Ring polymers in confined geometries

TL;DR

This paper studies how ring polymers behave in confined spaces and near colloidal particles, revealing that their topology causes different forces compared to linear polymers, with implications for understanding polymer-surface interactions.

Contribution

It provides a theoretical analysis of depletion forces exerted by ring polymers with and without excluded volume interactions in confined geometries using field theory.

Findings

Ring polymers exert different forces than linear polymers in confinement.

Excluded volume interactions significantly affect depletion forces.

Topology influences polymer-surface interaction behavior.

Abstract

The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size was performed. Taking into account the correspondence between the field theoretical $\phi^4$ $O(n)$-vector model in the limit $n\to 0$ and the behaviour of long-flexible polymers in a good solvent, the correspondent depletion forces and the forces which exert phantom ideal ring polymers and ring polymers with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions $d$=3 up to one-loop order. Besides, taking into account the Derjaguin approximation, the depletion forces between big colloidal particle and a wall and in the case of two big colloidal particles were calculated. The obtained results indicate that phantom ideal ring polymers and ring polymers with EVI due to the complexity of chain topology and for entropical reasons demonstrate a completely different behaviour in confined geometries compared with linear polymers.