Free energy of cylindrical polyions: analytical results

TL;DR

This paper derives an exact analytical expression for the grand potential of a charged cylindrical polyion in a binary electrolyte within the Poisson-Boltzmann framework, relevant for nucleic acid processes.

Contribution

It provides the first low-salt asymptotic analytical solution for the Coulombic grand potential of cylindrical polyions, extending understanding within the PB theory.

Findings

Exact low-salt asymptotic expression derived

Results applicable for arbitrary polyion charges with small radius

Enhances understanding of nucleic acid electrostatics

Abstract

Within the Poisson-Boltzmann (PB) framework useful for a wealth of charged soft matter problems, we work out the Coulombic grand potential of a long cylindrical charged polyion in a binary electrolyte solution of arbitrary valency and for low salt concentration. We obtain the exact analytical low-salt asymptotic expression for the grand potential, derived from known properties of the exact solutions to the cylindrical PB equation. These results are relevant for understanding nucleic acid processes. In practice, our expressions are accurate for arbitrary polyion charges, provided their radius is smaller than the Debye length defined by the electrolyte.