molecular dynamics simulations of sodium chloride …...properties.15,16 with respect to the...

Molecular dynamics simulations of sodium chloride solutions inwater–dimethyl sulphoxide mixtures: Potentials of mean force and solvationstructuresAshok K. Das and B. L. Tembe Citation: J. Chem. Phys. 111, 7526 (1999); doi: 10.1063/1.480079 View online: http://dx.doi.org/10.1063/1.480079 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v111/i16 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 16 22 OCTOBER 1999

Molecular dynamics simulations of sodium chloride solutionsin water–dimethyl sulphoxide mixtures: Potentials of mean forceand solvation structures

Ashok K. Das and B. L. Tembea)

Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai, 400 076, India

~Received 7 December 1998; accepted 19 July 1999!

Five solutions of sodium chloride in mixtures of water and dimethyl sulphoxide~DMSO! have beensimulated using the conventional molecular dynamics technique. The potentials of mean force~PMFs! of the sodium chloride ion pair in the presence of the five water–DMSO mixtures withDMSO mole fractions (xDMSO) of 0.10, 0.21, 0.35, 0.48 and 0.91 have been computed. The derivedPMFs have been confirmed by the long time dynamical ion-pair trajectories. The solvationstructures of the ions in the presence of these mixtures have been analyzed using the ion-solventradial distribution functions and the corresponding integration numbers. It has been found that theNa1 ion is always preferentially solvated by the water molecules in all the water–DMSO solventmixtures. The Cl2 ion is slightly preferred by the DMSO molecules in these mixed solvents.© 1999 American Institute of Physics.@S0021-9606~99!51038-6#

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I. INTRODUCTION

The solvation of sodium chloride and other electrolyin several one component solvents has been a subject otailed investigations, both theoretically and through simutions, for a considerably long time.1 Molecular dynamical~MD! simulation studies on NaCl in the presence of mopolar solvents,2 water,3–5 methanol,6 and dimethyl sulphox-ide ~DMSO!7 have been reported. These studies cover maspects of the NaCl solvation in the respective solventscluding the evaluation of the potential of mean force~PMF!,analysis of the solvation structure and dynamics, comption of solvent friction kernels, calculation of transmissiocoefficients across the PMF barriers and orientational disbutions of the solvent molecules around the ions. The solvmixtures like water–methanol, water–acetone and watammonia have been simulated by Ferrarioet al.8 Similarly,the water–DMSO mixture has been simulated by Vaismand Berkowitz9 and also by Luzar and Chandler.10 Interest-ingly, the simulations of NaCl solutions in solvent mixturare being reported only recently. The solvation of a sinNa1 ion and a single Cl2 ion in the presence of mixed sovents like water–methanol11 and water–formamide12 hasbeen reported in the recent past. Monte Carlo simulatiand neutron diffraction studies on a peptide forming systCuCl2–NaCl–H2O have appeared recently.13

The phenomenon of preferential solvation of NaCl in twater–methanol mixtures has been addressed by Hawand Wojcik.11 For the Na1 ion, the preferential solvation bymethanol decreases with increasing methanol mole fracand it vanishes atxmethanol50.9. The opposite behavior habeen noticed for the Cl2 ion. The most direct insight into thestructure of solutions is expected from x-ray and neutdiffraction experiments. But these techniques do not prov

a!Electronic mail: [email protected]

7520021-9606/99/111(16)/7526/11/$15.00

Downloaded 01 Mar 2012 to 14.139.97.79. Redistribution subject to AIP lic

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decisive results for electrolyte solutions in water–methamixtures.14 Computer simulation gives an opportunity to ditinguish between the properties of each subsystem insolution and to follow the effects of each component of tsystem. In the water–formamide mixture, both the Na1 cat-ion and Cl2 anion are preferentially solvated by formamideven if small amounts of formamide are present in the mixsolvent.12

