Inertial and memory effects in the hydrodynamic Brownian motion of rouse and 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 int 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.