Structural and Dynamical Properties of Alkaline Earth Metal Halides in

Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX-XXX

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Structural and Dynamical Properties of Alkaline Earth Metal Halides in Supercritical Water: Effect of Ion Size and Concentration Sonanki Keshri and B. L. Tembe* Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India S Supporting Information *

ABSTRACT: Constant temperature−constant pressure molecular dynamics simulations have been performed for aqueous alkaline earth metal chloride [M2+−Cl− (M = Mg, Ca, Sr, and Ba)] solutions over a wide range of concentrations (0.27−5.55 m) in supercritical (SC) and ambient conditions to investigate their structural and dynamical properties. A strong influence of the salt concentration is observed on the ion−ion pair correlation functions in both ambient and SC conditions. In SC conditions, significant clustering is observed in the 0.27 m solution, whereas the reverse situation is observed at room temperature and this is also supported by the residence times of the clusters. The concentration and ion size (cation size) seem to have opposite effects on the average number of hydrogen bonds. The simulation results show that the self-diffusion coefficients of water, cations, and the chloride ion increase with increasing temperature, whereas they decrease with increasing salt concentration. The cluster size distribution shows a strong density dependence in both ambient and SC conditions. In SC conditions, cluster sizes display a near-Gaussian distribution, whereas the distribution decays monotonically in ambient conditions.

1. INTRODUCTION Supercritical fluids (SCFs) refer to states of fluids in which their critical temperatures and pressures are exceeded. SCFs have been the subject of considerable research over the last few decades. The advantages of SCFs as environmentally friendly solvents arise from their nontoxicity and nonflammability and the possibilities of modulating the physical and chemical properties through minor changes in temperature and/or pressure. SCFs comprise an important class of solvents and reaction media, which have found many applications in basic and applied chemical sciences. SCFs and their mixtures have recently become a subject of growing scientific and industrial interest as safe and efficient solvents in a variety of industrial and technological processes. There have been a large number of industrial and technological applications of SCFs because of their fascinating properties.1−10 Among the various supercritical solvents of practical applications, supercritical water (SCW), in particular, has been the subject of intense research because of its low cost and environmentally friendly nature. The properties of supercritical water are very different from those in ambient conditions. Dramatic changes occur in the physical properties of water. Densities of SCW in the critical region can be varied from very low (gaslike) to high (liquidlike) values by changing the temperature and pressure. Thus, they provide a unique environment that enables control of reactions that depend on the dielectric constant of the medium. As density is varied, the extent of the hydrogen-bonding network of water molecules is © XXXX American Chemical Society

altered. As a result, the dielectric constant of water changes, which has a direct consequence on the solvation structure of water molecules around the solutes. Being benign, nonflammable and, nontoxic in nature for a large number of chemical reactions that are currently carried out in carcinogenic organic solvents, SCW is nowadays considered as an alternative and is widely being used in many industrial and chemical processes.11−15 An outstanding property of water in ambient conditions is its intrinsic ability to dissolve ionic and polar species due to its unusually large dielectric constant. However, at elevated temperature and pressure, i.e., in supercritical conditions, the dielectric constant of water decreases and ionic charges will not be shielded as effectively as in ambient conditions. This results in an increase in ion association and aggregation. Ion pair association at high temperature and pressure is of particular interest due to its importance in several disciplines, including geochemistry and hazardous waste destruction.16−18 Ion solvation in aqueous solutions governs many important biological, geological, and chemical processes.19−21 The most promising application of SCW is the destructive oxidation of hazardous waste using supercritical water oxidation.22−24 Alkali and alkaline earth metal chlorides are the most prevalent naturally occurring species in SCW. In recent years, Received: August 3, 2017 Revised: October 31, 2017 Published: October 31, 2017 A

DOI: 10.1021/acs.jpcb.7b07690 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

parameters of SPC/E water are Tc = 638.6 K and Pc = 139 bar.94 Because all our simulations are performed above the critical point of water, our simulations correspond to supercritical states. The force fields and geometrical parameters for water and the ions are given in Tables S1 and S2 in the Supporting Information. The force-field parameters for the ions are taken from Aqvist et al.118 The interatomic interactions between the ions and solvents are taken to be pairwise additive. The short-ranged interactions are described through the Lennard-Jones potential, and the long-ranged electrostatic interactions are modeled with a Coulombic potential. qiqj Aij Bij Uij(r ) = 12 − 6 + (1) r r r

