Density Fluctuation in Aqueous Solutions and Molecular Origin of

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Density Fluctuation in Aqueous Solutions and Molecular Origin of Salting-Out Effect for CO2 Tuan Anh Ho* and Anastasia Ilgen Geochemistry Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States ABSTRACT: Using molecular dynamics simulation, we studied the density fluctuations and cavity formation probabilities in aqueous solutions and their effect on the hydration of CO2. With increasing salt concentration, we report an increased probability of observing a larger than the average number of species in the probe volume. Our energetic analyses indicate that the van der Waals and electrostatic interactions between CO2 and aqueous solutions become more favorable with increasing salt concentration, favoring the solubility of CO2 (salting in). However, due to the decreasing number of cavities forming when salt concentration is increased, the solubility of CO2 decreases. The formation of cavities was found to be the primary control on the dissolution of gas, and is responsible for the observed CO2 salting-out effect. Our results provide the fundamental understanding of the density fluctuation in aqueous solutions and the molecular origin of the salting-out effect for real gas.

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INTRODUCTION Density fluctuation and cavity formation in liquid water have been used to characterize the molecular signatures of hydrophobicity.1−3 Due to thermal fluctuations, the number of water molecules in a small probe volume fluctuates (i.e., density fluctuation). For example, at 298 K, the average number of water molecules in a probe volume with the radius of 3.3 Å is ∼5 (i.e., density of water is ∼1 g mL−1). However, the number of water molecules n in that probe volume can vary from 0 to ∼10 at the molecular time scale.1−3 When there is no water molecule found in the probe volume (n = 0), the probe volume becomes a cavity. The probability P(n) of finding n water molecules in a small probe volume in bulk water follows the Gaussian distribution.3,4 The calculation of P(n) in a large probe volume is challenging because the probability of observing a very small number of water molecules is exponentially small.5 Numerous papers report calculations of the density fluctuation near solid/liquid and protein/liquid interfaces.1−3,6,7 These results indicate that the P(n) distribution is wider near the hydrophobic surfaces and becomes narrower with increasing hydrophilicity. For example, if n̅ is the average number of water molecules in the probe volume, then both P(n > n)̅ and P(n < n)̅ decrease with increasing hydrophilicity. In this report, we investigate how the P(n) distribution calculated for aqueous solutions change with increasing aqueous concentration of ions (i.e., hydrophilic species). We observed that with increasing ionic load, P(n > n)̅ increased and P(n < n)̅ decreased. We also tested the effect of changing temperature and pressure on the density fluctuation in the examined aqueous solutions. The probability P(n) for n = 0 has been used to calculate the excess chemical potential μ of the creation of cavities with the © XXXX American Chemical Society

same size and shape as a hard-sphere solute in aqueous solutions1−3 μ = −kBT ln[P(n = 0)]

(1)

where n is the number of water and ions, kB is the Boltzmann constant, and T is the temperature. Kalra et al.8 used the calculated excess chemical potential μ to explain the salting-in and salting-out effects of a hard-sphere solute (i.e., small idealized hydrophobic solute accommodates in hydrogenbonded network of water with negligible perturbation and little or no enthalpic cost, but a large entropic one9) in tetramethylammonium fluoride N(CH3)4F and tetramethylammonium chloride N(CH3)4Cl solutions. Jamadagni et al.10 observed a linear correlation between the binding energy of a hard-sphere solute (i.e., chemical potential of hard-sphere solute near surfaces) with macroscopic wettability (i.e., contact angle). It is not clear how these results will change when replacing a hard-sphere solute with a real gas molecule. In this work, we discuss the hydration of a real gas (i.e., CO2) to address this question. In aqueous solutions in contact with the gas phase, the chemical equilibria of CO2 occur as CO2 (g) ↔ CO2 (aq)

(2)

CO2 (aq) + H 2O ↔ H 2CO3 ↔ H+ + HCO3− ↔ 2H+ + CO32 −

(3)

