Saltingin/Saltingout Mechanism of Carbon Dioxide in Aqueous Electrolyte Solutions^{†}
Ⅰ. INTRODUCTION
The oceanic storage and adsorption of CO$_2$ is one important step in the carbon circle leading to the greenhouse gases on the earth [1]. Solubility of CO$_2$ in sea water is sensitive to the concentration and composition of the coexisting salts [2, 3]. Salteffect on the solubility of molecular solute in aqueous electrolyte solutions has been a topic of significant interest in many research fields [47], and different theories have been proposed for the underlying mechanism like the hydration theories, water dipole theories, and electrostatic theories [7]. None of these theories, however, is consistent with all the existing experimental observations, especially with the saltingin phenomenon [7]. The saltingeffect is usually attributed to the change of solvent density, structure and dynamics induced by ions. As a consequence, the solubility of solute changes in aqueous electrolytes. It is usually right for the saltingout effect, but it seems more complex for the saltingin effect than the saltingout [7, 8]. Molecular mechanism of the saltingeffect on the solubility of carbon dioxide at molecule level, therefore, remains elusive.
The saltingeffect on solubility of nonpolar solute like carbon dioxide in aqueous solution is often quantified by the Setschenow equation [9]:
$
\begin{eqnarray}
{\rm{lg}}\left(\frac{S_0}{S}\right)=\frac{K_{\rm{S}}}{C_{\rm{S}}}
\end{eqnarray}
$

(1) 
where $S_0$ and $S$ are the solubility of the CO$_2$ in pure water and in a salt solution at a finite concentration $C_{\rm{S}}$, respectively. Previous studies focused on rationalizing the correlations between the CO$_2$ solubility and the macroscopic properties such as activity coefficient, partial molar volume and viscosity [10]. For instance, ions with positive viscosity Bcoefficient, such as like F$^$ (0.107 at 25 ℃) and Na$^+$ (0.085 at 25 ℃) [11], are the socalled water ''structure makers'', while those with negative values, such as K$^+$ ($$0.009 at 25 ℃), Cl$^$ ($$0.005 at 25 ℃) and ClO$_4$$^$ ($$0.063 at 30 ℃) [11], are ''structure breakers''. From the thermodynamic view point, ions salt out the nonpolar solute such as CO$_2$ in electrolyte solutions by an indirect way [12, 13]: the structure maker ions strengthen the waterwater hydrogen bond network and reduce the entropy of water, then reduce the solubility of the nonpolar solutes. Mostly, there is a good correlation observed between saltingout coefficient $K_{\rm{S}}$ and viscosity Bcoefficient. However, exceptions do exist. For instance, there is a strong saltin effect on solubility of CO$_2$ in NaClO$_4$ aqueous solutions, but NaClO$_4$ has a positive value of the viscosity Bcoefficient (0.012) [11]. This inconsistency is not well understood due to the lack of knowledge on the molecular mechanism underlying.
Analysis of a carefully chosen molecular dynamic behavior, that is experimentally measurable (by spectroscopy e.g., ) and can be assigned to clear structural origins, helps us understand the definitive physical factors responsible for the important phenomenon in general [5, 14, 15]. The rotational time of water and the translational diffusion constant of water, measured by ultrafast infrared or NMR techniques, are found to nicely correlate with $K_{\rm{S}}$ in most cases: previous work indicates that a slower water molecular dynamics usually associates with the "structure maker" ions in the solution, with a positive value of $K_{\rm{S}}$ [5, 6, 11].
In this work, the chemical potentials of carbon dioxide, the water rotational time and water selfdiffusion constant are calculated for aqueous KF, NaCl and NaClO$_4$ solutions. We found a good correlation between the $K_{\rm{S}}$ coefficient and the molecular rotational time and the translational self diffusion constant of water in NaCl and KF aqueous solutions. On the other hand, similar to that observed in viscosity measurement, an inconsistency is observed between the salt concentration dependence of $K_{\rm{S}}$ coefficient and the microscopic dynamic properties of water for NaClO$_4$. Further analysis shows that in NaCl and KF solutions the direct association between CO$_2$ and cation and anion is not preferred compared to waterCO$_2$ pair. Mobility of water is retarded with respect to that in pure water, the solubility of carbon dioxide should therefore reduce due to the decrement of the water entropy induced by ions in an indirect way [57]. In the aqueous NaClO$_4$ solutions, a specific direct binding between anion and CO$_2$ exists according to the Kirkwood and Buff theory [16], which induces an increment of the solubility of carbon dioxide in aqueous NaClO$_4$ solutions.
Ⅱ. EXPERIMENTS
A. Simulation detail
The KF, NaCl and NaClO$_4$ aqueous solution at 0.2, 0.5, 1.00, and 2.00 mol/L, were selected in this work. Each empty cubic box was randomly inserted with 1000 water molecules, one carbon dioxide molecule and ions according to the molar concentration (for 1 mol/L box, the ratio of salt/water=1 salt:55 water). The force fields of alkali and halide ions are taken from ion JoungCheatham models [17]. The famous SPC/E model [18] and EPM2 model [19] are used for solvent water and solute CO$_2$. The geometry and the nonbond interaction parameters of ClO$_4$$^$ are directly obtained from Ref.[20] and Ref.[21] respectively. In running simulations, the geometries of water and ions were kept rigid by the LINCS Algorithm [22]. Each sample was kept at 1 atm and at 298 K weakly coupled to a bath with the NoseHoover thermostats [23, 24] at the interval of 0.1 ps. The equations of motion were integrated with 2 fs time step. Before the harvest simulations, a 5 ns NPT simulation was run to reach the equilibration. Then, additional 2 ns NVE simulations are carried out to get the dynamic properties of system. The longrange Coulombic interactions are calculated with the particlemesh Ewald method [25]. The nonbonded van der Waals interactions are truncated at 12 Å using the switching functions. All simulations are performed using the GROMACS simulation package [26].
B. The chemical potential of CO$_{2}$ in electrolyte solutions
The chemical potential of carbon dioxide in electrolyte solution at salt concentration $C_{\rm{S}}$ was calculated with the Bennett's acceptance ratio method (BAR) proposed by Bennett in 1976 [27(a)]. When the change from initial state A (the electrolytes solution with CO$_2$) to final state B (the electrolytes solution without CO$_2$) is large (unlike states), some intermediate states are chosen by a coupling parameter $\lambda$ according to a linear relationship:
$
\begin{eqnarray}
H(\lambda) = \lambda H_{\rm{B}}+ (1\lambda) H_\rm{A}
\end{eqnarray}
$