there have been several experimental and theoretical studies on the solvation structure and dynamics of alkali metal halides in SCW, but detailed studies of alkaline earth metal halides in high-temperature, high-pressure systems are rare. Several studies have been reported on the effect of solvent composition on the ion−ion (both alkali and alkaline earth metal halides) potentials of mean force (PMFs) in supercritical conditions via a constrained method (infinite dilution).25−49 It has been established that the contact ion pair (CIP) is the most stable structure in supercritical conditions as compared to that in ambient conditions. However, solvation in a concentrated salt solution may proceed in a different manner than in dilute solutions because the solutes may be present as ion clusters rather than as single ions. Concentration dependence of PMFs has been studied by several authors using different numbers of ion pairs in both ambient and supercritical conditions50−71 but that of alkaline earth metal halides has not been explored much.72−91 Concentrated solutions of calcium chloride have been studied a lot in ambient conditions by several research groups. Chialvo and co-workers83 performed molecular dynamics (MD) simulations of aqueous CaCl2 solutions over a wide range of concentration (0 < m ≤ 9.26) in ambient conditions. X-ray and neutron diffraction and molecular dynamics simulations of concentrated calcium chloride solutions (2.5 and 4.0 M) in aqueous media were performed by Megyes et al.90 The coordination number of the calcium ion was found to decrease with an increase in concentration. The effect of concentration on the solvation structure of Ca2+ in aqueous solution was studied using the neutron diffraction isotope substitution method by Badyal and co-workers.87 Seward and co-workers performed X-ray absorption fine structure measurements to study solvation and ion pairing in aqueous strontium solutions (0.10 m) from 25 to 300 °C.91 Molecular dynamics simulations of aqueous solutions of magnesium chloride over a wide range of concentrations (0.2−4.9 M) were performed by Bartczak et al.84 MD simulations of concentrated MgCl2 and CaCl2 aqueous solutions at various temperatures (298−573 K) and pressures (0.5−20.0 bar) were carried out by Dai et al.85 Their results indicate that ion association does not change with pressure in the case of MgCl2 but in the case of CaCl2 solutions, ion association changes slightly with pressure. Frequency-dependent electrical conductivities of aqueous strontium hydroxide and strontium chloride were measured by Arcis and co-workers over a wide range of ionic strengths (3 × 10−5−0.2 mol kg−1) from T = 295 to 625 K at P = 20 MPa using a high-precision flow AC conductivity instrument.81 To the best of our knowledge, detailed analysis of the solvation structure of alkaline earth metal halides in supercritical water as a function of salt concentration has not yet been reported. In the present work, we will focus our attention on the structural and dynamical properties of alkaline earth metal chlorides in supercritical water as a function of salt concentration and cation size and we will compare our results with those in ambient conditions. The methodology and computational details are described in Section 2. The results of the simulations are discussed in Section 3, followed by conclusions in Section 4.

Here, i and j denote a pair of interaction sites on different molecules, qi is the charge located at site i, qj is the charge located at site j, and r is the site−site separation. Terms Aij and Bij are determined from Aij = 4 × (εij) × (σij)12

(2)

Bij = 4 × (εij) × (σij)6

(3)

whereas εij and σij are calculated using the Lorentz−Berthelot mixing rules95 εij = (εi × εj)1/2

(4)

⎛ σi + σj ⎞ σij = ⎜ ⎟ ⎝ 2 ⎠

(5)

Half of the box length is used as a cutoff for Lennard-Jones forces. The electrostatic interactions are treated by the particle mesh Ewald method,96 with a Coulomb cutoff of 1.5 nm and an interpolation order of 4. For nonbonded van der Waals interactions, a 1.5 nm cutoff is used. The potential energy of our system is minimized using the steepest decent algorithm. Initially, MD simulations were performed for 50 ns in the NVT ensemble for thermal equilibration of each system. Subsequently, NPT simulations for 50 ns were carried out for the equilibration of the pressure for each system. Finally, we have generated trajectories of 100 ns for each system in the NPT ensemble. From these trajectories, we have computed the potentials of mean force (PMFs) between ions with the help of pair correlation functions, g(r)s. The relation between PMFs and g(r)s is W (r ) = −kBT ln g (r )

(6)

Periodic boundary conditions are used along with the minimum image criterion.97 The neighbor list is updated every 10 steps. The SHAKE algorithm98 is used to maintain the constant bond lengths and bond angles of the solvent molecules during simulations. The temperature of the system is maintained at 673 K using a velocity rescaling thermostat99 with a relaxation time of 0.1 ps. The pressure of the system is fixed at 350 bar using the Berendsen barostat100 with a relaxation time of 0.5 ps. The equations of motion are integrated using the leapfrog algorithm101 with a time step of 2 fs. A Parrinello−Rahman barostat102 is used for the production run. The details of simulation boxes in supercritical (SC) and ambient conditions (RT) are listed in Tables S3 and S4 in the Supporting Information, respectively. The simulated densities of the mixtures in ambient and supercritical conditions match well

2. METHODOLOGY AND COMPUTATIONAL DETAILS All of the MD simulations have been performed in an isothermal−isobaric ensemble at T = 673 K and P = 350 bar using the GROMACS package (version 4.5.4).92 In the present study, the SPC/E model has been used for water.93 The critical B


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Figure 1. Potentials of mean force between Ca2+ and Cl− ion pairs in water as a function of salt concentration in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar).

