Translational diffusivity from the Zimm model

Various approaches to the translational diffusion of polymers in a dilute solution are discussed for the Zimm model. The whole discussion is carried out for an arbitrary definition of the center of a polymer, for all homogeneous steady flows, and for constant external forces. It turns out that the result for the diffusion coefficient differs from the well-known Kirkwood expression, however, the numerical difference is less than 2%. We point out which approximations in the various derivations of the Kirkwood expression for the diffusion coefficient lead to this difference. The expression for the diffusion coefficient given in this paper can be generalized to arbitrary bead-spring models. Furthermore, we give the configurational distribution function for the Zimm model with time-dependent external forces in an arbitrary homogeneous flow field.