Force-Extension Relations for Polymers with Sliding Links

TL;DR

This paper investigates how sliding links in polymers affect their force-extension behavior, deriving exact and scaling results for different regimes and chain types, enhancing understanding of topological effects in polymer physics.

Contribution

It provides exact solutions for single-loop force-extension relations and extends the analysis to self-avoiding chains using scaling arguments.

Findings

Exact expressions for average end-to-end separation in single-loop phantom chains.

Linear response relates to unstressed chain properties.

Large force regime described by Pincus--de Gennes blobs with topological constraints.

Abstract

Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable size. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation: The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus--de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.