The Journal of
Physical Chemistry VOLUME 98, NUMBER 24, JUNE 16, 1994
0 Copyright 1994 by the American Chemical Society
LETTERS Simulation of the Na+CI- Ion Pair in Supercritical Water Jiali Gao Department of Chemistry, State University of New York at Buffalo. Amherst, New York 14260-3000 Received: February 25, 1994; In Final Form: April 26, 1994'
Potentials of mean force (pmf) for the Na+Cl- ion pair in supercritical water were obtained from Monte Carlo simulations at 400 OC and pressures of 350 and 1000atm. The usual oscillatory behavior for ion pairs in ambient water is found to be much less structured in supercritical water, which is accompanied by disappearance of the minimum corresponding to the solvent-separated ion pair and a much deeper well for the contact ion pair. Solvent clustering is predicted to be significant for this attractive supercritical solution from analyses of the pmf and radial distribution functions. The results should be useful for developing models of ionic interactions in supercritical water.
The ubiquitous properties of water as a solvent are the most intriguing and important because life itself evolves in such a medium. Undoubtedly, the solvating power of water depends strongly on the density of the liquid, which is about 1 g/cm3 at room temperatureand atmosphere.' Theconcept that electrolytic salts and polar organic compounds such as amino acids and nucleotides dissolve in water, while "nonpolar" organic molecules are insoluble in aqueous solution, is certainly not true at elevated temperature and pressure.2 Above or near the critical point, the behavior of water as a solvent is entirely reversed. Now, organic compounds includinghydrocarbonsand molecular oxygen become completely miscible with supercritical water (SCW), whereas inorganic salts precipitate out of the s ~ l u t i o n .Consequently, ~ a powerful and promising procedure for destruction of organicwaste materials has been developed. In supercritical water, organic compoundsare oxidized to form carbon dioxide,water, and simple inorganicacids and salts with remarkable efficiency (>99.99%1).~ Of particular interest is ion pair associationat high temperature and pressure, Le., in supercritical and subsupercritical water, due to its importance to several disciplines including geochemistry and hazardous wastedestruction. In addition,supercritical water provides a unique environment for studying solute-solvent interactions since the fluid dielectric constant (e) can vary from 80 to about 2 simply by changing the temperature or pressure,
* Abstract published in Advance ACS Abstracts, June 1, 1994.
without altering the chemical composition of the solvent? Numerous experimentalstudieshave been performed to determine the solubility of inorganic salts in SCW and to refine conditions for organic waste oxidation;'5.1&12 however, little is known about structural and energetic details of ion-ion and ion-water interactions at the atomic level. An important issue in supercritical hydration is the formation of solventclusters near the solutewhen solute-solvent interaction is stronger than solvent-solvent interaction (attractive supercritical solutions).1'16 Early studies have demonstrated the significance of solvent clustering around the~olute.'~ Another important aspect is the formation of solute solute ~1ustering.I~ To answer some of these questions, we extend early molecular dynamics calculation^^^ and report the results from Monte Carlo simulations of the potential of mean force for the Na+Cl- ion pair as a function of ion separation in SCW at 400 OC and pressures of 350 and 1000 atm. The findings are compared with the results obtained in ambient water. Computational Details
Recently, we investigated the possibility of Monte Carlo simulations of supercritical water and dilute solutions using an empirical, pairwise potential function.18 A molecular dynamics calculation of an S Nreaction ~ in SCW has been reported.'" It was found that the TIP4P model performs reasonably well in describing properties of SCW, despite the fact that this potential
0022-365419412098-6049$04.50/0 0 1994 American Chemical Society
Letters
6050 The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 was developed for liquid water at 25 OC and 1 atm.19 However, limitations of the TIP4P model also exist for simulation of supercritical solution. The results from that study indicate that the TIP4P model overestimates the fluid density at 400 OC and a pressure range of 350-2000 atm. Nevertheless, the computed dielectric constants under these conditions are in good accord with experimental data for the corresponding fluid densities. It appears that the TIP4P critical temperature is somewhat lower than the experimental value, a finding also obtained for the SPC model by de Pablo et al.*7b921To characterize the critical point of the TIP4P model, Monte Carlo or molecular dynamics simulations in the Gibbs ensemble should be employed to yield the critical temperature and density based upon the coexistence curve.17b These calculations have not been carried out for the TIP4P model. Statistical mechanical Monte Carlo simulationsof the Na+Clion pair in supercriticalwater werecarried out with the isothermalisobaric (NPT) ensemble at 400 OC and pressures of 350 and 1000 atm. This correspondsto bulk conditions of p = 0.23 g/cm3 (pr = 0.72) and e = 3.6 and p = 0.59 g/cm3 (pr = 1.84) and t = 9.2, respectively, for the TIP4P modeLt8J9 The potential of mean force (pmf) as a function of ion separation was obtained using statistical perturbation theory (eq 1)*2
