Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations

Abstract

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛr) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛr, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛr show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛr. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛr. Moreover, even in simulations with constant ɛr for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

Activity Coefficients and Solubilities of NaCl in Water–Methanol Solutions from Molecular Dynamics Simulations

“…Mean ionic activity coefficients (MIACs) and solubilities have been typically obtained in simulations using variations of the thermodynamic integration technique. − ,− The MIACswhich quantify deviations from ideal solution behaviorare obtained from the differences between chemical potentials at a finite concentration (μ) and at a standard state reference state (μ † ). We have recently demonstrated that a single ion insertion technique accompanied by a counteracting neutralizing background can provide significant insights into the behavior of individual ions , and have obtained individual ion activity coefficients (IIACs) in qualitative agreement with available experimental data. − The IIACs reveal disparities between the properties of anions and cations in solution and describe in detail the interactions between ions and solvent molecules.…”

“…We did not pursue this formal extrapolation here, in order to limit the computational cost of the study, but have investigated system size effects at a single composition, as indicated at the end of the Results and Discussion section. For the MIACs, any neutralizing-background or finite-size effects are expected to be small based on our prior studies. , …”

“…To obtain MIACs, we first computed IIACs following the framework developed in our earlier work. , The activity coefficient of an individual ion, γ i , in solution can be calculated from where μ i is the chemical potential in solution, μ i † is the standard state chemical potential, and m i is the (dimensionless) molality. The chemical potential μ i is calculated here from single ion insertions. , Briefly, at each of these ternary compositions, a single cation (Na + ) or anion (Cl – ) is inserted from an ideal gas state into the solution. Such an insertion must be accompanied by a neutralizing background to preserve electroneutrality.…”

“…The reference state chemical potentials μ i † were obtained by enforcing the Debye–Hückel limiting slope, as explained in our previous studies. , Thus, simulation results for μ i at the lowest salt concentration studied for each mixed-solvent composition were forced to pass through the Debye–Hückel limiting line with slope calculated from where q e is the elementary charge, N A is Avogadro’s number, ρ is the solution density, ε is the relative permittivity of the solution, ε 0 is the vacuum permittivity, and T is the temperature. The relative permittivity, ε, is calculated from total dipole moment fluctuations as presented in prior work. , The solubility was obtained from the condition of equality of the total chemical potential in solution to that of the pure NaCl solid crystal. The chemical potential of crystal NaCl (μ crystal ) using the JC force field has been previously calculated as −384.06 kJ/mol using the Einstein crystal method, and this value was adopted here.…”

“…Thus, results from the present study are pure predictions using unmodified force fields from the literature. IIAC values were calculated from the single ion insertion technique, as previously presented in our recent publications, , and MIACs were obtained from the corresponding IIACs. The solubility of NaCl in the ternary system at each concentration was obtained by matching the chemical potential of NaCl in solution with that of the solid crystal (μ crystal ), previously calculated from the Einstein crystal method …”