Network coordination number

Computer modelling of physisorption hysteresis is simplified if it is assumed that pore filling occurs reversibly (i.e. in accordance with the Kelvin equation) along the adsorption branch of the loop. Percolation theory has been applied by Mason (1988), Seaton (1991), Liu et al., (1993, 1994), Lopez-Ramon et al., (1997) and others (Zhdanov et al.,1987 Neimark 1991). One approach is to picture the pore space as a three-dimensional network (or lattice) of cavities and necks. If the total neck volume is relatively small, the location of the adsorption branch should be mainly determined by the cavity size distribution. On the other hand, if the evaporation process is controlled by percolation, the location of the desorption branch is determined by the network coordination number and neck size distribution. 

The structure of a-C H films may be thus pictured as sp--carbon atoms in condensed aromatic clusters, dispersed in an sp- -rich matrix, which confers to the network its characteristic rigidity. This situation can also be regarded as a random covalent network in which the sp" clusters of a defined size take part in the structure as an individual composed atom with its corresponding coordination number [17]. Such kinds of models have been successfully used to describe the dependence of a-C H film mechanical properties on composition, hybridization, and sp" clustering [23]. 

A series of zinc diphosphonate complexes were synthesized in the presence of diamines of varying chain length. 1-hydroxyethylidenediphosphonate bridges the metal ions with the proto-nated diamine (ethyl-, butyl-, pentyl-, or hexylenediamine) filling in channels or residing between chains. All four structures are different with one-, two-, and three-dimensional networks formed. The coordination number (4-6) and geometry also varies.418... 

Mercury(II) arsenate Hg3(As04)2 has three independent Hg particles with coordination numbers five and seven, but each of them has two short Hg O bonds (206 < r(HgO) < 214 pm) in a nearly linear arrangement linking of these polyhedra including the As04 tetrahedra leads to a 3-D network.300... 

The difference between V- and D-tessilations is as follows each of V-polyhedra includes one network point (or particle) and a void that is closer to this point than to others, each of D-polyhedra includes one cavity and parts of the particles that are the closest to the center of the cavity and all windows that are on the borders with other neighboring cavities. It is convenient to term the latter as PBU/C, where C means cavity. The local coordination number of cavities Zc is equal to the number of the faces of PBU/C (D-polyhedra or D-polygons), and their local porosity e (or eA in 2D space) is equal to the unoccupied volume. Typical D-polyhedra are shown in Figure 9.30 and Figure 9.31. 

The first model of porous space as a 2D lattice of interconnected pores with a variation of randomness and branchness was offered by Fatt [220], He used a network of resistors as an analog PS. Further, similar approaches were applied in a number of publications (see, e.g., Refs. [221-223]). Later Ksenjheck [224] used a 3D variant of such a model (simple cubic lattice with coordination number 6, formed from crossed cylindrical capillaries of different radii) for modeling MP with randomized psd. The plausible results were obtained in these works, but the quantitative consent with the experiment has not been achieved. 

Note added in proof. Earlier in the text it was mentioned that the model used to describe the structure function of low density H20(as) does not describe that of high density H20(as). However, Narten, Venkatesh and Rice 27) do show than an ice I-like network with a near neighbor distance of 2.76 A has the density and distance spectrum of high density H20(as) if one permits 45% of the cavities characteristic of this structure to be occupied by water molecules. These are not ordinary unbonded interstitials. If the cavity molecules are located on the c axis at a distance of 2.76 A from the nearest network molecule each cavity molecule would have second neighbor network molecules at a distance of 3.25 A. Moreover, since occupancy of 45% of the cavities implies that 81% of the water molecules are part of the tetrahedral network and 19% in cavity positions, the average coordination number of nearest neighbors in this model is 4.3, as is found for H20(as) 10 K/10 K. Structure functions calculated for this interstitial variant of a randomized ice I model (the randomization is effected as in the simple ice I... 

The case of boron as a network former cation is somewhat specific in that this element has no available d orbitals. However, a p orbital is available when the boron has a coordination number of 3, which allows stabilisation of an electronic doublet of the oxygen or sulphur introduced by the modifier. This oxygen or sulphur giving up a doublet to another boron atom increases the cross-linking by the formation of two BO4 tetrahedra. In hybridisation terms, the boron is altered from the sp configuration to the sp configuration. The coordination change of boron has been especially well observed by NMR (Bray and O Keefe, 1963 Muller-Warmuth and Eckert, 1982). 

In the mathematical theory of networks valence is defined as the number of links terminating at a node, and it was in this sense that the term was introduced into chemistry. However, chemists were later forced to distinguish between a chemical valence (bonding power) and a coordinative valence (number of bonds). They chose to keep the term valence for the chemical valence and introduced the term coordination number for the coordinative valence. This book follows the chemical convention. The term valence is always used in the sense of bonding power unless otherwise stated, and coordination number is used to indicate the number of bonds. 

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