Longitudinal vibrations independency

Comments are necessary concerning the significance of to and Oq in Eq, (8.21). Values of 10" to 10 s have been frequently determined for to , they have been assigned to longitudinal vibrational modes of the backbone chain. For PVC and PE extremely small values are obtained which certainly cannot be interpreted in the same manner. With flow processes it must be recognized that the activation energy is not temperature independent but decreases with temperature ... 

In an unbounded isotropic solid, two types of sound waves can be propagated. In the first type, called a longitudinal wave, the polymer vibrates in the direction of wave propagation. In the second type, called a shear wave, the polymer motion is perpendicular to the direction of propagation. Longitudinal waves are sometimes called dilatational, compressional, or irrotational waves. Shear waves are sometimes called distortional, isovoluminous, or transverse waves. These two types of waves propagate independently of one another and are the only two types possible in an unbounded soUd. 

Only 03 changed somewhat from the earlier fit by Wunderlich (1962). A third improvement was offered by Tucker and Reese (1967). They used a separate expression for the longitudinal and the transverse vibrations . Each was fitted to a sqiarate Tarasov expression. In order not to increase the number of constants to be fitted, the two independent asstunptions were made First, = 0.60 which is based on a... 

In molecular crystals or in crystals composed of complex ions it is necessary to take into account intramolecular vibrations in addition to the vibrations of the molecules with respect to each other. If both modes are approximately independent, the former can be treated using the Einstein model. In the case of covalent molecules specifically, it is necessary to pay attention to internal rotations. The behaviour is especially complicated in the case of the compounds discussed in Section 2.2.6. The pure lattice vibrations are also more complex than has been described so far . In addition to (transverse and longitudinal) acoustical phonons, i.e. vibrations by which the constituents are moved coherently in the same direction without charge separation, there are so-called optical phonons. The name is based on the fact that the latter lattice vibrations are — in polar compounds — now associated with a change in the dipole moment and, hence, with optical effects. The inset to Fig. 3.1 illustrates a real phonon spectrum for a very simple ionic crystal. A detailed treatment of the lattice dynamics lies outside the scope of this book. The formal treatment of phonons (cf. e(k), D(e)) is very similar to that of crystal electrons. (Observe the similarity of the vibration equation to the Schrodinger equation.) However, they obey Bose rather than Fermi statistics (cf. page 119). 

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