(2) 
$H_\rm{A}$ and $H_\rm{B}$ are the Hamiltonians at initial states A ($\lambda$=0) and final state B ($\lambda$=1). The difference of chemical potentials between two neighboring intermediate states $i$ and $j $ can be calculated at $\lambda_i$ and $\lambda_j$ as Eq.(1) with BAR method [27(a)].
$
\Delta \mu _{ij}^{{\rm{BAR}}} = {k_{\rm{B}}}T\ln \frac{{{{\left\langle {f\left( {{H_i}  {H_j} + C} \right)} \right\rangle }_j}}}{{{{\left\langle {f\left( {{H_j}  {H_i}  C} \right)} \right\rangle }_i}}}{\rm{ }} + C
$

(3) 
where $f$ is the Fermi function. $k_\rm{B}$ and $T$ are the Boltzmann constant and the temperature respectively. $H_i$ and $H_j$ are the Hamiltonians at intermediate states $i$ and $j$. The value for $C$ is determined iteratively until to meet
$
\begin{eqnarray}
\langle f(H_i  H_j + C)\rangle_j =\langle f(H_j  H_i  C)\rangle_i
\end{eqnarray}
$

(4) 
Then,
$
\begin{eqnarray}
\Delta \mu _{ij}^{\rm{BAR}} =  k_{\rm{B}} T\ln \left( \frac{{N_j }} {{N_i }} \right) + C
\end{eqnarray}
$

(5) 
The chemical potential of CO$_2$ at final state B relative to initial state A is evaluated with g_bar tool in GROMACS software [26, 27].
$
\begin{eqnarray}
\mu = \sum\limits_{i = 1}^{n  1} {\Delta \mu _{i + 1, i}^{\rm{BAR}} }
\end{eqnarray}
$

