Jamming of Knots along a Tensioned Chain

Abstract

We examine the motion of a knot along a tensioned chain whose backbone is corrugated due to excluded volume effects. At low applied tensions, the knot traverses the chain diffusively, while at higher tensions the knot makes slow, discrete hops that can be described as a Poisson process. In this “jammed” regime, the knot’s long-time diffusivity decreases exponentially with increasing tension. We quantify how these measurements are altered by chain rigidity and the corrugation of the polymer backbone. We also characterize the energy barrier of the reptation moves that gives rise to the knot’s motion. For the simple knot types examined thus far (31, 41, 51, 52), the dominant contribution to the energy landscape appears in the first step of reptation—i.e., polymer entering the knotted core. We hope this study gives insight into what physics contributes to the internal friction of highly jammed knots.