where H(R1) and H(R0) are enthalpies at ion separations of R1 and Ro and ( . . . ) ~represents (b) the ensemble average corresponding to H(R0). Consequently, H(R1) may be viewed as a perturbation toH(R0). Thecalculation wascarried out by moving the distance between Na+ and C1-, R, forward and backward at intervals of fO. 1or *O. 15Avia a double-wide sampling technique in a total of 56 Monte Carlo simulations for each pmf to cover R from 2.2 to 10 A.22b The systems consisted 390 TIP4P water molecules plus the ion pair situated along thez axis of a rectangular periodic cell. The OPLS potentials for Na+ and C1- were adopted in this study.23 Cutoff distances of 11 and 13 A were used for systems with high and low density, respectively, based on ionwater and water-water separations. Each simulation was equilibrated for 1 X lo6 - 2 X lo6 configurations, followed by an additional 2 X IO6 configurations of averaging. Standard deviationswere estimated from fluctuations of separate averages for blocks of 105 configurations, and these are about f0.3-0.4 kcal/mol for each pmf. To compare the ion-pair formation in ambient water, the simulations were repeated for a system containing 740 water molecules and the Na+Cl- ion pair at 25 OC and 1 atm. A cutoff distance of 10 A was used to evaluate the interaction energies. All pmf's are anchored at the longest separation distances studied in the simulation to the result from the continuum, "primitive model" obtained by dividing the Coulombic energy by the computed bulkdielectriccon~tant.~~ The simulationswere carried out on a SGI R4400 computer and a SUN Sparc 10 computer using BOSS.25 Results and Discussion The key results are displayed in Figure 1. Minima for the ion pair in ambient water (AW) are found at 2.6 and 4.5 A, corresponding to contact and solvent-separated ion pairs, respectively. There are no specific structural features beyond the solvent-separated species in the computed pmf. These observations are in good accord with the findingsfrom the first molecular dynamics simulationof the Na+Cl-ion pairs in water by Berkowitz et al. using importance sampling26 and by others in subsequent s t u d i e ~ . ~Similar ~ - ~ ~ features have been obtained for other ion pair systems.28 The present results indicate that the solventseparated ion pair is about 1.3 kcal/mol lower in energy than the
10.0
Ambient Water
3a g
0.0
-10.0
U
5I
-20.0
0
3 rEl
-30.0
-40.0 1.0
2.5
4.0
5.5
7.0
8.5
10.0
R (A) Figure 1. Computed potential of mean force for the Na+Cl- ion pair in ambient water (25 OC, 1 atm) and in supercritical water at reduced densities of pr = 1.84 (400 OC, loo0 atm) and pr = 0.72 (400 "C, 350 atm). Dashed curves are obtained by dividing the Coulombic energy by the fluid dielectric constant and are used to anchor the Monte Carlo potential of mean force.
contact ion pair, while the barrier separating the two species is 2 kcal/mol. Berkowitz et al. found that the contact minimum for theNa+Cl-systemis 1.3kcal/molmorestable than thesolventseparated minimum.26 The difference might be due to the fact that a different solvent model (TIPS2 model) was used in that study. Nevertheless, it is important to note that the energy barrier dividing these ion pairs is small (ca. 1-3 kcal/mol), allowing the ions to dissociate into the bulk. However, the pmfs for the Na+Cl- ion pair in SCW exhibit some remarkable differences in comparison with that in ambient water (Figure 1). First, the interaction between the two ions shows a progressive increase as the fluid density decreases and is much stronger in SCW than in AW. The minimum energies are -15.7 f 0.3 and -26.9 f 0.4 kcal/mol, respectively, for simulations at 1000 and 350 atm, as opposed to about -1 kcal/ mol under ambient conditions. This of course is not surprising in view of the much smaller fluid dielectric constant under supercritical conditions? which are 9.2 and 3.6 at 1000 and 350 atm for the TIP4P water at 400 OC.18 Clearly, such a strong interaction between Na+ and C1- would prevent the ions from dissociating into the bulk, severely reducing the solubility of inorganic salts in SCW. The pmfs shown in Figure 1 indicate solute-solute clustering should be significant in SCW. For comparison, the experimentally-determinedsolubility of sodium chloride in water vapor ranges from 1 to 100 ppm (by weight) for temperature and pressure ranges of 450-550 OC and 100-250 bar.12 Second, the free energy minimum of the solvent-separatedion pair is diminished as the fluid density decreases. There is only a very shallow well on the pmf at 1000 atm (p = 0.59 g/cm3), while no minimum is observed at 350 atm (p = 0.23 g/cm3), for the solvent-separated species. Nevertheless, the free energy change along the pmfs is small for ion separations between 3.5 and 5 A, producing a leveling effect. This suggests that ionwater interactions are still significant, although the energy cost to remove waters separating the ion pair is largely offset by the favorable Columbic attraction between the oppositely charged ions. Finally, it is informative to compare the results obtained from Monte Carlo simulations and from the continuum, primitive model. The importance of specific solute-solvent interaction is clearly reflected by the more structured features at high densities, particularly in AW. Accompanying the formation of contact and solvent-separatedion pairs is a progressive reduction of cation and anion attraction as the bulk density increases. In supercritical water, the agreement between the primitivemodel and simulation