Figure 2. Schematic representation of the contact ion pair (CIP), solvent-assisted ion pair (SAIP), solvent-shared ion pair (SShIP), and solventseparated ion pair (SSIP).

with the experimental densities.103−105 The initial configurations are generated using software Packmol.106

ion are calculated from the pair distribution function, gM−Cl(r), using eq 6. 3.1.1. Effect of Salt Concentration. The PMFs of the calcium chloride ion pair as a function of salt concentration in supercritical (SC) and ambient conditions (RT) are presented in Figure 1a,b respectively. Proper asymptotic behavior of W(r) in supercritical conditions is observed when we plot W(r) up to 2.00 nm, which is shown in the inset of Figure 1a. We have retained W(r) until r = 1 nm to show its detailed structure at short distances more clearly. It has been found that the solutes in solutions exist in four different stable solvated states. In contact ion pairs (CIPs), neither a solvent molecule nor even a part of it comes in between the solute molecules. In solvent-assisted ion pairs (SAIPs), a part of a solvent molecule comes in between the solute molecules. In solvent-shared ion pairs (SShIPs), one solvent molecule comes in between two solutes and it is shared by the solvation shells of both the solute molecules. In solvent-

3. RESULTS AND DISCUSSION The structural properties of the alkaline earth metal chlorides in supercritical and ambient water have been characterized by potentials of mean force, radial distribution functions (RDFs), and running coordination numbers (RCNs). Diffusion coefficients of the ions and solvent as a function of salt concentration and ion size were also obtained. The effect of salt concentration on the structure of water was analyzed in terms of hydrogen bonding as well. 3.1. Potentials of Mean Forces (PMFs). The potentials of mean force give detailed information about the effect of the aqueous solvent on the attraction/repulsion between the ions. The potentials of mean force between the alkaline earth metal cations, i.e., M2+ ions (M = Mg, Ca, Sr, and Ba), and the Cl− C


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The Journal of Physical Chemistry B separated ion pairs (SSIPs), the first solvation shells of both the solutes do not share any common solvent molecule.107 Representative pictures of these four different states are given below (Figure 2). Although there are several ways of classifying ion pairs, we are using a description of ion pairs based on the position of the minima in their PMFs. This approach has the advantage of being more quantitative. In the literature, the term “two solvent-separated ion pair” is used, and what this means is that both the ions have a completed single solvation shell for the individual ions. When solvent molecules are shared between the ion pair, in solvents such as water, the location of the second minimum in the PMF is at a distance less than that corresponding to the sum of the ionic radii and the diameter of the solvent. For monovalent + + ion pairs, the first minimum occurs at a distance less than the sum of the two ionic radii and the diameter of the solvent (water). We are referring this ion pair as solvent-assisted ion pair (SAIP). In solvents like dimethyl sulfoxide, the second minimum occurs at a distance equaling the sum of the ionic radii and the solvent diameter. For bivalent + + ion pairs, the first minimum occurs at a distance equal to the sum of the ionic radii and the solvent diameter. We are calling this the solvent-shared ion pair (SShIP). We think that such a classification based on the minima in the PMFs will be useful in the long run. Whether a configuration is SAIP or SShIP can be decided on the basis of the position of the minimum in the potentials of mean force. In each mixture, the position of the CIP is around 0.26−0.27 nm (Figure 1a,b). A striking feature of the PMF plots is that the stability of CIP increases with a decrease in salt concentration in supercritical conditions but the opposite is observed in ambient conditions. The CIPs in Figure 1a are more stable than the CIPs in Figure 1b. In the case of supercritical conditions, the depths of the CIPs range from −38.3 kJ mol−1 (0.27 m) to −18.8 kJ mol−1 (5.55 m). For the ambient case, the depths of the CIPs range from −0.31 kJ mol−1 (0.27 m) to −7.51 kJ mol−1 (5.55 m). The position of CIPs calculated in our simulations is in good agreement with corresponding results in previous studies.41,75,78 A rationale for the higher stability of CIP with a decrease in salt concentration in supercritical conditions will be given after analyzing the cluster size distributions (Section 3.2). The energy differences between the first transition states (TSs) and CIPs lie in the range of 37− 40 kJ mol−1 (for supercritical conditions). A notable feature of the PMFs in ambient conditions is that the first transition state is not easily simulated when the salt concentrations are low (0.27, 0.55, and 1.38 m). For systems with a fewer number of ion pairs, it is difficult to get good RDFs from simulations because of poor statistics and thus it is not possible to obtain PMFs over the entire range of distances. However, on going from ambient to supercritical conditions, i.e., with an increase in temperature, the discrepancy is not there anymore. This can be attributed to the high amounts of thermally available energy in supercritical conditions compared to those in ambient conditions. With the rise in temperature, the movement of ions increases and becomes faster, which results in covering all of the distances corresponding to ion pairing. From Figure 1a,b, it is observed that there is a presence of stable SAIPs in all of the compositions. The position of SAIP lies between 0.48 and 0.52 nm. The depths of SAIPs in ambient conditions range from −4.35 kJ mol−1 (0.27 m) to −2.04 kJ mol−1 (5.55 m), and in supercritical conditions, they range from −16.8 kJ mol−1 (0.27 m) to −1.87 kJ mol−1 (5.55 m). We also