(6) 
where $N_i$ and $N_j$ represent the number of configures at intermediate states $i$ and $j$ respectively. $n$ is the number of intermediate states. Convergence of this iterative process can only be reached if there is sufficient overlap between the forward and backward energy differences [27]. In order to enhance the accuracy of BAR, the coupling procedure is further divided into two stages, the discharging process and the neutral soft particle disappearing process. The coupling parameters $\lambda$ were chosen at $\lambda$=1.0, 0.95, 0.9, 0.8, 0.7, 0.65, 0.6, 0.55, 0.50, 0.45, 0.40, 0.35, 0.30, 0.25, 0.20, 0.15, 0.10, 0.05, 0.00 for the discharging process. $\lambda$=1.0, 0.95, 0.9, 0.85, 0.80, 0.75, 0.70, 0.65, 0.6, 0.55, 0.50, 0.45, 0.40, 0.30, 0.20, 0.10, and 0.00 are used for the neutral soft particle disappearing stage. For each value of $\lambda$, the ensemble average of chemical potential is collected within the time period of 2 ns. Simulations were carried out at the same pressure and temperatures as the dynamic properties in method part.
C. Dynamic properties
The rotational correlation functions of water along OH bond vector u and are written as:
$
\begin{eqnarray}
C_2(t) = \langle P_2[{{\boldsymbol{\rm{u}}}}(0){{\boldsymbol{\rm{u}}}}(t)]\rangle
\end{eqnarray}
$

(7) 
where $P_2$ is the secondrank Legendre polynomial. The rotational relaxation time of water ($\tau$) is approximately obtained by fitting double exponential functions as described in previous works [2830]. The selfdiffusion coefficient $D$ can be derived from the timedependent mean square displacements of the mass center of water molecule in aqueous electrolyte solutions, according to the Einstein relation [31].
Ⅲ. RESULTS AND DISCUSSION
A. The chemical potential of CO$_2$
The chemical potential of carbon dioxide in saturated CO$_2$ aqueous solution without salt ($\mu$($S_0$)) and with a finite salt concentration $C_{\rm{S}}$ ($\mu$($S$)) :
$
\mu^{\rm{g}}\;\; =\;\; \mu(S_0)=\mu^0_\infty + RT{{\rm{ln}}}\left(\frac{S_0}{c_\infty}\right)
$

(8) 
$
\mu^{\rm{g}} \;\;= \;\;\mu(S)=\mu^1_\infty + RT{{\rm{ln}}}\left(\frac{S}{c_\infty}\right)
$

(9) 
$\mu^0_\infty$ and $\mu^1_\infty$ are the chemical potential of CO$_2$ in pure water and in electrolyte solution at salt concentration $C_{\rm{S}}$, with dilute concentration of CO$_2$ $c_\infty$. They correspond to the chemical potential in Eq.(6), which is derived from the BAR method. Given CO$_2$ at the gasliquid equilibrium state, $\mu$($S_0$) and $\mu$($S$) are equal to the chemical potential of CO$_2$ ($\mu^\rm{g}$) in gas with same vapor pressure. Setchenow equation is then expressed as:
$
\begin{eqnarray}
\frac{\mu^1_\infty  \mu^0_\infty}{RT} = {\rm{ln}}\left(\frac{S_0}{S}\right)
= {\rm{ln}}(f)
= K_{{\rm{S}}}C_{\rm{S}}
\end{eqnarray}
$

