Distribution of ions between different dielectric media: Direct simulation of the Donnan equilibrium in the grand canonical ensemble

A modification of the original Grand Canonical Monte Carlo (GCMC) method to handle Donnan equilibrium is proposed that provides an equilibrium between two implicit-solvent bath electrolytes with different dielectric constants. A solvation energy penalty (described by the Born theory) and an electrical potential difference (Donnan potential) exist between the two baths, the 'system' under investigation and the 'reservoir'. These terms are deducted from the chemical potential of the 'reservoir', and the resulting chemical potential is used in the 'system'. The simulation performed with this chemical potential in the acceptance probabilities of the ion insertion/deletions is called Donnan GCMC and provides a thermodynamic state in the 'system' that is in equilibrium with the electrolyte in the 'reservoir'. The simulation provides the distribution of ions between the two baths (concentrations in both media) from a single run instead of a numerical procedure that requires several GCMC runs. Using individual ion insertion/deletions, the Donnan potential can be determined.