Counter-ion density profile around charged cylinders: the strong-coupling needle limit

TL;DR

This paper investigates counter-ion condensation around charged rods in the strong-coupling needle limit, combining Monte Carlo simulations and analytical methods to understand ion evaporation and density profiles.

Contribution

It provides a comprehensive analysis of counter-ion behavior in the strong-coupling regime, emphasizing the universal nature of ion evaporation across coupling strengths.

Findings

Excellent agreement between simulations and analytical calculations.

Counter-ion evaporation is a universal phenomenon in both weakly and strongly coupled systems.

The strong-coupling needle limit reveals distinct ion density profiles compared to the thick rod case.

Abstract

Charged rod-like polymers are not able to bind all their neutralizing counter-ions: a fraction of them evaporates while the others are said to be condensed. We study here counter-ion condensation and its ramifications, both numerically by means of Monte Carlo simulations employing a previously introduced powerful logarithmic sampling of radial coordinates, and analytically, with special emphasis on the strong-coupling regime. We focus on the thin rod, or needle limit, that is naturally reached under strong coulombic couplings, where the typical inter-particle spacing $a'$ along the rod is much larger than its radius R. This regime is complementary and opposite to the simpler thick rod case where $a'\ll R$. We show that due account of counter-ion evaporation, a universal phenomenon in the sense that it occurs in the same clothing for both weakly and strongly coupled systems, allows to obtain excellent agreement between the numerical simulations and the strong-coupling calculations.