Hydrodynamic Properties of Flexible-Ring Macromolecules

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Abstract
The sedimentation constant of a series of multiple‐ring macromolecules has been calculated by the method of Kirkwood. The multiple‐ring form consists of m subrings of equal size linearly connected by universal joints. In the limit of large intersegmental hydrodynamicinteraction, the ratio of the sedimentation constant of a multiple‐ring molecule to that of a linear chain of the same molecular weight is 1.18 for m=1, 1.32 for m=2, 1.40 for m=3, ··· and 2.00 for extremely large m. These values are found to be practically independent of the excluded volume effect. The intrinsic viscosity of a single‐ring macromolecule has also been calculated by the method of Zimm. The eigenvalue problem encountered in the Zimm theory can be solved exactly over the whole range of the hydrodynamicinteraction parameter, h=0 to ∞. The ratio of intrinsic viscosities of ring and linear molecules is 0.500 for h=0 (free‐draining case) and 0.645 for h= ∞ (non free‐draining case). The latter value is slightly modified if the hydrodynamicinteraction is treated by the Fixman method.

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