Solid structures packing efficiency

Fig. 3 Structures showing (a) the solid-state packing efficiency of HT-coupled P3HT and (b) steric repulsions in regioirregular P3HT that disrupt the solid-state packing...

Previously known as cyclopolyphosphates, these rings may contain up to 12 tetrahedra, but those with three, four, and six units are most common (see Table 1). The cyclotri- and cyclotetraphosphate rings adopt puckered geometries typical of saturated six and eight atom rings. The predominance of even membered cyciophosphates reflects their ability to pack efficiently in the solid state, rather than any inherent stability over odd membered ones. This is often reflected by a high internal symmetry in the crystalline state an analysis of thirty reliably determined cyclohexaphosphate structures shows that 18 have inversion symmetry and a further seven have threefold (Dsd) internal symmetry. ... 

To appreciate the scientists Interest In M Ms, we must consider the Importance of packing atoms, molecules, or microcrystals In understanding the structures of solids. The most efficient use of space Is the closest packing of uniform spheres, where 74% of the space Is occupied by the spheres and 26% of space Is left unoccupied. Although the structures of most pure metals can be explained In terms of closest packing, most other substances—such as many alloys and ceramics—consist of random arrays of microscopic particles. For this reason, it is of interest to study how such objects pack in a random way. 

Traditional methods to estimate solid-phase density from molecular structure are primarily based on a simple summation of appropriate atomic or group volumes. The basic disadvantage of these group or volume additivity procedures is that they disregard crystal-packing efficiency and molecular conformation. Thus, conformational isomras, or even different compounds with the same functional group composition, wiU aU be calculated to have the same density. To solve this problem, Ammon and coworkers have developed a scheme to estimate molecular densities by predicting possible crystal... 

For unsaturated carboxyhc adds, the nature of the monolayer film will depend of the configuration of the double bond. For a trans double bond, the hydrocarbon chain will be more or less straight, so that lateral interactions and good packing efficiency may lead to the formation of a solid or an L2 film. The corresponding cis isomer has a forced bent structure, reducing its... 

Figure 11.16(b) shows how the cep structure is identical to the face-centered cubic Bravais lattice. In this case, each of the eight corner atoms is shared by eight different unit cells and the six face-centers are each shared by two unit cells. Hence, there are a total of four atoms per unit cell within the cep structure. While the cep contains more atoms per unit cell than the hep, some of its edges are also longer, so that the two closest-packed structures have identical densities and packing efficiencies. Many—but not all—metallic solids will also assume one of the two closest-packed structures. 

The network approach to understanding solid-state structures has been an important factor in the development of crystal engineering. " In many cases, however, a structure contains not a single net, but rather multiple uets that iuter-penetrate, particularly if a single net would result iu au open framework structure. Indeed, a driving force for the formation of interpenetrating structures is the desire to maximize the packing efficiency of any solid. 

The most efficient solid-state packing is usually preferred in order to minimize the amount of "empty" space in a structure. The exact crystal structure type, however, can vary depending on the shapes and sizes of the ions, atoms, or molecules making up the solid. 

Metallic Solids Most metallic elements crystallize in one of the two closest packed structures (Figure 12.30). In contrast to the weak dispersion forces in atomic solids, powerM metallic bonding forces hold atoms together in metallic solids. The properties of metals— high electrical and thermal conductivity, luster, and malleability— result from their delocalized electrons (Section 9.1). Melting points and hardnesses of metallic solids are also related to packing efficiency and number of valence electrons. We discuss bonding models that explain these metallic properties in the next two subsections. 

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