The solvent mixtures of water and DMSO have specimportance because of their unique physical and chemproperties.15,16 With respect to the chemical properties, thformation of water–DMSO mixtures is exothermic with thmagnitude of the heat of mixing showing a strong negatdeviation from ideality.17 The other macroscopic propertiesuch as density,18 viscosity,18 refractive index,18 dielectricpermittivity19,20 and surface tension21 show positive devia-tions from ideality. An aqueous solution of DMSO witxDMSO > 0.25 has a freezing point270 °C in comparison tothe pure constituents~0 °C for water and118.6 °C forDMSO!.22 These solvent mixtures show maximum devtions from ideal behavior in the DMSO mole fraction ranof 0.20–0.45. There is no general agreement aboutmechanism by which the two solvents interact to accountthese macroscopic deviations.23 However, it has been welestablished that the water–DMSO hydrogen bond is mstronger than the water–water hydrogen bond,8 which hasbeen accepted to be one of the major reasons for the detions in macroscopic properties. The associative propertieDMSO responsible for the nonidealities in water–DMSmixtures are also found in its associations with polarizanonionic and ionic substances.15,16 The existence of stronglyhydrogen bonded one DMSO-2 water aggregates havebeen proved through molecular dynamical simulationsthese solvent mixtures.9 In order to probe this associativcharacter of DMSO and its influence on ion solvation, whave studied the solvation of the Na1 – Cl2 ion pair in the

6 © 1999 American Institute of Physics

ense or copyright; see http://jcp.aip.org/about/rights_and_permissions

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7527J. Chem. Phys., Vol. 111, No. 16, 22 October 1999 NaCl solutions in water-dimethyl sulphoxide mixtures

presence of five selected water–DMSO mixtures wxDMSO50.10, 0.21, 0.35, 0.48 and 0.91. The choice ofsodium and chloride ions is because of their importancechemistry and biochemistry.24,25

The PMF for the Na1 and Cl2 ion pair in pure water hasbeen reported by Berkowitzet al.,3 and by Karim andMcCammon4 using the umbrella sampling technique aalso by Guardia, Rey, and Padro5 using the constrained MDsimulations. These two sets of results differ only slighwith respect to the location of the contact ion pair~CIP!minimum, the transition state~TS! maximum, the solventseparated ion pair~SSIP! minimum and also with respect tthe magnitudes of dissociation and association barriers.differences arise largely because of the different interacpotential models used by these authors. While Berkowet al.3 and Karim and McCammon4 have used the TIPS2model for water, Guardia, Rey, and Padro5 have used theflexible SPC model for water.

The ion–ion PMF for the Na1 and Cl2 ion pair in pureDMSO has been reported by Madhusoodanan and Tem7

using the constrained MD simulations. Table I collectsmain characteristics of the ion–ion PMF for the Na1 andCl2 ion pair in these two solvents and the ion–ion PMFthe two solvents is shown in Fig. 1.

To our knowledge, ion-solvent interactions for this mocommonly used electrolyte~i.e., Na1Cl2) has not been re

FIG. 1. The potentials of mean forceW~r! for the Na1 – Cl2 ion pair in unitsof kBT in DMSO and water as a function of the ion–ion separation.

TABLE I. Characteristics of the Na1 – Cl2 PMF in water and in DMSO.

Location of Magnitude of

First First Second Dissociation AssociationSolvent minimum maximum minimum barrier barrier Referen

Watera 2.7 Å 3.5 Å 5.0 Å 5.6kBT 3.2 kBT 3,4Waterb 2.9 Å 3.7 Å 5.0 Å 2.8kBT 3.7 kBT 5DMSO 2.6 Å 4.9 Å 7.2 Å 28.7kBT 1.9kBT 7

aTIPS2 model.bFlexible SPC model.


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ported in mixed solvents such as water–DMSO. In orderexplore the nature of the solvation of the ion pair in themixed solvents with extreme nonideality we have derivedion–ion PMF at five selected compositions, which we rephere. Significantly, in all the compositions studied, the shdistance stable minimum~characteristic of the formation of aCIP! is not observed.

These studies will yield a comparison of the naturethe PMFs and the solvation structures of the ions in the pence of the mixed solvents of different compositions. Tpreferential solvation of the Na1 and Cl2 ions in thesemixed solvents and the orientational distributions of the svent molecules around a moving ion pair during its transfmation from one solvated configuration into another mayrevealed through these studies.

II. THE MODELS AND THE METHOD

The details of the methodology have been given inearlier papers. The five systems for which the Na1 – Cl2

ion–ion PMF have been derived contain the two ions inpresence of the five selected solvent compositions ofwater–DMSO mixture. The relevant details of the chossolvent mixtures are given in Table II.

