Dynamics of stiff polymer chains. I

Abstract

The nonlinear configurational diffusion equation is formulated with bond vector coordinates. Primarily the treatment focuses on low amplitude oscillatory shear flow of the freely jointed chain, but the high frequency limit is formulated also with the constraint of constant bond angles, and is calculable fairly readily for a freely rotating chain or rotational isomeric model. The only numerical result given here concerns the high frequency limit [η] N ∞ of freely jointed chains of N bonds. We find by perturbation theory that [η] N ∞ ≃ [η] 1 ∞ N[1+(N−1)/(6N)+⋯] (for the concentration measured in molecules/cubic centimeter; in conventional units of grams/cubic centimeter, [η] N ∞ is asymptotically independent of N). In the lowest approximation the relaxing part of the intrinsic viscosity is given by equations quantitatively close to those of Zimm for the Gaussian model.