Environment and Resource System Engineering, Kyoto University, Kyoto , Japan

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1 Supplementary Material Molecular Dynamics Study of Salt Solution Interface: Solubility and Surface Charge of Salt in Water Kazuya Kobayashi, 1 Yunfeng Liang, 1, * Tetsuo Sakka, and Toshifumi Matsuoka 1, * 1 Environment and Resource System Engineering, Kyoto University, Kyoto , Japan Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto , Japan * Corresponding author: Yunfeng Liang y_liang@earth.kumst.kyoto-u.ac.jp * Corresponding author: Toshifumi Matsuoka matsuoka@earth.kumst.kyoto-u.ac.jp 1

2 1. Sensitivity Analysis on Solubility Calculation by Chemical Potential Calculation Interpolating Gibbs free energy value into polynomial to get the chemical potential function with the number of ion pairs, we have to choose a narrow range (fitting window) of dataset because the chemical potential function cannot be always a single polynomial function or a single linear function. Here, in this supporting information, the sensitivity analysis on the dataset range at the time of fitting was executed. The whole of data is shown in Table S1. Focusing on the method in the manuscript (Method A), we divided the Gibbs free energy into an ideal and a residual contribution. First, we obtained the derivative of the ideal part numerically using the number density of solutions at different concentrations. In this case, we fix the fitting window 0.56 mol/kg to 7.78 mol/kg, which is close to that used by Aragones et al. The number density as function of the number of the sodium chloride pairs was obtained: N / A N N (1) This relationship is used in the calculation of the ideal part with the equation below 1 : solution id A solution k BT ln( ) k BTV ( H ) O N () T, P, N _ H O where V is the partial molar volume of sodium chloride, which is represented by V V N. T, P, N H O The ideal chemical potential is then employed throughout the analysis in this supporting information. Second, we obtained the residual free energy and fit it with a quadratic function of sodium chloride ions. Here, we will show that the fitting parameters are dependent on the fitting window. Since the calculated solubility values from direct calculation with JC model were 5.50 mol/kg in Aragones et al. s work 1, 6.0 mol/kg (this work) and 7.7 mol/kg in Joung and Cheatham III s one, respectively. Our calculated value is almost at the center of all calculations. At this concentration, there are about 56 pairs with 500 water molecules. The residual Gibbs free energy values around 56 should be used when we fit them into polynomial. Therefore, our first choice of the fitting window is from 5.77 mol/kg to 7.78 mol/kg. In this case, the residual Gibbs free energy as function of the number of sodium chloride ion pairs was obtained as: G N 0.488N N 1589 (3) res

3 The residual chemical potential as function of the number of sodium chloride pairs was the derivative of the residual Gibbs free energy: N N (4) res The total chemical potential of in solution is simply a summary of the ideal and residual chemical potentials. When the chemical potential of in the solution phase is equal to the chemical potential of the solid phase, the concentration of the solution system is the solubility. Figure S1 shows the chemical potential value as function of the ion pairs together with chemical potential of solid. The calculated solubility (with this particular fitting window) is around 6.4 mol/kg (Table S). Figure S1 also presents some other data of chemical potential values obtained with other fitting windows. The difference is small, if the fitting window is varied a little (towards the calculated solubility from the direct calculation). For example, the calculated solubility is around 6.5 mol/kg, if the fitting window is from 6.11 mol/kg to 7.78 mol/kg. If instead, we selected the full range of our calculated data, the calculated solubility is around.79 mol/kg. In the intermediate range there are some fitting windows (e.g. from 5.56 mol/kg to 7.78 mol/kg), the calculated chemical potential seems unphysical, that is, the chemical potential value decrease with increasing concentration. Because it is difficult to equilibrate the system above 7.0 mol/kg and the curvature in the chemical potential below 3.0 mol/kg is significant, we have chosen a fitting range of mol/kg. The obtained solubility value is 3.48 mol/kg. This value is very close to the previous one (3.7 mol/kg) calculated by osmotic ensemble Monte Carlo 3. The value of the chemical potential obtained from cubic fit (for the full range of our calculated data) is also shown in Figure S1. As can be seen, the difference with the results of the second order polynomial function fit is quite small and the solubility value is hardly affected by the choice of the polynomial. This further verifies the importance of the fitting window. To be sure that our calculations are indeed correct, we did the same analysis for the Aragones et al. s data, which was represented in Table VIII of Ref. [1]. As shown in Figure S and Table S3, similar conclusion can be reached. In addition, we calculated the free energy of a system with molecules of and 70 molecules of water as Aragones et al. used in their Monte Carlo calculations. As shown in Table S4, the data are in good agreement with each other within some uncertainties. 3

