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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 Bhalachandra Laxmanrao Tembe J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07690 • Publication Date (Web): 31 Oct 2017 Downloaded from http://pubs.acs.org on November 4, 2017

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The Journal of Physical Chemistry

Structural and Dynamical Properties of Alkaline Earth Metal Halides in Supercritical Water: Effect of Ion Size and Concentration

Sonanki Keshri and B. L. Tembe* Sonanki Keshri Graduate Student, Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India E-mail: [email protected]

*B. L. Tembe Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India Phone No: +91-22-2576-4199, Fax No: +91-22-2576-7152 E-mail: [email protected]

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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 molal to 5.55 molal) in supercritical and ambient conditions to investigate their structural and dynamical properties. A strong influence of the salt concentration is found on the ion-ion pair correlation functions in both ambient and supercritical conditions. In supercritical conditions, significant clustering is observed in 0.27 molal solution whereas, the reverse situation is observed at room temperature and this is also supported by the residence times of the clusters. 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 coefficient of water, the cations and the chloride ion increase with increasing temperature, whereas they decrease with increasing salt concentration. The cluster size distribution shows strong density dependence in both ambient and supercritical conditions. In supercritical conditions, cluster sizes display a near Gaussian distribution whereas, the distribution decays monotonically in ambient conditions.

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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, non-flammability 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 environmentfriendly nature. The properties of supercritical water are very different from those at ambient conditions. Dramatic changes occur in the physical properties of water. Densities of SCW in the critical region can be varied from very low (gas like) to high (liquid like) 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 hydrogen bonding network of water molecules is 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, non-flammable and non–toxic in nature for a large number of chemical reactions that are currently carried out in carcinogenic organic solvents, SCW is now a days considered as an alternative and is widely being used in many industrial and chemical processes.11-15 An outstanding property of water at ambient conditions is its intrinsic ability to dissolve ionic and polar species due to its unusually large dielectric constant. But at elevated temperature and pressure i.e. at 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 The ion solvation in aqueous solutions governs many important biological, geological, and chemical processes.19-21 The most



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promising application of SCW is the destructive oxidation of hazardous waste using supercritical water oxidation (SCWO).22-24 Alkali and alkaline earth metal chlorides are the most prevalent naturally occurring species in SCW. In recent years, 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 contact ion pair is the most stable structure in supercritical conditions as compared to those in ambient conditions. But 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 have been studied by several authors using different numbers of ion pairs in both ambient and supercritical conditions,50-71 but those of alkaline earth metal halides have not been explored much.72-91 Concentrated solutions of calcium chloride have been studied a lot at ambient conditions by several research groups. Chialvo and co-workers83 performed molecular dynamics simulations of aqueous CaCl2 solutions over a wide range of concentration (0 < m ≤ 9.26) at 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 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 neutron diffraction isotope substitution method by Badyal and co-workers.9 Seward and co-workers performed X-ray absorption fine structure measurements (EXAFS) to study solvation and ionpairing in aqueous strontium solutions (0.10 m) from 25 to 3000C.91 Molecular dynamics simulations of aqueous solutions of magnesium chloride over a wide range of concentrations (0.2 to 4.9 M) were performed by Bartczak et al.84 MD simulations of concentrated MgCl2 and CaCl2 aqueous solutions at various temperatures (298 K to 573 K) and pressures (0.5 bar to 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 to 0.2 mol kg-1) from T = 295 K to 625 K at P = 20 4 ACS Paragon Plus Environment

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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 at 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.

