Interfacial Tensions, Solubilities, and Transport Properties of the H2/H2O/NaCl System: A Molecular Simulation Study

Data for several key thermodynamic and transport properties needed for technologies using hydrogen (H2), such as underground H2 storage and H2O electrolysis are scarce or completely missing. Force field-based Molecular Dynamics (MD) and Continuous Fractional Component Monte Carlo (CFCMC) simulations are carried out in this work to cover this gap. Extensive new data sets are provided for (a) interfacial tensions of H2 gas in contact with aqueous NaCl solutions for temperatures of (298 to 523) K, pressures of (1 to 600) bar, and molalities of (0 to 6) mol NaCl/kg H2O, (b) self-diffusivities of infinitely diluted H2 in aqueous NaCl solutions for temperatures of (298 to 723) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O, and (c) solubilities of H2 in aqueous NaCl solutions for temperatures of (298 to 363) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O. The force fields used are the TIP4P/2005 for H2O, the Madrid-2019 and the Madrid-Transport for NaCl, and the Vrabec and Marx for H2. Excellent agreement between the simulation results and available experimental data is found with average deviations lower than 10%.

info MD and CFCMC simulations (Tables S6 -S8); Raw data MD simulations for Interfacial Tensions (Table S9); Density and viscosity data (Table S10); Raw data MD simulations for self-diffusivities (Tables S11 -S12); Raw data CFCMC simulations (Table S13); Solubilities of H 2 in pure water (Figure S1); Density profile of Na + and Cl − of a MD simulation to calculate interfacial tensions (Figure S2); Solubilities of H 2 in aqueous NaCl solution at H 2 partial pressures of 1-100 bar (Figure S3); Densities of NaCl solutions (Figure S4); Viscosities of NaCl solutions (Figure S5).Table S1: Computed solubilities of H 2 at a H 2 partial pressure of 1 bar in pure water using the TIP4P/2005 1 H 2 O force field in combination with the Marx 2 H 2 force field and the Vrabec 3 force field as a function of temperature T .T is in unit of K, x H 2 and σ x H 2 are reported with multiplication factors of 10 −5 .σ x H 2 is the uncertainty of x H 2 .The last column lists the calculated solubilities using the experimental correlation provided by Torín  S2: Parameters for the TIP4P/2005 1 water force field.σ and ϵ are the Lennard-Jones parameters, q is the atomic partial charge, and l is the bond length.σ and l are in units of Å, ϵ is in units of kJ/mol, and q is in units of the elementary charge e.In the TIP4P/2005 Table S3: Parameters for the single-site Vrabec 3 Hydrogen force field.σ and ϵ are the Lennard-Jones parameters.σ is in units of Å and ϵ is in units of kJ/mol.σ HH 3.0366 ϵ HH 0.214846 Table S4: Parameters for the three-site Marx 2 Hydrogen force field.σ and ϵ are the Lennard-Jones parameters, q is the atomic partial charge, dummy site L is the geometric center of mass, and l is the bond length.σ and l are in units of Å, ϵ is in units of kJ/mol, and q is in units of the elementary charge e. σ LL 2.958 ϵ LL 0.305141 q H 0.468 q L −0.936 l H−H 0.74 Table S5: Parameters for the Madrid-Transport 5,6 and Madrid-2019 7 force fields.σ and ϵ are the Lennard-Jones parameters and q is the atomic partial charge.σ is units of Å, ϵ is in units of kJ/mol, and q is in units of the elementary charge e.   Table S10: The densities ρ and viscosities η of aqueous NaCl solutions as computed using the NaCl Madrid-2019 7 and Madrid-Transport 5,6 force fields, compared with a fit to experimental data for densities 8 and viscosities. 9The TIP4P/2005 1 H 2 O force field and the Vrabec 3 H 2 force field were used.T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg H 2 O, ρ is in units of kg/m 3 and η is in units of mPa•s.σ x is the uncertainty of quantity x.

Figure S2 :Figure S3 :
Figure S1: Computed solubilities of H 2 in pure water using the TIP4P/2005 1 H 2 O force field in combination with either the Marx 2 H 2 force field (diamonds) or the Vrabec 3 force field (circles) as a function of temperature T at a H 2 partial pressure of 1 bar.The dashed lines represent the experimental correlation provided by Torín-Ollarves and Trusler 4 .