4 Table S1: Breakdown of calculated data from MD simulations, where the energy unit is (kj/mol) and the unit (N/Å) is used for number density, ρ. N ρ Gsolution A integral A res LJ,ref pvsolution A id solution m (mol/kg)

5 Figure S1. Calculated chemical potential of the in-solution phase as a function of sodium chloride ion pairs. Figure S. Calculated chemical potential of the in-solution as a function of sodium chloride ion pairs (using the data from Table VIII in Ref. 1). 5

6 Table S Calculated solubility values with changing concentration range (this work): Nan indicates chemical potential value get negative tendency with increasing concentration and N indicate the number of datasets used to fit polynomial. Concentration range [mol/kg] N Solubility [mol/kg] Nan Table S3 Calculated solubility values with changing concentration range (using the data from Table VIII in Ref. 1). Concentration range [mol/kg] N Solubility [mol/kg] a Nan a Calculated value from chemical potential is 4.8 mol/kg in the Ref. [1]. Table S4: Comparison between MD (This work) and Aragones et al. (01) 1, where the system include 70 water molecules and pairs of and the energy unit and the number density unit are kj/mol and (N/Å), respectively. ρ G solution A integral A res LJ,ref pv solution A id solution This work Aragones (01)

7 Furthermore, we examined the difference between the current method (Method A) and the original simplified method proposed by Sanz and Vega (Method B) 4. Method A was used in the manuscript, where the curvature of chemical potential was well reproduced. In Method B, we fitted the whole Gibbs free energy, Gres+Gideal, into nd order polynomial function. Fig. S3 shows the comparison between the two methods for the fitting windows from 0.56 mol/kg to 7.78 mol/kg and from 5.77 mol/kg to 7.78 kg/mol, respectively. We found that the solubility value itself was not affected by the method to calculate the chemical potential function. Fig. S3 also shows the chemical potential curve resulted from a fitting range of mol/kg. Similar to the calculated solubility, the overall chemical potential is very close to the previous calculations 1,5. Note: the solubility value from OEMC and the curve from OEMC were reported in two different papers (Ref. 3 and 5). The former used the Ewald summation (similiar to our work) and latter used the generalized reaction field. Figure S3. Calculated chemical potential of the in-solution as a function of sodium chloride ion pairs with comparisons of the two methods: Aragones et al. (01), Method A, and Sanz and Vega (007), Method B. 7

8 . Improving the Statistics on Solubility Calculation by Chemical Potential Calculation The above analysis highlighted the problem that the solubility had the variation with different range of fitting. The worst case is that there was unphysical (negative) trend with the fitting. The possible analysis to avoid such problems is the finite difference, where the chemical potential is represented by: * N G N G N N N solution solution 1 1 * N N N1 (6) The results were shown in Fig. S4. It can be seen that the chemical potential had large deviation in the high concentration range especially from N 40. We thus sought a data treatment method in order to improve the statistical accuracy. As we mentioned both in the manuscript and in the previous discussion, the Gibbs free energy fitting result should be correct if we focus on the narrow area of fitting. In other words, chemical potential from fitting have to be the most exact at the center of the fitting. Therefore the most possible chemical potential can be represented by weighted average of the chemical potential from the different fitting range. The mathematical representation can be written as: wi i N i N wi i (7) where subscript i means the different fitting results. w can must be small if N is far from the center of the fitting. The example of the curve was shown in Fig. S5, where the 0,, and 4 different fitting results are obtained by moving the range with keeping the width of the range as 4, 6, and 8 points, respectively. The function of weight was defined as: w i Center N 81 N where wi=0 when wi is less than zero. The deviation is calculated by following equation: wi N wi i i (9) We found that the chemical potential was fluctuated around the solid chemical potential at concentration from.77 mol/kg, where the fluctuation for 8 points presents lowest standard deviation. We thus fitted the result obtained from the 8 points weighted average into the function (Fig. S6): a log N bn c (10) It was found that the plateau of the chemical potential in the in-solution phase is very close to that in solid phase. This in turn results in the solubility variation with different fitting windows. Finally, we also studied the weighted function dependence of the chemical potential curve. It was found (in Fig. S7) that the chemical potential curve was not affected by the selection of the weighted function. 8 (5) (8)