observe a third minimum corresponding to SSIP. The depths of SSIPs range from −15.6 kJ mol−1 (0.27 m) to −1.98 kJ mol−1 (5.55 m) in supercritical conditions, and in ambient conditions, they range from −0.54 kJ mol−1 (0.27 m) to 0.04 kJ mol−1 (5.55 m). For each salt concentration studied here, the depth of the CIP minimum is more than the depth of the SAIP and SSIP. This shows that the CIP is more stable than any other configuration in both ambient and supercritical conditions. Depths of SAIPs and SSIPs also increase with an increase in temperature and with a decrease in salt concentration in supercritical conditions. In contrast to the CIP stability, SAIPs and SSIPs are more stable at low salt concentrations in ambient conditions. These observations on the effect of concentration are in agreement with other experimental findings.57,60,66,68,108 The increased stability of CIP, SAIP, and SSIP in supercritical conditions compared to that in ambient conditions can be explained on the basis of the decrease in the dielectric constant of water in supercritical conditions. The dielectric constant in ambient and supercritical conditions as a function of salt concentration is given in Table S5 in the Supporting Information. A hydration shell is formed by water molecules around the ions, and these shells screen the charges of the ions and significantly attenuate their Coulombic interactions with each other. In ambient conditions, the ions are screened from each other by water molecules. In supercritical conditions, the hydrogen-bonding network between water molecules is perturbed to a significant extent, which results in the reduction of the dielectric constant. In this situation, the electrostatic interaction acting between the ions is much stronger than the force acting between the ions and water and between water molecules. The ion pair cannot be screened effectively by solvents having lower dielectric constants and thus ion association is strengthened. Thus, electrolytes tend to associate at high temperatures and low densities. As a result, CIPs, SAIPs, and SSIPs are more stable in supercritical conditions compared to those in ambient conditions. This has been previously observed in ion pair association studies by several authors.17,28,29 Because the decrease in the dielectric constant facilitates ion association, one may expect the contact ion pair to be more stable in the 5.55 m solution in supercritical conditions, but in reality, we observe the opposite. There is hardly any decrease in the dielectric constants as we go from the 0.27 m (∼3.47) to 5.55 m solution (∼3.30) in the supercritical conditions. Thus, the dielectric constant of the solvent does not play a significant role here in providing stability to the CIPs in supercritical conditions. The overall structure in ambient and supercritical conditions can be roughly visualized with the help of the snapshots of different configurations given in Figure S1 in the Supporting Information. From Figure S1, we can see that ion association occurs easily in supercritical conditions compared to that in ambient conditions (at low salt concentrations). From the snapshots of the configurations at different times separated by several nanoseconds (Figure S1), we note that in supercritical conditions there is a continuous redistribution of clusters throughout the simulation, whereas in ambient conditions, clusters are formed only at higher salt concentrations. The PMFs for other alkaline earth metal chlorides in supercritical and ambient conditions are shown in Figures S2a,b−S4a,b in the Supporting Information. The deepest contact minima in both ambient and supercritical conditions are observed for D


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Figure 3. Potentials of mean force between Ca2+ and Ca2+ ion pairs in water as a function of salt concentration in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar).

Figure 4. Potentials of mean force between the Cl− and Cl− ion pair in water as a function of salt concentration in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar).

not the contact ion pair or SAIP. The solvent-shared ion pair is found to be most stable at a lower density, i.e., at a low salt concentration in supercritical conditions. The first minimum, which occurs at 0.50 nm in supercritical conditions, is absent in ambient conditions when the salt concentration is very low (0.27, 0.55, and 1.38 m). However, at higher salt concentrations, the first minimum occurs near 0.50 nm. The second minimum occurs near 0.68 nm (high salt concentration). We see that SShIPs become more stable with increasing density and salt concentration in ambient conditions. The SShIPs are found to be more stable in supercritical conditions compared to those in ambient conditions, which is mainly because of the low dielectric constant of water. From the above figures, it is also seen that the solvent-associated/separated state is more stable than the contact ion pair in ambient conditions. The probability of two highly charged ions staying in contact with each other is very unlikely and hence we see that the contact ion pair is not even formed for the cation− cation PMFs. In the solvent-separated state, the neighboring water molecules around the ions act as a bridge between the ions and thus provide stability to the configuration. The PMFs of the Mg2+−Mg2+, Sr2+−Sr2+, and Ba2+−Ba2+ ions as a function of salt concentration in supercritical and ambient conditions are given in Figures S5a,b−S7a,b in the Supporting Information. Because the cations are doubly charged, there is no scope for contact ion pair formation (as evidenced from the M2+−M2+ PMFs). The first minimum corresponds to a distance where the two ions are assisted by at least one solvent molecule and water molecule acts as a linear bridge between the two cations.

magnesium halides. Barium halides show the least-stable contact minima. We have also studied the association of the M2+−M2+ (M = Mg, Ca, Sr, and Ba) and Cl−−Cl− ions in both ambient and supercritical conditions. The PMFs for the Ca2+−Ca2+ ion pair as a function of salt concentration in supercritical and ambient conditions are shown in Figure 3a,b, respectively. In this case also, W(r) does not reach the value of zero until r = 1 nm. There is no specific structure formed beyond 1 nm in both ambient and supercritical conditions, and the structural information that we extract from PMFs is between 0.47 and 0.82 nm. However, if we plot W(r) up to 2 nm, asymptotic behavior is seen. In supercritical and ambient conditions, they show the first minimum near 0.50 nm and a second minimum near 0.68 nm. This corresponds to a situation wherein the ions are assisted by counter ions/solvent molecules. The potentials of mean force of Na+−Na+ and Cl−−Cl− ion pairs in water by a constrained MD approach have been studied by Guàrdia and co-workers.109 According to their findings, solvent molecules surrounding the Na+−Na+ pairs can stabilize configurations with two ion pairs of the same sign. In the case of the first minimum, the oxygen of the water molecule serves as a bridge between the two ions, whereas the second minimum corresponds to configurations where water molecules are uniformly distributed with the oxygen atoms closer to the Ca2+ ions than the hydrogen centres.109 The same argument justifies the stability of contact and solvent-separated ion pairs in the present work. In the case of alkaline earth metal cations, the first minimum is the solvent-shared ion pair (SShIP) and E


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Figure 5. Potentials of mean force between the alkaline earth metal ions and the chloride ion in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar) for 2.77 m salt concentration.

