Anchoring of Polymers by Traps Randomly Placed on a Line

We study the 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. Extensions of this model occur naturally in many fields, ranging from the spreading of polymer liquids on chemically active substrates to the binding of biomolecules by ligands. For our model we succeed in computing exactly the time evolution of the probability Psl(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.