Planar network

Figure 9.8 Planar network formed by extended 2D condensation of rings of 6 8104 tetrahedra to give 1205 ". (a) Plan as seen looking down the O- Si direction, and (b) side elevation.

Scheme 6 represents coordinate polymers. A low-molecular-weight compound with multidentate groups on both ends of the molecule grows into a linear polymer with metal ions, and the polymer chain is composed of coordinate bonds. The parquetlike polymer complexes, poly(metal-phthalocyanine) and poly(metal-tetracyano-ethylene), are classified into Scheme 7. They are formed by inserting metal ions into planar-network polymers or by causing a low-molecular-weight ligand derivative to react with a metal salt and a condensation reagent.

In principle, the negatively charged, presumably planar network I can be combined with one molar equivalent of tetraalkylammonium ion IGN"1" of the right size as interlayer template to yield a crystalline inclusion compound of stoichiometric formula (IGN+) I C(NIG ) ICO2 that is reminiscent of the graphite intercalates. Anionic network n, on the other hand, needs twice as many monovalent cations for charge balance, and furthermore possesses honeycomb-like host cavities of diameter 700 pm that must be filled by... 

Table 16 summarizes the complexes formed between the vinyl-type analogs of nucleic acid and polynucleotides465,466). Poly(VA)-Poly(U) was assumed to exhibit a planar network structure. In addition, some studies on the interactions occurring in nucleic acid systems and model compounds bearing phosphate ester units on the side chains or the main chains480, and on interactions of poly(A) and quaternized poly(4-vinylpyridine) with bases have been reported48. ... 

A planar network or circuit is one that can be drawn on a plane surface without any of the branches crossing each other. Conversely, a non-planar network or circuit cannot be drawn on a plane surface without the crossing of branches. 

A commonly used network analysis method is loop and mesh analysis, which is generally based on KVL. As defined previously, loop analysis refers to the general method of current analysis for both planar and non-planar networks, whereas mesh analysis is reserved for the analysis of planar networks. In loop or mesh analysis, the circulating currents are selected as the unknowns, and a circulating current is assigned to each independent loop or mesh of the network. Then a series of equations can be formed according to KVL. 

Figure 18 (a) Two dimeric units of the alternating chirality type are necessary to form a closed hexagon ring (b) the resulting planar network motif. 

Figure 8-24. The 17 symmetry classes of one-sided planar networks with the most important symmetry elements and the notations of the classes indicated. Along with the geometrical configurations, Hungarian needlework patterns are presented for illustration. A brief description of the origin of these patterns is given here [36] ...

Figure 8-27 shows three planar networks based on the same plane lattice. Two and only two lines intersect in each point of all three networks. Accordingly, the parallelograms of all three networks have the same area. All of them are unit cells, in fact, primitive cells. Each of these parallelograms is determined by two sides a and b, and the angle y between them. These are called the cell parameters. 

Figure 8-25. Scheme for establishing the symmetry of planar networks after Crowe [37],... 

Figure 9-16. Planar networks of regular polygons with up to eight-fold symmetry.

Figure 9-17. Octagonal planar network Hungarian needlework [21],...

Table 1.2 Relation between average ring size, n, connectivity, z, and Euler-Poincare cheuracteristic per vertex, xl i a range of networks that are regular tessellations of surfaces. The nature of the network is set by the value of cages, planar networks and three-dimensional frameworks are characterised by positive, zero and negative respectively.

The receptor mechanism involved in cell uptake of lipids from blood in the form of LDL (low-density lipoprotein) has been revealed by the work of Brown and Goldstein [71]. When the lipoprotein is boimd to the receptor, a "coated" pit deepens and buds off to form a "coated" vesicle inside the cell (endocytosis). The "coat" represents a general principle of cell transport that is known mainly from the work by Bretscher [72]. The protein forming this coat is clathrin, which aggregates into planar network (or basket-like cages, morphologically similar to "mesh" phases of lipids or surfactants in water, cf. Chapter 4) and the lipid bilayer can span these nets, like a soap film spanning a wire net. 

ResBrg is similar to Re3Cl9 but the iodide, which is a black solid and is similarly trinuclear, differs in that it is thermally less stable and only 2 Re atoms in each duster are linked to adjacent clusters, thereby forming infinite chains of trimeric units rather than planar networks. 

To proceed, consider two finite planar networks, a regular Euclidean triangular lattice (interior valence v — 6, but with boundary defect sites of valence v = A and v = 2) of dimension d — 2, and a fractal lattice... 

The binary indium-rich transition metal compounds show a variety of different indium networks. In the structures of T2lns (T = Ti, Hf), the indium atoms form infinite two-dimensional (2D) planar networks, which can be described as a tessalation of triangles, squares, and pentagons. The 2D network is also found in the structures of the Lasins compounds, which contain well-defined indium square pyramids and some intercluster indium-indium distances that are only 11-15% greater than the average intracluster bond lengths. The apparent Ins " cluster in Lasins can be described as a closed shell nido-deltahedron, and the compound structurally as a Zintl phase. The /S-Ysins compounds with a similar structure to Lasins present a slow first-order phase transition to a-YsIns at high temperature. Clusters in the low-temperature a-YsIns phase are twisted and Joined by short bonds at trans-basal positions into chains that are more weakly interconnected into a three-dimensional structure. 

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