Vibrational spectrum of chain molecules with conformational disorder: polyethylene

Abstract

The problem of the lattice dynamics of crystalline polyethylene containing a random distribution of geometrical defects is considered with a view to understanding some features of its infra-red and Raman spectra which cannot be explained in terms of k=0 spectroscopically active modes. A general method is proposed for the construction of the dynamical matrix of such a conformationally random polymer chain. The negative eigenvalue theorem is used for the calculation of the density of the vibrational eigenstates from the resulting very large matrices. Calculations are performed for several models containing the energetically more favoured conformational defects. The problem of the vibrational perturbations introduced by the defects in the lattice dynamics of the perfect crystal is discussed for crystals containing chain molecules. In addition to the activation of all band modes, gap and in-band resonances due to localized vibrations of the defects are found. Evidence is derived from calculations, and verifie...