Bending stiff charged polymers: the electrostatic persistence length

TL;DR

This paper derives a simple analytical formula for the electrostatic persistence length of charged polymers, accurately accounting for nonlinear effects and counter-ion condensation, improving upon classical models and refining DNA rigidity estimates.

Contribution

It introduces a new analytical expression for electrostatic persistence length that aligns well with numerical Poisson-Boltzmann results, addressing limitations of previous theories.

Findings

The formula agrees with numerical Poisson-Boltzmann results.

Counter-ion condensation significantly affects persistence length.

The typical DNA persistence length is overestimated by 20%."

Abstract

Many charged polymers, including nucleic acids, are locally stiff. Their bending rigidity -- quantified by the persistence length --, depends crucially on Coulombic features, such as the ionic strength of the solution which offers a convenient experimental route for tuning the rigidity. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. Specified to double-stranded DNA, our work reveals that the widely used bare persistence length of 500\,\AA\ is overestimated by some 20%