Dynamic relaxation of drifting polymers: A phenomenological approach

Abstract

We study the nonequilibrium dynamic fluctuations of a polymer subject to an external force, moving in a dilute solution at a uniform average velocity. Starting from general symmetry arguments, a set of nonlinear equations is proposed to describe the time evolution of the polymer. The dynamic scaling of fluctuations is studied analytically (by renormalization group) and numerically. In most physically relevant cases, the fluctuations are superdiffusive, governed by a swelling exponent ν=1/2 and a dynamic exponent z=3. The polymer exhibits ‘‘kinetic’’ form birefringence as it is stretched by the flow. The crossover to anisotropy is controlled by the scaling variable y=${\mathit{UN}}^{1/2}$/${\mathit{U}}^{\mathrm{*}}$, where U is the average velocity, n is the number of monomers, and ${\mathit{U}}^{\mathrm{*}}$ is a characteristic microscopic velocity that is roughly 10–20 m/s for polystyrene in benzene. Numerical simulations show that strong crossover behavior may produce larger swelling exponents along the force at intermediate length scales that may potentially give rise to a stretching transition.