Viscosity, Sedimentation, et Cetera, of Ring- and Straight-Chain Polymers in Dilute Solution

Abstract

The hydrodynamic properties of straight‐chain and ring‐chain polymers whose dimensions are expanded over those of similar Gaussian coils have been calculated by a perturbation method based on the normal‐coordinate treatment with hydrodynamic interaction. Expansion is characterized by a parameter ε, such that the mean‐square length is proportional to N 1+ε, N being the number of chain segments. For straight chains the intrinsic viscosity, expressed in terms of the Flory Φ (×10−23), decreases from 2.81 at ε=0 to 0.686 at ε=0.5, while for rings Φ varies from 1.85 to 0.422; the ratio straight:ring increases slowly from 1.5 to 2.0. The sedimentation coefficient of the straight chain increases by a factor of 2.4 over this range of ε, while that of the ring goes up 2.2‐fold. The ratio straight: ring rises slowly from 0.85 to 0.91. The results on straight chains agree with those of previous workers, and the straight:ring ratio agrees with several experiments on the sedimentation of straight and ring forms of various DNA's. It is apparent that viscosity should be a much more sensitive measure of ring formation than sedimentation, and that the effect of ring formation is roughly the same regardless of chain expansion (i.e., the same both in Gaussian coils and in a stiff chain such as DNA).