The grand canonical ensemble Monte Carlo method applied to the electrical double layer

The grand canonical ensemble Monte Carlo method is applied to the electrical double layer, using a discrete surface charge distribution and the restricted primitive model for the electrolyte. A systematic examination of the effects of the dimensions of the basic Monte Carlo cell shows that the usual minimum image technique, for determining the potential energy of the system, must be supplemented by long range corrections. Alternatively, very large dimensions or numbers of ions must be employed. The calculated ion distribution functions are compared with the Gouy–Chapman theory for bulk electrolyte concentrations up to 0.2 C/m2. The Gouy–Chapman theory compares very well with the Monte Carlo results for electrolyte concentrations up to 0.1 mole/dm3, but quantitatvive differences appear at 1 mole/dm3. These differences are more pronounced at 2 mole/dm3 for which the Monte Carlo results indicate an inversion of the positive and negative charge distribution functions.