Dynamic Intrinsic Viscosity of Macromolecules with Internal Viscosity. III. Effect of Molecular Weight, Excluded Volume, and Hydrodynamic Interaction

Abstract

The frequency dependence of the complex intrinsic viscosity and elastic modulus of a macromolecule with internal viscosity is calculated for the Gaussian coil and the coil with excluded volume in a wide range of molecular weight and hydrodynamic interaction. Due to limitations in eigenvalues and because of coil rotation in laminar flow the results obtained are sufficiently accurate only for a large number of coil segments and for small internal viscosity. Hydrodynamic interaction enhances the effect of internal viscosity so that the macromolecule seems to be stiffer than in the free-draining case. The non-Gaussian character of intrachain distances has a very small effect. Finite internal viscosity yields a nonvanishing limiting viscosity at ω→∞ which at sufficiently large M increases as M1/6. The relative limiting viscosity [η]∞′/[η]0 as a function of molecular weight (Z∼M), hydrodynamic interaction (h), non-Gaussian character of the coil (ε), and internal viscosity (φ) can be well represented by a single master curve if plotted against ν1φ/Zf. The eigenvalue ν1 is unity for the free-draining coil and asymptotically increases as a linear function of h and ε. Molecular weight enters the abscissa of the master curve implicitly through ν1 and explicitly through Z.