The PMFs of Cl−−Cl− ions (the counter ion being Ca2+) in supercritical and ambient conditions are presented in Figure 4a,b, respectively. In supercritical conditions, the first minimum occurs at around 0.36 nm, followed by a broad minimum at around 0.65−0.67 nm. In ambient conditions for low salt concentrations (0.27 and 0.55 m), we do not observe the first minimum at 0.36 nm. As we increase the salt concentration further, the first minimum appears at 0.36 nm. Because the first minimum occurs at around 0.36 nm, which corresponds to the interionic distance between two chloride ions (the ionic radius of the Cl− ion is 0.184 nm), we can say that the contact ion pair (CIP) is formed in the case of Cl−−Cl− PMFs. Here also, the Cl−−Cl− configurations are stabilized by surrounding water molecules. The stability of CIPs increases as the salt concentration decreases in supercritical conditions, whereas in ambient conditions, the CIP is the most stable at the highest concentration. The nature and shape of the Cl−−Cl− PMFs for all other counter cations (Mg2+, Sr2+, and Ba2+) are found to be almost the same. 3.1.2. Effect of Cation Size. The PMFs of different alkaline earth metal chlorides are shown in Figure 5a,b for supercritical and ambient conditions. The PMFs for alkaline earth metal halides in ambient and supercritical conditions are characterized by three minima (CIP, SAIP, and SSIP). From the figures, it is evident that contact minima shift to larger interionic distances with increasing ionic radii. Stabilities of CIPs decrease with an increase in the size of the cations. This result indicates that the CIP is likely to be the most stable for the cation with the smallest size as the interaction between the anion and cation is maximum in that case. This is because of the high charge density on a cation of smaller size (maximum ionic potential) as compared to that on a larger one, which favors the CIP formation. In supercritical conditions, the depths of the CIPs range from −25.6 kJ mol−1 (Mg2+−Cl− ion pair) to −19.8 kJ mol−1 (Ba2+−Cl− ion pair) (Figure 5a). For the ambient case, the depths of the CIPs range from −8.3 kJ mol−1 (Mg2+−Cl− ion pair) to −7.3 kJ mol−1 (Ba2+− Cl− ion pair) (Figure 5b). CIPs in supercritical conditions are 3 times more stable than those in ambient conditions. A similar trend of CIP stability is observed in previous studies.41,78,82 3.2. Cluster Size Distributions. The ion clusters were identified to see how their sizes change with concentration and temperature. A cluster is defined as a set of ions with each ion connected with at least one other ion in the same cluster

regardless of its charge and species. Two ions are considered to be connected if they are separated by a distance smaller than a certain cutoff. The first minimum of the cation−anion RDF was used as the cutoff for connected ions. The cluster size distributions as a function of concentration are shown in Figure 6a,b in both supercritical and ambient conditions. These distributions are normalized by the length of the analyzed trajectory and hence they represent the frequency of occurrence of clusters of different sizes. From the above figures, we see that the cluster size distributions in ambient and supercritical conditions have distinctly different density dependence. At room temperature, an increase in density leads to a dominance of certain ion cluster sizes. For example, for a 1.38 m solution, the cluster sizes of 3 and 4 dominate. For 2.77 and 5.55 m solutions, cluster sizes of 6 and 11 (respectively) dominate. In supercritical conditions, there is a strong dominance of largesized clusters and the distribution of cluster sizes is much wider, almost appearing like a Gaussian distribution. For a 5.55 m solution in supercritical conditions, the cluster sizes are distributed between 50 and 260 with the dominant cluster size being 120. This feature is in qualitative agreement with those reported earlier for the univalent electrolytes.26,63,110 This is also evident if we look at the distribution of r(Ca2+−Cl−) as a function of time, which is shown in Figure 7a,b. We have calculated several such trajectories of different ion pairs in different clusters and given a few representative examples in these figures. From the above figures, it is clear that the distance between the ion pair is fixed at around 0.27 nm and it hardly shows any change in the 0.27 m solution (in supercritical conditions) and 5.55 m solution (in ambient conditions). This indicates that ion pairing in supercritical conditions is favored in less concentrated solutions, whereas in ambient conditions, it is favored at high concentrations. The interionic separation distance shows a large fluctuation from the equilibrium distance in ambient conditions for 0.27 m solutions, which suggests that ions are, on the average, far apart from each other and that no significant, long-lived ion pairing/clustering is observed. This is also clear from Figure S1, where all of the ions tend to remain as a single ion cluster in less concentrated solutions (0.27 m) in supercritical conditions, but in ambient conditions, they are far apart from each other. Although the ion pair resides at ∼0.27 nm for a significant period of time in 5.55 m solutions in supercritical conditions, fluctuations from the contact ion pairing distance (i.e., 0.27 nm) are still observed (Figure 7b). F


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Figure 6. Cluster size distributions as a function of salt concentration in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar).

would also like to note that the solutions studied here are homogeneous and clusters of different sizes span the entire simulation cell. In the alkaline earth metal chloride solutions studied here as well in the case of NaCl solution investigated by Nahtigal et al.,111 it is interesting to note that the largest clusters seem to contain nearly one-third of the total number of

This is why the contact ion pair is the least stable in highly concentrated solutions in supercritical conditions. Although the distribution of cluster sizes ranges from a small value (∼50) to a very large value (∼250) in highly concentrated solutions (say 5.55 m), the rate of interconversion from one size to the other is quite high, which results in the lower stability of CIP. We G


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Figure 7. Distributions of the distance between the ion pair (Ca2+−Cl−) as a function of time in supercritical and ambient conditions in (a) 0.27 m and (b) 5.55 m solutions.

