Twist bending vibration

Bending vibrations in one plane (symbol 8), changing bond angles but leaving bond lengths unaltered (in larger molecules further divided into rock, twist and wag vibrations),... 

An in-plane bending An out-of-plane bending vibration (scissoring) vibration (twisting)... 

In the Raman spectrum of polyethylene the main peak of the bending vibrations is observed at 1437 cm, while a wagging vibration shows a weak band at 1370 cm and a twisting vibration gives a strong band at 1295 cm The stretching vibrations of the C-C chain are observed at 1126 and 1059 cm, respectively, in the Raman spectrum (Figs. 4.1-2A and 4.1-3). A normal coordinate calculation of polyethylene is published by Tasumi et al. (1962). 

Fig. 19 Examples of symmetrised distortions of a hexa-aqua complex (a) the Qg component of the V2(MOg), eg(Th) stretching vibration (b) The component of the V5(M06), tg (Th) bending vibration (c) the Qt component of the x[M(OH2)6], tg (Tjj) twisting libration...

Fig. 4.36. Pattern of observed transitions between the energy levels for the twisting and bending vibrations in dioxene. Many of the checks on the self-consistency of the assignments are provided by the difference band in the far-infrared spectrum (Fig. 4.34c).

The vibrations of a molecule containing three or more atoms are more complex (Figure 13.12). Such molecules can experience symmetric and asymmetric stretches and bends, and their bending vibrations can be either in-plane or out-of-plane. Bending vibrations are often referred to by the descriptive terms rock, scissor, wag, and twist. 

Biphenyl The molecule (Fig. 5.16) is not planar in the gas phase the angle between the two planes is about 45°. In the biphenyl crystal, the molecules are planar. At 40 K and at 17 K, there are structural phase transitions within the biphenyl crystal. The molecules thereby lose their centres of inversion. Below 40 K, the molecule is twisted by about 10° around the central C-C axis. This means that the inter-molecular coupling is larger than the intramolecular torsion potential and that the coupling between torsional and lattice oscUlations cannot be neglected in every case, but instead can even induce phase transitions. A similar conclusion holds for the coupling of low-frequency bending vibrations (Fig. 5.16, lower part) to external lattice vibrations (see e.g. [19, 20]). 

The bending vibrational modes of methylene group The top two dii rams frrocking modes. The bottom two dii rams show wagging and twisting modes. 

Figure 4.3 Principal modes of vibration between carbon and hydrogen in an alkane (a) symmetrical stretching, (b) asymmetrical stretching and the bending vibrations, (c) scissoring, (d) rocking, (e) wagging, and (f) twisting.

Figure 14 Raman spectra, measured in the spectral ranges for the C—C stretching vibration (I), the — CH2— twisting vibration (II), and the —CH2— bending vibration (III) for a sample of an extended-chain polyethylene at 25°C (a) the melt at 150°C (b) and a branched, partially crystalline polyethylene at 25°C (c). The dotted line represents the amorphous component.

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