3 @Figure S4 :
Figure S4: Densities of aqueous sodium chloride solutions as a function of (a) pressure for a solution molality of 3 mol/kg water and (b) sodium chloride molality at a pressure of 1000 bar computed using the NaCl Madrid-Transport 5,6 force field, the TIP4P/2005 1 water force field, and the Vrabec 3 hydrogen force field.

Figure S5 :
Figure S5: Viscosities of aqueous sodium chloride solutions as a function of (a) pressure at a solution molality of 3 mol NaCl/kg water and (b) sodium chloride molality computed at a pressure of 400 bar using the NaCl Madrid-Transport 5,6 force field, the TIP4P/2005 1 water force field, and the Vrabec 3 hydrogen force field.

Table S6 :
The numbers of H 2 , H 2 O molecules, and Na + and Cl − ions N H 2 , N H 2 O , N NaCl .The different columns represent different NaCl molalities.The last column reports the average simulation cell sizes L x , L y and L z for a molality of 1.01 mol NaCl/kg H 2 O. T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg H 2 O, and L is in Å.

Table S7 :
The numbers of molecules or ions N used in the MD simulations to compute selfdiffusivities.mNaCl is in units of mol NaCl/kg water.For each molality, the same numbers of molecules and ions are used for all temperatures and pressuresm NaCl N H 2 N H 2 O N Na + N Cl −

Table S8 :
The numbers of molecules or ions N used in the CFCMC simulations.m NaCl is in units of mol NaCl/kg water.For each molality, the same numbers of molecules and ions are used for all temperatures and pressures.In every simulation, a single fractional molecule of H 2 used.

Table S9 :
The interfacial tensions γ of H 2 in contact with aqueous NaCl solutions as computed using the NaCl Madrid-2019 7 force field, the TIP4P/2005 1 water force field, and the Vrabec 3 hydrogen force field.T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg H 2 O, and γ is in units of mN/m.σ γ is the uncertainty of γ.Conditions at which simulations are not performed are denoted by -.Uncertainties in pressure and temperature are zero as these are imposed in the simulations (N P T ensemble).

Table S11
5,6esults of MD simulations to compute self-diffusivities of H 2 in aqueous NaCl solutions as computed using the NaCl Madrid-Transport5,6force field, the TIP4P/2005 1 H 2 O force field, and the Vrabec 3 H 2 force field.The densities ρ, viscosities η, and H 2 finite-size corrected 10 self-diffusion coefficients D H 2 for a wide range of temperatures T , pressures P , NaCl molalities m NaCl , and corresponding molarities M NaCl .T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg water, M NaCl is in units of mol NaCl/L solution, ρ is in units of kg/m 3 , η is in units of mPa•s, and D is in units of 10 −9 m 2 /s.σ x is the uncertainty of quantity x.Uncertainties in pressure and temperature are zero as these are imposed in the simulations (N P T ensemble).

Table S12 :
Results of MD simulations used to compute self-diffusivities of H 2 in aqueous NaCl solutions as computed using the NaCl Madrid-2019 7 force field, the TIP4P/2005 1 H 2 O force field, and the Vrabec 3 H 2 force field.The densities ρ, viscosities η, and H 2 finite-size corrected self-diffusion coefficients D H 2 for a wide range of temperatures T , pressures P , NaCl molalities m NaCl , and corresponding molarities M NaCl .T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg H 2 O, M NaCl is in units of mol NaCl/L solution, ρ is in units of kg/m 3 , η is in units of mPa•s and D is in units of 10 −9 m 2 /s.σ x is the uncertainty of quantity x.Uncertainties in pressure and temperature are zero as these are imposed in the simulations (N P T ensemble).

Table S13 :
Results of the CFCMC simulations using the NaCl Madrid-2019 force field, 7 TIP4P/2005 1 H 2 O force field and Marx 2 H 2 force field.The fluid densities ρ, infinite dilution chemical potentials µ ex of H 2 , the solubilities of H 2 s H 2 , and mole fractions x H 2 are reported for a wide range of temperatures T , pressures P , and NaCl molalities m NaCl , and corresponding molarities M NaCl .The standard deviations σ are reported.T is in units of K, P is in units of bar, m NaCl is in units of mol NaCl/kg water, M NaCl is in units of mol NaCl/L solution, ρ is in units of kg/m 3 , µ ex is in units of k B T s H 2 is in units of mol/L, and x H 2 is in units of 10 −4 .Uncertainties in pressure and temperature are zero as these are imposed in the simulations (N P T ensemble).Computed solubilities of H 2 in pure water using the TIP4P/2005 1 H 2 O force field in combination with either theMarx 2