Figure 8. Ion cluster residence time correlation functions for CaCl2 solutions as a function of concentration in (a) supercritical (SC) conditions (T = 673 K and P = 350 bar) and (b) ambient conditions (RT) (T = 298 K and P = 1 bar).

solvent radial distribution functions (RDFs) in supercritical and ambient conditions. The ion-solvent RDFs for all of the ions and the solvent molecules are given in Figures S8a,b−S11a,b in the Supporting Information. The positions of the peak maxima of the ion-solvent radial distribution functions are in good agreement with those reported previously by other authors.27,28,41,55 From Figures S8a,b−S11a,b, we note that the ion-water structure is markedly dependent on the salt concentration in both ambient and supercritical conditions. The heights of the RDFs for these pairs decrease as the salt concentration increases. With an increase in concentration, the number of water molecules available for the ions decreases, which results in a decrease in the peak height. There is a rapid decrease in the peak heights in supercritical conditions compared to those in ambient conditions. The formation of clusters of larger sizes in supercritical conditions is responsible for the rapid decrease of the ion-solvent RDFs. The coordination numbers of water around the cations at CIPs in ambient and supercritical conditions are presented in Tables S6−S9. From the tables, it can be noticed that in both ambient and supercritical conditions the local solvent density around the cations is steadily decreasing with an increase in the salt concentration. In ambient conditions, the decrease in the hydration number is around 36%, whereas in supercritical conditions, it decreases by around 10%. In supercritical conditions, the solutes are present as ion clusters rather than as single ions (even at low salt concentration). However, in ambient conditions, when the concentration is low (say 0.27 m), no significant clustering is observed (Section 3.2) and most of the ions are present as single ions, which explains the higher

ions present in the supercritical solutions. It would be interesting to check this result for other halides. The ion cluster residence time correlation functions, c(t), which characterize the lifetimes of the ion pair, are shown in Figure 8a,b in supercritical and ambient conditions, respectively, as a function of salt concentration. This function is defined as c(t ) = ⟨p(0)p(t )⟩

(7)

where p(t) = 1 if a given ion is still in the shell of the same ion at time t and 0 otherwise and the angular brackets denote ensemble averaging over all trajectories. In ambient conditions, the lifetimes of ion pairs increase with an increase in salt concentration, indicating a higher stability of the clusters, whereas the reverse is observed in supercritical conditions. The higher stability of the contact ion pair with increasing concentration in ambient conditions is supported by Figure 8b. The cluster size correlation times in supercritical conditions are shorter than the corresponding times in ambient conditions. These are the indicators of homogeneity of the salt solutions in supercritical conditions. Only at small concentrations (due to a very small value of the dielectric constant), there is predominantly a single cluster, and this seems to be a feature of most ionic solutions at low concentrations in supercritical conditions. Figure S1 illustrates these features at different concentrations in supercritical and ambient conditions. 3.3. Ion-Solvent Radial Distribution Functions. To analyze the local solvation structures around M2+ and Cl− ions as a function of salt concentration, we have computed the ionH