2. Methodology and Computational Details All the MD simulations have been performed in an isothermal-isobaric ensemble at T = 673 K and P = 350 bar using GROMACS package (version 4.5.4).92 In the present study, the SPC/E model has been used for water.93 The critical parameters of SPC/E water are Tc = 638.6 K and Pc = 139 bar.94 Since 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 Table S1 and Table S2 in the Supplementary 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 Lennard-Jones potential and the long-ranged electrostatic interactions are modeled with a Coulombic potential. U ij (r ) =

Aij r

12

−

Bij r

6

+

qi q j

(1)

r

here, i and j denote a pair of interaction sites on different molecules, qi = charge located at site i and qj = charge located at site j, r = site-site separation. The terms Aij and Bij are determined from,

Aij = 4 × (ε ij ) × (σ ij )12 Bij = 4 × (ε ij ) × (σ ij ) 6

(2) (3)

whereas, ε ij and σij are calculated using the Lorentz-Berthelot mixing rules,95 (4)

ε ij = (ε i × ε j )1 / 2 σ ij = (

σi +σ j 2

(5)

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Half of the box length is used as a cut-off for Lennard-Jones forces. The electrostatic interactions are treated by particle Mesh Ewald (PME) method,96 with a Coulomb cut-off of 1.5 nm and an interpolation order of 4. For non-bonded van der Waals interactions, a 1.5 nm cut-off 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 ) = − k BT ln g ( r )

(6)

Periodic boundary conditions (PBC) are used along with the minimum image criterion.97 The neighbor list is updated every 10 steps. 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. 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. Parrinello-Rahman barostat102 is used for production run. The details of simulation boxes in supercritical (SC) and ambient conditions (RT) are listed in the Supplementary Information in Table S3 and Table S4 respectively. The simulated densities of the mixtures in ambient and supercritical conditions match well with the experimental densities.103-105 the initial configurations are generated using the software PACKMOL.106

3. Results and Discussions 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 and running coordination numbers. Diffusion coefficients of the ions and solvent as a function of salt concentration and ion size were also obtained. 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) 6 ACS Paragon Plus Environment

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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- ion are calculated from the pair distribution function, gM-Cl(r), using equation (6).

3.1.1. Effect of salt concentration The PMFs of calcium chloride ion pair as a function of salt concentration in supercritical (SC) and ambient conditions (RT) are presented in Fig. 1(a) and Fig. 1(b) respectively.

0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

0

-15

20

0

-30

(b) Ca2+ - Cl- PMFs (RT)

20 W (r) / kJ mol -1

(a) Ca2+ - Cl- PMFs (SC)

15 W (r) / kJ mol-1

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0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

10

0

-20

-40 0.4

0.2

0.4

0.6 r / nm

0.8

0.8

1.2

1.6

2.0

-10 0.2

1.0

0.4

0.6

0.8

1.0

r / nm

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

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 Fig. 1(a). We have retained W(r) till 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 separated ion pairs (SSIPs), the first solvation shells of both the solutes



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do not share any common solvent molecule.107 Representative pictures of these four different states are given below (Fig. 2).

Fig. 2. Schematic representation of contact ion pair (CIP), solvent assisted ion pair (SAIP), solvent shared ion pair (SShIP) and solvent separated ion pair (SSIP).

While 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 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 a solvent diameter (water). We are referring this ion pair as solvent assisted ion pair (SAIP). In solvents like DMSO, the second minimum comes 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 8 ACS Paragon Plus Environment

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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 [Fig. 1(a) and Fig. 1(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 Fig. 1(a) are more stable than the CIPs in Fig. 1(b). In the case of supercritical conditions, the depths of the CIPs range from -38.3 kJ/mol (0.27 molal) to -18.8 kJ/mol (5.55 molal). For the ambient case, the depths of the CIPs range from -0.31 kJ/mol (0.27 molal) to 7.51 kJ/mol (5.55 molal). 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 (for supercritical conditions). A notable feature of the PMFs in ambient conditions is that first transition state is not easily simulated when the salt concentrations are low (0.27 m, 0.55 m 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. But 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 thermal 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 the distances corresponding to ion-pairing. From Fig. 1(a) and Fig. 1(b), it is observed that there is a presence of stable SAIPs in all 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 (0.27 molal) to -2.04 kJ/mol (5.55 molal) and in supercritical conditions, they range from -16.8 kJ/mol (0.27 molal) to -1.87 kJ/mol (5.55 molal). We also observe a third minimum corresponding to SSIP. The depths of SSIPs range from -15.6 kJ/mol (0.27 molal) to -1.98 kJ/mol (5.55 molal) in supercritical conditions and in ambient conditions they range from -0.54 kJ/mol (0.27 molal) to 0.04 kJ/mol (5.55 molal). In 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 9 ACS Paragon Plus Environment


