| Abstract: | The sedimentation of an unperturbed polymer chain in dilute solution is reformulated by using Burgers' method, in which the no-slip boundary condition on the surface of each chain element is taken into account approximately. It is shown that the forcevelocity proportionality relation employed so far as the basis of theoretical developments in polymer hydrodynamics can be justified as a first approximation to the no-slip condition. The derived expression for the translational friction coefficient ft is a complex function of n and a/b, where n is the number of chain elements in a single molecule and a/b is the ratio of the Stokes radius of a chain element to the effective bond length. Three special cases corresponding mathematically to b = ∞ (no hydrodynamic interaction), a ? b (Kirkwood-Riseman theory), and b = 2a (touching-sphere model) are examined in detail. Finally, it is shown that when a/b = 0.2360, our ft varies linearly with n1/2 over the entire range of n. |
