Molecular dynamics simulation of the limiting conductance of NaCl in supercritical water

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28 August 1998 Chemical Phsics Letters 293 1998 289 294 Molecular dnamics simulation of the limiting conductance of NaCl in supercritical water S.H. Lee a,1, P.T. Cummings a,b,), J.M. Simonson c, R.E.

Chemical and Analtical Sciences DiÕision, Oak Ridge National Laborator, Oak Ridge, TN 37831-6110, USA Received 23 March 1998; in final form 29 June 1998 Abstract We report molecular dnamics

1 28 August 1998 Chemical Phsics Letters Molecular dnamics simulation of the limiting conductance of NaCl in supercritical water S.H. Lee a,1, P.T. Cummings a,b,), J.M. Simonson c, R.E. Mesmer c a Department of Chemical Engineering, UniÕersit of Tennessee, KnoxÕille, TN , USA b Chemical Technolog DiÕision, Oak Ridge National Laborator, Oak Ridge, TN , USA c Chemical and Analtical Sciences DiÕision, Oak Ridge National Laborator, Oak Ridge, TN , USA Received 23 March 1998; in final form 29 June 1998 Abstract We report molecular dnamics calculations of the ionic mobilit and limiting conductance of NaCl in supercritical water as a function of densit along an isotherm 5% above the critical temperature. The number of hdration water molecules around ions is found to dominate the behavior of the limiting conductance in the higher-densit region while the interaction between the ions and hdration water molecules is found to dominate in the lower-densit region. The different effects in the lower- and higher-densit regimes lead to different slopes for the limiting conductance as a function of densit in the two regimes Published b Elsevier Science B.V. All rights reserved. 1. Introduction Much of the prior research interest in ionic mobilit at infinite dilution has been focused on its dependence on ion size at ambient conditions. Stokes law wx 1 predicts that the ionic mobilit is inversel proportional to the radius of the ion. However, it is found experimentall that the ionic mobilities in aueous solution have two distinct maxima Žone for cations and another for anions. as a function of ion size w1 4 x. The existence of these maxima leads to consideration of the anomalousl low mobilities of small ions at infinite dilution. The dielectric friction effect of the solvent on an ion was proposed b Born wx wx wx 5 and further developed b Fuoss 6, Bod 7, and ) Corresponding author. ptc@urk.edu 1 Permanent Address: Department of Chemistr, Kungsung Universit, Pusan, South Korea Zwanzig w8,9 x. The continuum treatment of Hubbard and Onsager Ž HO. w10,11x permits self-consistent examination of the set of electrohdrodnamic euations that satisf the smmetr principle. Wolnes molecular approach w12x is the first and onl existing treatment of limiting ionic mobilit that starts from the consideration of a microscopic expression for the drag coefficient which is given in terms of a random force autocorrelation function. In previous work w13,14 x, Lee and Rasaiah performed molecular dnamics Ž MD. simulations of the Ž mobilities of the alkali metal ions Li, Na, K, Rb, and Cs. and the halides ŽF, Cl, Br, and I. at 258C. The used the TIP4P w15x and the SPCrE w16x models for water and Pettit Rossk w17x ion water potential parameters. The mobilities calculated from the mean suared displacements Ž MSD. and the velocit autocorrelation Ž VAC. functions were found to be in good agreement with each other r98r$ - see front matter 1998 Published b Elsevier Science B.V. All rights reserved. PII: S