(10) 
The Setchenow saltingout coefficient $K_{\rm{S}}$ is the slope of linear function ln($f$) over the salt concentration $C_{\rm{S}}$ and usually can be obtained according to the linear relationship ln($f$)$\propto$$C_{\rm{S}}$ [7, 32].
The calculated chemical potential of CO$_2$ in pure water in this work is (1.88$\pm$0.22) kJ/mol. It is in agreement with the experimental value of 1.00 kJ/mol [34]. The calculated values of ln($f$) in the Setchenow saltingout equation in KF, NaCl and NaClO$_4$ aqueous solution at 0.2, 0.5, 1.00, and 2.00 mol/L are shown in FIG. 1, which is also consistent with the tendency of the experimental ln($f$) with concentration [32, 33]. ln($f$) of both KF and NaCl solutions increase monotonously with concentration in FIG. 1(a), while the value of NaClO$_4$ decreases with concentration FIG. 1(b). This suggests that NaCl and KF both have saltingout effect on the carbon dioxide and have positive values of the Setchenow saltingout coefficient $K_{\rm{S}}$. KF has the strongest ability to reduce the solubility of CO$_2$ at each concentration. NaClO$_4$ has a saltingin effect on CO$_2$ with concentration and negative value of the Setchenow saltingout coefficient $K_{\rm{S}}$. The slight deviation from the linear relationship between ln($f$)$\propto$$C_{\rm{S}}$ at high concentration is probably due to the artifact of the force field used in simulation.
B. Water dynamics induced by salts
We next calculated the rotational time and the translational selfdiffusion constant of water, and discussed the correlation between the change of these dynamic behaviors of water induced by ions and the saltingeffect of on the solubility of CO$_2$.
The rotational times and the self diffusion constants of water in KF, NaCl and NaClO$_4$ aqueous solution at 0.2, 0.5, 1.00, and 2.00 m are shown in FIG. 2. With adding KF and NaCl into water, the rotational time of water increases monotonously with concentration. The translational selfdiffusion constant of water decreases correspondingly. Slower water dynamics is observed in KF than in NaCl solution. The dynamic properties with concentration from simulations are consistent with the predictions of Hofmerster Series as well as the viscosity Bcoefficients (Bcoefficients of KF and NaCl are 0.098 and 0.080, respectively). On the other hand, the rotation and the translation of water in aqueous NaClO$_4$ electrolyte solutions are both retarded, while a negative value of the Setchenow saltingout coefficient $K_{\rm{S}}$ is observed (FIG. 1). This is a controversy between the predictions by Hofmerster Series [32] and the viscosity Bcoefficients for NaClO$_4$ [11, 12].
C. Specific and direct effect of anion
To rationalize the observed correlations between the CO$_2$ solubility and water molecular dynamics, we need to relate the solubility with a molecular structure factor. According to the KirkwoodBuff theory [16, 35], the Setchenow saltingout coefficient (the slope of Setchenow equation in Eq.(10)) is proportional to the first order derivative of the chemical potential of carbon dioxide in electrolyte solution (Eq.(11)), when the concentration of carbon dioxide approaches zero and at constant pressure $P$ and temperature $T$ [16, 35].
$
\begin{eqnarray}
\mathop {\lim }\limits_{\rho _C \to 0} \left( {\frac{{\partial \mu }}{{\partial x_{\rm{S}} }}} \right)_{T, P} &=& \frac{{RT\left( {\rho _\rm{W} + \rho _{\rm{S}} } \right)}}{\eta }\left( {G_{\rm{CW}}  G_{\rm{CS}} } \right) \nonumber\\
&\cong& K_{\rm{S}} C_{\rm{S}}
\end{eqnarray}
$

(11) 
where $x$ and $C$ is the molar fraction density and the molarity of salt. $\rho _\rm{W}$, $\rho_{\rm{S}}$, and $\rho_\rm{C}$ are the number densities of water, salt, and carbon dioxide. $R$ is the gas constant. $G_{\rm{CW}}$ and $G_{\rm{CS}}$ are the CO$_2$water and CO$_2$salt KB integrals (KBIs), which are defined as:
$
\begin{eqnarray}
G_{ij} = \int_0^\infty {4\pi \left[{g_{ij} \left( r \right)1} \right]r^2 {\rm{d}}r}
\end{eqnarray}
$

(12) 
$g_{ij}$($r$) is the pair radial distribution function between components $i$ and $j$.
$\eta$ is a positive constant at the limit of concentration of CO$_2$ for ideal solution.
$
\begin{eqnarray}
\eta = \rho _{\rm{W}} + \rho _{\rm{S}} + \rho _{\rm{S}} \rho _{\rm{S}} \left( {G_{\rm{WW}} + G_{\rm{SS}}  2G_{\rm{SW}} } \right)
\end{eqnarray}
$

