Molecular packing

We present here some of the highlights of Kitaigorodskii s considerations [88], First, the problem of dense packing is examined for the plane groups of symmetry. The distinction between dense-packed, densest-packed, and maximum density was introduced for the plane layer of molecules. The plane was called dense-packed when coordination of six was achieved for the molecules. The term densest-packed meant six-coordination with any orientation of the molecules with respect to the unit cell axes. The term maximum density was used for the packing if six-coordination was possible at any orientation of the molecules with respect to the unit cell axes while the molecules retained their symmetry. 

The criteria for the suitability as well as incompatibility of plane groups for achieving molecular six-coordination have been considered. The next step is to apply the geometrical model to the examination of the suitability of three-dimensional space groups for densest 

Low-symmetry crystal classes are typical for organic compounds. Densest packing of the layers may be achieved either by translation at an arbitrary angle formed with the layer plane, or by inversion, glide plane, or by screw-axis rotation. In rare cases closest packing may also be achieved by twofold rotation. 

Kitaigorodskii [94] analyzed all 230 three-dimensional space groups from the point of view of densest packing. Only the following space groups were found to be available for the densest packing of molecules of arbitrary form  

For molecules with symmetry centers, there are even fewer suitable three-dimensional space groups, namely  

We present here some of the highlights of Kitaigorodskii s considerations [9-22]. First, the problem of dense packing is examined for the plane groups of symmetry. The distinction between dense-packed, densest packed, and maximum density was introduced for the plane layer of molecules. The plane was 

Due to the low solubility of the longer Ts, single crystals could only be successfully grown by using a sublimation technique [15], the so called Lipsett technique. For 6T [61] and 8T [96] single crystals (plates) of macroscopic dimensions were obtained with a length of a few millimeters and a thickness of some tens of microns. 

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Molecular packing of surfactants in crystals has been reviewed at some length [1 ]. An almost universal factor... 

Figure C2.3.3. Molecular packing of SDS monohydrate viewed as projected on the ac plane. This polymoriDh crystallizes in a triclinic cell with unit cell constants a, b and c of 10.423 A, 5.662 A and 28.913 A, respectively, and with a = 86.70°, (3 = 93.44°, y = 89.55°. There are four molecules per unit cell. Adapted from figure 2 of [18].

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

The early Hartley model [2, 3] of a spherical micellar stmcture resulted, in later years, in some considerable debate. The self-consistency (inconsistency) of spherical symmetry witli molecular packing constraints was subsequently noted [4, 5 and 6]. There is now no serious question of tlie tenet tliat unswollen micelles may readily deviate from spherical geometry, and ellipsoidal geometries are now commonly reported. Many micelles are essentially spherical, however, as deduced from many light and neutron scattering studies. Even ellipsoidal objects will appear... 

The probable crystal stmcture of this salt has been described (14) as a complex of two dianions and two cations forming a large polyatomic ring. By implication this type of molecular packing probably appHes to many other similar pigments. 

Eurther heat treatment in excess of 2000°C is referred to as graphitization. Eiber stmcture further densifies as molecular packing and orientation increase. At temperatures of 3000°C or above, the fiber stmcture begins to approach a truly graphitic stmcture with three-dimensional order. Typically, fiber strain to failure decreases as the carbonization temperature exceeds 1500°C because of reaction of impurities with the carbon fiber and the development of an increasingly flaw-sensitive graphitic stmcture (31,34)... 

Figure 18.3 Protein crystals contain large channels and holes filled with solvent molecules, as shown in this diagram of the molecular packing in crystals of the enzyme glycolate oxidase. The subunits (colored disks) form octamers of molecular weight around 300 kDa, with a hole in the middle of each of about 15 A diameter. Between the molecules there are channels (white) of around 70 A diameter through the crystal. (Courtesy of Ylva Lindqvist, who determined the structure of this enzyme to 2.0 A resolution in the laboratory of Carl Branden, Uppsala.)...

