Off-center charge model revisited: Electrical double layer with multivalent cations.

The off-center charge model of ions is a relatively simple model for introducing asymmetry in Coulomb interaction while retaining the simplicity and convenience of the spherical hard core geometry. A Monte Carlo simulation analysis of the planar electric double layer formed by this ionic model for 1+:1- valence systems [S. Lamperski et al., Langmuir 33, 11554-11560 (2017)] is extended to include solutions of multivalent (2+, 3+) hard spherical cations and single valence (1-) hard spherical anions near a uniformly charged, planar electrode. The solvent is modelled as a uniform dielectric continuum with a dielectric constant equal to that of the pure solvent, viz., the primitive model. Results are reported for the ion density, the cation charge profile, and the electrostatic potential profile at 1 mol/dm3 salt concentration. Additionally, the double layer potential drop, that is, the electrode potential, and the integral and the differential capacitances are computed as functions of the electrode surface charge density. The latter two quantities show an expected asymmetry as long as the cation valence is not too great and the charge of the off-center ion cannot approach too close to the electrode surface. It is unusual that the integral and differential capacitances are negative for high valence cations and a negatively charged electrode when the off-center charge is large and can be very near the surface of the electrode. The corresponding electrode potential versus surface charge density curve becomes non-monotonic and shows a change of slope, and thus the resultant integral and differential capacitances can become negative. This nonphysical result is the result of an incipient singularity when a large positive charge is too near a negatively charged electrode. Overall, the off-center charge model suggests a useful recipe to model electrical asymmetry within the broader context of the primitive model provided that the off-center charge is not too near the surface of the electrode.