Variational Treatment of Hydrodynamic Interaction in Polymers

It has recently been pointed out by several authors that the Kirkwood–Riseman diffusion tensor normally used to treat hydrodynamic interactions in polymer molecules is not necessarily positive definite, an unphysical behavior which results from the neglect of short-range contributions to the interaction between chain segments. The problem can be reformulated as a minimization of the rate at which energy is dissipated by the motion of the suspending fluid, and in this way we have obtained an approximate diffusion tensor which (1) is positive definite for all configurations of the polymer molecule, (2) approaches the Kirkwood–Riseman diffusion tensor at large separations between the interacting segments, and (3) can be written as the true diffusion tensor plus a positive definite correction. The last feature can be used to obtain variational bounds on relaxation times and sedimentation rates.