Phonon green's function for polymer chains. I. Treatment of conformational defects

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Abstract
It is shown that the Green's function (GF) method of Lifshitz can be applied to conformational defects in polymers by taking correctly into account the actual geometrical configuration of the molecules. In contrast with methods currently in use in polymer dynamics, this method is not restricted to the calculation of the density of states, allows the treatment of infinitely long chains, and provides a direct assignment of typical frequencies to certain defect types. Furthermore, arbitrary frequency accuracy can be obtained with computer time drastically reduced from that required by other methods. A short review is given of the computation of experimental quantities which are related to phonons (in harmonic approximation, but in the presence of defects) and which can be obtained from the GF. Expressions are derived for the matrix elements of the harmonic GF of zigzag chains, valid for a general force field. The symmetry of the defects is taken advantages of by introducing symmetry coordinates.

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