STRUCTURE OF CUBIC PHASES IN THE TERNARY-SYSTEM DIDODECYLDIMETHYLAMMONIUM BROMIDE WATER HYDROCARBON

We have studied the structure of the ternary cubic phases formed by the system didodecyldimethylammonium bromide (DDAB)/D2O/hydrocarbon oil by small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS). Different oils (octane, dodecane, tetradecane, and toluene) of varying molecular size and degree of penetration into the hydrophobic tail region were used, and systematic trends were observed both in the phase behavior and structure of the cubic phase. This structure is well-described by the topology of triply periodic minimal surfaces, and either a parallel surface construction in which the surfactant bilayer decorates a minimal surface or one based on a constant mean curvature family of surfaces can be invoked to describe the data. The diffraction data reveal Bragg reflections which index to well-known cubic structures, and transitions between different cubic symmetries are observed on changing the composition of the system. It is found that highly penetrating oils such as toluene are fully absorbed into the surfactant region, while nonpenetrating oils such as tetradecane reside largely in the middle of the bilayer, thus causing it to swell appreciably on increasing the oil content of the system. The transitions between different cubic symmetries are primarily driven by interfacial curvature and occur in a systematic manner with composition. The aqueous volume fraction is mainly responsible for setting the mean curvature of the interface, but the interaction of the oil with the surfactant tails is also important in determining the structure through its effect on the spontaneous curvature. The system adopts that structure which best optimizes the (generally) divergent values of the actual and preferred curvatures at the expense of alternative structures. The observed cubic structures include triply periodic ones based on the gyroid (G), diamond (D), and the Schwarz-P (P) minimal surfaces. Regions with an unresolved cubic symmetry as well as biphasic regions with two coexisting cubic symmetries are also found in the phase diagrams. The phase behavior and structure of ternary cubic phases can thus be accounted for solely on topological considerations, with the particular composition of each system merely setting the values of parameters such as curvature, lattice constant, etc.