2 290 ( ) S.H. Lee et al.rchemical Phsics Letters The results showed, for the first time, that cation and anion mobilities fall on separate curves, as functions of ion size, with distinct maxima. This is in complete agreement with experimental results observed in waw1 4 x. The calculated residence times of ter at 258C water in the first hdration shells around the ion were found to decrease dramaticall with increasing size. The mobilit of Li ion in water is described adeuatel b the classical solventberg model but not those of the other ions. Our understanding of solute speciation of dilute aueous alkali halides at supercritical conditions is mostl based on conductimetric measurements w18,19 x. Two experimental results for the limiting molar conductances as a function of the densit of water at high temperatures Ž supercritical points. showed two different trends w20,21 x. One displaed a clear change of slope from the assumed linear dependence of limiting euivalent conductances of LiCl, NaCl, NaBr, and CsBr on the water densit w20x and the other had a clear maximum in limiting euivalent conductance of NaOH w21 x. This phenomenon is closel related to the structure of water around an ion and to the shape of the anion, OH. There have been man molecular dnamics studies of ions in supercritical water. For example, Na Cl ion pair association in supercritical water w22x and ion solvation in supercritical water based on an adsorption analog w23x have been investigated. The former studied three different ion water models for the anion cation potential of mean force of an infinitel dilute aueous NaCl solution in the vicinit of the solvent s critical point. The latter focused on the solvation structure and free energ for Li,Na, F, Cl, Be 2, Mg 2, and Ca 2 in supercritical aueous solutions described b a dielectric concentric shell model incorporating solvent adsorption analogous to a Langmuir model. However, we are unaware of an molecular dnamics studies of ionic mobilit in supercritical water. In this Letter, we report MD simulations of NaCl in supercritical water. The ionic mobilities are calculated in order to explain the experimental observations of the limiting conductances as a function of the densit of water supercritical state points. In the following section, we described the technical details of the simulations. In Section 3, we present our results, followed b conclusions in Section Molecular models and molecular dnamics simulation details The SPCrE Ž extended simple point charge. model w16x was adopted for the water molecule. All ions were represented b a point charge having a Lennard-Jones Ž LJ. center. The potential parameters for ion water of Na and Cl are the same as those w x used in Ref. 14 : for Na and Cl, the ion oxgen s is and A, IO respectivel, and IO s kjrmol for both ions. A spherical cutoff r c of half the simulation box length was emploed for all the pair interactions. This is a simple truncation in which two molecules are considered as interacting if the distance between their centers is less than the cutoff radius rc and all interactions are neglected if the distance is larger than r c. This simple truncation of all interactions for water containing a single ion was shown b Perera et al. w35x to be comparable in accurac to the use of Ewald summation or reaction field methods. The experimental critical properties of water are Tcs K, rcs0.322 grcc, and Pcs bar w24x and the critical properties of SPCrE water are Tcs640 K, rcs0.29 grcc, and Pcs160 bar w25 x. Simulations to calculate the limiting conductance of NaCl were performed at the reduced temperature, T strt s1.05 Ž 673 K. r c and at reduced densities, rrs rrrcs 0.76, 1.07, 1.38, 1.66, 2.10, and 2.55, corresponding to densities of about 0.22, 0.31, 0.40, 0.48, 0.61, and 0.74 grcc for the SPCrE model. This spans the range of densities around 0.45 grcc where the clear change of slope from the assumed linear dependence of limiting euivalent conductances of LiCl, NaCl, NaBr, and CsBr on densit w20x and the maximum in limiting euivalent conductance of NaOH w21x are located. We used Gaussian isokinetics w26 29x to keep the temperature of the sstem constant and the uaterw30,31x of the euations of rota- nion formulation tional motion about the center of mass of the SPCrE water molecules. For the integration over time, we adopted Gear s fifth-order predictor corrector algow x 15 rithm 32,33 with a time step of 0.5=10 s Ž0.5 fs.. Each MD simulation of a single ion sstem with 215 SPCrE water molecules was carried out for Na and Cl ions for time steps after euilibration of time steps. The euilibrium

