Rotational crystalline state

When all the rotations are possible in the solid state the symmetry increases to hexagonal. This form corresponds to the close packing of spheres or cylinders and the molecule is in a rotational crystalline state, characterized by rigorous order in the arrangement of the center (axes) of the molecules and by disordered azimuthal rotations [118]. If the chain molecules are azimuthally chaotic (they rotate freely around their axes), their average cross sections are circular and, for this reason, they choose hexagonal packing. The ease of rotation of molecules in the crystal depends merely on the molecular shape, as in molecules of an almost spherical shape like methane and ethane derivatives with small substituents, or molecules of a shape close to that of a cylinder (e.g., paraffin-like molecules). 

Figure 5. Formation of centrosymmetric crystals by noncentric molecules and relations among ordered state, rigid disordered state, and rotational crystalline state.

PHBA goes through an orthorhombic-to-hexagonal phase transformation (a rotational crystalline phase or a smectic liquid-crystalline phase). Other structures [720-/22] were recently described as belonging to the rotational crystalline state. 

Study of the structure and physicochemical properties of comb-shaped polymers in dilute solutions, gels, and the solid phase genoalized in [8] permitted describing the structural features of this special class of branched polym systems in detail within the framework of the so-called rotational-crystalline state, a variety of the LC state. 

In the foregoing discussion polymers have been used as a medium for smaU molecules in comparison with the crystalline state. It has also been observed that there are changes in polymeric geometry and various rotational motions introduced by pressure (10—14). These are at times reflected in the absorption spectmm (usuaUy in the ultraviolet) or in the emission spectmm and are a form of piezochromism. 

Fig. 7. Molecular model of cyclododecane in the (gag)4 conformation of the crystalline state according to Dunitz and Shearer (Ref. 12>). The numbers at the bonds indicate the rotational angles...

With concern to the high internal mobility of the molecules in the high temperature solid state phase, some parallelism to n-alkanes can be stated. In the pseudohexagonal (rotator) phase the latter are also characterized by fast molecular motions. For discrimination and according to Pfitzer 14) and Dale 13) in the following the term pseudorotator phase is used for the mobil crystalline state of cyclic molecules. 

From X-ray diffraction experiments28 it is known that in the crystalline phase the erythrodiisotactic poly(l,2-dimethyltetramethylene) has a (g+aaa g aaa)n structure as shown in Fig. 13. The bold printed letters in the denotation give the conformation of the CH—CH bond. In agreement with this structure and low temperature solution state spectra of 2,3-dimethylbutane, 3,4-dimethylhexane, and 4,5-dimethyloctane 29 30) in which the CHCH bond rotation is frozen the crystalline signals can be assigned conclusively. Like for the crystalline state of poly(l,2-... 

Tetravinylmethane (TVM) is a very interesting compound with respect to its conformational and structural parameters. All the assumptions on the symmetry of TVM are based on D2d and S4 conformations10,11. Surprisingly, none of these conformations is observed in the crystalline state instead, C symmetry was found in an orthorhombic crystal lattice (space group Pbca). If one of the vinyl groups (C3-C8-C9) is rotated by ca 150°, the Ci symmetry can be transferred to S4 symmetry (or vice versa). This is evident from Figure 2 where DVC is also shown in the same projection which demonstrates that the C1 symmetry is no coincidence of packing effects. 

It has been shown frequently that without the presence of strong intermolecular interactions, discotic molecules are highly mobile in the liquid crystalline state.1 They undergo both lateral as well as rotational translations, resulting in the absence of positional order. Similarly, such discotics also freely rotate in the columnar aggregates they form in solution. This lack of positional order in the columns accounts for the absence of chiral or helical supramolecular order. We will demonstrate this characteristic using results obtained for triphenylenes. 

Molecular Theory of Surface Tension (Harasima) Molecules, Barriers to Internal Rotation in (Wilson) Molecules, Convex, in Gaseous and Crystalline States (Kihara). ... 

For vacuum sublimed thin films, Grabuzov et al. [138] reported a photoluminescence quantum efficiency of 32 2%. In the same paper, data on the absorption coefficient at the maximum, a = (4.4 0.1) x 104 cm 1, and the refractive index at 633 nm (n = 1.73 0.05) can be found. Other reported values for the photoluminescence quantum efficiency that can be found in the literature are 30 5% [124] and 25 5% [139]. Naito et al. [109] reported a quantum yield of 5% in the amorphous film compared to 35% in the crystalline state. The fluorescence lifetime is reported to be biexponential with x = 3.4 and 8.4 ns, which is much shorter than in the crystal (17.0 ns). In the amorphous state, the larger free volume allows more vibrations and rotations to take place, which favors nonradiative decay. 

Because of the orientational freedom, plastic crystals usually crystallize in cubic structures (Table 4.2). It is significant that cubic structures are adopted even when the molecular symmetry is incompatible with the cubic crystal symmetry. For example, t-butyl chloride in the plastic crystalline state has a fee structure even though the isolated molecule has a three-fold rotation axis which is incompatible with the cubic structure. Such apparent discrepancies between the lattice symmetry and molecular symmetry provide clear indications of the rotational disorder in the plastic crystalline state. It should, however, be remarked that molecular rotation in plastic crystals is rarely free rather it appears that there is more than one minimum potential energy configuration which allows the molecules to tumble rapidly from one orientation to another, the different orientations being random in the plastic crystal. 

Existence of a high degree of orientational freedom is the most characteristic feature of the plastic crystalline state. We can visualize three types of rotational motions in crystals free rotation, rotational diffusion and jump reorientation. Free rotation is possible when interactions are weak, and this situation would not be applicable to plastic crystals. In classical rotational diffusion (proposed by Debye to explain dielectric relaxation in liquids), orientational motion of molecules is expected to follow a diffusion equation described by an Einstein-type relation. This type of diffusion is not known to be applicable to plastic crystals. What would be more appropriate to consider in the case of plastic crystals is collision-interrupted molecular rotation. 

The isolation of three isomers of this type is completely consistent with the concept that the two cyclopentadienyl rings in ferrocene are rotating in all but the crystalline state. From the amounts of each isomer formed and the number of nonequivalent ring positions, site reactivities can be calculated, the l -position being arbitrarily assigned a value of unity. 

If only one, or none, of the forms is known in the crystalline state, polarimetry does not yield any useful results. It was not even certain, for example, before the advent of n.m.r. spectroscopy, whether the one known crystalline form of D-ribose is the a- or the / -pyranose its muta-rotational change is small, but complex.5... 

Rotational restriction of the amino group has been observed by the NMR spectroscopy technique in a number of cytosines in solution as well as in the crystalline state.64,86,88,89 194 Shoup et al. 89,90 measured the activation parameters for the rotation of the dimethylamino group in N8-dimethylcytosine derivatives. With one exception, the range of activation energies is 15-18 kcal/mole. The activation energies found for 26a and 26b are about twice those reported by Martin and Reese195 for 26c. In this last case, however, the method by which the activation energy was obtained has not been described (usually approximate... 

---