Approximate methods for calculating hydrodynamic properties of macromolecules in dilute solution. Theory and application to rigid structures

TLDR: In this paper, the authors examined several approximate methods that can be used to calculate hydrodynamic properties of macromolecules in solution and compared the relative performance of the methods.

Abstract: In this work we examine several approximate methods that can be used to calculate hydrodynamic properties of macromolecules in solution. We consider some well-known approximations such as the preaveraging approximation and the double-sum formula of Kirkwood for translation. We also consider newer methods such as the diagonal approximation and other double-sum formulas for rotation and viscosity. The obvious advantage of the approximate methods is that they require much less computational effort than the rigorous treatments. We first describe the nature of the approximations used in the various methods. Then we calculate translational and rotational coefficients and intrinsic viscosities of rigid rods and rings and other polygonal or polyhedral structures, using both the rigorous theory and the approximate methods. This enables us to determine the errors of the methods in terms of the geometry and size of the structures. The relative performance of the methods is discussed. A remarkable finding is the large effect from preaveraging the interaction tensor on the rotational coefficients and intrinsic viscosities. This effect is generally larger than that caused by the approximations used to derive the double-sum formulas.