(13) 
where $G_{\rm{WW}}$+$G_{\rm{SS}}$$$2$G_{\rm{SW}}$=0 in ideal solutions. At this condition, the term ($G_{\rm{CW}}$$G_{\rm{CS}}$) in Eq.(11) can be used to examine the salting effect on the solubility.
The radial distribution functions $g$($r$) of waterwater, CO$_2$water, CO$_2$anion and CO$_2$cation pairs, are shown in FIG. 3. There are weak changes observed for the waterwater and CO$_2$water radial distributions at different salt solutions. In aqueous solutions, F$^$, Cl$^$, K$^+$ and Na$^+$ stay far away from the carbon dioxide, which is suggested by lower first solvation peaks ($<$1) of their CO$_2$anion and CO$_2$cation radial distribution functions. There is lower possibility to directly bind to carbon dioxide for them. The saltingout effect of KF and NaCl on the solubility CO$_2$ is imposed by the surrounding solvent water in an indirect way. The large positive value ($G_{\rm{CW}}$$$$G_{\rm{CS}}$) is observed in KF, NaCl solutions (FIG. 4). This means that the affinity between CO$_2$ and water is higher than that between water molecules themselves.
In the solution of NaClO$_4$, there is a much stronger shortrange correlation, within first solvation shell, observed for the CO$_2$ClO$_4$$^$ pair than the CO$_2$water pair in FIG. 3. Additionally, a negative value ($G_{\rm{CW}}$$$$G_{\rm{CS}}$) is found for NaClO$_4$. Given the connection between the saltingout coefficient and the microscopic structure ($g$($r$)) in Eq.(11), the direct binding is the main factor for the saltingin effect of NaClO$_4$ on the solubility of carbon dioxide. On the other hand, the mobility of water is retarded by NaClO$_4$. The structure analysis therefore suggests that the specific interaction of CO$_2$ClO$_4$$^$ leads to the controversial expectations according to the Hofmerster Series and the ion induced water dynamics for NaClO$_4$.
A further analysis is made for the orientation of CO$_2$ within the first solvation shell of ClO$_4$$^$ according to the anionwater radial distribution. The orientation is described by the angle of the vector of C=O bond (the nearest oxygen atom of CO$_2$ from the chloride atom) of CO$_2$ and the Cl$$O bond vector (the nearest oxygen atom of ClO$_4$$^$ from the carbon atom) of ClO$_4$$^$ in FIG. 5. The orientation angle ($\theta$) has the highest population around 90$^{\circ}$. This means that CO$_2$ molecule prefers a perpendicular orientation to the nearest Cl$$O bond around ClO$_4$$^$. Namely, it tends to be tangent to the surface of ClO$_4$$^$ sphere.
Ⅳ. CONCLUSION
In this work, the chemical potential of carbon dioxide in electrolyte solutions and pure water, the rotational time of water and the self diffusion constant of water, as well as the microscopic structures in aqueous KF, NaCl and NaClO$_4$ solutions, are explored to uncover the saltingin or saltingout mechanism of different salts by molecular simulations. Hofmerster Series and the viscosity Bcoefficients both can reasonably predict the saltingout ability of salt and the dynamic properties induced by salt respectively. However, it is not consistent for some saltingin salts like NaClO$_4$. The mechanism is due to the role of water in the solubility of carbon dioxide. The saltout salt like NaCl and KF usually reduces the solubility of carbon dioxide by making the water more structuring than pure water, which results in the nonpolar CO$_2$ uncomfortably in electrolyte solution relative to in pure water. The saltingout salts reduce the solubility of CO$_2$ by the indirect way, but the saltingin effect is more specific and complex than the saltingout effect of ions. A specific direct interaction between anion and CO$_2$ is the real reason for the saltingin effect like NaClO$_4$, according to the Kirkwood and Buff theory. This indicates that we can't predict the saltingin or saltingout effect by the viscosity Bcoefficients of salts, which is valid most for saltingout salts.
Ⅴ. Acknowledgments
This work was supported by the National Key Research and Development Program of China (No.2017YFA0206801), the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDB20000000 and No.XDB10040304) and the National Natural Science Foundation of China (No.21373201 and No.21433014). Q. Zhang thanks the support of Scientific Research Foundation for Returned Scholars, Ministry of Education of China and Liaoning BaiQianWan Talents Program (No.2015294).