching the critical point at k(c) = 0, whereas monodisperse globular micelles (small length-to-width ratio) are expected to be present at large k(c) values. The spontaneous curvature mainly determines the width of tablet-shaped or ribbonlike micelles, or the radius of disklike micelles, whereas the saddle-splay constant primarily influences the size but not the shape of the micelles.