The bending energy of a semi-flexible polymer chain and the polygons of the polymer chain

TL;DR

This paper models semi-flexible polymers using random walks on lattices, deriving a simple relation for the minimum bending energy that incorporates dimensionality, step fugacity, and persistence length.

Contribution

It introduces a lattice-based model for semi-flexible polymers and derives a simple formula for the minimum bending energy considering key physical parameters.

Findings

Derived a relation for minimum bending energy involving dimensionality and persistence length

Quantified the average chain length between bends in the model

Provided insights into the energy costs of polymer conformations

Abstract

We consider random walk model of a semi-flexible polymer chain on a square and a cubic lattice to enumerate conformations of the polymer chain in two and three dimensions, respectively. The bending energy of the chain is assumed as the key factor which controls the minimum average length of the chain in between two successive bends in the chain; and the average length of the chains per unit bend is defined as the persistence length of the polymer chain. It has been found that the minimum energy required to bend the chain is expressed in the form of simple relation which includes space dimensionality, step fugacity and persistence length.