THE MECHANICAL SURFACE-TENSION AND STABILITY OF MINIMAL SURFACE-STRUCTURES

The principal components of the surface stress tenser, sigma, in surfa ctant systems with internal interfaces in the form of infinite periodi c minimal surfaces have been determined from general relations derived by Gurkov and Kralchevsky (Colloids Surf, 47, 45, 1990), and by emplo ying a Helfrich kind of second-order expression for the thermodynamic surface tension, gamma, as a function of the mean curvature, H, and th e Gaussian curvature, K. For this hypothetical case it is found that t he surface stress tenser, sigma, is isotropic with a constant, positiv e value everywhere on the surface. However, in order to avoid mechanic al instability, an extra term, e.g., proportional to K-2 has to be ent ailed in the expression for gamma causing the surface stress tenser, s igma, to vary somewhat with the position on the surface. Moreover, bec ause of the necessary inclusion of, e.g., a K-2 term, in reality the e quilibrium interfacial structure of a bicontinuous microemulsion or an L(3) (sponge) phase will correspond to a slightly distorted infinite periodic minimal surface. (C) 1994 Academic Press, Inc.