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increase in temperature and decrease in salt concentration in supercritical conditions. In contrast to the CIP stability, SAIPs and SSIPs are more stable in 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 based on the decrease in 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 Supplementary 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 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 in supercritical conditions are more stable compared to those in ambient conditions. This has been previously observed in ion-pair association studies by several authors.17, 28, 29 Since the decrease in the dielectric constant facilitates ion association, one may expect contact ion pair to be more stable in 5.55 molal solution in supercritical conditions but in reality, we observe the opposite. There is hardly any decrease in the dielectric constants as we go from 0.27 molal (~3.47) to 5.55 molal solution (~3.30) in the supercritical conditions. Thus, dielectric constant of the solvent does not play a significant role here in providing stability of the CIPs in supercritical conditions. The overall structure in ambient and supercritical conditions can be roughly visualized with the help of snapshot of different configurations given in the Supplementary Information in Fig. S1. From Fig. 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 (Fig. 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 10 ACS Paragon Plus Environment

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concentrations. The PMFs for other alkaline earth metal chlorides in supercritical and ambient conditions are shown in Figs. S2 [(a) and (b)] to Figs. S4 [(a) and (b)] in the Supplementary Information. The deepest contact minima in both ambient and supercritical conditions are observed for magnesium halides. Barium halides show the least stable contact minima. We have also studied association for the M2+-M2+ (M = Mg, Ca, Sr and Ba) and Cl- - Cl- ions in both ambient and supercritical conditions. The PMFs for Ca2+-Ca2+ ion-pair as a function of salt concentration in supercritical and ambient conditions are shown in Fig. 3(a) and Fig. 3(b) respectively. (a) Ca2+ - Ca2+ PMFs (SC)

20 10 0 -10

0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

(b) Ca2+ - Ca2+ PMFs (RT)

20 W (r) / kJ mol-1

30

W(r) / kJ mol-1

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0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

10

0

-20 -30 0.4

0.6

0.8

1.0

0.4

0.6

0.8

1.0

r / nm

r / nm

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

In this case also, W(r) does not reach the value of zero till r = 1 nm. There is no specific structure formed beyond 1 nm in both ambient and supercritical conditions and the structural information which we extract from PMFs is between 0.47 – 0.82 nm. But if we plot W(r) up to 2 nm, asymptotic behavior is seen. At 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. Potentials of mean force of Na+-Na+ and Cl- - Cl- ion pairs in water by constrained MD approach have been studied by Guardia 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 11 ACS Paragon Plus Environment


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 the alkaline earth metal cations, the first minimum is solvent shared ion pair (SShIP) and not contact ion pair or a SAIP. Solvent shared ion pair is found to be most stable at lower density i.e. at a low salt concentration in supercritical conditions. The first minimum which occurs at 0.50 nm in supercritical condition is absent in ambient condition when the salt concentration is very low (0.27m, 0.55 m and 1.38 m). But at higher salt concentrations, the first minimum occurs near 0.50 nm. A 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 an ambient condition which is mainly because of the low dielectric constant of water. From the above figures, it is also seen that 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 neighbouring water molecules around the ions act as a bridge between the ions and thus provide stability to the configuration. The PMFs of Mg2+-Mg2+, Sr2+-Sr2+ and Ba2+-Ba2+ ions as a function of salt concentration in supercritical and ambient conditions are given in Figs. S5 [(a) and (b)] to Figs. S7 [(a) and (b)] in the Supplementary Information. Since 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. The PMFs of Cl--Cl- ions (the counter ion being Ca2+) in supercritical and ambient conditions are presented in Fig. 4(a) and Fig. 4(b) respectively.

