Frequency anharmonic chain

Figure 5.17 Calculated frequency shifts of OH stretches, involving the bridging hydrogen. Solid lines refer to anharmonic and broken to harmonic frequencies. The first molecule in the chain is designated 1, and the central molecule corresponds to that with largest frequency near center of chain" . ...

Resonant raman spectroscopy has proved to be another valuable tool for the study of the structure of the polydiacetylene chain. Due to the resonance enhancement the spectra are compared to greatly simplified, infrared spectra and show as principle feature only the in-plane modes of the polymer chain. The correlation of the CsC and C = C stretching modes and their temperature dependence have been interpreted as resonances between the mesomeric structures (I) and (II) i32) Hoy(rever, a model using simple anharmonic force constants for the acetylene structure (II) is in good agreement with the experiment, e.g, the temperature and pressure dependence of the vibration frequency and the mechanical properties... 

Apart from the bilinear connection between acoustic and optical vibrations, the usual phonon anharmonicity takes place in the chain. The acoustic vibrations modulate the distances between A atoms and thus influence the frequency of proton vibrations on hydrogen bonds. The proton vibration frequency can be presented as... 

L. Ojamae and K. Hermansson, J. Phys. Chem., 98, 4271 (1994). Ab Initio Study of Cooperativity in Water Chains Binding Energies and Anharmonic Frequencies. 

The spectral changes in the frequency range of 150-280 cm , which characterizes a torsional vibrations in the CH2 sequences contacted with the CONH group, also point to an elevated mobility of chains in Nylon 12 prestrained, while the breaking of H-bonds (110 cm band) in this polymer may be ob rved only for loaded sample (Fig. 33, curve 5). Also the FIR spectra of loaded Nylon 12 show a narrowing of the translational and torsional vibration bands which is connected with a decrease in the amplitudes (and anharmonicity) of these motions because of an increase in the chain rigidity uncter Vision on account of so-called nechanical vitrification ... 

As an introduction, the chapter begins with the anharmonic diatomic molecule. Then we study the thermal properties (free energy, equation of state, thermal expansion and specific heat) of the classical anharnx)nic linear chain. Two important concepts are introduced the Gvuneisen pavametev and the quasiharmonic approximation. In this approximation, the temperature dependence of the force constants and phonon frequencies is only due to the... 

More recently. Green s function methods have been applied to evaluate analytic expressions of phonon frequencies and widths as well as of thermodynamic properties of the linear chain [5.7-9]. These studies have shown that the complex anharmonic self-energies, that is, the shifts and widths of the phonon energies, depend on q and on the applied frequency w. The results of such calculations for three-dimensional crystals will be discussed in Sect.5.5. 

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