Model calculations of the spontaneous curvature, mean and Gaussian bending constants for a thermodynamically open surfactant film

The spontaneous curvature (H(0)), mean and Gaussian bending constants (k(c) and k (c)), as defined in the well-known Helfrich expression, have been calculated from a detailed model for a thermodynamically open surfactant layer. The effect of head group cross-section area, surfactant tail length and electrolyte concentration for monovalent ionic surfactants have been investigated. Geometrical packing constraints subjected to the aggregated hydrocarbon tails and electrostatics are found to be the dominant contributions to H(0), k(c) and k (c). In addition, the transition from spherocylindrical micelles to vesicles were investigated in terms of the three parameters and the following simple expressions were derived as criteria for coexistence between micelles and vesicles H(0)=1/4 xi and N(ves)/N(mic)=exp4 pi(k(c)+k (c))/kT], where xi is the thickness of the hydrocarbon part of the film and N(mic) and N(ves) the average aggregation numbers of micelles and vesicles, respectively. However, it is found that the ratio N(ves)/N(mic) is order of magnitudes too large for vesicles to form at all in charged single-surfactant systems where the surfactant head is of moderate size.