The counterion density profile in the dilute limit (no coions). The dotted lines demarcate the limiting behaviors in Eqs. (23) and (24) . The wall charge is positive and the counterions have negative charge. As R increases, the profile takes the exponential shape.
The counterion density profile near a charged wall. R = 0 corresponds to point ions. The relevant lengths are: κ−1 = 0.3 nm, λ B = 0.72 nm, and λGC = 0.09 nm.
The coion distribution at a charged wall corresponding to the system in Fig. 2 . The coions are in excess to neutralize the inverted charge. Note that the density profile exhibits oscillations.
Electrostatic potential near a charged wall corresponding to the system in Fig. 2 . The minimum corresponds to a point of vanishing electrostatic field.
Counterion density profiles. The system parameters are: λGC = 0.09 nm and λ B = 0.72 nm. The symbols designate the simulation data points and the lines are the numerical results for the FSPB equation.
The coion density profile for R = 0.8 nm obtained from the simulation (symbols) and the FSPB equation (solid line). The remaining parameters are as in Fig. 7 .
Configuration snapshot of counterions adsorbed on the charged wall at x < 0.35 nm. The diameter of particles is σ = 0.5 nm and is selected arbitrarily for visualization. The configuration on left is for R/λ B = 0.14 and the one on the right is for R/λ B = 1.1. The 2D densities are ρ2d = 2.34 nm−2 and ρ2d = 2.68 nm−2, respectively. For comparison, the surface charge density is σ c = 2.50 nm−2. The system parameters are as in Fig. 7 .
Correlation function for counterions in the lateral plane adjacent to the wall. The layer thickness is 0.35 nm. The remaining parameters are the same as in Fig. 7 . The dashed lines guide the eye.
The nearest neighbor separation distribution for different ω(r) functions. R = 0.8 nm and the same parameters as in Fig. 7 .
Counterion distribution function for symmetric solution with ion charge ±eZ. The remaining parameters are the same as in Fig. 7 . The circles are the simulation data points and the lines are obtained from the FSPB.
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