Abstract

Numerical simulations are employed to study the Brownian motion of a bead-rod polymer chain dissolved in a solvent. An investigation is conducted of the relaxation of the stress for an initially straight chain as it begins to coil. For a numerical time step delta t in the simulations, conventional formulae for the stress involve averaging large +/- O(1/(delta t)(1/2)) contributions over many realizations, in order to yield an O(1) average. An alternative formula for the stress is derived which only contains O(1) contributions, thereby improving the quality of the statistics. For a chain consisting of n rods in a solvent at temperature (T) over cap, the component of the bulk stress along the initial chain direction arising from tensions in the rods at the initial instant is k (T) over cap x n(1/3n(2) + n + 2/3). Thus the bead-rod model yields results very different from other polymer models, such as the entropic spring of Flory (1969), which would assign an infinite stress to a fully aligned chain. For rods of length and beads of friction factor (zeta)over cap>, the stress decays at first on O((zeta)over cap>(l) over cap(2)/k (T) over cap x 1/n(2)) time scales. On longer time scales, this behaviour gives way to a more gradual stress decay, characterized by an O(k (T) over cap x n) stress following a simple exponential decay with an O(k (T) over cap/(zeta)over cap>(l) over cap(2) x 1/n(2)) rate. Matching these two limiting regimes, a power law decay in time (t) over cap is found with stress O(k (T) over cap x n(2) x (k (T) over cap (t) over cap/(zeta)over cap>(l) over cap(2))(-1/2)). The dominant physical processes occurring in these separate short, long and intermediate time regimes are identified.