Received: September 15, 2017 Revised: October 12, 2017

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(constant number of atoms, pressure, and temperature) ensemble using LAMMPS17 simulation package. A number of ions, chosen based on the concentration, were randomly placed in a simulation box that includes 1000 water molecules. After an energy minimization, the system was equilibrated in the NPT ensemble. Our simulations were performed at 298, 308, 328, and 338 K (as specified in the Results and Discussion section), and 1 atm using Nosé−Hoover scheme.18,19 Short-range interaction was calculated using a cutoff distance of 10 Å with tail corrections.20 Long-range electrostatic interaction was calculated using PPPM (particle−particle−particles−mesh) solver.21 Force field parameters for all of the species simulated in this work are reported in Table 2. The ability to reproduce hydration energy of ions in water is the criterion used to select ion force field. Understanding ion solubility using molecular dynamics simulation is an interesting topic and requires further investigation.22 Water molecules were simulated by SPC water model23 and kept rigid using Shake algorithm.24 Note that Na+,25 K+,26 Ca2+,27 Cl−,25 and HCO3− 28 ions used in this work are developed with SPC/E water;29 and Li+,30 Mg2+,30 and Ba2+ 30 ions are developed with SPC water. The flexible SPC water model is also used with Na+, Cl−, Ba2+, and Ca2+ ions in CLAYFF force field31 and in the study of the cation solvation energy.32 We selected the SPC water model to provide consistent results for all of the ions studied in this work. However, when possible, the water model that was used to develop ion force field in the original work should be implemented. The TraPPE force field33 was used to simulate CO2 molecule because it can reproduce CO2 density. The rigidity of HCO3− and CO2 was maintained by using the algorithm proposed by Kamberaj.34 Interaction parameter for unlike atoms was calculated using the arithmetic mixing rule (unless specified in Results and Discussion section). Note that Lennard-Jones (L-J) effective radius for the cross interaction between Mg2+ and Cl− was scaled by a factor of 1.6.35 Simulations were conducted with a time step of 1 fs for 20 ns. The simulation trajectories were recorded every 1000 steps. The interaction energies of a CO2 molecule with aqueous

At low pH, the main species present in the aqueous solutions is CO2(aq).11−13 Therefore, understanding the CO2 transfer from gas phase into aqueous solutions (i.e., eq 2) is an important step for understanding chemical controls on the CO2 solubility. The CO2 partitioning into water at 25 °C and 1 atm results in a free energy difference of 1.95 kcal/mol.12 From a thermodynamics point of view, dissolving CO2 in an aqueous solution (i.e., eq 2) can be divided into two steps: first, a cavity forms in the aqueous solution and then a CO2 molecule is inserted into the cavity and interacts with the solvent. The free energy ΔG (i.e., hydration energy) of dissolving CO2 can be calculated as14−16 ΔG = ΔGcavity + E int

(4)

where ΔGcavity is the work required to form a cavity and Eint is the interaction energy between CO2 and solvent. Note that Eint includes the work of solvent reorganization around the solute, but this term is small and can be ignored.14 Using molecular dynamics simulation, we analyzed these terms to understand the molecular origin of the salting-out effect for CO2.

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METHOD Molecular dynamics simulations of LiCl, NaCl, KCl, MgCl2, CaCl2, BaCl2, and NaHCO3 aqueous solutions at concentration below the solubility limit (Table 1) were conducted in NPT Table 1. Aqueous Solutions Simulated in This Work solutions

concentrations (M)

solubility in water at 25 °C (M)36

NaCl KCl LiCl CaCl2 MgCl2 BaCl2 NaHCO3

1, 2, 3, 4 1, 2, 3 1, 2, 3 1, 2, 2.5, 3 1, 2, 2.5, 3 0.5, 1, 1.22, 1.33, 1.556 0.11, 0.22, 0.33, 0.44

6.15 4.76 19.93 7.32 5.88 1.77 1.22

Table 2. Geometry, Lennard-Jones Parameters εi and σi, Charge qi, and Equivalent Hard-Sphere Radii ri of Species Simulated in This Work

H2O, CO2, and HCO3− are rigid and therefore have no intramolecular interactions. bWhen calculating cross interaction between Mg2+ and Cl− ions, the L-J effective radius (σij) is scaled by a factor of 1.6 using the parameter provided in Table 2.35 a

B

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Figure 1. Density fluctuation in NaCl solutions (A). Calculated cavity formation energy as a function of concentration for different aqueous solutions at 298 K (B) and 308 K (C). Density fluctuation in 2 M NaCl aqueous solution as a function of temperature (D). Cavity formation energy as a function of concentrations for NaCl solution at temperatures from 298 to 338 K (E). Density fluctuations in 2 M NaCl aqueous solution simulated at pressures from 1 to 300 atm and at 298 K (F). Calculated cavity formation energy for 2 M NaCl aqueous solution as a function of pressure at 298 K (G). In (D) and (F), the P(n) distributions are only shown for n < 5.

