The Distribution of Ions between a Bulk Electrolyte Solution and Charged Microcapillaries in Solvents with Low Dielectric Constant

The distribution of ions between charged cylindrical micropores modeling an adsorbing material and a bulk electrolyte was calculated. For this purpose the Grand Canonical Monte Carlo method and the method based on solution of the nonlinear Poisson-Boltzmann equation were utilized. The focus was on the effect of the solvent, characterized here merely by its dielectric constant. The Donnan exclusion coefficient and mean activity coefficient of an electrolyte confined in a microcapillary were calculated as functions of the electrolyte concentration and the dielectric constant of the solvent. The exclusion coefficient was found to decrease with increasing electrolyte concentration and with decreasing dielectric constant of the solvent. In other words, the desalination mechanism becomes very inefficient in solvents with dielectric constant lower than that of water. In comparison with Monte Carlo simulations the Poisson-Boltzmann theory was able to predict correct trends for the Donnan exclusion coefficient, but it grossly overestimated Monte Carlo results. The microscopic picture which emerged on the basis of the distributions of small ions in the microcapillary was helpful in explaining these results.