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10−5 cm2 s−1, DCl− = 0.447 ± 0.015 × 10−5 cm2 s−1). Scaling the charges increases the self-diffusion coefficient value (DCa2+ = 0.55 ± 0.02 × 10−5 cm2 s−1, DCl− = 1.15 ± 0.01 × 10−5 cm2 s−1), whereas the electronic continuum correction with rescaling approach results in values (DCa2+ = 0.259 ± 0.003 × 10−5 cm2 s−1, DCl− = 0.56 ± 0.03 × 10−5 cm2 s−1) that are in good agreement with the experiment. The self-diffusion coefficient of the calcium and chloride ions in aqueous solutions of calcium chloride in ambient conditions as a function of salt concentration is in excellent agreement with the experimental results reported by Wang.114 The experimental and simulation results are presented in Figure S13. MD simulations of 1.1 M aqueous solutions of SrCl2 were studied by Spohr et al.116 The self-diffusion coefficient of the Sr2+ and Cl− ions were found to be DSr2+ = 0.60 ± 0.1 × 10−5 cm2 s−1 and DCl− = 1.2 ± 0.3 × 10−5 cm2 s−1 in ambient conditions. Muller et al. calculated the self-diffusion coefficient of water in a number of electrolyte solutions.115 The results obtained by them are in good agreement with our results for MgCl2 and CaCl2 electrolyte solutions in ambient conditions. 3.5. Hydrogen Bonding. The presence of ionic species produces important modifications in both the structure and dynamics of water, which is mainly attributed to the changes in the hydrogen bond network. In supercritical conditions, the decrease in the density of water produces a remarkable reduction in the dielectric constant of water as well as the hydrogen-bonding network of water. Definitions of hydrogen bonds in molecules are usually based on either the energetic or the geometric criterion. We have used the geometric criterion suggested by Ma et al.,117 which is based on both the distance and the angle, and is found to be as efficient as the energetic criterion for hydrogen bond calculations in the supercritical conditions. Addition of electrolytes also changes the hydrogen-bonding network of water. The average number of hydrogen bonds as a function of salt concentration in both ambient and supercritical conditions is given in the Supplementary Information in Table S11. From Table S11, it is seen that in supercritical conditions the average number of hydrogen bonds per water molecule is ∼1.45 at low salt concentrations, whereas the same number at room temperature is ∼3.49. The addition of ionic solutes creates a strong local structure around themselves, and as a result, the H-bonding structure of water is disrupted in both ambient and supercritical conditions. As seen from Table S6, an increase in salt concentration is accompanied by a decrease in the average number of hydrogen bonds in both ambient and supercritical conditions. The average number of hydrogen bonds decreases by ∼64% as we go from ambient to supercritical conditions (when the concentration is low), but at a higher salt concentration, the decrease is ∼43%. The number of hydrogen bonds in supercritical conditions is ∼2.5 times less compared to that in ambient conditions. The decrease in the extent of an average number of hydrogen bonds in supercritical conditions can be explained by weaker intermolecular interactions between solvent molecules resulting from a lower solvent density in supercritical conditions. In ambient conditions, the hydrogen bonding decreases by around ∼61% for MgCl2, whereas for BaCl2, the decrease is around ∼39%. In supercritical conditions, the hydrogen bonding decreases by around ∼21% for MgCl2, whereas for BaCl2, the decrease is around ∼8%. The effect of ions on the structural properties of water can be explained by a competition between ion-water interactions (governed by charge density effects) and

coordination number of cations at room temperature. With increasing salt concentration, RCNs decrease as the hydration shells are now substituted by chloride ions. A lower decrease in the hydration number of the cations in supercritical conditions compared to that in ambient conditions implies that the cations form the cores of the clusters and there is not much change in the vicinity of these cores as the concentration is increased. For the Cl− ion, the anion−oxygen peak is centered at 0.33 nm, which is in good agreement with that deduced from MD simulations5,6,28,29,78,81 and from X-ray diffraction studies. The first peaks of the Cl−−O (H2O) radial distribution functions are centered at around 0.33 nm in both the thermodynamic states under study. Similar to the cation−water RDFs, the Cl−−water RDFs are also dependent on the salt concentration in both ambient and supercritical conditions. The g(r) peak height decreases with an increase in salt concentration in both ambient and supercritical conditions. The running coordination numbers of water around Cl− at CIPs in ambient and supercritical conditions are presented in Table S10. The RCNs of water around the anion decrease with an increase in salt concentration in both ambient and supercritical conditions. Clustering increases with an increase in concentration in both ambient and supercritical conditions, which results in a decrease in the hydration numbers of the anion. The larger decrease in RCNs of anions (compared to those of cations) in supercritical conditions (with an increasing concentration) indicates a greater exposure of anions to solvent molecules in the clusters. 3.4. Diffusion Constants. The diffusion coefficients of the ions and the solvent molecules in ambient as well in supercritical conditions are calculated from the mean square displacements, using Einstein’s relation. The variation of the diffusion constants of the cations, anions, and solvent molecules in supercritical and ambient conditions are presented in Figure S12a−d The self-diffusion coefficients increase with an increase in temperature and decrease with an increase in concentration. The increase of salt concentration causes an enhancement of oscillations of particles and consequently a decrease of the selfdiffusion coefficients. In ambient conditions, the self-diffusion coefficients of the M2+ ions are lower than those of the Cl− ion, yet the values are close to each other at high concentrations. This phenomenon can be related to the fact that at higher concentrations the M2+−Cl− pairing is increased (as evidenced in Figure 1a). However, in supercritical conditions, the selfdiffusion coefficients of M2+ ions and Cl− ion are close to each at lower salt concentrations (Figure 1b) as the association in supercritical conditions is favored when the concentration is low (i.e., low density). There exists other simulation data of self-diffusion coefficients of ions, calculated at infinite dilution (a single ion in the cell or an ion pair in the cell). The results of Obst and Bradaczek112 from MD simulations using the CHARMM22 force field for an infinite dilute solution (DMg2+ = 0.62 ± 0.09 × 10−5 cm2 s−1, DCa2+ = 0.55 ± 0.04 × 10−5 cm2 s−1, DSr2+ = 0.54 ± 0.07 × 10−5 cm2 s−1) are lower than the experimental values (DMg2+ = 0.71 × 10−5 cm2 s−1, DCa2+ = 0.79 × 10−5 cm2 s−1) reported by Mills and Lobo.113 Self-diffusion coefficients of the calcium ion, chloride ion, and water for a 4 m solution were calculated by Kohagen and co-workers. 75 In ambient conditions, in the system with full charges, the self-diffusion coefficients for Cl− and Ca2+ ions are too small (DCa2+ = 0.067 ± 0.001 × 10−5 cm2 s−1, DCl− = 0.15 ± 0.01 × 10−5 cm2 s−1) compared to the experimental values (DCa2+ = 0.225 ± 0.002 × I


