On the Swelling of Bicontinuous Lyotropic Mesophases

The swelling of sponge-like bicontinuous mesophases of bilayers of surfactant (or lipid) in water as a function of dilution is analyzed. Analytic formulae for the swelling are derived assuming ii) constant aggregate thickness and (it) fixed surface area per surfactant molecule at an imaginary surface located within the bilayer. Approximate swelling laws are derived for bicontinuous films and compared with swelling behaviour of disconnected sheet-like, rod-like and globular aggregates. It is shown that sponge-like "oil-in-water" bicontinuous aggregates can be readily distinguished from rods, sheets or globules in surfactant/lipid aggregates; the morphologies of aggregates of reversed curvature ("water-in-oil") are less easily deduced from swelling data. Accurate scaling laws for (ordered or disordered) symmetric and asymmetric