Monte Carlo and Density Functional Theory Study of the Electrical Double Layer: The Dependence of the Charge/Voltage Relation on the Diameter of the Ions

Abstract

According to the well known Gouy–Chapman theory (GCT) for ions modeled as charged hard spheres that are of equal diameter, the diffuse layer potential (DLP), the potential at the distance of closest approach, is independent of the ionic diameter. In this paper, the question of the dependence of the diffuse layer DLP on the ion diameter is examined by means of a Monte Carlo (MC) simulation for three values of the diameter, d=2, 3 and 4.25 Å, for three ion concentrations, 0.1, 1 and 2 M, for the cases of 1:1 and 2:1 salts. For 1:1 salts at the lower concentrations, the dependence of the MC DLP on d is found to be rather weak. Thus, for these salts, the GCT is reasonably successful on this point even though the actual GCT values for the DLP are less satisfactory. For 1:1 salts, density functional theory (DFT), which is generally more accurate than the GCT, gives a dependence of the DLP on d that, at large electrode charge, is too great. The MC results for 2:1 salts show an appreciable dependence of the DLP on d at higher concentrations, especially when the divalent ions are the counterions. For these salts the GCT fails to describe both the actual values of the DLP and its d dependence; here DFT is more successful. Interestingly, at high concentrations, for 2:1 salts the MC and DFT (but not the GCT) values of the DLP can have the opposite sign to that of the electrode charge.