Dodecahedral shape

Complexes of molybdenum and tungsten with eight ligands are known. These complexes have antiprismatic (6) or dodecahedral shapes (7). However, complexes with more than six ligands are rare. 

A down to about 50 A, at which point the layer breaks apart, and the bubble collapses. Layers of 200 to 2,000 A are typical. Once the gas bubbles collect into a foam and press against each other, they assume a dodecahedral shape, the liquid between them starts to drain away. 

Ekwall and Baltcheffsky [265] have discussed the formation of cholesterol mesomorphous phases in the presence of protein-surfactant complexes. In some cases when cholesterol is added to these solutions a mesomorphous phase forms, e.g. in serum albumin-sodium dodecyl sulphate systems, but this does not occur in serum albumin-sodium taurocholate solutions [266]. Cholesterol solubility in bile salt solutions is increased by the addition of lecithin [236]. The bile salt micelle is said to be swollen by the lecithin until the micellar structure breaks down and lamellar aggregates form in solution the solution is anisotropic. Bile salt-cholesterol-lecithin systems have been studied in detail by Small and coworkers [267-269]. The system sodium cholate-lecithin-water studied by these workers gives three paracrystalline phases I, II, and III shown in Fig. 4.37. Phase I is equivalent to a neat-soap phase, phase II is isotropic and is probably made up of dodecahedrally shaped lecithin micelles and bile salts. Phase III is of middle soap form. The isotropic micellar solution is represented by phase IV. The addition of cholesterol in increasing quantities reduces the extent of the isotropic... 

The edges of this dodecahedron sized a - 8.5 cm. When the volume of the rubber balloon at inflation became bigger than the volume of the sphere inscribed in the dodecahedron, the balloon was deformed by the dedecahedron faces and took a shape close to the respective shape of a bubble in a monodisperse dodecahedral foam with a definite expansion ratio. The expansion ratio of the foam was determined by the volume of liquid (surfactant solution or black ink in the presence of sodium dodecylsulphate) poured into the dodecahedron. An electric bulb fixed in the centre of the balloon was used to take pictures of the model of the foam cell obtained. The film shape and the projection of the borders and vertexes on the dodecahedron face are clearly seen in Fig. 1.10. 

Based on the studies of border and film shape in the dodecahedral model Kruglyakov et al. [18] and Kachalova et al. [19] have proposed an expression for foam expansion ratio, using a cylindrical border model with the same cross-sectional radius of curvature. The volume of excess vertex parts was considered in order to estimate the effect of the longitudinal radius of curvature on the border shape... 

Structural foams are usually produced as fabricated articles in injection molding or extrusion processes they vary in properties (see Table 10.2). Again, the most important structural variables are polymer composition, density, and cell size and shape. Structural foams have relatively high densities (more than 320 kg/m3), and cell structures are primarily comprised of holes, in contrast to the pentagonal dodecahedral structure characteristic of low-density plastic foams. Because structural foams are generally not uniform in cell structure, they exhibit a considerable variation in properties with particle geometry (see Table 10.5) [24] these relations can provide valuable guidance. 

This preparation gives the potassium bis(nitrilotriacetato)-zirconate(IV) as very small irregular crystals. However, if the solution is evaporated slowly during the recrystallization, large diamond-shaped crystals are formed. In the rubidium and the potassium salts, the two nitrilotriacetate ligands are coordinated to the zirconium in a slightly distorted dodecahedral arrangement. 

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