Anchoring of polymers by traps randomly placed on a line

TL;DR

This paper models the diffusion of a polymer chain constrained by a line of randomly placed traps, providing an exact calculation of the probability that the chain remains untrapped over time, which informs its mobility dynamics.

Contribution

It introduces a novel model of polymer dynamics with a one-dimensional trap line and derives an exact solution for the survival probability of the chain's slip-link.

Findings

Exact time evolution of the survival probability $P_{sl}(t)$ is obtained.

The model reveals how trap distribution affects polymer mobility.

Provides insights into constrained polymer diffusion in complex environments.

Abstract

We study dynamics of a Rouse polymer chain, which diffuses in a three-dimensional space under the constraint that one of its ends, referred to as the slip-link, may move only along a one-dimensional line containing randomly placed, immobile, perfect traps. For such a model we compute exactly the time evolution of the probability $P_{sl}(t)$ that the chain slip-link will not encounter any of the traps until time $t$ and consequently, that until this time the chain will remain mobile.