Thermodynamics and bending energetics of toruslike micelles

The self-assembly of surfactants forming toruslike or toroidal micelles has been investigated from a theoretical point of view, in particular the structural behaviour and stability of tori in terms of the three bending elasticity constants spontaneous curvature (H(0)), bending rigidity (k(c)) and saddle-splay constant (k(c)). It is demonstrated that the size of toruslike micelles increases with an increasing bending rigidity, but is independent of both spontaneous curvature and saddle-splay constant. Similar to conventional micelles, toruslike micelles are found to be stable over bilayers as the spontaneous curvature times the surfactant layer thickness exceeds 1/4. Moreover, it is shown that toruslike micelles, in general, are favoured at the expense of long spherocylindrical micelles as a result of elimination of the unfavourable end-caps. However, conventional micelles that are able to grow with respect to both width and length (tablets) may be stable over tori as well as spheres in much wider regimes of different bending elasticity constants. As a result, toruslike micelles are predicted to be stable over conventional micelles, including rods, at large values of the effective bending constant k(eff) identical with 2k(c)+k(c), i.e. in the same region where infinite cylinders are expected to be observed. This result is consistent with the fact that toruslike micelles have usually been observed to coexist with large networks of branched cylinders.