Linear and nonlinear excitations in a polyethylene crystal, 1. Vibrational modes and linear equations

Linear excitations in a polyethylene crystal are investigated by a new analytical method from the “first principles”. Elastic moduli are calculated from the parameters of molecular potentials of interaction. High anisotropy allows to derive comparatively simple approximate equations describing the dynamics of the crystal. Approximate expressions for the low-frequency branches of vibrational spectra are obtained. The role of internal degrees of freedom is revealed. Approximate expressions governing the dynamics of all degrees of freedom considered are obtained in analytic form suitable for nonlinear generalizations.