3 ( ) S.H. Lee et al.rchemical Phsics Letters properties are averaged over six blocks of time steps and the configurations of water molecules and an ion are stored ever 10 time steps for further analsis. The diffusion coefficient, D i, of each ion is calcu- lated from the mean suare displacement Ž MSD. and the ion mobilit is obtained b uisdizerk i BTs DzFrRT Ž Einstein relation. where k is the Boltzi i B mann constant, R is the gas constant, F is the Farada constant, zi is the charge on the ion in units of the electronic charge e, T is the absolute temperature and is and. The limiting conductance of each ion can be calculated from l o suzf. The i i i total limiting conductance of NaCl is the sum of each ion, l o sl o l o. It is worth mentioning that the ions cross the simulation box, on average, two times ever 8000 time steps. As a result, care must be exercised to calculate the diffusion coefficients correctl w34 x. 3. Results and discussion The diffusion coefficients Di of Na and Cl, calculated from the mean suare displacement Ž MSD. and from the velocit autocorrelation function Ž VAC., are listed in Table 1. The limiting conductances l o determined from these diffusion coefficients are also listed in the same table. The limiting conductances calculated from the simulation MSDs Table 1 Diffusion coefficient Di and molar conductance l 0 i of Na and Cl at infinite dilution in supercritical water at 673 K calculated from MSD and VAC Ž 5 2. o Ž 2. i i Ion Densit D =10 cm rs l =Scmrmol Ž grcc. MSD VAC MSD VAC Na " " " "58 Na " " "80 650"83 Na " " "75 637"98 Na " " "95 625"92 Na " " "81 506"69 Na " " "45 452"51 Cl " " "58 700"69 Cl " " "83 712"69 Cl " " "98 709"81 Cl " " "92 669"106 Cl " " "69 616"58 Cl " " "51 551"57 Fig. 1. Limiting molar conductance of NaCl at infinite dilution as a function of densit of supercritical water at 673 K obtained from MSD. are compared, in Fig. 1, with the experimental rew20 x. Fig. 1 shows that the limiting conductance of sults NaCl calculated from our MD simulations is in good agreement with the experimental results over the full range of densities of supercritical water at 673 K. In particular, the experimental trends in the limiting conductances as a function of water densities are reproduced in our simulations a clear change of slope from the assumed linear dependence of limiting conductances of NaCl on the water densit. The calculated values are essentiall exact in the higherand medium-densit regions, and are about 5% higher than the experimental values in the lower-densit region. In order to explain the deviation from the assumed linear dependence of limiting conductances of NaCl below the densit of 0.45 grcc, several thermodnamic, structural, and dnamic uantities have been calculated. First the average ion water potential energies are listed in Table 2 and shown in Fig. 2. These potential energies for both ions increase almost linearl with decreasing densit of water except for a relativel sudden increment at 0.22 grcc. The hdration number n is found b integrating the water number densit from the inner to the outer boundar of the first solvation shell w23 x: b H IO 2 a ns4pr g r r dr 1

4 292 ( ) S.H. Lee et al.rchemical Phsics Letters Table 2 Average ion water potential energ, hdration number, ion water potential energ divided b hdration number, and residence time of water molecules in hdration shell of an ion at 673 K Ion Densit Ion water PE Hdration number Ion water PE Residence time of water Ž grcc. Ž kjrmol. Ž n. Ž n. Ž ps. Na " " " " 0.09 Na " " " " 0.03 Na " " " " 0.07 Na " " " " 0.06 Na " " " " 0.06 Na " " " " 0.04 Cl " " " " 0.02 Cl " " " " 0.05 Cl " " " " 0.07 Cl " " " " 0.06 Cl " " " " 0.07 Cl " " " " 0.03 where r is the bulk water number densit, a is the point at which the ion oxgen radial distribution function g Ž r. IO first rises from zero, and b is the point at which the first minimum in g Ž r. IO occurs. Table 2 shows the hdration number of water in the first solvation shell around both ions. As can be seen in Fig. 2, the hdration numbers for both ions decrease monotonicall with decreasing water densit, but the slopes are different in the ranges of densit above and below 0.45 grcc. The average ion water potential energ divided b the hdration number is also listed in Table 2 and shown in Fig. 3. The difference between these potential energies at densities above and below 0.45 grcc is clear. The low limiting conductance in the lower densit region is due to the strong interaction between an ion and the hdrated water molecules around the ion, compared to the higher densit region. In the high densit regime, the large number of hdration water molecules restricts ionic mobilit. As the densit of water decreases, the ion should diffuse more easil due to the decreasing number of the hdration water molecules. However, in the lower densit region, increase in the interaction between an ion and the hdrated water, reflected in the average potential energ per hdration water molecule, strongl decreases ionic mobilit and leads to a decrease in the limiting euivalent conductance. Fig. 2. Ion water potential energ for Na Ž '. and Cl Ž v. and hdration number for Na Ž ^. and Cl Ž `.. Horizontal lines are drawn through the data points to aid the reader in identifing changes in slope between the low- and high-densit regimes. Fig. 3. Ion water potential energ divided b hdration number Na ' and Cl v and residence time for Na ^ and Cl Ž `.. Horizontal lines are drawn through the data points to aid the reader in identifing changes in slope between the low- and high-densit regimes.