of radius r for pure water (n̅ varies from 4.48 for pure water to 4.78 for 4 M NaCl solution). Increasing NaCl concentration increased the probability of observing n > n̅ species and decreases the probability of observing n < n̅ species in the probe volume (Figure 1A). As opposed to our results, density fluctuation calculated for water near hydrophobic objects indicates an enhanced density fluctuation (i.e., probabilities of finding n water molecules are higher on both sides of the average value, whereas more narrow probability distribution was found near hydrophilic surfaces).1,2 We also observed that with increasing salt concentration, the probability of observing the cavity P(n = 0) decreased. This observation agrees with the previous reports of hydrophilic objects suppressing the cavity formation.1 The ions simulated in this work are hydrophilic species that pull in water tightly within their hydration shells. The P(n) distributions for NaCl at different concentrations also indicated that water is more compressible than NaCl solutions. This observation agrees with the conclusion that water confined between hydrophobic plates is more compressible than bulk water or water confined between hydrophilic surfaces.39−41 In Figure 1B,C, we plot the cavity formation energy, calculated using eq 1, as a function of salt concentration for aqueous solutions at 298 and 308 K, respectively. The results indicate that cavity formation energy increases linearly with increasing salt concentration. Our results also suggest that at the same concentration CaCl2, MgCl2, and BaCl2 solutions yield comparable cavity formation energy at both simulated temperatures. This is a surprising result because both experimental and simulation studies suggested different hydration properties for Ca2+, Mg2+, and Ba2+ ions.42−44 For

solutions including Lennard-Jones and electrostatic interactions were recorded every 100 time steps. The last 15 ns trajectories and interaction energies were divided into three blocks to calculate the cavity formation energy and standard deviation. To quantify the density fluctuation in simulated solutions, we calculated the probability P(n) of finding n number of water molecules and ions in the probe volumes of radius r = rCO2 + rw/ions, where rCO2 and rw/ions are the equivalent hard-sphere radii of a CO2 molecule and of water molecule or ions, respectively (see Table 2). The probe volumes were centered at the grid points that are 1 Å away from each other throughout the simulation box. The diameter of SPC water model is 2.6 Å, which is the shortest distance at which the radial distribution function (RDF) of oxygen−oxygen reach unity.8 The radii of other species were calculated from the RDF with water oxygen (Ow). For example, if the shortest distance at which the RDF of K+-Ow reaches unity is 2.63 Å, then the radius of K+ is 1.33 Å.

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RESULTS AND DISCUSSION

Density Fluctuation and Cavity Formation in Aqueous Solutions. In Figure 1A, we show the probability P(n) of observing n number of species (water and ions) in the spherical probe volume of radius r for NaCl solutions at 298 K, 1 atm. Interestingly, the density fluctuation calculated for NaCl solutions exhibits trends not previously reported in the studies of liquid density fluctuation (e.g., water density fluctuation calculated for water near hydrophobic and hydrophilic objects). On average, we calculated n̅ = 4.48 species in the probe volume C

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Figure 2. Interaction energy including the van der Waals and electrostatic interactions of a CO2 molecule with aqueous solutions at 298 K (A) and 308 K (B).

al.13 used ab initio calculations and reported interaction energy between a water and a CO2 molecule of −3 kcal/mol. Their comparison of the results calculated using literature CO2 models with the results obtained using ab initio simulation indicates the failure of literature CO2 models to reproduce the interaction of CO2 with water in the gas phase. In our work, we develop a new pairwise interaction between CO2 and H2O based on the hydration energy ΔG of CO2 in pure water. The hydration energy ΔG is computed using eq 4, with ΔGcavity reported in Figure 1. To obtain Eint, we conducted simulation of a system including a CO2 molecule (TRaPPE model33) and 1000 water molecules. The Eint, including L-J and electrostatic interactions between water and CO2, were recorded and reported herein. In these simulations, the unlike-pair parameters were computed using the following rules

