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We report on a ternary isothermal system consisting of a poly(ethylene oxide)/poly(propylene oxide) (PEO/PPO) amphiphilic block copolymer, "water", and "oil" (where "water" and "oil" are selective solvents for the different blocks), which exhibits the richest structural polymorphism ever observed (in equilibrium) in mixtures containing amphiphiles (such as block copolymers, surfactants, or lipids). The microstructure resulting from the self-assembly of the PEO/PPO block copolymer can vary from normal (oil-in-water) micelles in solution, through all types of normal and reverse (water-in-oil) lyotropic liquid crystals (normal micellar cubic, normal hexagonal, normal bicontinuous cubic, lamellar, reverse bicontinuous cubic, reverse hexagonal, reverse micellar cubic), to reverse micelles, as the relative volume fraction of the apolar ("oil"-like) components increases over that of the polar ("water"-like) components. The structure in the liquid crystalline phases has been established with small-angle X-ray scattering; both the normal and the reverse bicontinuous cubic structures are consistent with the Ia3d crystallographic space group (and the Gyroid minimal surface), while the normal and reverse micellar cubic structures are consistent with the Im3m and Fd3m space groups, respectively. The self-assembly of amphiphilic block copolymer in selective solvents described here provides a link between the self-assembly of surfactants in water (and oil/cosurfactant) and the self-assembly of block copolymers in the absence of any solvent. Furthermore, the ability of the PEO/ PPO amphiphilic block copolymers to attain diverse microstructures is of great importance to numerous practical applications, especially since such copolymers are commercially available (as poloxamers, Pluronics, or Synperonics).

The self-assembly of a polyethylene oxide)-Wocfe-poly(propylene oxide j-biocfe-poly( ethylene oxide) copolymer (Pluronic L64, (EO)i3(PO)3o(EO)i3) in the presence of water and p-xylene was investigated. The phase boundaries were identified using 2H NMR of heavy water (2H20) and inspection under polarized light. Small-angle X-ray scattering was employed to ascertain the structure of the various liquid crystalline phases formed and to determine the structural lengths involved. A rich phase behavior with normal hexagonal, lamellar, bicontinuous cubic, and reverse hexagonal liquid crystalline regions, in addition to three separate liquid phases, was observed at 25 °C. The cubic phase was identified as having a structure associated with the Gyroid minimal surface. A very small liquid region, found between the normal hexagonal and lamellar phases on the binary water-polymer axis, is identified as a melted analogue of a bicontinuous cubic phase often present in this part of the phase diagram. The pure polymer exists at 25 °C as a disordered melt. Structure and segregation are induced by the addition of water. p-Xylene is soluble in the polymer melt but does not induce structure when added alone. For polymer concentrations above ~50%, a sequence of liquid crystalline phases is observed when the water-to-oil ratio is varied. Here we can identify the volume fraction of apolar components, given by the sum of the PPO and oil volume fractions, as the major parameter governing the phase behavior.

A reverse (water-in-oil) cubic phase was observed in a ternary system consisting of an amphiphilic diblock copolymer (EO17BO10, where EO represents ethylene oxide and BO represents butylene oxide), water, and p-xylene in the following composition range: 47-62 wt % polymer and 7-12 wt % water. This cubic phase occurs between a reverse hexagonal liquid crystalline (H2) and a reverse micellar solution (L2) region and can be considered the result of crystallization of the reverse micelles as they swell with increasing water content. Small-angle X-ray spectra from samples of this cubic phase can be indexed to the crystallographic space group Fd3m (Q227). This is one of the first times a cubic structure consisting of distinct reverse micelles has been observed in a ternary amphiphile-water-oil system; bicontinuous reverse cubic structures, such as the Gyroid (Ia3d, Q230), are more common and have been previously identified in such ternary systems between the lamellar (L R) and the H2 phases.

