Spontaneous curvature and thermodynamic stability of mixed amphiphilic layers

The elastic behavior of mixed bilayers composed of two amphiphilic components with different chain length ~and identical head groups! is studied using two molecular level models. In both, the bilayer free energy is expressed as a sum of chain, head group and interfacial contributions as well as a mixing entropy term. The head group and interfacial terms are modeled using simple phenomenological but general expressions. The models differ in their treatment of the chain conformational free energy. In one it is calculated using a detailed mean-field molecular theory. The other is based on a simple ‘‘compression’’ model. Both models lead to similar conclusions. Expressing the bilayer free energy as a sum of its two monolayer contributions, a thermodynamic stability analysis is performed to examine the possibility of spontaneous vesicle formation. To this end, we expand the bilayer free energy as a power series ~up to second order! in terms of the monolayer curvatures, their amphiphilic compositions and the average cross sectional areas per molecule; all variables are coupled, with the molecular composition and areas treated as degrees of freedom which are allowed to relax during bending. Using reasonable molecular interaction parameters we find that a second order transition from a planar to a curved ~vesicle! geometry in a randomly mixed bilayer is unlikely. Most of our analysis is devoted to calculating the spontaneous curvature and the bending rigidity of the bilayer as a function of its amphiphile chain composition. We find that adding short chain amphiphiles to a layer of long chain molecules reduces considerably its bending rigidity, as already known from calculations involving only the chain contributions. However, we find that inclusion of head group and interfacial interactions moderates the effect of the added short chains. We also find that the bending rigidity of pure monolayers is approximately linear in chain length, as compared to the nearly cubic dependence implied by the chain free energy alone ~at constant head group area!. Our main result involves the calculation of the spontaneous curvature as a function of composition. We find, for different chain mixtures, that upon adding short chains to long chain monolayers, the spontaneous curvature first increases nearly linearly with composition and then ~beyond mole fraction of about 0.5! begins to saturate towards the spontaneous curvature of a pure short chain layer. Qualitative arguments are provided to explain this behavior. © 1995 American Institute of Physics.