The mechanics and thermodynamics of disc-shaped micelles

Abstract

A theory of disc-shaped micelles is developed similar to that presented earlier for spherical and rod-shaped micelles. Here, a disc micelle is assumed to be composed of a bilayer part ended by a quasi-hemicylindrical, toroidal rim. The mechanical equilibrium state is considered in detail by means of the pressure tensor, and a surface-thermodynamic description based on the surface tension and the disjoining pressure is derived. Further, by applying the thermodynamics of small systems and making some rather general assumptions about the free energy properties of an ensemble of disc-shaped micelles, we conclude that such micelles can be present in appreciable amounts in a surfactant solution only when the free-energy cost per monomer of forming the bilayer part and the toroidal part, respectively, are each < ca. 10^–2kT. The size distribution is found to be broad and quite skew, and of a similar nature to that for rod-shaped micelles. Our numerical calculations for SDS solutions containing added salt show that the size distribution and overall volume fraction of disc-shaped micelles are very sensitive to the choice of the actual solution conditions. Moreover, the toroidal rim of a disc-shaped micelle is likely to be swollen compared with the central bilayer part, and it is subject to a positive net (line) tension.