Molecular Interpretation of the Mean Bending Constant for a Thermodynamically Open Vesicle Bilayer

Expressions for the various molecular contributions to the mean bending constant k c of a thermodynamically open vesicle bilayer have been derived, from which k c may be calculated from an appropriate molecular-thermodynamic model as a function of the structure of the surfactants making up the aggregates as well as the solution state. It is demonstrated that k c determines the shape of a vesicle bilayer insofar as spherical vesicles form when k c is large and positive whereas nonspherical vesicles predominate at values of k c close to or below zero. It is found that contributions due to electrostatics and residual headgroup effects, which are present for one-component as well as mixed aggregates, mainly give rise to a positive value of k c whereas geometrical packing constraints are less important. However, the mixing of two or more surfactants can significantly reduce k c to values where nonspherical vesicles may begin to form. The magnitude of the reduction of k c due to mixing increases with increasing asymmetry with respect to headgroup cross-section area, charge number, and hydrocarbon tail volume between two surfactants in a binary surfactant mixture. The asymmetry is most pronounced for a binary mixture where the surfactant that carries the charge has the larger headgroup and the smaller tail. The reduction of k c due to mixing is, however, expected to be less than the corresponding effect for the bilayer bending constant of a spherical vesicle as a result of an additional positive contribution in the expression for the compositional contribution to k c .