5 ( ) S.H. Lee et al.rchemical Phsics Letters Another uantit that is useful in elucidating the local environment around an ion is the residence time of the hdration water molecules. The residence time correlation function is defined b Refs. w13,14x N 1 r Ý N i i r is1 RŽ r,t. u Ž r,t. u Ž r,0. Ž 2. where u Ž r,t. i is the Heaviside unit function, which s1 if water molecule i is in a region r within the first hdration shell of the ion and s 0 otherwise, and Nr is the number of water molecules in this region r at t s 0. The characteristic deca time Ž residence time., t, is obtained b fitting the time correlation function to an exponential deca ² RŽ r,t.:(expž trt. which is useful particularl when t is large. The residence time, also listed in Table 2 and shown in Fig. 3, reinforces the clear difference between the higher- and lower-densit regions above and below 0.45 grcc, respectivel. At lower densit, the hdration water molecules remain close to the ion for relativel long periods and move together with the ion, thus impeding ion diffusion. In order to visualize the increasing hdration with decreasing densit, in Fig. 4 we present the ion water radial distribution functions for the sodium and chloride ions at a low densit Ž 0.22 grcc. and a high densit Ž 0.74 grcc.. The ion water structure is obtained b calculating g Ž r. IO, the radial distribution function between the ion Ž. I and the oxgen site Ž O. in the water molecules. We observe a large enhancement of water densit at 2.5 A Žthat is, in the first. hdration shell in both the Na O and Cl O radial distributions at a low densit. The large peak in g Ž r. IO at low densit suggests that the degree of densit enhancement in the hdration shell is much greater at lower densit than at higher densit, and is consistent with the densit dependence in the average ion water potential energ per hdration number and the residence time of the hdration water molecules. 4. Concluding remarks In explaining the limiting conductance of NaCl in supercritical water at 673 K, there are two important competing factors the number of hdration water molecules around ions and the interaction between the ions and the hdration water molecules. The competition between these two factors is seen in the residence time of the water in the first hdration shell around the ions. The interaction between the ions and the hdration water molecules dominates in the lower densit region while the number of hdration water molecules around the ions dominates in the higher densit region. Similar considerations explain the dependence of ionic mobilit on ion size at ambient conditions, where an analogous competition between hdration number and ion water interaction is found as a function of ion diameter w13,14 x. In the case of NaCl, the interaction between the ions and the hdration water molecules is not a strong enough factor to result in a maximum of limiting conductance in the middle densit region. In the case of NaOH, experiment exhibits a clear maximum in limiting conductance w21 x. We expect that the same factors will be observed in the case of OH in addition to the effect of the ion shape on the hdrated water around it. This sstem is presentl under stud. Acknowledgements Fig. 4. Ion water radial distribution functions, g Ž r. IO around the Na and Cl ions at a low densit Ž 0.22 grcc. and a high densit Ž 0.74 grcc.. The work of SHL was supported b the Nondirected Research Fund of the Korea Research Foundation, This work was supported b the Division of Chemical Sciences, Office of Basic Energ Sciences, US Department of Energ. The work of JMS

