Measuring the elastic parameters for inverse bicontinuous cubic phases

Abstract

A second-order curvature elastic energy description for the inverse bicontinuous cubic phases has been developed from existing theories. Using this model it is possible to determine curvature elastic parameters from X-ray diffraction measurements on these phases, and we present a preliminary analysis of data from a 2:1 (mol: mol) mixture of lauric acid and dilauroylphosphatidylcholine. A curvature elastic free energy model developed by Turner and co-workers uses as a starting point the same physical principles as the model presented here, but the equations are developed in a very different manner. By re-analysing some of Turner's data using our model we have found a discrepancy between the models, which at present remains unexplained. It has been shown by others that the curvature elastic parameters are related to the variation in lateral stress through the bilayer by three integrals involving the first and second moments of the stress profile and its first derivative with respect to mean curvature. It is our long term aim to measure the stress profile from curvature elasticity determinations. We show that the elastic parameters will only give rise to values wh relate directly to the lateral stress profile when the cubic phase is sufficiently swollen, since otherwise the elastic approximations become inaccurate and transverse forces may make significant contributions to the total free energy. A set of diagnostic measurements is suggested which indicates whether or not the cubic phase is sufficiently swollen for the approximations to hold. Using these it seems clear that so far no data have been published in which the cubic phase is sufficently swollen. However, we show measurements which indicate that such systems do exist.