Cubic Strut Phases

Very few rheological data have been reported for ordered cubic phases of surfactant solutions. However, Radiman et al. (1994) have reported dynamic oscillatory data for solutions of didodecyldimethylammonium bromide (DDAB) in deuterated water and octane. Their data for type II cubic P and D phases are shown in Fig. 12-29. They report that the samples 

If these cubic-phase gels are heated, they melt into isotropic liquid-like phases. As the melting point is approached, the storage and loss moduli become equal to each other and follow a power law in frequency, reminiscent of critical gels (see Section 5.3). This suggests that the melting transition for these cubic phases is not far from being second order. 

The structural units of surfactant-containing liquids are self-assembled aggregates, such as spherical or cylindrical micelles, or bilayers. These supramolecular structural units can then further self assemble into ordered phases, with cubic, hexagonal, smectic, or other symmetry. Consequently, the structural and flow properties of such liquids are amazingly rich. Laws of mass action, combined with geometric packing arguments, allow rationalization, if not prediction, of the phase behavior of many surfactant solutions. 

The flow properties of disordered micellar phases are now reasonably well understood. For spherical micelles the viscosity can be estimated from modified hard-sphere-suspension theories, while for disordered semidilute cylindrical micelles the Cates theory of entangled living polymers provides at least a good starting point, and in some cases nearly quantitative prediction of rheological properties. 

Andelman D, Cates ME, Roux D, Safran SA (1987). J Chem Phys 87 7229. 

---

Exotic phases are found at compositions between lamellae and hexagonal cylinders (see Figs. 12-19 and 12-20). Some examples of the morphologies of these phases are shown in Fig. 12-22 these include cubic strut phases, tetragonal and rhombohedral mesh phases, and rectangular ribbon phases. 

Cubic strut phases are common in the phase diagrams of two-tailed surfactants. These surfactants have a relatively high value of the vfaolc parameter, because the volume-to-length ratio v/i(. of the double tail is twice that of a single tail. A high value of v/aoic is consistent with the formation of type II bicontinuous and other inverse phases, such as the inverse hexagonal phase in Fig. 12-24. 

Figure 12.25 Phase diagram of didodecyldimethylammonium bromide (DDAB) in water and styrene at 20°C. The phases include an oil-rich isotropic phase L2, lamellar phases, and five distinct cubic strut phases, including the G, D, P, C(P), and an unknown phase C5. Above the cubic phases are regions of two- and three-phase coexistence. (From Strom and Anderson 1992, reprinted with permission from Langmuir 8 691. Copyright 1992, American Chemical Society.)...

---