Letters is remarkable for ion separations beyond 7 A, indicating that the computed fluid dielectric constant is quite reasonable and the simulations are well-converged. Examination of deviation from the primitive model shown in Figure 1 is also interesting. At low density (pr = 0.72), the calculated interaction energy is predicted to be about 6 kcal/mol smaller than that of the primitive model, suggesting that the local dielectric constant at regions surrounding the ions is higher than the bulkvalue. Consequently,it is a strong indication that there is an enhanced local solvent clustering or charisma near the solute in supercritical water.l5J7 This is consistent with the notion of attractive supercritical solutions in which solute-solvent attraction is stronger than solvent-solvent interactions, resulting in solvent clustering and large, negative partial v01ume.l~Note that at longer Na+Cl- separations local solvent clustering around the ions will no longer effect the pmf, leading to an agreement between the simulation and continuum models. Consequently, it seems to be reasonable to anchor the computed pmfs to the primitive model. For the pmf corresponding to a bulk reduced density of pr = 1.84, the Monte Carlo simulation predict that the contact ion pair is about 3 kcal/mol more stable than the Coulombic model. This is the result of a delicate balance of the energy costs to remove water molecules separating the two ions and the favorable ion-ion Coulombic attraction. In supercritical water, there is significant solvent clustering around each ion, as demonstrated here and by others in previous studies.17 Thus, one would expect to find similar behaviors in the region between contact and solventseparated ion pairs. Indeed, the shapes of the two SCW pmf s are similar in the ion-pair region. However, at low bulk density, the energy cost to remove hydrogen-bonding waters for the "realisticn system will be much larger than that predicted by the continuum model, which assumes a unique dielectric constant for the entire fluid, i.e., identical local and bulk density from the ions. Consequently, the continuum,primitive model yields a much more attractive energy profile. On the other hand, in a dense supercritical solution, the difference between the two models is much smaller since the fluid dielectric constant is very high. Here, consideration of specific intermolecular interactions becomes important. In fact, after crossing the barrier spearating the two ion pairs, the continuum model is no longer valid because there are no water molecules between the two ions, and the dielectric constant should be unity. The association constant for the ion pair may be computed by integrating the potential of mean force according to eq 218930
where R,is a distance defining the geometric limit of association. If R, is chosen to be at the maximum separating the contact and solvent-separated ion pairs at room temperature (3.3 A), the computed associationconstants are 8.2 X 2.0 X 103, and 7.8 X 106 M-1 for Na+Cl- in ambient water and SCW at 1000 and 350 atm, respectively. Extending the integration to an &value of 5.0 A, the Ka's would be 5.5, 2.1 X lo3, and 8.0 X 106 M-1. For comparison, the experimental values in SCW at similar fluid densities are about 1.1 X 102 (p = 0.55 g/cm3)lla and 1.6 X 105 M-1 (p = 0.23).llb The difference between the computed and experimental binding constants might be due to deficiency of empirical potential functions and perhaps more likely due to the use of a nonpolarizable solvent model. Additional insights on the solutesolvent interactions can be obtained by examining the computed radial distribution functions (rdfs). Shown in Figures 2-5 are the ion-water rdfs from simulations at an ion separation of 4.4 A, which corresponds to the minimum of the solvent-separated ion pair observed in ambient water. In these figures, the rdf gxy(r),wherex represents a solute atom and y is either water oxygen or hydrogen, gives the probability of finding an atom y at a distance r from atom x.
The Journal of Physical Chemistry, Vol. 98, No. 24, 1994 6051 8.0 7
c1-0Radial Distribution Functions
I
6.0
8
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2.0
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8
M
4.0
1
350atm
1
-
2.0
0.0 0.0
2.0
6.0
4.0
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10.0
R (A)
Figure3.. Computed chloride-water hydrogen radial distribution functions from a simulation at an ion separation of 4.4 A.