10

15

(a) Cl- - Cl- PMFs (SC)

0

W(r) / kJ mol-1

W(r) / kJ mol-1

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-10 0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

-20 -30

(b) Cl- - Cl- PMFs (RT)

0.27 m 0.55 m 1.38 m 2.77 m 4.16 m 5.55 m

10

5

0

-5 0.4

0.6 r / nm

0.8

1.0

12

0.3


0.6

0.9 r / nm

1.2

1.5

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Fig. 4. Potentials of mean force between Cl- and Cl- ion pair in water as a function of salt concentration in (a) supercritical condition (SC) [T = 673 K and P = 350 bar] and (b) ambient condition (RT) [T = 298 K and P = 1 bar].

In supercritical condition, the first minimum occurs at around 0.36 nm followed by a broad minimum at around 0.65 - 0.67 nm. At ambient conditions for low salt concentrations (0.27 m 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. Since the first minimum occurs at around 0.36 nm which corresponds to the interionic distance between two chloride ions (the ionic radius of Cl- ion is 0.184 nm), so we can say that 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 at supercritical conditions whereas at ambient conditions CIP is 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 Fig. 5(a) and Fig. 5(b) for supercritical and ambient conditions.

(b) RT (2.77 molal)

(a) SC (2.77 molal)

20 10 0

Mg2+ - Cl-

-10

Ca2+ - ClSr2+ - Cl-

-20

W (r) / kJ mol-1

20

W(r) / kJ mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Mg2+ - ClCa2+ - Cl-

10

Sr2+ - ClBa2+ - Cl-

0

Ba2+ - Cl-

-30

-10

0.2

0.4

0.6 0.8 r / nm

1.0

1.2

1.4

0.2

0.4


0.6

0.8 r / nm

1.0

1.2

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Fig. 5. Potentials of mean force between the alkaline earth metal ions and the chloride ion in (a) supercritical condition (SC) [T = 673 K and P = 350 bar] and (b) ambient condition (RT) [T = 298 K and P = 1 bar] for 2.77 molal salt concentration. 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 increase in the size of the cations. This result indicates that the CIP is likely to be 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 a larger one, which favors the CIP formation. In supercritical condition, the depths of the CIPs range from -25.6 kJ/mol (Mg2+- Cl- ion pair) to -19.8 kJ/mol (Ba2+- Cl- ion pair) [Fig. 5(a)]. For the ambient case, the depths of the CIPs range from -8.3 kJ/mol (Mg2+- Cl- ion pair) to -7.3 kJ/mol (Ba2+- Cl- ion pair) [Fig. 5(b)]. CIPs in supercritical condition are 3 times more stable than those in ambient condition. 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 cut-off. The first minimum of the cation-anion RDF was used as the cut-off for connected ions. The cluster size distributions as a function of concentration are shown in Fig. 6(a) and Fig. 6(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.


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

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 1.38 molal solution, the cluster sizes of 3 and 4 dominate. For 2.77 and 5.55 molal solutions, cluster sizes of 6 and 11 (respectively) dominate. In supercritical conditions, there is a strong dominance of large sized clusters and the distribution of cluster sizes is much wider, almost appearing like a Gaussian distribution. For 5.55 molal in supercritical conditions, the cluster sizes are distributed between 50 to 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 Fig. 7(a) and Fig. 7(b). We have calculated several such trajectories of different ion pairs in different clusters and given a few representative examples in these figures.

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1.5 1.2 0.9 0.6 0.3

0.0 0

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400 600 Time / ps

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400 600 Time / ps

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Fig. 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 molal and (b) 5.55 molal solutions.