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diffusion coefficients of M2+ and Cl− ions are seen to be quite close to each other at high salt concentrations, which supports the fact that ion association is stronger at higher salt concentrations. However, in supercritical conditions, the diffusion coefficient of M2+ and Cl− ions are close to each other at low salt concentrations. Thus, we observe a stronger ion−ion association in low salt concentrations in supercritical conditions, whereas in ambient conditions, the situation is reversed. It is thus seen that temperature, dielectric constant, ionic size, ion concentration, and solvent density bring out interesting and some unique features of ion association, which do have impact on tunability of solvent media. Our results of the structural and dynamical aspects of ion hydration in ambient and supercritical conditions as a function of salt concentration lead to several insights into the microscopic processes in these solutions.

water−water interactions (governed by hydrogen bonding). Small ions (commonly known as Kosmotropes) cause strong electrostatic ordering of neighboring water molecules because of their high charge densities and thus the hydrogen-bonding network in water is significantly perturbed. However, in the case of large ions (also known as chaotropes), because of their low charge densities, the tetrahedral network of water is not affected much and neighboring water molecules are predominantly hydrogen-bonded. As a result, the average number of hydrogen bonds is smaller in aqueous MgCl2 solutions compared to that in BaCl2 solutions in both ambient and supercritical conditions. As the concentration increases from 0.27 to 5.55 m, the number of ions increases from 15 to 300 but the number of solvent molecules is the same (1000). Thus, in a 5.55 m solution, there are 300 ions that are solvated and the relative number of solvent molecules decreases. This results in a fewer number of hydrogen bonds.

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4. CONCLUSIONS The potentials of mean force between the M2+ ion and Cl− ion show that the fraction of contact ion pairs (CIPs) increases and that of solvent-separated ion pairs (SSIPs) decreases with increasing ion concentration in ambient conditions. In supercritical conditions, both CIPs and SSIPs become less stable with an increase in ion concentration. The higher stability of CIPs at low salt concentrations (i.e., solutions having a lower density) is consistent with the tendency for cluster formation in supercritical solutions at low densities. With increasing concentration, the cluster size increases in both ambient and supercritical conditions, but the lifetimes follow an opposite trend. The longest lifetime in ambient conditions is observed for the 5.55 m solution, whereas in supercritical conditions, the longest lifetime is observed for the 0.27 m solution, which explains the trend in the stabilities of contact ion pairs. The stabilities of CIPs are found to decrease with an increase in the size of the cations in both ambient and supercritical conditions, which is because of the higher charge densities of cations of smaller size, which favors CIP formation. In the case of Na+−Na+ PMFs, the first minimum corresponds to the solvent-assisted ion pair (SAIP),109 whereas in the case of M2+−M2+ (M = Mg, Ca, Sr, and Ba) PMFs, the first minimum corresponds to the solvent-shared ion pair (SShIP). It is very unlikely that two highly positive charged cations will stay in contact with each other and hence solvent molecules have to act as a bridge between the ions. Cations of smaller size lead to higher local densities than the cations of larger size in both ambient and supercritical conditions. An increase in concentration and temperature (i.e., going from ambient to supercritical conditions) results in a decrease in cation hydration numbers and an increase in the Cl− hydration number. The coordination number of the cations decreases with an increase in concentration but that of the Cl− ion increases with an increase in concentration. The coordination numbers of the ions decrease with an increase in temperature. Salt concentration is seen to have a strong effect on the hydrogen-bonding network of water in both ambient and supercritical conditions. The difference in the number of hydrogen bonds for small (Mg2+) and large ions (Ba2+) is explained on the basis of ion-water and water−water interactions. The self-diffusion coefficients of water and M2+ and Cl− ions increase with an increase in temperature at all concentrations, whereas they decrease with an increasing concentration and cation size. In ambient conditions, the

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b07690. Force-field and geometric parameters of solvent and solute molecules (Tables S1 and S2); details of simulation boxes (Tables S3 and S4); dielectric constant as a function of salt concentration in ambient and supercritical conditions (Table S5); hydration numbers of cations and anions in ambient and supercritical conditions (Tables S6−S10); hydrogen bonds as a function of concentration (Table S11); snapshots of configurations (Figure S1); PMFs as a function of molality for Mg2+−Cl−, Sr2+−Cl−, and Ba2+−Cl− ion pairs (Figures S2−S4) in supercritical and ambient conditions; PMFs as a function of molality for Mg2+− Mg2+, Sr2+−Sr2+, and Ba2+−Ba2+ ion pairs (Figures S5− S7) in supercritical and ambient conditions; radial distribution functions of cations and Cl− ions with the oxygen site of water in supercritical and ambient conditions (Figures S8−S11); diffusion coefficients of the ions (Figure S12); and a comparison of diffusion coefficients (experiment and simulation) of calcium and chloride ions in ambient conditions as a function of salt concentration (Figure S13) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-22-2576-4199. Fax: +91-22-2576-7152. ORCID

B. L. Tembe: 0000-0002-6730-2981 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank high computing facility of the Indian Institute of Technology Bombay and Chemistry Department of IIT Bombay.

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