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We report on the shear-induced transition from an oriented lamellar phase (Lα phase) to multilamellar vesicles (MLV) in two nonionic surfactant systems, namely, a 40 wt % sample of triethylene glycol monodecyl ether (C10E3) and a 40 wt % sample of tetraethylene glycol monododecyl ether (C12E4) in D2O. This transition was studied by time-resolved small-angle neutron and light scattering under shear. Within a range of shear rates from 2 to 100 s-1 at 25 °C the transition from the Lα phase to MLVs in the C10E3 system apparently is controlled by strain. This transition involves an intermediate structure with cylindrical scattering symmetry. This can be interpreted as multilamellar cylinders (MLCs) or as a coherent stripe buckling with the wave vector of the undulation in a neutral direction. The intermediate structures found along the transition path are stable for long times, when shear is turned off. This allows for studies on trapped intermediate structures and experiments where different positions within the gap of a couette shear cell were examined in so-called gap-scan experiments. These experiments revealed that the transition from planar lamellae to MLVs is homogeneous throughout the gap. A temperature increase to 32 °C changes neither the pathway nor the strain control in comparison with experiments run at 25 °C. Upon a further increase in temperature to 38 °C, the transition leads to a mixture of MLC and planar lamellae or a weakly buckled state. With C12E4 as surfactant, and therefore with changed bilayer properties, a strain control is still observed, but less strain is needed for the transition compared to that of the C10E3 system. A comparison of the transition for the two systems, their transient as well as their steady-state viscosities, indicates that the transition is controlled by the stress.

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The structure of the isotropic L3 phase observed in many surfactant-water or surfactant-water-oil systems is analyzed. It is pointed out that the L3 phase generally appears in equilibrium with a dilute solvent phase on one hand and a lamellar liquid crystalline phase on the other. Irrespective of the detailed chemical nature of the system, the one-phase region is remarkably narrow in one direction, indicating that the thermodynamic degrees of freedom are effectively reduced by one due to an internal constraint in the phase. In accordance with previous work it is argued that the basic structural unit in the L3 phase is a surfactant bilayer. Furthermore, we conclude that the L3 phase appears when there is a spontaneous mean curvature toward the solvent at the polar/apolar interface. It is shown that, for a system which has such a curvature toward the solvent, the surface formed by the bilayer midplane has a negative average Gaussian curvature {K). By virtue of the Gauss-Bonnet theorem the bilayer under such circumstances has a multiply connected structure. The conclusion is then that, under conditions when there is a spontaneous mean curvature toward the solvent, it is possible to reach a low free energy state by forming multiply connected bilayer structures, as in many cubic phases, rather than planar bilayers. When interbilayer forces are weak, the structure tends to be disordered, leading to an isotropic solution (L3) rather than an ordered cubic structure. To minimize local variations in curvature at the polar/apolar interface, we demonstrate that the midplane surface should be close to a minimal surface. We then show that a certain dimensionless group associated with a given periodic minimal surface has approximately the same value for all of the well-known isotropic minimal surfaces. Assuming a minimal midplane surface, we can then show that, for a given thickness, a bilayer structure with a prescribed area-averaged mean curvature can only exist at a single volume fraction. This explains the internal constraint in the L3 phase, which is manifested in the narrow character of the L3 phase. Applying the equations that express this constraint, and using results from a theory due to Cantor to account for the effect of water/head-group interactions on water penetration, we present fits of these narrow phase-existence regions to the theory and rationalize the temperature dependence of the L3 phases in a variety of nonionic surfactant systems. For a microemulsion system the analysis shows that the spontaneous monolayer curvature'increases strongly on the addition of hydrocarbon. The emerging picture of the L3 phase is that the solution structure is characterized by a highly connected bilayer, extending in three dimensions, thus appearing bicontinuous in, e.g., NMR self-diffusion experiments, and having an average mean curvature at the polar/apolar interface toward the solvent. The basic driving force forming an L3 rather than a lamellar phase is thus not an entropy increase associated with disorder, as previously sug...