Title: Hydrodynamic Brownian motion of Rouse-Zimm polymer coils

Abstract:
Traditional bead-spring models of the polymer dynamics are based on the
Einstein theory of the Brownian motion (BM), valid only at the times much
larger than the particle´s relaxation time. The reason is in neglecting the
inertial and memory effects in the dynamics. In the present work we use a
generalized theory of the BM to build models of the dynamics of flexible
polymers in dilute solution. The equations of motion for the polymer
segments include the friction force that follows from the linearized
Navier-Stokes hydrodynamics. It has a form of a memory integral. To get a
correct description of the short-time dynamics, inertial effects are
included into the consideration. For negligible hydrodynamic interactions
(HI) between the beads the motion of the polymer center of mass is not
influenced by internal forces within the chain and has been considered
exactly. Then we include the HI into the description of motion of chains,
which are assumed Gaussian in equilibrium. Analytical solutions for the
observable time correlation functions describing the movement of the polymer
coils significantly differ from the classical results showing, in
particular, algebraic long-time tails and ballistic motion at short times.