example, hydration energies of alkali earth ions increase (become more negative) with decreasing ionic size: Ba2+ (−315.1 kcal/mol), Ca2+ (−380.8 kcal/mol), Mg2+ (−455.5 kcal/mol).44 The ions-Ow RDF peak positions decrease in the sequence Ba2+ (2.75 Å) > Ca2+ (2.39 Å) > Mg2+ (2.05 Å),30 as well as the coordination numbers: Ba2+ (9.5) > Ca2+ (7−8.1) > Mg2+ (6).42,45 For alkali metal aqueous solutions, the energy of cavity formation increased in the order of Li+ < K+ < Na+ (in this study). Again, there was no correlation between cavity formation energy with typical hydration properties for Li+, K+, and Na+ ions. For instance, the hydration energy increased (became more negative) in the order of K+ (−80.6 kcal/mol), Na+ (−98.2 kcal/mol), Li+ (−122.1 kcal/mol).44 The ions-Ow RDF peak positions decreased in the order K+ (2.73 Å) > Na+ (2.35 Å) > Li+ (2 Å).30 The changes in the density fluctuation and cavity formation energy as a function of temperature and pressure are illustrated in Figure 1D−G. With increasing temperature, the probability P(n < 5) in 2 M NaCl aqueous solution increased (Figure 1D). In other words, when temperature increases, more cavities can be found in aqueous solutions. However, the cavity formation energy increased with increasing temperature (Figure 1E) because of the T term in eq 1. With increasing pressure, the probability P(n < 5) in 2 M NaCl aqueous solution decreased (Figure 1F) and cavity formation energy increased (Figure 1G) (i.e., higher energy is required to create cavities when pressure increases). Effect of Cavity Formation on the Hydration of CO2. The cavity formation energies, such as those presented in Figure 1B,C, are important in understanding hydrophobic effect and hydration of hard-sphere solutes.1,2,8,10 The main difference between hydration of an idealized hard-sphere solute and that of a real gas in aqueous solution is the interaction of real gas with the aqueous solution (i.e., Eint in eq 4). Small idealized hydrophobic solutes are accommodated in hydrogen-bonded network of water with negligible perturbation and little or no enthalpic cost, but a large entropic one.9 As a result, hydration energy of small hard-sphere solutes is comparable with the cavity work.3,9 In the rest of the report, we investigate how cavity formation energy ΔGcavity and interaction energy Eint determine hydration of real gas CO2 and demonstrate the molecular origin of the salting-out effect for CO2. There is limited research on the hydration of CO2, especially in aqueous solutions. Jiao and Rempe46 studied CO2 solvation free energy in pure water using quasi-chemical theory. Dick et

εij = γ εiiεjj σij = β(σii + σjj)/2

(5) (6)

where ε and σ are the depth of the potential well and the distance at which the interparticle potential is zero, respectively; and γ and β are two factors used to tune the interaction between CO2 and H2O. When γ = β = 1 (i.e., Lorentz−Berthelot combining rule), we were unable to reproduce the hydration energy of CO2 in pure water (i.e., 1.95 kcal/mol12), as expected.13 We then adjusted γ and β, a common approach to tune the interaction energy of the unlike atoms in molecular simulations, to obtain the right hydration energy for CO2 in pure water. When β = 1.06, γ = 0.3 at 298 K and 1 atm, we got Eint = −3.441 ± 0.03 kcal/mol, which is close to the value reported for gas phase interaction (−3 kcal/mol).13 The resulting hydration energy ΔG was 1.955 kcal/mol (ΔGcavity = 5.396 kcal/mol; Figure 1). We then used β = 1.06, γ = 0.3 to compute the cross interaction between an atom belonging to CO2 molecule and an atom belonging to H2O molecule (eqs 5 and 6) in the calculation of interaction energy Eint between CO2 and aqueous solutions (note that γ = β = 1 was used to compute the interaction between an atom in CO2 molecule with ion). In Figure 2, we report the interaction energy Eint of a CO2 molecule with aqueous solutions at 298 and 308 K. The results indicate that with increasing salt concentrations, Eint becomes more negative. In other words, with increasing salt concentration, interaction energy Eint between CO2 and aqueous D

