The intrinsic viscosity of dilute solutions of stiff polymers

Abstract

The intrinsic viscosity of a dilute polymer solution is studied for a polymer model with rigid constraints on some quantities, such as bond lengths and bond angles. The constraints are introduced via a harmonic constraining potential; the strength of this potential is taken to infinity at the end of the calculation. Expressions for the frequency dependent intrinsic viscosity are obtained with the correlation function formalism. The limiting form for the case in which the constraints become rigid is obtained via a systematic expansion procedure. In the limit we obtain a contracted description in terms of the unconstrained variables only. We discuss the form of the polymer diffusion equation and various expressions for the stress tensor that may be used in the context of such a contracted description, as well as expressions for both the frequency dependent and the frequency independent part of the intrinsic viscosity. We compare our results with those of other authors. Complete agreement is found with the results of Fixman and Kovac, and with the corrected version of the theory of Erpenbeck and Kirkwood. Discrepancies are found with results of Doi, Nakajima, and Wada, and of Hassager. The origin of these discrepancies is explained.