Crystalline solids parallel directions

Diffraction is a scattering phenomenon. When x-rays are incident on crystalline solids, they are scattered in all directions. In some of these directions, the scattered beams are completely in phase and reinforce one another to form the diffracted beams [1,2]. Bragg s law describes the conditions under which this would occur. It is assumed that a perfectly parallel and monochromatic x-ray beam, of wavelength A, is incident on a crystalline sample at an angle 0. Diffraction will occur if... 

Very often these initiations avoid the difficulties presented by the more common protonic and aprotonic add catalysts, in that they are chemically well defined and allow a quantitative initiation reaction to proceed without complicating side reactions or the need for co-catalysts and promoters. Furthermore, since these salts are stable crystalline solids, physicochemical analysis of their solutions can be undertaken, in parallel with kinetic investigations of polymerisation. For example, ultraviolet/visible absorption spectrophotometry can be used to monitor directly the concentration of species such as Ph3C+ in solution (19—23). 

On this conceptual premise, uptake and release of solvent can be paralleled to a solid-gas reaction, whereby the reactants are the molecules in the crystalline solid and the molecules in the gas phase and the product is the solvated crystal. Clearly, the same reasoning applies to the reverse process, i.e. generation of a new crystalline form by means of gas release. In gas-solid reactions, gases are reacted directly with crystals or amorphous phases to give complete conversion and usually quantitative yields. What would then be the difference between a solvation reaction and a reaction leading to new molecular/ionic species if not the energetic scale of the processes and the fact that in solvation processes molecules retain their chemical identity ... 

Crystalline solids need not be single crystals. Usually they are composed of an aggregate of crystals which can be distinguished as separate entities under the microscope. They can also be composed of crystallites, that is, of crystals in which the pattern repeats itself a few times in each direction. In this case, they cannot be resolved by ordinary microscopic examination. Crystallite size is extremely variable and not easily measurable. However, sometimes crystallites are so nearly parallel to each other that the solid as a whole can be called a single crystal (L4). 

In crystalline solids the magnetic susceptibility forms a tensor which is not necessarily symmetric. In the presence of axial symmetry two different susceptibility components are experimentally distinguishable Xu parallel, and Xi perpendicular to the field direction. If the symmetry is even lower, three components of the susceptibility tensor should be considered. 

A solid surface is intrinsically an imperfection of a crystalline solid by destroying the three-dimensional (3D) periodicity of the structure. That is, the unit cell of a crystal is usually chosen such that two vectors are parallel to the surface and the third vector is normal or oblique to the surface. Since there is no periodicity in the direction normal or oblique on the surface, a surface has a 2D periodicity that is parallel to the surface. By considering the symmetry properties of 2D lattices, one obtains the possible five 2D Bravais lattices shown in Figure 2. The combination of these five Bravais lattices with the 10 possible point groups leads to the possible 17 2D space groups. The symmetry of the surface is described by one of these 17 2D symmetry groups. 

Rather than having a situation where a unit cell consists of one or more molecules, as in small molecule crystals, the situation is reversed a single molecule participates in many unit cells. This has significant ramifications for the correlations, both structural and dynamical, between unit cells. Second, the periodicity of the crystal lattice usually implies a periodicity for the conformation of the polymer chain itself. This condition places a severe restriction on the conformation space available to the chain in a crystalline solid. Polymer chains in crystals are more appropriately described as helices rather than coils. A helix conformation consists of a regular repetition of the torsion angles characteristic of a small subsection of the chain, the helix repeat unit [4,5]. Each helix has an axis and a handedness of rotation (the direction in which the chain backbone winds around the helix axis). The helix itself is characterized by the translational displacement parallel to the helix axis, d, and the angle of rotation about the helix axis, a, executed by a single helix repeat unit. The coordinates of Eq. (1) may be expressed in terms of these helical parameters as follows ... 

The transition moment directions of some of the absorption bands of PBLG in liquid crystalline state have been investigated in a CaF2 cell by means of the infra-red dichroic ratio (56). All the transition moment directions measured at 1 °C are very similar to those observed 32) on mechanically oriented films of PBLG (Table 2), verifying that all the polymer molecules present a parallel or nearly parallel orientation in the molecular cluster and that the main chain and the side chains of the polymer molecule are fixed as in the solid film. No significant difference is observed between the systems of solution testing. The orientation of the solvent molecules (methylene moletules) is detected in an electric field in accordance with the NMR observation (56). 

Crystalline samples of the dimer, trimer, tetramer, and hexamer were also polymerized by heating to temperatures below the melting point (18). The dimer and trimer react increasingly slower parallel with the decrease in vapor pressure of these molecules which again form unreactive zwitter ions in the solid state. The tetramer and hexamer form polymer at a faster rate and it is expected that now a different mechanism not involving the gas phase is followed. The tetramer and hexamer do not form zwitter ions and should thus be able to react directly. Unfortunately no details on the reactions of the latter are available. It is not known whether the polymer formed in this case is crystalline. 

Whereas most homodimers have been shown to exhibit host-guest behavior, Feldman and Campbell have described a crystalline homodimer that exhibits chemical reactivity (Fig. 24).44 In particular, two J-shaped dicarboxylic acids based on 1,8-disubstituted naphthalene units directed the assembly of two olefinic groups via two carboxylic acid synthons in an arrangement suitable for a [2 + 2] photodimerization.45 The two double bonds of the homodimer were organized parallel and separated by 3.65 A. Ultraviolet (UV) irradiation of the solid induced the... 

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