THE CUBIC PHASE REGION IN THE SYSTEM DIDODECYLDIMETHYLAMMONIUM BROMIDE WATER STYRENE

The determination of five separate one-phase regions, corresponding to five distinct bicontinuous cubic phase microstructures, in the phase diagram of DDAB (didodecyldimethylammonium bromide)-water-styrene at 20-degrees-C, provides a unique opportunity to study progression between distinct cubic phases. A thorough phase behavior study of this region is reported, involving hundreds of samples and aided by the NMR self-diffusion technique and small-angle X-ray scattering (SAXS) technique. Two-phase samples have been found in each of the four two-phase regions separating these different monophasic regions, as well as the requried three-phase samples involving cubic, lamellar, water-rich, and microemulsion phases. The structural sequence for the four cubic regions starting at lowest water content and increasing, identified by reference to the minimal surface dividing the infinitely connected bilayer, is proposed to be G (Ia3d) --> D (Pn3m) --> P (Im3m) --> C(P) (Im3m) (Neovius' surface). The structure of the fifth cubic phase is unknown, but it is shown that the minimal surface describing this structure has a low value of gamma = -(2/pi)(S/V2/3)3/chi-E, more specifically gamma < 1.7 and probably gamma < 1.5, where the dimensionless area and the Euler characteristic are measured over any representative patch of surface. We conjecture that the "C(D)" minimal surface describes this cubic phase. A free energy theory based on surfactant chain lengths and head group areas gives quanitative agreement with the observed phase boundaries and with lattice parameters reported in the literature with cyclohexane and octane as hydrophobe. This progression can also be qualitatively understood in terms of simple arguments focusing on the mean curvature of the polar-apolar interface and does not require the introduction of a second curvature free energy contribution such as a Gaussian curvature term; a more precise interpretation is that the mean curvature term far outweighs the "difference curvature" term. The same two theoretical approaches also explain the strong slope of the phase boundaries with respect to the lines of constant water content, the "slowing down" of the lattice parameter increase as the phase boundaries are approached, and the tell-tale jump in the monolayer mean curvature across each of the two-phase regions. The water self-diffusion rate plotted as a function of water volume fraction falls on five curves corresponding to the five one-phase regions, with discontinuities at the phase boundaries. These discontinuities facilitate precise structural comparisons between different microstructures. A quantitative fit of the water self-diffusion is obtained, using the results of recent solutions to the diffusion equation in cubic phase models, and the results show that the interconnected-rod description is best at low water and the parallel or H-surface description is best at high water. Polymerization of styrene was performed in samples from the first four cubic phase regions, and SAXS, deuterium NMR (on samples containing D2O), and water self-diffusion rates for the polymerized samples were indistinguishable from unpolymerized samples.