Pj. Maddaford et C. Toprakcioglu, STRUCTURE OF CUBIC PHASES IN THE TERNARY-SYSTEM DIDODECYLDIMETHYLAMMONIUM BROMIDE WATER HYDROCARBON, Langmuir, 9(11), 1993, pp. 2868-2878
We have studied the structure of the ternary cubic phases formed by th
e system didodecyldimethylammonium bromide (DDAB)/D2O/hydrocarbon oil
by small-angle X-ray scattering (SAXS) and small-angle neutron scatter
ing (SANS). Different oils (octane, dodecane, tetradecane, and toluene
) of varying molecular size and degree of penetration into the hydroph
obic tail region were used, and systematic trends were observed both i
n 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 bi
layer decorates a minimal surface or one based on a constant mean curv
ature family of surfaces can be invoked to describe the data. The diff
raction data reveal Bragg reflections which index to well-known cubic
structures, and transitions between different cubic symmetries are obs
erved on changing the composition of the system. It is found that high
ly penetrating oils such as toluene are fully absorbed into the surfac
tant region, while nonpenetrating oils such as tetradecane reside larg
ely 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 curvatu
re and occur in a systematic manner with composition. The aqueous volu
me fraction is mainly responsible for setting the mean curvature of th
e interface, but the interaction of the oil with the surfactant tails
is also important in determining the structure through its effect on t
he 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 cub
ic structures include triply periodic ones based on the gyroid (G), di
amond (D), and the Schwarz-P (P) minimal surfaces. Regions with an unr
esolved cubic symmetry as well as biphasic regions with two coexisting
cubic symmetries are also found in the phase diagrams. The phase beha
vior and structure of ternary cubic phases can thus be accounted for s
olely on topological considerations, with the particular composition o
f each system merely setting the values of parameters such as curvatur
e, lattice constant, etc.