Analytical results for torsional vibrations of polymers: dynamical matrix for random conformations and phonon Green function for Pitzer's model

Abstract

The matrix elements of the lattice Green function for Pitzer's model (describing the out-of-plane skeletal vibrations of an extended polyethylene chain) have been calculated analytically and discussed as to singularities, asymptotic behaviour, density of states, incoherent neutron scattering cross section and localized modes due to an isotropic mass defect. In addition, analytical formulae are presented for the torsional part of the dynamical matrix for a chain in arbitrary conformation.