Elasticity of semiflexible polymers in two dimensions

TL;DR

This paper provides an exact analytical study of the entropic elasticity of two-dimensional semi-flexible polymers like DNA, including force-extension relations and interactions with nematic fields, using the worm-like-chain model.

Contribution

It derives an exact analytical expression for the partition function and force-extension relation of 2D semi-flexible polymers, extending understanding of their elastic behavior.

Findings

Exact partition function derived using Mathieu functions.

Force-extension relation characterized in the long chain limit.

Applications to polymer-nematic field interactions and order parameters.

Abstract

We study theoretically the entropic elasticity of a semi-flexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semi-flexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.