6 294 ( ) S.H. Lee et al.rchemical Phsics Letters and REM was supported b the Division of Chemical Sciences, Office of Basic Energ Sciences, US Department of Energ at Oak Ridge National Laborator, managed b Lockheed Martin Energ Research for the US Department of Energ under contract DE-AC05-96OR SHL is on sabbatical leave at the Universit of Tennessee. SHL thanks the Tongmung Universit of Information Technolog Ž Pusan, South Korea. for access to its IBM SPr2 computer. References wx 1 R. Lorenz, Z. Phs. Chem. 37 Ž wx 2 H.S. Frank, Chemical Phsics of Ionic Solutions, Wile, New York, wx 3 R.A. Robinson, R.H. Stokes, Electrolte Solutions, Butterworth, London, wx 4 R.L. Ka, in: F. Franks Ž Ed.., Water, A Comprehensive Treatise, Vol. 3, Plenum, New York, wx 5 M. Born, Z. Phs. 1 Ž wx 6 R.M. Fuoss, Proc. Natl. Acad. Sci. 45 Ž wx 7 R.H. Bod, J. Chem. Phs. 35 Ž wx 8 R. Zwanzig, J. Chem. Phs. 38 Ž wx 9 R. Zwanzig, J. Chem. Phs. 52 Ž w10x J.B. Hubbard, L. Onsager, J. Chem. Phs. 67 Ž w11x J.B. Hubbard, J. Chem. Phs. 68 Ž w12x P.G. Wolnes, J. Chem. Phs. 68 Ž w13x S.H. Lee, J.C. Rasaiah, J. Chem. Phs. 101 Ž w14x S.H. Lee, J.C. Rasaiah, J. Phs. Chem. 100 Ž w15x W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impe, M.L. Klein, J. Chem. Phs. 79 Ž w16x H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phs. Chem. 91 Ž w17x B.M. Pettitt, P.J. Rossk, J. Chem. Phs. 84 Ž w18x A.S. Quist, W.L. Marshall, J. Phs. Chem. 72 Ž w19x P.C. Ho, D.A. Palmer, R.E. Mesmer, J. Sol. Chem. 23 Ž w20x G.H. Zimmerman, M.S. Gruszkiewicz, R.H. Wood, J. Phs. Chem. 99 Ž w21x P.C. Ho, D.A. Palmer, J. Solution Chem. 25 Ž w22x A.A. Chialvo, P.T. Cummings, H.D. Cochran, J.M. Simonson, R.E. Mesmer, J. Chem. Phs. 103 Ž w23x L.W. Flanagin, P.B. Balbuena, K.P. Johnston, P.J. Rossk, J. Phs. Chem. B 101 Ž w24x R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Liuids and Gases, McGraw Hill, New York, w25x Y. Guissani, B. Guillot, J. Chem. Phs. 98 Ž w26x K.F. Gauss, J. Reine Angew. Math. IV Ž w27x W.G. Hoover, A.J.C. Ladd, B. Moran, Phs. Rev. Lett. 48 Ž w28x D.J. Evans, J. Chem. Phs. 78 Ž w29x D.J. Evans, W.G. Hoover, B.H. Failor, B. Moran, A.J.C. Ladd, Phs. Rev. A. 28 Ž w30x D.J. Evans, S. Murad, Mol. Phs. 34 Ž w31x D.J. Evans, Mol. Phs. 34 Ž w32x W.C. Gear, Numerical Initial Value Problems in Ordinar Differential Euations, McGraw Hill, New York, w33x D.J. Evans, G.P. Morriss, Computer Phs. Rep. 1 Ž w34x M.P. Allen, D.J. Tildesle, Computer Simulation of Liuids, Oxford Universit Press, Oxford, w35x L. Perera, U. Essmann, M.L. Berkowitz, J. Chem. Phs. 102 Ž

Molecular dynamics simulation of limiting conductances for LiCl, NaBr, and CsBr in supercritical water

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 2 8 JANUARY 2000 Molecular dynamics simulation of limiting conductances for LiCl, NaBr, and CsBr in supercritical water S. H. Lee Department of Chemistry,