Chain Packing and the Compressional Elasticity of Surfactant Films

Abstract

We summarize briefly our work on the effect of excluded volume on the conformational statistics and thermodynamics of semi-flexible chain packing in surfactant layers. Our aim is to establish the important extent to which “tails” compete with “heads” in determining the equilibrium state and compressional properties of mono- and bi-layer amphiphilic films. Using the mean-field theory developed originally for micellar systems [1] we present first some typical results for chain free energies in bilayers as a function of area per molecule. Ensuing estimates for the optimum area per molecule and compression (stretching) force constant are compared with those arising from head-group interactions alone. Then, in order to treat the dependence of these properties on chain contour length (e.g. alkyl carbon number) we discuss a diffusion-equation approach to conformational statistics which takes into account the constraint of uniform segment density. This description provides a natural justification for a scaling of layer thickness which leads to approximately universal compressional behavior. It also allows new insights into the way in which lateral pressure profiles serve to “squeeze” “free” chains into uniformly packed ones. We then treat the important case of mixed-chain systems and derive the corresponding surface-volume relations and their consequences for relative stabilities of planar and curved layers. Finally, we present a simple but accurate model for calculating bending elastic properties of surfactant films in terms of their compressional force constants.