Ring polymer chains confined in a slit geometry of two parallel walls: the massive field theory approach

Abstract

The investigation of a dilute solution of phantom ideal ring polymer chains confined in a slit geometry of two parallel repulsive walls, two inert walls, and for the mixed case of one inert and the other one repulsive wall, was performed. Taking into account the well known correspondence between the field theoretical O(n)-vector model in the limit and the behaviour of long-flexible polymer chains in a good solvent, the investigation of a dilute solution of long-flexible ring polymer chains with the excluded volume interaction (EVI) confined in a slit geometry of two parallel repulsive walls was performed in the framework of the massive field theory approach at fixed space dimensions d = 3 up to one-loop order. For all the above mentioned cases, the correspondent depletion interaction potentials, the depletion forces and the forces which exert the phantom ideal ring polymers and the ring polymers with the EVI on the walls were calculated, respectively. The obtained results indicate that the phantom ideal ring polymer chains and the ring polymer chains with the EVI due to the complexity of chain topology and because of the entropical reason demonstrate completely different behaviour in confined geometries than linear polymer chains. For example, the phantom ideal ring polymers prefer to escape from the space not only between two repulsive walls but also in the case of two inert walls, which leads to the attractive depletion forces. The ring polymer chains with less complex knot types (with the bigger radius of gyration) in a ring topology in the wide slit region exert higher forces on the confining repulsive walls. The depletion force in the case of mixed boundary conditions becomes repulsive in contrast to the case of linear polymer chains.