Corrections to Some Models of the Curvature Elastic Energy of Inverse Bicontinuous Cubic Phases

Abstract

― Recently a number of papers have appeared which have attempted to measure the curvature elastic coefficients of lipid monolayers from the structural data of inverse bicontinuous cubic phases [1-3]. It has subsequently become apparent that these efforts have been flawed in at least two ways. Firstly, errors have been made in setting physically inappropriate constraints on the differential geometry of the bicontinuous cubic phases and secondly, it has not been appreciated that in the systems which have been studied, the degree and variance of the mean and Gaussian curvature at the interface are so great that three curvature elastic coefficients are insufficient to correctly describe the bending energetics. In this paper we have re-cast and corrected the curvature elastic description used in references [1-3] and then re-analysed the experimental data with the revised theory. Of course as we have already stated these analyses are inadequate measurements of the curvature elasticity, both in terms of the model used and also because of the relative increase in the energetic contribution from packing frustration and forces acting between bilayers when the lattice parameter is relatively small. However, all is not lost and we show that inverse bicontinuous cubic structures do exist of sufficient size that a simple curvature elastic model may be an adequate description of the mesophase and hence allow one to measure the curvature elastic moduli.