Extended Arrays of Molecules

The communal metallic electrons come into their own when private sharing between pairs of individuals becomes too cumbrous for stability. It predominates when the valency electrons are few, as in groups 1, 2, and 3, and in the transition elements, or where some tend to remain in inert sub-groups, as in the heavier elements of group 4. 

With the elementary halogens the sharing of electrons is confined normally to a single pair. The diatomic molecules so formed have no valencies left to knit the lattices of the solids into continuous frameworks, and van der Waals forces are left to dictate the structure of the crystals. 

In such a manner the general disposition of metallic properties and the variation in the mode of linking throughout the periodic system of the elements can be explained. On the overall pattern there are many embroideries, and highly specific influences play their parts. 

Oxygen and nitrogen, for example, form diatomic molecules which do not, in the solid state, participate in more extended covalent arrays like the continuous spirals of selenium. This is because, for specific reasons, the diatomic molecules are very stable. The double link of the oxygen molecule is in fact more than twice as strong as the single link. Thus a large number of separate O2 molecules are more stable than a long chain—0—0—O—0—0—O—. 

That the pictures of covalent bonds, on the one hand, and of the communal electrons, on the other, are not necessarily quite so different as might at first sight appear is suggested by the views of Pauling on the nature of the bonds in metals. He postulates a state 

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Section 1.4 introduced the idea of symmetry, both in individual molecules and for extended arrays of molecules, such as are found in crystals. Before going on to discuss three-dimensional lattices and unit cells, it is important to introduce two more symmetry elements these elements involve translation and are only found in the solid state. 

All substances, except helium, if cooled sufficiently form a solid phase the vast majority form one or more crystalline phases, where the atoms, molecules, or ions pack together to form a regular repeating array. This book is concerned mostly with the structures of metals, ionic solids, and extended covalent structures structures which do not contain discrete molecules as such, but which comprise extended arrays of atoms or ions. We look at the structure and bonding in these solids, how the properties of a solid depend on its structure, and how the properties can be modified by changes to the structure. 

Finally, we consider crystal structures that do not contain any extended arrays of atoms. The example of graphite in the previous section in a way forms a bridge between these structures and the structures with infinite three-dimensional arrays. Many crystals contain small, discrete, covalently bonded molecules that are held together only by weak forces. 

Two different of supramolecular synthons have been detected in the two polymorphs of the carbamazepine-saccharin cocrystal system [45]. In the Form-I structure, the carbamazepine molecules formed a homo-synthon, with the saccharine molecules also forming a hydrogen-bonded homodimer. The interaction of these two synthons resulted in formation of a one-dimensional array of molecules in a crinkled tape motif. In the Form-II structure, a heterosynthon is formed by the interaction of a carbamazepine and a saccharin molecule. This latter synthon packs in one-dimensional chains that extended along the crystallographic c-axis. 

As a kind of extension of this particular type of trinuclear structure, there are numerous compounds that contain two such units fused together on a common edge to give either a discrete molecule as in W4(OEt)i6 (Fig. 16-23), and Mo408(OPr )4py4 or extended arrays of such a unit, joined by shared nonmetal atoms, as in MNb4Cln (Fig. 18-B-13) or certain mixed oxides of molybdenum such as Bai.i4Mo80i6. 

The ideal crystal is a rigid, three-dimensional array of molecules extending infinitely in all directions. This is the model used to evaluate the symmetry of a group of real atoms. The infinite extent of this array allows us to add new symmetry operations to our list of point group symmetry elements (Section 6.1). Previously, we counted only operations that leave the center of mass unchanged. However, the center of mass is not defined for an infinite number of atoms, so we can ignore that constraint now by adding translational symmetry elements to the list. 

An alternative way of deriving the BET equation is to express the problem in statistical-mechanical rather than kinetic terms. Adsorption is explicitly assumed to be localized the surface is regarded as an array of identical adsorption sites, and each of these sites is assumed to form the base of a stack of sites extending out from the surface each stack is treated as a separate system, i.e. the occupancy of any site is independent of the occupancy of sites in neighbouring stacks—a condition which corresponds to the neglect of lateral interactions in the BET model. The further postulate that in any stack the site in the ith layer can be occupied only if all the underlying sites are already occupied, corresponds to the BET picture in which condensation of molecules to form the ith layer can only take place on to molecules which are present in the (i — l)th layer. 

In principle, emission spectroscopy can be applied to both atoms and molecules. Molecular infrared emission, or blackbody radiation played an important role in the early development of quantum mechanics and has been used for the analysis of hot gases generated by flames and rocket exhausts. Although the availability of FT-IR instrumentation extended the application of IR emission spectroscopy to a wider array of samples, its applications remain limited. For this reason IR emission is not considered further in this text. Molecular UV/Vis emission spectroscopy is of little importance since the thermal energies needed for excitation generally result in the sample s decomposition. 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

The competition between the polar and steric dipoles of molecules may also lead to internal frustration. In this case, the local energetically ideal configuration cannot be extended to the whole space, but tends to be accomodated by the appearance of a periodic array of defects. For example, the presence of the strong steric dipole at the head of a molecule forming bilayers will induce local curvature. As the size of the curved areas increases, an increase in the corresponding elastic energy makes energetically preferable the... 

Ai-Stearoylamino acids and their methyl esters were synthesized from enantiomeric and racemic forms of tyrosine, serine, alanine, and tryptophan (Fig. 16). Analogs of these molecules were investigated initially over 30 years ago by Zeelen and Havinga, who found stereochemical differentiation in the monolayer HjA isotherms of these materials (Zeelen, 1956 Zeelen and Havinga, 1958). We have extended this study using more sensitive Langmuir balances, a wider array of dynamic and equilibrium techniques, and the A-stearoyl methyl esters of the amino acids (Harvey et al., 1989 Harvey and Arnett, 1989). 

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