Molecular model of internal viscosity

Abstract

Internal viscosity was introduced in the model of randomly coiled macromolecule by Kuhn and Kuhn (1) in order to explain the gradient dependence of intrinsic viscosity. In laminar flow with transverse gradient the molecule rotates with an angular velocity equal to half the gradient and during each rotation gets twice extended and twice compressed. Hence the amplitude and the frequency of shape change are increasing almost linearly, the rate of deformation quadratically with the gradient. The resistance of the macro-molecular chain to rapid change of shape reduces the coil deformation below the value expected for a completely flexible elastic dumbbell or necklace model. As a consequence, the increase of end-to-end distance cannot compensate the decrease of viscosity contribution caused by chain orientation so that with increasing gradient the intrinsic viscosity drops below the initial value at zero gradient. The effect is extreme for perfectly rigid molecule and disappears for ideally flexible coil.