(a) Radial distribution functions for force field Cs9I1 at 0.31 m and four different values of the LJ energy scaling factor λɛ. Dotted(black), dashed(red), dot-dashed(blue), and solid(green) lines correspond to values of λɛ 0.5, 0.6, 0.8, and 1.0, respectively. The different RDFs for all components of the solution, anions, cations, and water are shown. (b) The different Kirkwood-Buff integrals for Cs9I1 at 0.31 m and four different parameters of the scaling factor λɛ as a function of the upper integral boundary. Lines, colors and labeling are the same as in panel (a). (c) The composite Kirkwood-Buff integrals G cc and G c w as defined in Eq. (5) for Cs9I1 at 0.31 m, which enter the calculation of the activity derivative in Eq. (4a). The curves are shown again for four different values of λɛ, with line and color coding as in panel (a). The insets zoom into the values for λɛ = 0.6, 0.8, 1.0. All Kirkwood-Buff integrals are given in units nm3.
Results for the activity derivative a cc for different values of the scaling prefactor λɛ at 0.31 m for (a) the Na+-salts, (b) the K+-salts, and (c) the Cs+-salts, respectively. The lines are the respective experimental data as denoted by the labels, the data points denote simulation results. In all panels, the inset image shows the sizes of all ion-pairs with all cation radii increased by 0.04 nm (see text for discussion), while the inset graph shows two representative RDFs, for λɛ = 1 (see text). In panel (a), the label KBBF denotes an alternative Kirkwood-Buff-derived force field42 (see text). In panel (c), results are shown for all combinations of two force field sets for Cs+ and I−. In panel (b) the error bar is shown only for one data point for clarity. The error bar is similar for all data points.
Activity derivatives a cc for the salts KF and NaF as a function of the LJ ion-water energy parameter ɛ iO with LJ radius σ iO constrained to the line on which the experimental ion solvation free energy is reproduced, similar to our previous study in Ref. 48. For K11F data the K11 force field is fixed and ɛ FO is varied, for KCl the Cl force field is fixed and ɛ KO is varied. The horizontal lines correspond to the experimental values for KCl and KF. The results are shown for 1.03 m (1 M) as in Ref. 48. For KF, results are also shown for 0.31 m (0.3 M). All data are given for unmodified mixing rules, i.e., λɛ = 1, except for K11F at 1 M with ɛ FO = 0.1585 kJ/mol, where additional data for the values λɛ = 1.2 and λɛ = 1.5 are shown (cyan filled squares).
Activity derivatives a cc for the KF solutions as a function of the scaling factors λɛ and λσ. Note that only one of the factors is varied, the other is fixed at unity. The line shows the respective experimental value. The concentration is 0.31 m (0.3 M).
Cation-anion radial distribution functions g +−, Lennard-Jones potentials V LJ , and total (Lennard-Jones plus Coulomb) potentials V LJ + V C for the salt K11F5 at 0.31 m (0.3 M). Note that V LJ (red dotted lines) has been magnified 10 times for clarity. The uppermost panel shows results for unmodified mixing rules with scaling factors λɛ, λσ = 1.0. The left and right panels correspond to the modifications λɛ > 1, and λσ > 1, respectively, where the other scaling factor is unity.
(a) Experimental activity derivatives a cc as a function of the difference r + − r −, where r + and r − denote the Pauling radii of the cation and anion, respectively. All salt solutions considered in this work are shown at concentrations of 0.31 m (0.3 M) (upper panel) and 1.03 m (1 M) (lower panel), respectively. The color-coding is for fixed cations. (b) Same as in (a), except for the color-coding which corresponds to fixed anions. (c) Experimental activity coefficients as a function of r + − r − for different monovalent and divalent salt solutions at 0.31 m (0.3 M) (upper panel) and 1 m (lower panel) concentration.
Ion-water and bare ionic parameters for the anions and cations used in the current MD simulations. The parameters for Na+, Cl−, and Br− are taken from Refs. 51 and 52, while the rest is taken from Ref. 48. The Pauling radii of the ions are also given.60
Optimal λɛ, λσ scaling prefactors for the cation-anion combinations studied in this work.
Excess coordination numbers for the optimized scaling prefactors given in Table II from our simulation results, denoted as = ρ c G cc and = ρ w G c w , and experimental values as taken from the analysis in Ref. 23, denoted by and . Most data are shown for 0.31 m, numbers in parentheses correspond to solutions of 1 m concentration. The activity derivatives are computed through Eq. (4a) using the , MD data, and can be compared to the experimental data given in Refs. 23,64, denoted as 64 and 23, respectively.
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