(451a) Individual and Mean Ionic Activity Coefficients: Insight from Molecular Dynamics Simulations

Aqueous electrolyte solutions are widely present in many technological, environmental, and biological phenomena. Understanding the thermodynamic behavior of such complex fluids is essential in carrying out in-depth phenomenological studies, particularly on a molecular level, as well as performing feasible design, optimization, and process simulations for industrial purposes. Mean ionic activity coefficients (MIAC) are unique properties of electrolyte solutions which quantify deviations from the ideal solution behavior. There are numerous experimental, theoretical, and simulation studies in the literature reporting MIAC for variety of symmetric and asymmetric aqueous salts, over wide ranges of concentrations and temperatures. Molecular dynamics (MD) simulations, in particular, have long been utilized for predicting various “collective” properties of electrolyte solutions, including among others, the MIAC.

Despite the presence of a fairly established framework for quantifying critical properties of aqueous electrolytes as neutral salts, there still remains a knowledge gap when it comes to breaking down the contributions of individual anions and cations to solution nonideality. This is rather unfortunate as understanding the behavior of individual ions and specifically quantifying their activity coefficients are of great interest in studying many electrochemical and biological phenomena. Unlike the experimental data reported for MIAC, the measurements¹ for individual ionic activity coefficients (IIAC) are rather controversial and not widely accepted. That is in part attributed to the extra thermodynamic hypotheses employed for the calculation of liquid junction potential in an electrochemical cell, which is a crucial quantity in measuring the IIAC. On the other hand, there are a number of simulation studies in the literature that have aimed at calculating IIAC for aqueous electrolytes from MD and Monte Carlo (MC) simulations. Most of these studies have utilized implicit-water simulations with variations of the primitive model for electrolytes in conjunction with MC, while only a few have used explicit-water MD simulations. Implicit-water simulations, though computationally favorable, fail to provide insight into the solution structure on a microscopic scale, as well as hydration of anions and cations. Furthermore, such simulations have shown not to render correct magnitudes for chemical potentials, despite predicting somewhat reasonable MIAC.

In this work, we propose a thermodynamically consistent methodology for the calculation of IIAC from explicit-water molecular dynamics simulations. We select four aqueous solutions, namely NaCl, KCl, NaF, and KF to calculate IIAC over wide ranges of concentrations up to the solubility limit, at 25 and 1 bar. The activity coefficients are calculated from deviation of chemical potentials at finite concentrations from an infinite dilution reference state. Chemical potentials are in turn obtained from free energy change for insertion of a single ion into the aqueous solutions. Although inserting a single ion into a neutral solution violates the electroneutrality, a static neutralizing background charge would naturally arise when using Ewald summation under periodic boundary conditions. The perturbation to the Hamiltonian of the system attributed to the added background charge would be vanished in the thermodynamic limit. Therefore, we perform multiple simulations for each concentration and extrapolate to infinite system size. The results for the MIAC from single ion insertions are consistent with the previous results from pair insertion^2,3, as well as with the experimental data⁴. IIAC results demonstrate only qualitative agreement with the experimental measurements¹ in terms of relative positions for activity coefficients of anions and cations in different solutions, but generally carry larger magnitudes. Furthermore, we will demonstrate that the gap between activity coefficients of anions and cations are narrower in systems with more tendency to form ion hydration, whereas larger such gaps are observed in solutions with stronger ionic association.

In another investigation, we have pursued calculations of IIAC and MIAC using implicit-water simulations. Two aqueous salts, namely NaCl and KCl are selected over similar concentration ranges as those considered for the explicit-water simulations. The single ion is placed in a dielectric continuum―representing implicitly the water molecules―with the number of existing anions and cations varying as per the target salt concentration. Two separate approaches have been undertaken: one with a constant relative permittivity (ε_r) equal to that of pure water, and the second approach with a concentration-dependent ε_r, calculated previously in our explicit-water simulations from total dipole moment fluctuations. The ε_r obtained from MD simulations agree well the experimental data, showing a linear decline versus square root of concentration in molality. In continuum with constant ε_r, the MIAC results show satisfactory agreement for NaCl and KCl solutions when compared to the experimental data. The results however reveal wrong positionings for the IIAC of Na⁺ and Cl^– in NaCl, while correct orders are observed for K⁺ and Cl^– in KCl. On the other hand, the simulations with concentration-dependent ε_r demonstrate a systematic negative deviation for both MIAC and IIAC for all ionic species in NaCl and KCl solutions.

References:

¹G. Wilczek‐Vera, E. Rodil, and J. H. Vera, On the activity of ions and the junction potential: Revised values for all data. AIChE journal, 2004, 50(2), 445-462.

²Z. Mester and A. Z. Panagiotopoulos, Mean ionic activity coefficients in aqueous NaCl solutions from molecular dynamics simulations, J. Chem. Phys. 2015, 142, 044507.

³Z. Mester and A. Z. Panagiotopoulos, Temperature-dependent solubilities and mean ionic activity coefficients of alkali halides in water from molecular dynamics simulations, J. Chem. Phys. 2015, 143, 044505.

⁴R. A. Robinson and R. H. Stokes, Electrolyte solutions. Courier Corporation: 2002.