Double diamond phase

Suppose two diamond lattices composed of carbon-type atoms and bonds. Set the bond directions of the two lattices to be the same. Fix one of the lattices in space. One can imagine the displacement of the other lattice there remain degrees of freedom of relative positions of the two lattices. Corresponding to this geometric consideration, we found a phase transition between the low-temperature phase (DD I) and the high-temperature phase (DD II). DD I is a symmetric double-diamond phase One-diamond lattice occupies the centers of voids of the other lattice. In other words, two lattices are placed at the most symmetric positions. DD II is a shifted double-diamond phase topologically equivalent but shifted lattices from the symmetric positions say, one shifts in the x-direction from the other. 

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]. 

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.]...

PFS block co-polymers in which the blocks are immiscible (which is generally the case) would be expected to self-assemble to form phase-separated organometallic domains in the solid state. Based on the classical behavior of organic block co-polymers, thin films of polyferrocene diblock co-polymers would be expected to form domains such as spheres, cylinders (or their anti-structures), double diamonds (or gyroids), or lamellae (Section 1.2.5). The preferred domain structure would be expected to be controlled by the ratio of the blocks, their degree of immiscibility (as defined by the Flory-Huggins interaction parameter y), and the overall molecular weight of the block co-polymer. 

Figure 6.26. Block copol5mier morphologies. L, C and S (lamellae, cylinders and spheres, respectively) are the classical morphologies whose stability limits were determined in the strong segregation limit by Helfand and Wasserman (1982). PL, G and D (perforated lamellae, gyroid and bi-continuous double diamond) are complex, non-classical phases that have subsequently been identified. Diagram courtesy of M. Matsen.

Several ordered states distinguished by their symmetries have been identified the preferred one depends primarily on the polymer composition [29,38,39]. Some common patterns are lamellar sheets, ordered bicontinuous double diamond (OBDD), hexagonally packed cylindrical arrays, and body-centered-cubic spherical microstructures. If the volume fractions of the two halves of the polymer chain are similar, the interface between the two regions will be flat and the lamellar phase will form. However, if one block is much smaller than the other, then for packing reasons, the interface will curve toward the smaller half (see Fig. 19b), giving, in order of increasing curvature, the OBDD, cylindrical, and spherical microstructure. 

For the 7-16-7 polymers, the microphase was lamellar. Both these sets of results are consistent with the NSCFT predictions for these compositions. The 10-10-10 chains formed the bicontinous double-diamond structure. This contrasts with the NSCFT prediction that the gyroid phase is stable, but it is modest disagreement given that the NSCFT predicts that the double-diamond structure is metastable, and the energy difference between the two is small. 

Copolymer systems based on blocks which behave in a coil-like fashion (including di- and triblock copolymers) have been widely studied (Chapter 9). Coil-coil multiblock systems build of incompatible coil segments have been found to exist in a wide range of microphase separated supramolecular structures, such as spheres, cylinders, double diamond (DD), double gyroid (DG), and lamella. Their phase behavior mostly results from the packing constraints imposed by the connectivity of each block... 

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