Rotational disorder

A conformationally disordered mesomorphic form is present, for instance, in the high-temperature phase I of PTFE. In this form, a long-range 3-D order is present only in the periodic pseudohexagonal placement of the chain axes [49]. In fact intramolecular helix reversals would produce the conformational disorder [50-52] and a complete intermolecular rotational disorder would be also present [49, 52,53]. 

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... 

The delocalization may be assumed to occur in a box of dimensions Lx x LyxLz, containing the carbon skeleton, freely rotating about its x-axis. The dimensions Ly = Lz are assumed equal to l, the diameter of the rotationally disordered skeleton. The length of the box, for a C/v chain is assumed to be Lx — Nl. The delocalized electrons are confined by the Pauli principle to N/2 energy levels with wave functions... 

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. 

Benzene forms a rotationally disordered structure on the reconstructed (100) platinum surface. However, the work function changes with increasing surface coverage are similar to that of benzene on the (111) crystal face. 

Obviously, if R is large enough to affect the packing of tbe molecule in the crystal then tbe possibility of rotational disorder does not exist. 

In the same way the N-methylimidazole ligand (the group below the iron atom) shows a two-fold disorder with respect to where the methyl group is located. The model compound has pseudo-four-fold symmetry and the rotational disorder can have no effect on the molecular packing. This is especially evident looking at the 02 buried in the molecule see Fig. 19.4 for the complete structure. 

The problem of rotational disorder was solved by making an osmyl derivative of buckyball. Osmic acid, OsO. will add across double honds ... 

There are four independent molecules in the crystal of205 at 138 K two of them show rotational disorder about their central bonds3 8. Another phase formed on cooling consists of twinned crystals, which cannot be used for a structure determination318. Approximate Z)3h sysmmetry and bond lengths of about 1.60 and 1.53 A (corrected for the large thermal motion) in the ordered molecules at 138 K correspond to those in the gas phase. 

Polyoxybenzoate is a stiff chain, lyotropic liquid crystalline material, as was discussed on the basis of its copolymers with ethylene terephthalate (see Sect. 5.1.4). The crystal structure of the homopolymer polyoxybenzoate was shown by Lieser 157) to have a high temperature phase III, described as liquid crystalline. X-ray and electron diffraction data on single crystals suggested that reversible conformational disorder is introduced, i.e. a condis crystal exists. Phase III, which is stable above about 560 K, has hexagonal symmetry and shows an 11 % lower density than the low temperature phases I and II. It is also possible to find sometimes the rotational disorder at low temperature in crystals grown during polymerization (CD-glass). 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

This intermolecular potential for ADN ionic crystal has further been developed to describe the lowest phase of ammonium nitrate (phase V) [150]. The intermolecular potential contains similar potential terms as for the ADN crystal. This potential was extended to include intramolecular potential terms for bond stretches, bond bending and torsional motions. The corresponding set of force constants used in the intramolecular part of the potential was parameterized based on the ab initio calculated vibrational frequencies of the isolated ammonium and nitrate ions. The temperature dependence of the structural parameters indicate that experimental unit cell dimensions can be well reproduced, with little translational and rotational disorder of the ions in the crystal over the temperature range 4.2-250 K. Moreover, the anisotropic expansion of the lattice dimensions, predominantly along a and b axes were also found in agreement with experimental data. These were interpreted as being due to the out-of-plane motions of the nitrate ions which are positions perpendicular on both these axes. 

Crystals of most polar lipids can swell in the presence of water. The corresponding phases, gel-phases, with lamellarly packed lipid, and water layers, are sometimes thermodynamically stable (Larsson, 1994, p. 41). Also, the hydrocarbon chain packing of gel-phases usually show some axial rotational disorder. The alkyl chain cross-sectional area is close to 20 A2 in a plane perpendicular... 

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