Kinetics of dilute polymers with the viscous memory

Abstract

The Zimm equation for the position vector of a polymer segment is generalized taking into account the effect of viscous memory. The Oseen tensor is built on the basis of the nonstationary Navier-Stokes equation. After the preliminary averaging of the tensor a non-Markovian equation for the time correlation function of the Fourier components of the segment position is derived. The viscous memory essentially affects the long-time asymptote of the correlation function of the Fourier amplitudes of the chain fragments: the time behavior is of a fractional power character instead of the traditional exponential. The relaxation time and the diffusion coefficient of the macromolecule as a whole are the same as in the Zimm model.