A. The interaction potentials

The present work considers the interactions betweenions, DMSO and water molecules to be composed of pwise additive potential functions between the sites. Fortails, the reader may refer to our earlier work7 and the refer-ences cited.26–32 In all the five mixture compositionsconsidered here, water–water interactions are taken tothose of the SPC model of water due to Berendsenet al.33

For the DMSO–DMSO interactions, the potential functioused by other authors9,10,32 has been chosen. The ion–iodirect potential between the Na1 and Cl2 ions is taken to bethat of the Huggins–Mayer form31

Ui j ~r !5qiqj

r1Bi j expS 2

r

r i jD2

Ci j

r 6 , ~1!

whereqi is the charge on theith ion at a distancer from thejth ion andB, C, and r are parameters. The site–site iosolvent and solvent–solvent potential is represented as

TABLE II. Compositions of the water–DMSO mixtures. Solvent[ DMSO; solvent 2[ water;xi[ mole fraction of solventi; ni[ numberof molecules of solventi in the cubic simulation cell of edge lengthL; r[ density at298 K; e[ dielectric constant.

Composition x1 x2 n1 n2

L~Å!

ra

(gm ml21) eb

3 0.10 0.90 25 225 21.228 1.0425 77.52 0.21 0.79 53 197 22.784 1.0725 74.81 0.35 0.65 88 162 24.764 1.0927 69.95 0.48 0.52 120 130 26.066 1.0983 65.04 0.91 0.09 228 22 30.211 1.0965 49.5

aReference 18.bReferences 19 and 20.


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7528 J. Chem. Phys., Vol. 111, No. 16, 22 October 1999 A. K. Das and B. L. Tembe

Uab~r !5qaqb

r1

Aab

r 12 2Cab

r 6 , ~2!

wherea andb denote a pair of interaction sites on differemolecules,r is the site-site separation,qa is a point chargelocated at sitea. The termsAab andCab are given by

Aab54«ab~sab!12, ~3a!

Cab54«ab~sab!6, ~3b!

whereeab andsab are the energy and distance parameterthe Lennard-Jones potential. The cross interactions hbeen obtained by using the Lorentz–Berthelot rules34

sab5 12 ~saa1sbb!, ~4a!

«ab5~«aa«bb!1/2. ~4b!

The various potential parameters in Eqs.~1! and ~2! used inthis work are presented in Table III.

The choice of the intersolvent potential is consistent wthe usual combining rules used in the statistical mechanicmixtures34,35 and with the independent determination of tintermolecular DMSO—DMSO, water–water, ion-DMSand ion-water potentials. Earlier MD simulation studiessolvent mixtures performed by Ferrarioet al.8 proved thatsuch choice of the intersolvent potential is reasonably acrate for simulating water–methanol, water–acetonewater–ammonia mixtures.

B. Preparation of the solvent mixtures

The starting solvent configurations for the five compotions of the mixtures have been chosen according tospecifications given in Table II. In all the compositions, tNa1 and Cl2 ions have been placed at the center of the cusimulation box. For placing the solvent molecules into tsimulation box, the following three procedures have beadopted.

H1 „Hetero1…: Keeping the two ions at the center of thbox, n1 DMSO molecules are placed around them. Tmakes up the box size up toL1 . This central box of DMSOis then covered byn2 water molecules in the form of asheath, to make up the full box length ofL. ~For example, incomposition 1,n1588, L1521.8 Å, n25162, L524.564 Å;in composition 2,n1553, L1518.4 Å, n25197, L522.784Å and so on!.

TABLE III. Site–site potential parameters.

Salt Bi j /~kJ! r i j /Å Ci j /~kJ/ Å6)Na1–Cl2 2.01310219 0.317 1.12310221

Solvent Site e/~kJ mol21) s/~Å! q/ea

Water O 0.6502 3.156 20.82H 0.0 0.0 10.41

Solvent Site e/~kJ mol21) s/~Å! q/ea

DMSO S 0.844 03 3.56 10.139O 0.275 86 2.94 20.459

CH3 0.668 52 3.60 10.160

aThe terme is the magnitude of the electronic charge.


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H2 „Hetero2…: Similar to H1, heren2 molecules of wa-ter surround the ions in the inner box up to a box size ofL2 .This water box is then covered byn1 DMSO molecules as asheath, up to the net box length ofL. ~For example, in com-position 1,n25162, L2516.9 Å, n1588, L524.564 Å; incomposition 2,n25197, L2518.1 Å, n1553, L522.784 Åand so on!.

