FIG. 6.

(a,b) The mean residence time τ_p (bottom two lines) for a counterion to stay within a distance of r_c +δ (r_c=counterion radius) from the surface of the respective phosphate group, and the mean residence time τ_⊥ (upper two lines) for a counterion to stay within a radial distance of r_c+δ from the polyelectrolyte surface. Solution conditions are (a) Na⁺ and (b) Mg²⁺, with salt concentrations c⁰=0.001M (solid lines) and 0.1M (dashed lines). Both τ_⊥ and τ_p are scaled as number of Monte Carlo steps. (c–f) Three characteristic distances of counterions (in unit of angstrom): the distance Δp of tightly bound counterions from the respective phosphate sphere centers (black lines); the distance Δz in the axis direction (gray lines); and the radial distance Δr of counterions from DNA axis (light gray lines). (c) [Na⁺]=0.001M; (d) [Na⁺]=0.1M; (e) [Mg²⁺]=0.001M; (f) [Mg²⁺]=0.1M. The counterions, which reside in the layer with thickness δ=2 Å, are tracked in the simulations, and the tracking process is performed after the system reaches thermal equilibrium.