Effect of Geometrical Constraint on Conformational Properties of a Polymer Chain

TL;DR

This study investigates how geometrical constraints affect the conformational behavior of an infinitely long semiflexible polymer chain in two dimensions, considering factors like bending energy, persistence length, and polymerization conditions.

Contribution

It provides exact critical fugacity values and analyzes the impact of constraints on the chain's persistence length and bending energy in a two-dimensional setting.

Findings

Calculated exact critical fugacity for polymerization under constraints.

Determined maximum and minimum persistence lengths for constrained chains.

Identified maximum bending energy per turn for various constraint separations.

Abstract

In this paper, we analyze the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The constraints are two impenetrable stair shaped surface and for two dimensional space, the surface is a one dimensional line. The semiflexibility of the chain is accounted by introducing a Boltzmann weight of bending energy required to produce each turn in the chain and good solvent condition was accounted by using self avoiding walk model of the chain. We have calculated exact critical value of step fugacity required for polymerization of an infinitely long polymer chain confined in between the constraints for different values of separation between the constraints for directed version of the model. We have also calculated possible maximum, minimum values of the persistent length for such chains and the maximum value of bending energy required for each turn in the chain for few values of separation between the constraints.