R „Random…: For the random configuration, two equilbrated solvent boxes are taken; one of which containsDMSO molecules in a cubic box of edge length 31.039and the other which contains 300 water molecules in a cubox of edge length 20.77 Å. From the DMSO box,n1 mol-ecules are picked up at random. Then for thesen1 DMSOmolecules, we have located the water molecules wS~DMSO!–O~water! distance less than;2.5 Å and deletedthese water molecules from the water box. Out of themaining water molecules, onlyn2 are retained for preparingthe mixture, and the rest are deleted. Finally, then1 DMSOmolecules and then2 water molecules are placed into thsimulation box along with the Na1 and Cl2 ions at the centerof the box.

In all these three procedures, about 1000 Monte Camoves are performed in order to eliminate any site-site clcontacts. In the case ofH2 andR, the system reaches equlibrium ~tested with the constancy of the total energy of tsystem!34 within 10 ps of MD simulation at 298 K. On theother hand,H1 ~with DMSO molecules forming an innesheath to the ions! takes a considerably long time~more than50 ps! to reach equilibrium. This is because of the presenof the very deep potential minimum~depth of 28.7kBT)existing in the PMF of the Na1 – Cl2 in DMSO at a shortinterionic separation~2.6 Å!. However, the equilibration ofH1 can be achieved faster by increasing the temperaturthe system gradually followed by slow cooling to 298 K.

All these three strategies have been tested for givingidentical PMF for the Na1 – Cl2 ion pair in all five mixturecompositions.

C. Details of the simulations

In order to simulate the ion pair dynamics in the preence of the mixed solvents we have used the constrainedmethodology36 in all the simulations. The method requirethe MD simulation of the system consisting of the ions athe solvent molecules in which not only the intrasolveatom–atom or site–site separations are held constant,also the ion–ion separation is kept fixed. This was achieby using the SHAKE algorithm.37 The short range interactions were truncated using a spherical cutoff with half tbox length as the cutoff radius. The long range interactiowere computed using the reaction field technique.35 Theequations of motion were solved numerically using the Vlet algorithm38 using a time step of 0.5 fs.

For the system consisting of two ions~A,B! andN sol-vent molecules, the force due to the solute–solvent intetions, acting along the interionic axis is evaluated as39

DF~r ,t !5mFFAS~r ,t !

mA2

FBS~r ,t !

mBG• r̂ , ~5!


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whereFAS(r ,t) andFBS(r ,t) are the total forces on the soute particles A and B due to the solvent molecules;mA andmB are the individual masses of the ions;m is the reducedmass of the ion pair andr̂ is the unit vector along the ABdirection. TheDF(r ,t) values are calculated at each timstep and then averaged over the whole simulation. The tmean force between the ions is the sum of the direct~bare!ion–ion force,Fd(r ) and the solvent contribution,DF(r ).That is

F~r !5Fd~r !1DF~r !, ~6!

whereDF(r )[,DF(r ,t)., the angular brackets denotinan ensemble average. The potential of mean force,W~r!, ofthe ion pair in the presence of the solvent can then be calated as39

W~r !52E F~r !dr5W~r 0!2Er 0

r

F~r !dr. ~7!

The choice ofW(r 0) is required to be done in such a wathat the calculated mean force potential matches the mascopic Coulombic potential at long distances

W~r 0!5qiqj

r 0«, ~8!

whereqi is the charge on theith ion ande is the dielectricconstant of the solvent. The experimental values of theelectric constants19,20 have been given in Table II. We havfound that the ion–ion PMFs for the solvent compositiostudied are not sensitive to the choice ofr 0 if r 0 is greaterthan 8.0 Å.

Interionic separations~r! from 2.0 to 9.0 Å with incre-ments of 0.2 Å were considered for the estimation ofPMFs. This constitutes a series of 36 MD simulationseach of the solvent compositions. Several initial configutions were generated for a given interionic separation.each case after an initial equilibration period of 20 ps,ion–ion separation was increased and/or decreased to cthe whole range of distances. For each value ofr, the systemwas further equilibrated for 20 ps which was followed byproduction period ranging from 60 to 80 ps, during which tion-solvent mean forceDF(r ) was computed. We have determined the errors inDF(r ) by repeating the productionruns over several initial solvent configurations. Typical vues of the standard deviations ofDF(r ) range from about 5kBT ~at smallerr between 2.6 and 4.0 Å! to about 1kBT ~atlonger r!.

