Molecular theory of curvature elasticity in surfactant films

We develop a microscopic-level formulation for the curvature elasticity of monolayer and bilayer systems of typical surfactant molecules. It is argued that both the bending and saddle-splay force constants k and k̄ are determined primarily by the conformational entropy of the flexible hydrocarbon chain rather than by the electrostatic interactions associated with hydrophilic head groups. A priori estimates of the chain contributions are made for the first time, without the use of any adjustable parameters. Both k and k̄ are shown to be calculable wholly from the conformational statistics describing the planar film. In particular, these constants are expressed in terms of the derivatives and moments of the lateral pressure profile characterizing chain packing in the unbent layers. By considering the dependence of the curvature elasticity on chain length, area per molecule, and composition in mixed films, we are able to account for the order-of-magnitude variations in k observed in a variety of different surfactant systems. The replacement of long chain molecules by short ones is shown to be especially efficient in lowering the bending energy from 10’s of kBT to kBT. The effect of ‘‘free’’ vs ‘‘blocked’’ exchange are also presented and contrasted with the case of fixed area-per-molecule bending deformation. Finally, monolayer vs bilayer results are compared and the calculated signs and magnitudes of k and k̄ are discussed in the context of planar bilayer stability.