Packing space filling

While not overcrowded, the polyethylene structure uses space with admirable efficiency, the atoms filling the available space with 73% efficiency. For contrast, recall that close-packed spheres fill space with 74% efficiency, so polyethylene does about as well as is possible in its utilization of space. 

The densities of common engineering materials are listed in Table 5.1 and shown in Fig. 5.12. These reflect the mass and diameter of the atoms that make them up and the efficiency with which they are packed to fill space. Metals, most of them, have high densities because the atoms are heavy and closely packed. Polymers are much less dense because the atoms of which they are made (C, H, O) are light, and because they generally adopt structures which are not close-packed. Ceramics - even the ones in which atoms are packed closely - are, on average, a little less dense then metals because most of them contain light atoms like O, N and C. Composites have densities which are simply an average of the materials of which they are made. 

The tower pressure losses are (1) tower packing or fill (70-80% of loss) (2) air inlet if induced draft (3) mist eliminators at top (4) air direction change losses and entrance to packing on forced draft units. These losses are a function of air velocity, number and spacing of packing decks, liquid rate and the relation between L and Ga. 

If atoms are considered as hard spheres, the packing density can be expressed by the space filling SF of the spheres. It is ... 

The space filling in the body-centered cubic packing of spheres is less than in the closest packings, but the difference is moderate. The fraction of space filled amounts to ns/3 = 0.6802 or 68.02 %. The reduction of the coordination number from 12 to 8 seems to be more serious however, the difference is actually not so serious because in addition to the 8 directly adjacent spheres every sphere has 6 further neighbors that are only 15.5 % more distant (Fig. 14.3). The coordination number can be designated by 8 + 6. 

Corresponding to its inferior space filling, the body-centered cubic packing of spheres is less frequent among the element structures. None the less, 15 elements crystallize with this structure. As tungsten is one of them, the term tungsten type is sometimes used for this kind of packing. 

Although the space filling of the body-centered cubic sphere packing is somewhat inferior to that of a closest-packing, the CsCl type thus turns out to be excellently suited for compounds with a 1 1 composition. Due to the occupation of the positions 0,0,0 and with different kinds of atoms, the structure is not... 

Fig. 27. Packing relations in the crystal structure of 47 benzene (1 1) 64>. Stereo drawing of complementary stick style and space filling representations of host and guest molecules, respectively (atomic radii of the corresponding guest atoms in the space filling style are set to about half of their common van der Waals values the H atoms of the host molecules are omitted)...

Fig. 32. Packing relations and steric fit of the 26 acetic acid (1 1) clathrate (isomorphous with the corresponding propionic acid clathrate of 26)1U- (a) Stereoscopic packing illustration acetic acid (shown in stick style) forms dimers in the tunnel running along the c crystal axis of the 26 host matrix (space filling representation, O atoms shaded), (b) Electron density contours in the plane of the acetic acid dimer sa First contour (solid line) is at 0.4 eA" while subsequent ones are with arbitrary spacings of either 0.5 and 1 eA 3. Density of the enclosing walls comes from C and H atoms of host molecules.

Fig. 34. Stereo drawing of the packing in the 20 DMSO clathrate 851 (complementary space filling and stick style representations of host and guest molecules, respectively O atoms of the host are shaded). Space around guest molecules in the center of the drawing, related by the symmetry center operator, indicates the opportunity for disorder...

Although the bond-orientational metrics defined above have proven useful for identifying numerous space-filling crystalline morphologies43 like face-centered cubic, body-centered cubic, simple cubic, and hexagonally close-packed lattices, they are inadequate for detecting order in systems that organize... 

Fig. 20. Space-filling views of distal pockets in NP4-NO (left) and NP4—NH3 (right) structures. View is from above the distal pocket, with heme, solvent, and ligands shown in black. Waters 1-3 (right) are expelled as L130 and loop 31-37 pack against NO (left). Reproduced with permission from Ref. (47).

Estimation of ligand thickness. The simplest method consists in measuring the thickness s of the ligand layer on space-filling molecular models. When X-ray structures are available, the thickness may be obtained from crystal packing data. However, ligands often have regions of different thicknesses and contain crevasses in which solvent molecules may or may not penetrate. 

Figure 5. The packing structure of 11 with anions showing in space-filling mode the coordinated water and non-coordinated bpy molecules were omitted for clarity.

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