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This paper reports grand canonical Monte Carlo computations on the diffuse double layer in an ionic system next to a uniformly charged plane surface. The boundary conditions and the grand canonical techniques are discussed. Calculations were carried out for the 1:1 restricted primitive model at several concentrations and over a range of surface charge densities. The results are compared with the modified Gouy–Chapman theory, and some remarks are also possible with respect to the modified Poisson–Boltzmann and the hypernetted chain approaches. At high concentrations and surface charge densities the counterions are packed closely at the surface and begin to show a layered structure. This results in a large electrostatic potential drop, but only very slight charge oscillations are observed in the solution. None of the theories seems able to describe this behavior.

This paper reports Monte Carlo (MC) calculations of the charge distribution and mean potential of the diffuse double layer for the restricted primitive model of 2:1 and 2:2 aqueous electrolytes next to a uniformly charged plane surface. In the latter case the parameters that we have used in the primitive model correspond also to 1:1 electrolytes in nonaqueous solvents. The MC results are compared with the modified Gouy-Chapman (MGC) and modified Poisson-Boltzmann (MPB) theories of these systems for surface charges up to 25 pC cm'1 2 3and electrolyte concentrations up to 0.5 M. When the counterions in the 2:1 system are singly charged, the success of the MPB theory and the relatively mild shortcomings of the MGC theory are similar to those found previously for 1:1 electrolytes. For doubly charged counterions in both the 2:2 and 2:1 systems, however, the MC results show the MGC theory to be totally inadequate; the MGC greatly overestimates the surface potential even at quite low surface charges and electrolyte concentrations. In fact, the MC diffuse-layer potential as a function of surface charge has an extremum, and oscillations occur in the ion densities at concentrations as low as 0.05 M. The MPB theory is successful in predicting some of these qualitative features but differs quantitatively from the MC results in several respects.

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