Transport of finite chains with free ends through thin channels

Abstract

We describe the transport of a finite chain of [Formula: see text] identical particles in a thermal bath, through thin channels that forbid any crossing with a conceptually and technically simple method, that is neither restricted to the thermodynamic limit (infinite systems with finite density) nor to overdamped systems. We obtain analytically the mean squared displacement of each particle. Regardless of the damping, we identify a correlated regime for which chain transport is dominated by the correlations between individual particles. At large damping, the mean squared displacement evidences the typical single file behavior, with a time dependence that scales as [Formula: see text]. At small damping, the correlated regime is rather described by a diffusion-like behavior, with a diffusivity which is neither the individual particle diffusivity nor the Fickian diffusivity of the chain as a whole. We emphasize that, for a chain with free ends, the fluctuations of the chain ends are larger by a factor two than the fluctuations of its center. This effect is observed whatever the damping [Formula: see text], but the duration of this fluctuations enhancement is found to scale as [Formula: see text] for low damping and as [Formula: see text] for high damping. We discuss the relevance of this model to the transport of actual systems in confined geometries.