What Do We Learn from Calculations

We have just outlined the way theoreticians in polymer dynamics face the problem of the understanding of the vibrational spectra of polymers in their realistic state. The reader interested in the theoretical aspects will find in the references quoted all indications which will enable him or her to grasp the theory and to carry out the calculations. 

However, a larger number of reader do not wish to play with calculations, but simply to know what we have learned about polymer structure and spectra using these calculations and to apply quickly and directly the knowledge acquired to their own problems. We report here the concepts of general validity in polymer spectroscopy which were derived from calculations and which can be applied to any polymer (for a general discussion, see [16, 19, 66]). 

The reader is certainly familiar with the traditional group-frequency approach generally used in the past 50 years for the chemical application of the infrared spectra (Section 3.4). Correlation tables and books have been written which discuss group-frequency correlations and provide the way to carry out a chemical diagnosis from the vibrational spectrum (so far, the infrared spectra have enjoyed great popularity the reader is advised to extend their interest to the very useful and easily available Raman spectra). 

The vibrations of disordered pol3uner chains follow the same kind of conceptual path which, on the other hand, was also found earlier by physicists in the study of lattice dynamics of very simple disordered lattices [98]. 

Let us make the problem simpler by considering briefly the small molecular unit which contains the defect as an isolated entity consisting of n atoms which generate 3n normal vibrations that occur somewhere in the vibrational spectrum. Next, we insert just one defect unit into the otherwise perfect polymer chain and allow the whole system to display its own new dynamics through the observed (or calculated) vibrational spectra. 

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