DOI: 10.1021/acs.jpcb.7b09215 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 3. CO2 solubility as a function of CO2 hydration energy in aqueous solutions at 298 K (A) and 308 K (B). The plotted CO2 solubilities for chloride solutions were those experimentally obtained by Yasunishi et al.47 and CO2 solubility in NaHCO3 solution was reported by Wong et al.48

solutions provide another angle for understanding the saltingout effect for CO2 in aqueous solutions. As expected, when there are HCO3− ions in the aqueous solution (e.g., NaHCO3 solution), they will reduce the concentration of CO2(aq) in the aqueous solution due to the chemical equilibria (i.e., eq 3). As shown in Figure 3A, the energy−solubility curve for NaHCO3 deviates from the energy−solubility curves for all of the simulated chloride solutions. The higher the concentration of NaHCO3, the stronger the deviation. For example, for 0.3, 0.4, and 0.5 M NaHCO3 solutions, the actual measured solubility of CO2 deviates by 12, 16, and 23%, respectively, from the predicted solubility obtained from energy−solubility correlation for simulated chloride solutions.

solution favors the CO2 solubility (i.e., salting in). Jamadagni et al.10 observed that the binding energy of realistic hydrophobic solutes have contributions from cavity formation and from van der Waals interactions. The latter does not change significantly at the interface of different condensed systems. However, we found that the interaction energy of CO2 with aqueous solutions depends not only on the salt concentration but also on the ionic species present. The magnitude of Eint calculated for NaCl and KCl solutions are comparable, and lower than those computed for CaCl2, MgCl2, BaCl2, and NaHCO3 solutions. The results shown in Figure 1 indicate that cavity formation energy ΔGcavity positively increases with increasing salt concentrations (salting out). The results presented in Figure 2 suggest that interaction energy Eint becomes more negative when salt concentration increases (salting in). Because the magnitude of ΔGcavity is larger than that of Eint, ΔGcavity term is the dominant contributor controlling the CO2 salting-out effect. To demonstrate the accuracy of our energies calculation, we plotted the solubility of CO2 as a function of hydration energy ΔG at 298 and 308 K (Figure 3). Note that the plotted CO2 solubilities for the chloride solutions were those experimentally obtained by Yasunishi et al.47 and CO2 solubility in NaHCO3 solution was reported by Wong et al.48 The results indicate that for NaCl, KaCl, MgCl2, CaCl2, and BaCl2 solutions (NaHCO3 will be discussed later), the relationship between ΔG and solubility collapse onto a single line, following the equation12 ΔG = −RT ln

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CONCLUSIONS In conclusion, we investigated the density fluctuation and cavity formation in aqueous solutions and the molecular origin of salting-out effect for CO2. The results indicate that with increasing salt concentration, the probability of finding small n species (n < n)̅ in the probe volume decreased and the probability of finding large n species (n > n)̅ increased. With increasing temperature, we observed an increasing number of cavities, whereas with increasing pressure, the formation of cavities was suppressed. Our energetic analyses indicated that interactions of CO2 with aqueous solutions including the van der Waals and electrostatic interactions favor the solubility of CO2 when the salt concentration increases (salting in). However, cavity formation, which is found to be the dominant process controlling the dissolution of gas, decreased with increasing salt concentration. We, therefore, conclude that the formation of cavities is the primary factor responsible for the CO2 salting-out effect.

[CO2(aq)] PCO2

(7)

where [CO2(aq)] (mol L−1) is the concentration of CO2 in the aqueous solution, PCO2 is the pressure of CO2, R is the gas constant, and T is the temperature. One of the mechanistic explanations for the salting-out phenomenon was based on the changes in water activity. Ions in a solution retain water molecules in their hydration shells and reduce the number of “free” water molecules available to interact with others.49 Gilbert et al. found that CO2 solubility is related to the number of “free” water molecules available for CO2 hydration.11 Our results based on the density fluctuation, cavity formation, and interaction of CO2 with aqueous

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 505-284-2339. ORCID

Tuan Anh Ho: 0000-0002-8129-1027 Anastasia Ilgen: 0000-0001-7876-9387 Notes

The authors declare no competing financial interest. E

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ACKNOWLEDGMENTS We thank Drs. Louise Criscenti, Craig Tenney, and Anh Phan for insightful discussions. This work was funded by the Center for Frontiers in Subsurface Energy Security, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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DOI: 10.1021/acs.jpcb.7b09215 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcb.7b09215 J. Phys. Chem. B XXXX, XXX, XXX−XXX