Crystals, intermolecular interactions

For rigid-chain crystallizable polymers, spontaneous transition into the nematic phase is accompanied by crystallization intermolecular interactions should lead to the formation of a three-dimensional ordered crystalline phase. 

Desiraju, G.R. Designer crystals intermolecular interactions, network structures and supramolecular synthons. Chem. Comm. 1997, 16, 1475-1482. 

In less violent encounters, such as crystallization, intermolecular interaction is just sufficient to establish a more extended whole, without completely destroying the partial molecular wholes. In a case such as this, interactions separate into strong intramolecular and weaker intermolecular interactions. 

In liquid crystals intermolecular interactions are short-range and Cp is dominantly related to short-range order fluctuations. Since fluctuations in local order occur above and below the transition, one expects, in contrast to the mean-field situation, anomalous Cp behavior above as well as below T. Unfortunately models taking short-range order parameter fluctuations into account are much more difficult to handle and analytic solutions are only available for some special cases. However, sophisticated renormalization group (RG) analyses have been carried out for several types of n vector order parameter models of which the three-dimensional cases are of particular relevance for liquid crystals [7, 10, 11]. 

Small needle-shaped single crystals were examined by transmission electron microscopy (TEM) and electron diffraction (ED) (see Fig. 16-17). The results show that the crystals are elongated along the b-axis, which is the direction of weak intermolecular n-n interactions, and have a well-developed (ab) top surface. It corresponds to the surface of aliphatic tails (direction of weak intermolecular interactions). There are indications of displacement of successive ( / )-laycrs along the fl-axis, in line with the other signs of disorder in the aliphatic layer. 

The substituted five-ring OPVs have been processed into poly crystal line thin films by vacuum deposition onto a substrate from the vapor phase. Optical absorption and photolumincscence of the films are significantly different from dilute solution spectra, which indicates that intermolecular interactions play an important role in the solid-state spectra. The molecular orientation and crystal domain size can be increased by thermal annealing of the films. This control of the microstruc-ture is essential for the use of such films in photonic devices. 

The diazonio group of one zwitterion is stabilized by intermolecular interactions with the carboxylato oxygens of two neighbouring zwitterions. The same type of coordination is observed in crystals of benzene diazonium chloride, tribromide, and tetrafluoroborate (Andresen and Romming, 1962 Romming, 1963 Cygler et al., 1982). 

Another important consideration is the comparison between gaseous and crystalline sulfoxides and sulfones. Such a comparison may yield information about intermolecular interactions in the crystal1. Unfortunately, very few data are yet available for confident use in such comparisons. The first requirement is, of course, that the same compound has been investigated both in the gaseous state and in the crystal. In addition, it is necessary that all the structural data correspond to the same physical meaning (cf. Reference 1). When these conditions are fulfilled, interesting conclusions2 may be reached on the basis of even small differences. 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

It is clear from the forgoing discussions that the important material properties of liquid crystals are closely related to the details of the structure and bonding of the individual molecules. However, emphasis in computer simulations has focused on refining and implementing intermolecular interactions for condensed phase simulations. It is clear that further work aimed at better understanding of molecular electronic structure of liquid crystal molecules will be a major step forward in the design and application of new materials. In the following section we outline a number of techniques for predictive calculation of molecular properties. 

Finally, there are groups of liquid crystals where, at the current time, force fields are not particularly useful. These include most metal-containing liquid crystals. Some attempts have been made to generalise traditional force fields to allow them to cover more of the periodic table [40, 43]. However, many of these attempts are simple extensions of the force fields used for simple organic systems, and do not attempt to take into account the additional strong polarisation effects that occur in many metal-containing liquid crystals, and which strongly influence both molecular structure and intermolecular interactions. 

Baumeister et al. [116] described the crystal structure of 4-(2-cyanoethyl)-cyclohexyl 4-n-pentylcyclohexanecarboxylate. The almost fully stretched molecule is only distorted by the gauche conformation of the cyanoethyl group. The crystal packing is characterised by a discrete layered arrangement with an antiparallel orientation of neighbouring molecules. With respect to intermolecular interactions, no remarkable contacts between the cyano groups can be observed. 

From the X-ray data of single crystals, it is possible to obtain information about the intermolecular interactions and the overlapping between the polar groups of neighbouring molecules. In Sects. 2.1.1, 2.1.2 and 2.1.3 the crystal structures of cyanobiphenyls were described. No cyano-phenyl overlapping of type 1 can be observed in the solid state of the compounds. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

It is concluded that the cooperative effect observed is of long-range nature and therefore of elastic rather than of electronic origin. Recently, the additional suggestion has been made [138] that, due to intermolecular interactions in the crystal environment of [Fe(ptz)g](BF4)2, domains of iron(II) complexes interconvert together. The observed kinetics would then correspond to a first- or higher-order phase transition rather than to the kinetics which are characteristic for the conversion of isolated molecules. 

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