Log-periodic oscillations for biased diffusion of a polymer chain in a porous medium

A coarse-grained off-lattice bead-spring model is used to reveal the complex dynamics of a polymer chain in a quenched porous medium in the presence of an external field B. The behavior of the mean square displacement (MSD) of the center chain bead and that of the center of mass of the chain as a function of time is studied at different values of the barrier concentration C, the field strength B and the chain length N. In a field, important information on the way in which chains move between obstacles and overcome them is gained from the MSD vs. time analysis in the directions parallel and perpendicular to the flow. Instead of a steady approach to uniform drift-like motion at low C, for sufficiently strong held B we observe logarithmic oscillations in the effective exponents describing the time dependence of the MSD along and perpendicular to field. A common nature of this phenomenon with oscillatory behavior, observed earlier for biased diffusion of tracers on random lattices, is suggested.