Vibrational spectroscopy branched-chain

The concentration of this species in liquid sulfur was estimated from the calculated Gibbs energy of formation as ca. 1% of all Ss species at the boihng point [35]. In this context it is interesting to note that the structurally related homocyclic sulfur oxide Sy=0 is known as a pure compound and has been characterized by X-ray crystallography and vibrational spectroscopy [48, 49]. Similarly, branched long chains of the type -S-S-S(=S)-S-S- must be components of the polymeric S o present in liquid sulfur at higher temperatures since the model compound H-S-S-S(=S)-S-S-H was calculated to be by only 53 kJ mol less stable at the G3X(MP2) level than the unbranched helical isomer of HySs [35]. 

Spectroscopic techniques are of great importance in polymer science, as they are in all branches of the chemical sciences, and these are dealt with in chapters 3 and 4. NMR is of prime importance as a method for identification and elucidation of the structure of polymer chains, and a complete chapter has been devoted to this technique. In recent years it has become an increasingly sophisticated and correspondingly expensive technique, requiring considerable skill in operating the spectrometer and in interpreting spectra, but it is still available in a simple and routine form in many laboratories. Vibrational spectroscopy encompasses infrared (IR) and Raman. These techniques, IR in... 

Since dispersion curves have been clearly discussed in Sections 3.5 and 3.6, the concepts which form the grounds of LAM spectroscopy can be easily defined. Let us consider an a -trans polymethylene chain and focus our attention on the branch cu8 of the phonon dispersion curve. The branch starts as mostly C-C stretching and ends as CCC bending. For a finite chain of N chemical units we expect to locate on this branch a band progression of N vibrational modes characterized by the phase coupling pj = jn/N. The most in-phase mode occurs at very small frequencies its frequency approaches zero when the chain tends to be of infinite length. Let 1,2,3. .. N label the components of the band progression of the modes which lie on the co% branch. 

Also Raman spectroscopy has greatly contributed to our knowledge of the conformational structure of polyethylene in the solid state. In the range below 250 cm there appear the so-called acoustic branches of chain vibrations from their position, the length of uninterrupted sequences of t structure can be determined by means of the expression originally proposed by Schaufele and Shimanouchi [8] ... 

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