Divergence Of Persistent Length Of A Semiflexible Homopolymer Chain In The Stiff Chain Limit

TL;DR

This paper analytically investigates the divergence of the persistent length of a semiflexible homopolymer chain in the stiff chain limit across different lattice dimensions, revealing a universal divergence pattern independent of space dimension.

Contribution

It provides a detailed analytical calculation of the persistent length divergence in the stiff chain limit for directed walk lattice models in 2D and 3D, extending previous work.

Findings

Persistent length diverges as (1 - g_c)^{-1}

Divergence pattern is independent of spatial dimension

In the stiff limit, the polymer behaves like a rigid rod

Abstract

In this brief report, we revisit analytical calculation [Mishra, {\it et al.}, Physica A {\bf 323} (2003) 453 and Mishra, NewYork Sci. J. {\bf{3(1)}} (2010) 32.] of the persistent length of a semiflexible homopolymer chain in %the extremely stiff chain limit, {\bf $k\to0$ (where, $k$ is stiffness of the chain)} for directed walk lattice model the extremely stiff chain limit, $k\to0$ (where, $k$ is stiffness of the chain) for directed walk lattice model in two and three dimensions. Our study for two dimensional (square and rectangular) and three dimensional (cubic) lattice case clearly indicates that the persistent length diverges according to expression $(1-g_c)^{-1}$, where $g_c$ is the critical value of step fugacity required for polymerization of an infinitely long linear semiflexible homopolymer chain and nature of the divergence is independent of the space dimension. This is obviously true because in the case of extremely stiff chain limit the polymer chain is a one dimensional object and its shape is like a rigid rod.