Derivation of expressions for the spontaneous curvature, mean and Gaussian bending constants of thermodynamically open surfactant monolayers and bilayers

Abstract

We have derived expressions for the spontaneous curvature H0, the mean and Gaussian bending constants, kc and k̄c, respectively, for a surfactant film of finite thickness that is open in a thermodynamic sense. Geometrical packing constraints are taken into account and give rise to explicit large and important contributions to kc, k̄c, and kcH0. From its contribution to the latter quantity we may deduce that surfactant aggregates (micelles, vesicles, microemulsion droplets) are expected to dramatically increase their size with increasing surfactant tail length. Moreover, the coupling between free energy contributions related to surfactant head group and tail with geometrical packing constraints give rise to dominant terms on the form 2ξpH0, where ξp is the thickness of a planar film, in the expressions for kc. In the case of repulsive head group effects that favor a large spontaneous curvature, such as electrostatics, these terms raise kc and thus increase the rigidity of the film. Due to the constraint of constant free monomer chemical potentials, the composition of the film becomes a function of curvature. As a result, the ability of a surfactant film to have different surfactant compositions in differently curved parts (e.g., inner and outer layer of a vesicle, central parts and end caps of rod or threadlike micelles, etc.) may considerably reduce kc, whereas k̄c and kcH0 are mainly unaffected by mixing. The magnitude of the reduction of kc of a binary surfactant film increases with increasing asymmetry between the two surfactants with respect to charge number, head group size, and tail volume.