Polymer chain in a random array of topological obstacles : 1. Collapse of loops

(Received 7 June 1992, revised 8 October 1992, accepted 12 October 1992)

Abstract
The thermodynamic properties of closed 3 D polymer loops topologically entangled with an array of immobile randomly distributed parallel rods are considered in the framework of an effective potential approach. The free energy of the loop in a quenched array of rods and for a quenched distribution in the number of rods enclosed by the loop has been calculated by means of the replica trick. We obtain that the disorder-induced collapse transition of the loop occurs at some critical length of the polymer chain, number of enclosed rods, dispersion in winding number and spatial dispersion of the density of rods.