It must be pointed out that deviations from such a simple relationship do occur. For example, since random copolymerisation tends to promote disorder, reduce molecular packing and also reduce the interchain forces of attraction, the Tg of copolymers is often lower than would be predicted by the linear relationship. Examples are also known where the Tg of the copolymer is higher than predicted. This could occur where hydrogen bonding or dipole attraction is possible between dissimilar comonomer residues in the chain but not between similar residues, i.e. special interchain forces exist with the copolymers. 

Crystalline structures have a much greater degree of molecular packing and the individual lamellae can be considered as almost impermeable so that diffusion can occur only in amorphous zones or through zones of imperfection. Hence crystalline polymers will tend to resist diffusion more than either rubbers or glassy polymers. 

With crystalline polymers the more orderly molecular packing leads to much greater shrinkage. Variations in moulding conditions can lead to large variations in shrinkage and need to be closely controlled. The main factors which cause an increase in shrinkage are ... 

The regular structure of the alternating copolymer with its absence of side chains enables the polymer to crystallise with close molecular packing and with interchain attraction augmented by the carbonyl groups. As a result these polymers exhibit the following characteristics ... 

Dielectric relaxation measurements of polyethylene grafted with acrylic acid(AA), 2-hydroxyethyl methacrylate (HEMA) and their binary mixture were carried out in a trial to explore the molecular dynamics of the grafted samples [125]. Such measurements provide information about their molecular packing and interaction. It was possible to predict that the binary mixture used yields a random copolymer PE—g—P(AA/HEMA), which is greatly enriched with HEMA. This method of characterization is very interesting and is going to be developed in different polymer/monomer systems. 

The close molecular packing makes diffusion more difficult than with amorphous polymers compared in similar circumstances, i.e. both below Tg or both above (but below of the crystalline polymer). Thermodynamic considerations lead to considerable restriction in the range of solvents available for such polymers. 

These model compounds can also be used in device fabrication, since thin films of appropriate thickness can be obtained by sublimation and subsequent deposition onto a substrate in vacuum. Electrical as well as optical properties of such devices have turned out to be strongly dependent on both the molecular packing within the crystallites and the polycrystalline morphology. Understanding and control of this aspect is one of the current scientific challenges. 

Figure 16-20. Molecular packing of Oocl-OPV3. Four molecules are shown, viewed nearly along Ihe long molecular axis (left) and perpendicular lo dial axis (right).

Figure 16-21. Molecular packing of Omc-OPV3. Tire four molecules lhal make up one unit cell arc shown, viewed al a slight angle with respect lo the long molecular axes (let ) and perpendicular to the plane of the central ring (right).

Figure 16-24. Molecular packing of ocl-OPV3. Tlie iwo molecules llial make up one unit cell have nearly perpendicular n-syslems.

Figure 16-16. Molecular packing of Oocl-OPV5 in the crystal lattice. Lett oblique view of (he unit cell of Oocl-OPV5 right projection of the unit cell on a plane perpendicular to the ci-axis.

Figure 16-22. Molecular packing of Oocl-OPV3-CN. The oclyloxy side-chains separate (lie non-planar ir-systcms.

The problem-solving approach that ties the processing variables to products properties includes considering melt orientation, polymer degradation, free volume/molecular packing and relaxation, cooling stresses, and other such factors. The most influential of these four conditions is melt orientation, which can be related to molded-in stress or strain. 

This is, for instance, the case of PTFE, which at atmospheric pressure presents two reversible first-order transitions at 19 °C and 30 °C [67], In the transition at 19 °C the molecular conformation changes slightly, from a 13/6 to a 15/7 helix and the molecular packing changes from an ordered structure with a triclinic unit cell (corresponding to a positioning of the chain axes nearly hexagonal) toward a partially disordered structure (partial intermolecular rotational disorder) with a... 

Molecular Packing and Ring Interconversion by Solid State and Solntion State... 

The purpose of this article is to discuss conformational shift variations in some selected solid state spectra on the basis of discrete rotational isomeric states and to compare them with molecular packing effects. 

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