Vibrations of crystallographic defects associated with a single chain in polyethylene

The vibrational behaviour of crystallographic defects associated with a single chain were investigated for a dispiration, disclination, and dislocation in polyethylene. An approximate longitudinal modulus for the defects was determined by using conformational calculations to estimate the energy changes associated with changes in the length of a defect. This modulus, combined with the mass per unit length of the defect, was used to estimate the lowest longitudinal frequency of the defect, which was found to be around 100 cm^?1 for all the defects considered. Normal mode vibrational calculations for oligomers containing defects showed that the predicted lowest longitudinal modes could be identified by examination of the displacements associated with modes occurring in the estimated frequency range. It was shown that the defects could be considered as localized oscillators embedded in the crystal and coupled to the vibrational modes of the crystal. The presence of defects provides special mechanisms for coupling light waves and lattice vibrations in the crystal which may affect the Raman spectrum.