Figures 2 and 3 give the C1-0 and Cl-H rdfs, which reveal progressive changes of hydrogen-bonding interaction between chloride ion and water as the density of the fluid varies. The positions of the first peaks in Figure 3 are about 2.3 A under supercritical conditions, while it is 2.2 A in ambient water. However, the heights of the first peaks in the CCH and C1-0 rdfs are substantially different at various fluid densities. The first peaks in each case are indicativeof strong hydrogen-bonding interactions between the ion and water. Integration of the first peaks of the Cl-H rdfs to minima at about 3.0 A yields coordination numbers of 5.9,6.2, and 7.3 waters in the first solvation layer for C1- at fluid densities of 0.23, 0.59,and 0.99 g / ~ m - respectively. ~, Note that although the heights of the rdfs in SCW are much greater than that in ambient water, which supports the idea of solvent clustering in SCW, the integral values are actually smaller than that in ambient water because of the much smaller fluid density. It should also be noted that the radial distribution functions become somewhat more structured as the fluid density increases. The second peaks in the CI-H rdfs may be assigned to water hydrogens not directly forminghydrogen bonds withC1-in the first solvation layer. Similar general features are observed in Figures 4 and 5 for the Na-0 and Na-H rdfs. Now, water oxygen is closer to the cation than hydrogen due to electrostatic interactions. The maxima of the first peaks in these distributions occur at 2.3 A. Again, there is clearly a high solvent population around Na+ in the first solvation layer. Integration of the rdfs in Figure 4 to about 3.3 A produces 5.2,5.6,and 5.9 water molecules nearest Na+ from simulations at low, intermediate, and high densities. Cummings et al. investigated supercritical aqueous solutions of Na+ and C1- using the SPC water model and Pettitt-Rossky potential for the i0ns.~~G27a The computed number of excess water molecules in the first solvation shell (about 4 for Na+ and 5 for C1-) is in accord with our estimate of the total coordination
I 350atm
-
16.0
12.0
-
8.0
-
4.0
-
density decreases. Significantly, the computed potentials of mean force as a function of ion separation mirror nicely the macroscopic behavior of electrostatic interactions, particularly at large ion separations, suggestingthe computed dielectric constant for TIP4P SCW is reasonable. Further analyses of the pmfs and radial distribution functions indicate that there is significant solvent clustering around the ions, leading to higher local density than the bulk. The coordination number and structure in the first solvation layer in SCW for Na+ and Cl- are similar to that in ambient water. These results are in accord with previous findings of dilute supercritical aqueous solutions of these ions and provide additional insight into the behavior of ionic interactions in supercritical water.
-
]Warm - - - - - .
ambient
.-.......... ~
h
% 80
i
ii I1
0.0
8.0 I
h
M
Na-H Radial Distribution Functions
References and Notes (1) (a) Franks, F., Ed. Water. A Comprehensive Treatise;Plenum: New York, 1972; Vols. 1-6. (b) Eisenberg, D.; Kauzmann, W. TheStructureand Properties of Water,Oxford University Press: New York, 1969. (c) Szwarc, M., Ed. Ions and Ion Pairs in Organic Chemistry; Wiley: New York, 1972. (2) Shaw, R. W.; Brill, T. B.; Clifford, A. A,; Eckert, C. A.; Franck, E. U. Supercritical Water: A Medium for Chemistry. Chem. Eng. News 1991,
4*0i
6.0 8.0 10.0 R (A) Figure 5. Computed sodium-water hydrogen radial distribution functions from a simulation at an ion separation of 4.4 A. 0.0
2.0
4.0
TABLE 1: Computed Coordination Numbers in Ambient and Supercritical Water
400 OC, 350 atm
400 OC, 1000 atm
25 OC
&,A
Na+
c1-
Na+
C1-
Na+
C1-
2.4 2.6 3.0 3.6 4.4 5.0 6.0 7.0
3.6 3.9 4.5 4.9 5.2 5.2 5.3 5.3 5.3 5.2
3.3 3.6 4.5 5.3 5.9
3.9 4.0 4.4 5.1 5.6 5.5 5.4 5.4 5.3 5.4
3.9 4.2 4.8 6.2 6.2 6.2 5.4 5.2 5.7 5.3
4.2 5.0 5.5 5.9 5.9 6.0 6.0
5.8 4.2
8.0 9.8
6.1 5.7 5.8 5.3 5.2
6.1 6.5 7.3 6.7 7.5
numbers. Hummer et al.17c carried out simulations and integral equation calculations of pair correlations in the NaClSPC system a t 823 Kandadensityof0.876 g/cm3. Table 1 shows thevariation of coordination numbers in the first solvation layer as a function of ion separation from this study. In supercritical water (high and low pressures), there are on average 5.3 nearest neighbors around both Na+ and C1-, which may be compared with a coordination number of 6.0 for Na+ and 7.5 for C1- in ambient water reported by Chandrasekhar et al.23 Evidently, the solvent density in the first solvation layer in SCW is similar to that in AW, which, of course, yields a much higher local density than the fluid bulk. Concluding Remarks Monte Carlo simulations of the Na+Cl- ion pair have been carried out in supercritical water, modeled by the TIP4P model. The minimum corresponding to the solvent-separated ion pair,
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