ITERATIVE CONVOLUTION DETERMINATION OF THE MOBILITY OF KNOTTED MACROMOLECULES

A statistical mechanical calculation of the mobility of a knotted macromolecule is presented on the basis of the iterative convolution approximation utilizing the Kirkwood-Riseman estimate of the translational friction coefficient. The linear relationship between mobility and the irreducible number of nodes or loops observed experimentally is confirmed. The magnitude of the diffusion coefficient appears to be a sensitive function of the excluded-volume processes operating within the entanglement, while the linear behavior derives from the specification of the central core of the knot from which the solvent is largely excluded.