Dynamics of stiff polymer chains. V. Interaction between local and global modes

Abstract

Relaxation spectra are analyzed for vector and tensor modes of a polymer chain with rigidly constrained bond lengths and angles in dilute solution. Illustrative approximate calculations are made for a chain with independent bond rotational potentials, and the constraints are found to reduce the relaxation rates of local modes to values that overlap the rate spectrum of some global modes significant to mechanical shear response. We conjecture that mixing of local and global modes occurs in the region of overlap, and that as a consequence of mixing a gap develops in the spectrum of relaxation rates. Pending a quantitative study of mixing, a crude approximation is made that the global modes with small relaxation rates retain a Rouse–Zimm form, while modes in the region of overlap have rates elevated significantly above the frequencies used in mechanical shear experiments. Then numerical values of the enhanced rates are unnecessary for the calculation of the complex dynamic viscosity. The latter is given by a formula of the Rouse–Zimm type, truncated at a specified mode number κD, and enhanced by a frequency independent real viscosity, the latter calculable Rouse–Zimm (low frequency) relaxation rates, and the cutoff κD. With κD determined from the experimental dielectric relaxation rate of poly (p-chlorostyrene), the theoretical complex dynamic viscosity of polystyrene was calculated and found to be in good agreement with experimental values.