Chinese Journal of Chemical Physics  2017, Vol. 30 Issue (6): 811-816

#### The article information

Xia Zhang, Lu Zhang, Tan Jin, Zhi-jun Pan, Zhe-ning Chen, Qiang Zhang, Wei Zhuang

Salting-in/Salting-out Mechanism of Carbon Dioxide in Aqueous Electrolyte Solutions

Chinese Journal of Chemical Physics, 2017, 30(6): 811-816

http://dx.doi.org/10.1063/1674-0068/30/cjcp1711230

### Article history

Accepted on: December 27, 2017
Salting-in/Salting-out Mechanism of Carbon Dioxide in Aqueous Electrolyte Solutions
Xia Zhanga, Lu Zhangb, Tan Jinb, Zhi-jun Panb, Zhe-ning Chenb, Qiang Zhanga, Wei Zhuangb
Dated: Received on November 27, 2017; Accepted on December 27, 2017
1. Department of Chemistry, Bohai University, Jinzhou 121013, China;
2. State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China
*Author to whom correspondence should be addressed. Qiang Zhang, E-mail: zhangqiang@bhu.edu.cn; Wei Zhuang, E-mail: wzhuang@fjirsm.ac.cn
Abstract: The solvation of carbon dioxide in sea water plays an important role in the carbon circle and the world climate. The salting-out/salting-in mechanism of CO2 in electrolyte solutions still remains elusive at molecule level. The ability of ion salting-out/salting-in CO2 in electrolyte solution follows Hofmeister Series and the change of water mobility induced by salts can be predicted by the viscosity B-coefficients. In this work, the chemical potential of carbon dioxide and the dynamic properties of water in aqueous NaCl, KF and NaClO4 solutions are calculated and analyzed. According to the viscosity B-coefficients, NaClO4 (0.012) should salt out the carbon dioxide relative to in pure water, but the opposite effect is observed for it. Our simulation results suggest that the salting-in effect of NaClO4 is due to the strongly direct anion-CO2 interaction. The inconsistency between Hofmeister Series and the viscosity B-coefficient suggests that it is not always right to indicate whether a salt belongs to salting-in or salting-out just from these properties of the salt solution in the absence of solute.
Key words: Salting effect    Viscosity B-coefficient    Hofmeister Series    Water dynamics
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 co-existing salts [2, 3]. Salt-effect on the solubility of molecular solute in aqueous electrolyte solutions has been a topic of significant interest in many research fields [4-7], 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 salting-in phenomenon [7]. The salting-effect 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 salting-out effect, but it seems more complex for the salting-in effect than the salting-out [7, 8]. Molecular mechanism of the salting-effect on the solubility of carbon dioxide at molecule level, therefore, remains elusive.

The salting-effect on solubility of non-polar 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 B-coefficient, such as like F$^-$ (0.107 at 25 ℃) and Na$^+$ (0.085 at 25 ℃) [11], are the so-called 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 non-polar solute such as CO_2 in electrolyte solutions by an indirect way [12, 13]: the structure maker ions strengthen the water-water hydrogen bond network and reduce the entropy of water, then reduce the solubility of the non-polar solutes. Mostly, there is a good correlation observed between salting-out coefficient K_{\rm{S}} and viscosity B-coefficient. However, exceptions do exist. For instance, there is a strong salt-in effect on solubility of CO_2 in NaClO_4 aqueous solutions, but NaClO_4 has a positive value of the viscosity B-coefficient (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 self-diffusion 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 water-CO_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 [5-7]. 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 Joung-Cheatham 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 non-bond 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 Nose-Hoover 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 long-range Coulombic interactions are calculated with the particle-mesh Ewald method [25]. The non-bonded 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 second-rank Legendre polynomial. The rotational relaxation time of water ($\tau$) is approximately obtained by fitting double exponential functions as described in previous works [28-30]. The self-diffusion coefficient $D$ can be derived from the time-dependent 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 gas-liquid 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 salting-out 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$$C_{\rm{S}} [7, 32]. The calculated chemical potential of CO_2 in pure water in this work is (1.88\pm0.22) kJ/mol. It is in agreement with the experimental value of 1.00 kJ/mol [34]. The calculated values of ln(f) in the Setchenow salting-out equation in KF, NaCl and NaClO_4 aqueous solution at 0.2, 0.5, 1.00, and 2.00 mol/L are shown in FIG. 1, which is also consistent with the tendency of the experimental ln(f) with concentration [32, 33]. ln(f) of both KF and NaCl solutions increase monotonously with concentration in FIG. 1(a), while the value of NaClO_4 decreases with concentration FIG. 1(b). This suggests that NaCl and KF both have salting-out effect on the carbon dioxide and have positive values of the Setchenow salting-out coefficient K_{\rm{S}}. KF has the strongest ability to reduce the solubility of CO_2 at each concentration. NaClO_4 has a salting-in effect on CO_2 with concentration and negative value of the Setchenow salting-out coefficient K_{\rm{S}}. The slight deviation from the linear relationship between ln(f)\propto$$C_{\rm{S}}$ at high concentration is probably due to the artifact of the force field used in simulation.

