Finite-Width Bundle is Most Stable in a Solution with Salt

TL;DR

This study uses a mean-field approach to analyze the stability of finite-width polyelectrolyte bundles in salt solutions, revealing that charge distribution and long-range electrostatic effects prevent indefinite bundle growth.

Contribution

It introduces a local self-consistent method to determine counter-ion distribution inside polyelectrolyte bundles, highlighting the role of electrostatics in finite bundle stability.

Findings

Finite-width bundles are most stable in salt solutions.

Charge distribution remains inhomogeneous within the bundle.

Long-range electrostatic effects prevent infinite bundle growth.

Abstract

We applied the mean-field approach to a columnar bundle assembled by the parallel arrangement of stiff polyelectrolyte rods in a salt bath. The electrostatic potential can be divided into two regions: inside the bundle for condensed counter-ions, and outside the bundle for free small ions. To determine the distribution of condensed counter-ions inside the bundle, we use a local self-consistent condition that depends on the charge density, the electrostatic potential, and the net polarization. The results showed that, upon bundle formation, the electric charge of polyelectrolytes, even those inside the bundle, tend to survive in an inhomogeneous manner, and thus their width remains finite under thermal equilibrium because of the long-range effect of charge instability.