From restricted towards realistic models of salt solutions: Corrected Debye–Hückel theory and Monte Carlo simulations

Abstract

The properties of bulk salt solutions over wide concentration ranges are explored by a combination of simple physical theory and Monte Carlo (MC) simulations. The corrected Debye–Hückel (CDH) theory which incorporates ion size effects in a linear response approximation is extended to yield free energy and other thermodynamic properties by integration of the chemical potential over concentration. Charging integration which is usually used to obtain an electrostatic contribution of total free energy of electrolytes is avoided in this new direct approach. MC simulations are performed with a modified Widom particle insertion method, which also provides directly the ionic activity coefficients. The validity of the CDH theory is tested by comparison with the MC simulation data for 1:1, 2:1, 2:2 and 3:1 restricted primitive model (RPM) electrolytes over a wide concentration range and at various ion sizes. Mean ionic activity and osmotic coefficients calculated by the CDH theory in RPM approximation of electrolyte are fitted to experimental data by adjusting only a mean ionic diameter. Good fits up to 1 molal (m) concentration are obtained for a large number of salt solutions. MC simulations data for unrestricted primitive model (UPM) of 1:1 and 2:1 electrolytes are also fitted to the experimental data by varying the cation radius while keeping the anion radius fixed at a crystallographic value. The success of this approach is found to be salt specific. For example good fits up to 2 and 3.5 m concentrations were obtained for LiCl and LiBr, respectively. However in the case of less dissociated salts such as NaCl and KI the experimental data could only be fitted up to one molal concentration. Possibility of extending the applicability range of the CDH theory to concentrations >2 m is explored by including a concentration dependent dielectric constant as measured in experiments. Mean ionic activity coefficients for a number of salts could successfully be fitted up to 3 m concentration by adjusting only a mean ionic diameter. Difficulties encountered in simultaneously fitting the mean ionic activity and osmotic coefficients at salt concentrations > 2 m are discussed.