9 Fig. S4: Chemical potentials from finite difference. Figure S5: Chemical potentials obtained by weighted average method. 9

10 Figure S6. Weighted average fitted by Eq. (10), where a=7.57, b=-0.137, and c= Figure S7. Chemical potential with the different weight function: Non-gauss represent 8 points result shown in Fig. S5. σ=3.0 was used as Gaussian width. 10

11 3. Charge Density Profile in the Direct Method Calculation Figure S8 shows the charge density profile from initial stage of the simulation to the end of simulation, where the sodium rich surface could be found at the surface (from 3.3 nm to 3.6 nm) during the simulation time. The time evolution of Na + and Cl - ion number densities in the range of every 0.5 nm at different distances is then presented in Figure 7. It is shown that the sodium ions at the interface with a distance from 0.5 nm are always higher than that of the chloride ions. (a) (b) (c) (d) Figure S8. Charge density profiles. Result in (a) is initial charge distribution made by the first frame coordination, while 1ns is used for the other three cases, namely at ns, ns and ns, respectively. The integration is executed to the z-coordinate from left to right. 11

12 4. Input Files of GROMACS for Thermodynamic Integration Finally, we show the relevant part of input files for thermodynamic integration implemented in GROMACS. The following shows the relevant part of.top file: [atomtypes] ; Name, mass, charge, type, sigma, epsilon Na A Cl A OW A H A DUM A DUM A DUM A DUM A where Na, Cl, OW, and H are transformed into DUM1, DUM, DUM3, and DUM4, respectively. DUM1 to DUM3 are the LJ particle. And we also switched off the charge on H atom in water molecule by transforming it into DUM4 during thermodynamic integration. The relevant part of.mdp file follows: free energy=yes init lambda=*** delta lambda=0 foreign_lambda= sc alpha=0 sc power=0 sc sigma=0.3 nstdhdl=10 separate dhdl file=yes dhdl derivatives=yes dh_hist_size=0 dh_hist_spacing=0.1 couple moltype= couple lambda0=vdw q couple lambda1=vdw q 1

13 couple intramol=no where we fixed the lambda during a simulation. In our specific case, we did calculations for a set of given lambdas (i.e. ini-lambda). 13

14 References 1. J. L. Aragones, E. Sanz, and C. Vega, Solubility of in water by molecular simulation revisited. J. Chem. Phys. 136, (01).. I. S. Joung and T. E. Cheatham III, Molecular dynamics simulations of the dynamic and energetic properties of alkali and halide ions using water-model-specific ion parameters. J. Phys. Chem. B 113, 1379 (009). 3. F. Moucka, I. Nezbeda, and W. R. Smith, Molecular force fields for aqueous eletrolytes: SPC/Ecompatible charged LJ sphere models and their limitations. J. Chem. Phys. 138, (013). 4. E. Sanz and C. Vega, Solubility of KF and in water by molecular simulation. J. Chem. Phys. 16, (007). 5. F. Moucka, M. Lisal, J. Skvor, J. Jirsak, I. Nezbeda, and W. R. Smith, Molecular Simulation of Aqueous Electrolyte Solubility.. Osmotic Ensemble Monte Carlo Methodology for Free Energy and Solubility Calculations and Application to. J. Phys. Chem. B 115, 7849 (011). 14