Double-diamond

Figure C2.1.11. Morjrhologies of a microphase-separated di-block copolymer as function of tire volume fraction of one component. The values here refer to a polystyrene-polyisoprene di-block copolymer and ( )pg is tire volume fraction of the polystyrene blocks. OBDD denotes tire ordered bicontinuous double diamond stmcture. (Figure from [78], reprinted by pemrission of Annual Reviews.)...

The model has been successfully used to describe wetting behavior of the microemulsion at the oil-water interface [12,18-20], to investigate a few ordered phases such as lamellar, double diamond, simple cubic, hexagonal, or crystals of spherical micelles [21,22], and to study the mixtures containing surfactant in confined geometry [23]. 

It is well known that block copolymers and graft copolymers composed of incompatible sequences form the self-assemblies (the microphase separations). These morphologies of the microphase separation are governed by Molau s law [1] in the solid state. Nowadays, not only the three basic morphologies but also novel morphologies, such as ordered bicontinuous double diamond structure, are reported [2-6]. The applications of the microphase separation are also investigated [7-12]. As one of the applications of the microphase separation of AB diblock copolymers, it is possible to synthesize coreshell type polymer microspheres upon crosslinking the spherical microdomains [13-16]. 

Star molecules containing branches made of two blocks have also been prepared by these methods102 103. Recently it was shown that such star-block copolymers exhibit very interesting so-called double-diamond structures in the bulk owing to segregation due to incompatibility between chemically unlike blocks 104. ... 

O. Ermer, L Lindenberg, Lorenz, "Double-diamond inclusion compounds of 2,6-dimethylideneadaman-tane-l,35,7-tetracarboxylic acid , Helv. Chim. Acta 1991, 74, 825-8277. 

Fig. 2.19 Structures belonging to space group laid (gyroid) and space group Pnlm ( double diamond ) (after Seddon 1990).

Figure 1 shows the now familiar sequence of equilibrium morphologies (spheres, rods, lamellae) as a function of copolymer composition also included is the newly proposed bicontinuous double-diamond morphology which exists in certain cases in a narrow composition range between the rod-like and lamellar morphologies. 

Figure 12.24 Phase diagrams for (a) 1-monoolein in water and (b) di-dodecyl alkyl-j8-D-glucopyranosyl-rac-glycerol in water, Hn is the inverse hexagonal phase, Gn is the inverse gyroid Ia3d, and Du is the inverse double-diamond Pn3m phase. In the inverse phases, the aqueous phase is inside the channels. [Part (a) Reprinted with permission from Larsson et al.. Journal of Physical Chemistry 93 7304 Copyright 1989, American Chemical Society. Part (b) Reprinted with permission from EDP Sciences.]...

Many more examples of interpenetration in inorganic chemistry lead to a recognition of the ubiquity of hyperbolic surfaces of infinite genus -exemplified by three-periodic minimal surfaces - that demands consideration. In the giant structure of Cu4Cd3 the Cu atoms are separated from the Cd atoms by a surface that resembles a minimal surface. In diamond, cubic ice and cristobalite, all the atoms are located on one side of the surface and the space on the other side is empty. If ice is subjected to very high pressure, the same structure appears on both sides of a minimal surface (double ice or ice IX), with almost double the density of ordinary ice (Fig. 2.8). Similarly, diamond is expected to transform to a double-diamond structure with metallic properties at sufficiently high pressure. 

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