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 0.27 molal solution (in supercritical conditions) and 5.55 molal solution (in ambient conditions). This indicates that ion-pairing in supercritical 16 ACS Paragon Plus Environment

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conditions is favored in low concentrated solutions, whereas in ambient conditions it is favored at high concentrations. The interionic separation distance shows a large fluctuation from equilibrium distance in ambient conditions for 0.27 molal 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 Fig. S1, where all the ions tend to remain as a single ion cluster in low concentrated solutions (0.27 molal) 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 molal solutions in supercritical conditions, fluctuations from the contact ion pairing distance (i.e., 0.27 nm) are still observed (Fig. 7(b)). This is why contact ion pair is 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 molal), the rate of interconversion from one size to the other is quite high which results in the lower stability of CIP. We would also like to note that the solutions studied here are homogeneous and clusters of different size 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 1/3rd of the total number of ions present in the supercritical solutions. It would be interesting to check this result for other halides. The ion cluster residence times correlation functions, c(t), which characterize the lifetimes of the ion pair are shown in Fig. 8(a) and Fig. 8(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. 1.0

1.0 (a) SC 0.8

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Fig. 8. Ion-cluster residence times correlation functions for the CaCl2 solutions as a function of concentration in (a) supercritical condition (SC) [T = 673 K and P = 350 bar] and (b) ambient condition (RT) [T = 298 K and P = 1 bar].

In ambient conditions, the lifetimes of ion pairs increase with an increase in salt concentration indicating higher stability of the clusters whereas, the reverse is observed in supercritical conditions. Higher stability of contact ion pair with increasing concentration in ambient conditions is supported by Fig. 8(b). The cluster size correlation times in supercritical conditions are shorter than the corresponding times in ambient conditions. These are 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. Fig. S1 at different concentrations in supercritical and ambient conditions illustrate these features.

3.3. Ion-Solvent Radial Distribution Functions In order to analyze the local solvation structures around M2+ and Cl- ions as a function of salt concentration, we have computed the ion-solvent radial distribution functions (RDFs) in supercritical and ambient conditions. The ion-solvent RDFs for all the ions and the solvent molecules are given in the Supplementary Information in Figs. S8 [(a) and (b)] to Figs. S11 [(a) and (b)]. 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 Figs. S8 [(a) and (b)] to Figs. S11 [(a) and (b)], we note that ion-water structure is markedly dependent on 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 to 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. 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 18 ACS Paragon Plus Environment

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conditions are presented in Tables S6 to 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 of the salt concentration. In ambient conditions, the decrease in 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 in low salt concentration). But in ambient conditions, when the concentration is low (say 0.27 molal), no significant clustering is observed (Section 3.2) and most of the ions are present as single ions which explains the higher coordination number of cations in room temperature. With increasing salt concentration, and 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 those 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 concentration is increased. For Cl- ion, the anion-oxygen peak is centered at 0.33 nm which is in good agreement 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 as well as in supercritical conditions. The g(r) peak height decreases with an increase in salt concentration in both ambient and supercritical conditions. The running co-ordination 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 decreases in the hydration numbers of the anion. The larger decrease in RCNs of anions (compared to cations) in supercritical condition (with 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 the supercritical conditions are calculated from the mean square displacements, using the Einstein’s relation. The variation of the diffusion constants of the cations, anions and the solvent molecules in supercritical and ambient conditions are presented in Fig. S12(a) to Fig. 19 ACS Paragon Plus Environment


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S12(d). The self-diffusion coefficients increase with increasing temperature and decrease with increase in concentration. The increase of salt concentration causes an enhancement of oscillations of particles and consequently a decrease of the self-diffusion coefficients. In ambient conditions, the self-diffusion coefficient of the M2+ ions are lower than those of Clion, 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 Fig. 1(a)). But in supercritical conditions, the self-diffusion coefficients of M2+ ions and Clion are close to each in lower salt concentrations (Fig. 1(b)) 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 calcium ion, chloride ion and of 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 coefficient for Cl- and Ca2+ ions are much 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 × 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 ECCR (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] in good agreement with experiment. The self-diffusion coefficient of calcium ion 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 Fig. S13. MD simulations of 1.1 molar aqueous solutions of SrCl2 was studied by Spohr et al.115 The self-diffusion coefficient of Sr2+ and Cl- ions were found to be DSr2+ = 0.60 ± 0.1 × 10-5 cm2 s-1, DCl- = 1.2 ± 0.3 × 10-5 cm2 s-1 in ambient conditions. Muller et al. calculated self-diffusion coefficient of water in a number of electrolyte solutions.116 The results obtained by them are in good agreement with our results for MgCl2 and CaCl2 electrolyte solutions at ambient conditions.


