Counterion Density Profile around Charged Cylinders: The Strong-Coupling Needle Limit

Abstract

Charged rod-like polymers are not able to bind all their neutralizing counterions: a fraction of them evaporates, while the others are said to be condensed. We study here counterion 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 intercounterion 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' ≪ R. We show that due account of counterion evaporation, a universal phenomenon in the sense that it occurs in the same clothing for both weakly and strongly coupled systems, allows one to obtain excellent agreement between the numerical simulations and the strong-coupling calculations.