CORRECTIONS TO SOME MODELS OF THE CURVATURE ELASTIC ENERGY OF INVERSEBICONTINUOUS CUBIC PHASES

Recently a number of papers have appeared which have attempted to meas ure the curvature elastic coefficients of lipid monolayers from the st ructural data of inverse bicontinuous cubic phases [1-3]. It has subse quently become apparent that these efforts have been flawed in at leas t two ways. Firstly, errors have been made in setting physically inapp ropriate constraints on the differential geometry of the bicontinuous cubic phases and secondly, it has not been appreciated that in the sys tems 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 bendin g energetics. In this paper we have re-cast and corrected the curvatur e elastic description used in references [1-3] and then re-analysed th e experimental data with the revised theory. Of course as we have alre ady stated these analyses are inadequate measurements of the curvature elasticity, both in terms of the model used and also because of the r elative increase in the energetic contribution from packing frustratio n and forces acting between bilayers when the lattice parameter is rel atively small. However, all is not lost and Ne show that inverse bicon tinuous cubic structures do exist of sufficient size that a simple cur vature elastic model may be an adequate description of the mesophase a nd hence allow one to measure the curvature elastic moduli.