Cubic phases structure

Figure 1. A. Computer graphic portion of a periodic surface of constant mean curvature, having the same space group and topological type as the Schwarz D minimal surfhce. This surbce, together with an identical displaced copy, would represent the polar/apolar dividing surface in a cubic phase with space group 224 (Pn3m). The two graphs shown would thread the two aqueous subspaces. B. Computer graphic of a portion of the Schwarz D minimal sur ce (mean curvature identically zero). In the 224 cubic phase structure, this sur ce would bisect the surfactant bilayer.

The Known Bicontinuous Cubic Phase Structures. Recording the structures that have been proposed for bicontinuous cubic phases ... 

It is interesting to note that, in contrast to the number of bicontinuous cuHc phase structures which apparently exist, only one cubic phase structure is now recognized that is not bicontinuous. Furthermore, this structure does not consist of FCC close-packed micelles, but rather a complicated packing of nonspherical micelles (311. 

If we turn to the isotropic phases, several possibilities exist with respect to both liquid solution phases and cubic liquid crystalline phases. Cubic phases, which have long-range order, can be distinguished from microemulsions in giving rise to low-angle X-ray diffraction patterns. A number of different cubic phase structures are possible, but the X-ray low-angle... 

The room-temperature tetragonal structure was first solved by Atoji and Medrud for LaC2 and takes the CaC2-type crystal structure (space group I4/mmm). The high-temperature cubic phase structure is that of the KCN-type (space group Fm3m). RC2 has been reported to form for the rare earth elements of R = Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu. 

A great many short-chain surfactants do not display either the hexagonal or lamellar liquid crystal as the separating phase above the Krafft eutectic they exhibit a cubic phase instead. Because the hexagonal liquid crystal is often found next to this cubic phase (at higher compositions), it may be presumed that this cubic phase has the discontinuous phase structure. The discontinuous cubic-phase structure consists of discrete micelle-like structural elements arrayed in various ways to form isotropic phase structures having cubic symmetry. A large family of such cubic structures exists [81,82]. 

As described in the introduction, OD ceria nanoparticles are easy to obtain because the cubic phase structure has no special favorite growth direction. 

Fig. 10.39 Cubic phase structure model for the BABH8 molecular phase...

Fohner, B. M. and Nyden, M. (2008) Structure and dynamics of micelles and cubic phase structures with ethoxylated phytosterol surfactant in water. Langmuir, 24, 6441-6446. 

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