Polyhedral structures

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

While most vesicles are formed from double-tail amphiphiles such as lipids, they can also be made from some single chain fatty acids [73], surfactant-cosurfactant mixtures [71], and bola (two-headed) amphiphiles [74]. In addition to the more common spherical shells, tubular vesicles have been observed in DMPC-alcohol mixtures [70]. Polymerizable lipids allow photo- or chemical polymerization that can sometimes stabilize the vesicle [65] however, the structural change in the bilayer on polymerization can cause giant vesicles to bud into smaller shells [76]. Multivesicular liposomes are collections of hundreds of bilayer enclosed water-filled compartments that are suitable for localized drug delivery [77]. The structures of these water-in-water vesicles resemble those of foams (see Section XIV-7) with the polyhedral structure persisting down to molecular dimensions as shown in Fig. XV-11. 

The structure of the bimetallic 10-vertex cluster was shown by X-ray diffraction to be (84). When the icosahedral carborane l,2-C2BioHi2 was used, the reaction led to the first supraicosahedral metallocarboranes with 13- and 14-vertex polyhedral structures (85)-(89). Facile isomerism of the 13-vertex monometallodicarbaboranes was observed as indicated in the scheme above (in which = CH and O = BH). 

Although the polyhedral structure of 3b seems to point to a bonding situation as described by Wade for a precloso or nido structure,13 the calculations... 

A possible explanation for the formation of this planar ladder structure can be found in the close geometrical similarity of 7 to (3-gallium. The relative positions of the Ga atoms in 7 are comparable to those found in (3-gallium (see Fig. 18), but as expected, the Ga-Ga distances in 7 are all shorter than in (3-gallium due to a more molecular kind of bonding. This means that in 7 the formation of metalloid structures is preferred over the formation of polyhedral structures, which results in the unusual arrangement of the Ga atoms. 

Figure 1. Polyhedral structure of ECS-2 view along the [110] direction (left) dark gray small spheres are atoms of sodium. View of a six phenylene cage (right) with ethanol molecules inside the cage in the two statistical conformations light gray are oxygen, dark gray are carbon.

Although the products in these equations are written as if they were simple ionic binary compounds, this is not always the case. For example, some nonmetals form clusters containing several atoms arranged in polyhedral structures. One such species is the P73- cluster, which has six phosphorus atoms at the vertices of a trigonal prism with the seventh occupying a position above a triangular face... 

Intermediate between the extended four-coordinate connectivities that dominate the low- T solid phase and the two-coordinate ring/chain connectivities that dominate at higher T are certain //jree-coordinate polyhedral structures that retain a degree of cooperative proton ordering. Two examples of such trigonally coordinated buckyball clusters, a 24-mer and a 28-mer, are shown in Fig. 5.31. The... 

The relationship of the wheel-rim-type structure of 62 to the metal can be demonstrated by a 30° rotation of the two centered Alg rings followed by a shift of the six rings towards each other (cf. Figure 2.3-13) [92], The other possibility of the formation of an Al14 polyhedron with point symmetry by displacement of the two naked central atoms in the direction of a polyhedral entity has been shown to be energetically unfavorable by quantum chemical calculations i.e., the observed metalloid structure (Figure 2.3-13) is favored over the anticipated polyhedral structure as described by Wade-Mingos [5, 96] (see Chapter 1.1.2). 

Some proteins are imported into cells from the surrounding medium examples in eukaryotes include low-density lipoprotein (LDL), the iron-carrying protein transferrin, peptide hormones, and circulating proteins destined for degradation. The proteins bind to receptors in invaginations of the membrane called coated pits, which concentrate endocytic receptors in preference to other cell-surface proteins. The pits are coated on their cytosolic side with a lattice of the protein clathrin, which forms closed polyhedral structures (Fig. 27-40). The clathrin lattice grows as more recep-... 

Gosed polyhedral structure with triangular faces only known only as with molecular formula (B HJ2- ( + I skeletal electron-pairs for polyhedron. 

Nest-like, nonclosed polyhedral structure molecular formula B H + 4 ( + 2) skeletal electron-pairs n vertices of the parent (n + l)-atom c/oro-polyhedron occupied. 

Net-like, nonclosed polyhedral structure molecular formula B H,I + 8 ... 

Open branch-like polyhedral structure molecular formula BnHn+ )0 ... 

Schaeffer, Smith, and Polley (64) observe from electron micrographs that carbon black particles heated to 3000° C. change from spherical to polyhedral in shape. Kmetko (40) makes similar observations and has shown that the polyhedral structure extends throughout the body of the particle in some cases. 

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