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3.5. Hydrogen Bonding The presence of ionic species produces important modifications in both the structure and dynamics of water, 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 energetic or geometric criterion. We have used the geometric criterion suggested by Ma et al.117 which is based on both 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 in low salt concentrations, whereas the same number at room temperature is ~3.49. Addition of ionic solutes creates a strong local structure around themselves and as a result, H-bonding structure of water is disrupted in both ambient and supercritical conditions. As seen from table 6, 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 higher salt concentration the decrease is ~ 43 %. The number of hydrogen bonds in supercritical conditions is ~2.5 times less compared to those 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 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 hydrogen bonding network in water is significantly perturbed. But in the case of large ions (also known as Chaotropes), because of 21 ACS Paragon Plus Environment


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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 those in BaCl2 solutions in both ambient and supercritical conditions. As the concentration increases from 0.27 molal to 5.55 molal, the number of ions increases from 15 to 300 but the number of solvent molecules is the same (1000). Thus in a 5.55 molal solution, there are 300 ions which are solvated and the relative number of solvent molecules decreases. This results in a fewer number of hydrogen bonds.

4. Conclusions The potentials of mean force between 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. Higher stability of CIPs in 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, cluster size increases in both ambient and supercritical conditions but the lifetimes follow an opposite trend. Longest lifetime in ambient conditions is observed for 5.55 molal solution, whereas in supercritical conditions, longest lifetime is observed for 0.27 molal solution which explains the trend in the stabilities of contact ion pairs. Stabilities of CIPs are found to decrease with an increase in the size of the cations in both ambient as well as in 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 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 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 of cation hydration numbers and an increase in the Cl- hydration number. The coordination number of the cations decreases with an increase concentration but that of Cl- ion increases with an increase in concentration. The coordination numbers of the ions decrease with a rise in temperature. Salt concentration is seen to have a strong effect on the 22 ACS Paragon Plus Environment

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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, M2+ and Cl- ions increase with an increase in temperature at all concentrations, whereas they decrease with increasing concentration and cation size. In ambient conditions, the diffusion coefficients of M2+ and Cl- ions are seen to be quite close to each other at high salt concentrations which support the fact that ion association is stronger in higher salt concentrations. But in supercritical conditions, the diffusion coefficient of M2+ and Cl- ions are close to each other in 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 the ion hydration in ambient and supercritical conditions as a function of salt concentration lead to several insights of the microscopic processes in these solutions.

Associated content Supplementary Information In the Supplementary Information, we have given the force field and geometric parameters of solvent and solute molecules (Table S1 and S2), details of simulation boxes (Table 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 (Table S6 to S10), hydrogen bonds as a function of concentration (Table S11), Snapshots of configurations (Fig. S1), PMFs as a function of molality for Mg2+-Cl- , Sr2+-Cland Ba2+-Cl- ion pair [Figs. S2 to Figs. S4 ] in supercritical and ambient conditions, , PMFs as a function of molality for Mg2+-Mg2+, Sr2+-Sr2+ and Ba2+-Ba2+ ion pair [Fig. S5 to Fig. S7] in supercritical and ambient conditions, radial distribution functions of cations and Cl- ions with oxygen site of water in supercritical and ambient conditions [Fig. S8 to Fig. S11], Diffusion coefficients of the ions (Fig. S12) and comparison of diffusion coefficients (experiment and



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simulation) of calcium and chloride ions in ambient conditions as a function of salt concentration (Fig. S13).

Author Information Corresponding Author *B.L.Tembe. Phone No.: +91-22-2576-4199. Fax No.: +91-22-2576-7152. Email: [email protected] Notes: The authors declare no competing financial interest.

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

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Structural and Dynamical Properties of Alkaline Earth Metal Halides in

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