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.

Counter-Ions Between or at Asymmetrically Charged Walls: 2D Free-Fermion Point

“…Conversely, in dimension ν = 3, the standard argument on the asymptotic validity of meanfield may well apply. We note that it is backed up by recent accurate Monte Carlo results [29]. As concerns the constrained model, the net charge density on each of the two lines is nonzero for every finite distance d and vanishes only at d → ∞.…”

Counterion density profile around a charged disk: From the weak to the strong association regime

“…This behavior is different from the prediction of the Poisson-Boltzmann equation: the mean field regime does not applies even at large distances from the inner disk. This can be contrasted to the situation for a three dimensional system of a charged cylinder, where at large distances the density profile behaves as the mean field prediction [20] a fact that can be understood as a sign that the coupling is independent of the density in two dimensions.…”

“…An important rationale then for condensation is that this particle is neither condensed nor evaporated and, thus, the integrated charge will exhibit a constant slope form when this occurs. This situation does not take place in the three-dimensional case [20,26,27].…”

“…The code uses the so-called centrifugal sampling [27], that uses y = log(r/R) as variable, necessary to sample large box sizes (D ≫ R). Also, besides the usual Monte Carlo moves, the codes implements moves that exchanges particles between the condensed and un-condensed populations (y −→ ∆ − y), necessary to properly sample the configuration space [20]. The ions are point-like particles of a single type in order to avoid the introduction of hard-core interactions.…”

“…Furthermore, we know from previous works in mean field [2,20,26,27] that the ratio of condensed ions is the well-known Manning relationship f M . In other words, from eq.…”