Some Rigorous Results on Semiflexible Polymers. I. Free and confined polymers

TL;DR

This paper introduces models for semiflexible polymers with high rigidity, analyzes their macroscopic behavior, and provides bounds on free energy when confined in narrow tubes.

Contribution

It rigorously characterizes the scaling limit of semiflexible polymers and derives bounds on free energy for confined configurations.

Findings

Determined the macroscopic scaling limit of semiflexible polymers.

Established bounds on free energy for polymers confined in narrow tubes.

Provided a rigorous mathematical framework for semiflexible polymer models.

Abstract

We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated to the gradient-gradient correlations, called the persistence length, being of the same order as the polymer length. We determine the macroscopic scaling limit, from which we deduce bounds on the free energy of a polymer confined inside a narrow tube.