 FIG. 1 The values of ln($f$) in Setchenow salting-out equation calculated with Eq.(10) for the MD simulations in KF, NaCl and NaClO$_4$ aqueous solution at 0.02, 0.05, 1.00, and 2.00 mol/L. The corresponding experimental values are taken from Refs.[32, 33].
B. Water dynamics induced by salts

We next calculated the rotational time and the translational self-diffusion constant of water, and discussed the correlation between the change of these dynamic behaviors of water induced by ions and the salting-effect 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 self-diffusion 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 B-coefficients (B-coefficients 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 salting-out coefficient $K_{\rm{S}}$ is observed (FIG. 1). This is a controversy between the predictions by Hofmerster Series [32] and the viscosity B-coefficients for NaClO$_4$ [11, 12].

 FIG. 2 (a) The rotational time of water and (b) the self diffusion constants of water in KF, NaCl and NaClO$_4$ aqueous solution at 0.2, 0.5, 1.00, and 2.00 mol/L.
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 Kirkwood-Buff theory [16, 35], the Setchenow salting-out 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}}$$-2G_{\rm{SW}}=0 in ideal solutions. At this condition, the term (G_{\rm{CW}}-G_{\rm{CS}}) in Eq.(11) can be used to examine the salting effect on the solubility. The radial distribution functions g(r) of water-water, CO_2-water, CO_2-anion and CO_2-cation pairs, are shown in FIG. 3. There are weak changes observed for the water-water and CO_2-water radial distributions at different salt solutions. In aqueous solutions, F^-, Cl^-, K^+ and Na^+ stay far away from the carbon dioxide, which is suggested by lower first solvation peaks (<1) of their CO_2-anion and CO_2-cation radial distribution functions. There is lower possibility to directly bind to carbon dioxide for them. The salting-out effect of KF and NaCl on the solubility CO_2 is imposed by the surrounding solvent water in an indirect way. The large positive value (G_{\rm{CW}}$$-$$G_{\rm{CS}}) is observed in KF, NaCl solutions (FIG. 4). This means that the affinity between CO_2 and water is higher than that between water molecules themselves.  FIG. 3 The radial distribution functions of CO_2-water, water-water, CO_2-anion and CO_2-cation pairs in KF, NaCl and NaClO_4 aqueous solution at 0.5 mol/L.  FIG. 4 The values of the Kirkwood and Buff integrations (G_{\rm{CW}}$$-$$G_{\rm{CS}}) in KF, NaCl and NaClO_4 aqueous solution at 0.5 mol/L. In the solution of NaClO_4, there is a much stronger short-range correlation, within first solvation shell, observed for the CO_2-ClO_4$$^-$ 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$. Given the connection between the salting-out coefficient and the microscopic structure ($g$($r$)) in Eq.(11), the direct binding is the main factor for the salting-in effect of NaClO$_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 anion-water 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.

 FIG. 5 The orientation of carbon dioxide around ClO$_4$$^-$ in NaClO$_4$ aqueous solution at 0.5 mol/L.
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 salting-in or salting-out mechanism of different salts by molecular simulations. Hofmerster Series and the viscosity B-coefficients both can reasonably predict the salting-out ability of salt and the dynamic properties induced by salt respectively. However, it is not consistent for some salting-in salts like NaClO$_4$. The mechanism is due to the role of water in the solubility of carbon dioxide. The salt-out 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 non-polar CO$_2$ uncomfortably in electrolyte solution relative to in pure water. The salting-out salts reduce the solubility of CO$_2$ by the indirect way, but the salting-in effect is more specific and complex than the salting-out effect of ions. A specific direct interaction between anion and CO$_2$ is the real reason for the salting-in effect like NaClO$_4$, according to the Kirkwood and Buff theory. This indicates that we can't predict the salting-in or salting-out effect by the viscosity B-coefficients of salts, which is valid most for salting-out 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.2015-294).

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1. 渤海大学化学化工学院学院, 锦州 121013;
2. 中国科学院福建物质结构研究所, 结构化学国家重点实验室, 福州 350002