On the Swelling of Bicontinuous Lyotropic Mesophases

(Received 6 June 1994, accepted in final form 19 September 1994)

Abstract
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 (i) constant aggregate thickness and (ii) 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 sponges, sheets, rods and globules are compared with experimental data of bicontinuous cubic phases in the binary glycerol monooleate - water system and the pseudo-binary didodecyl dimethyl ammonium bromide - cyclohexane - water system as well as some data within dilute sponge-like phases. In the latter cases, scattering data as a function of composition admit identification of symmetric and asymmetric sponge phases.