III. RESULTS AND DISCUSSION

A. The solvent contributions to the mean force

The mean forceF~r! on the Na1 and Cl2 ions in thepresence of the five mixed solvents~whose compositions arindicated on the curves! are displayed in Fig. 2 together witthe directFd(r ) contribution. Similar results were obtainefor the Na1- Cl2 ion pair in model polar solvents by Ciccotet al,36 in pure water by Guardia, Rey, and Padro5 and inpure DMSO by Madhusoodanan and Tembe.7 The sign ofDF(r ) @which isF(r )2Fd(r ) and is not shown in the graph#is positive for all the mixed solvent compositions. Positi


tal

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DF(r ) was also observed in the case of pure water5 as wellas in pure DMSO7 at all the interionic separations. This implies that for a system of charged particles~i.e., ions! in thepresence of polar solvents, the characteristics ofDF(r ) arethe manifestations of the electrostatic forces on the iwhich are dictated by the equilibrium solvent configuratioat that particular interionic separation. From the nature ofF~r! in all the solvent compositions, it is evident that thcontributions of the solvent forces are important for valuesr up to 8.0 Å. The repulsive character ofF~r! @which is dueto DF(r )] in all the solvent compositions can be understoby the fact that the polar mixed solvent assists in separathe oppositely charged Na1 and Cl2 ions. Total mean forceF~r! on the ions has the composite effect of two contribtions, namely, the bare attractive ion–ion forceFd(r ) and therepulsive ion-solvent forceDF(r ). These two are of opposite signs for all ion–ion separations greater than 2.3hence the resultingF~r! may be sensitive to the choice of thion–ion (Ui j ), ion-solvent and solvent–solvent (Uab) inter-action potentials which are responsible for the magnitudewell as the sign ofFd(r ) and DF(r ), respectively. Thisneeds further investigation.

From the curves in Fig. 2, it can be seen that the solvcontributionsDF(r ) differ only at small ion–ion separationsA shallow minimum inDF(r ) or F~r! near 3.0 Å is observedin the first three compositions. A local maximum is noticonly for xDMSO50.21 atr Na12Cl256.6 Å. A small barrier inDF(r ) is observed between 4.0 and 5.5 Å in all the compsitions. In the first three compositions,F~r! rises significantly

FIG. 2. Ion–ion total mean forceF~r! on the Na1 – Cl2 ion pair in units ofkBT/Å in the presence of the five water–DMSO mixed solvents as a fution of the interionic separation~r!. The mole fraction of DMSO (xDMSO) isindicated on each curve and the successive curves are shifted by 60The F~r!50 line is shown on each curve. The direct ion–ion forceFd(r ) isshown by dotted lines.


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above zero between 3.5 to 5.0 Å and this leads to theirresponding PMFs to be above zero forr,4.0 Å ~Fig. 3!. ForxDMSO50.48 and 0.91, theF~r!s are flatter in the region 3.0Å,r,5.0 Å and hence the corresponding PMFs are bezero in the distance range 3.0 Å,r,5.0 Å. Beyond about 8.0Å, the DF(r ) decays to small magnitude for all the solvecompositions. However, for composition withxDMSO50.21,the appearance of a small barrier inDF(r ) at around 6.6 Å isa significant characteristic of the mixed solvent atxDMSO

50.21.

B. The potentials of mean force

The ion–ion PMFs,W~r!s, for the five solvent compositions have been obtained by direct integration of the toforce, F~r!, according to Eq.~7!, taking r 058.0 Å, and sat-isfying Eq. ~8!. These are displayed in Fig. 3 for the fivsolvent compositions. From these figures it is evident thatfirst short-distance minimum in the Na1 – Cl2 PMF seen inpure water~at 2.9 Å! and in pure DMSO~at 2.6 Å! does notappear in any of the mixture compositions. The mixtucompositions withxDMSO50.10, 0.21 and 0.35 show narroshoulder regions between 3.0 and 4.0 Å very near theconfigurations observed in the pure solvents. The characistics of the Na1 – Cl2 PMFs in the presence of the mixesolvents are given in Table IV.

All these observations point to the fact that none ofsolvent mixtures permit the Na1 and Cl2 ions to remain‘‘intimate’’ within a short ion–ion distance correspondingthe CIP in the pure solvents. In pure water, the ions can eboth as a CIP and as a SSIP with an equilibrium constan7.7 at 298 K for the CIP⇔ SSIP equilibrium.5 The corre-

FIG. 3. Na1 – Cl2 potentials of mean force~PMFs! W~r!, as a function ofthe ion–ion separation~r! in the presence of the five water–DMSO mixesolvents. The mole fraction of DMSO (xDMSO) is indicated on each curveand the successive curves are shifted by 20 units. TheW~r!50 line is shownon each curve.


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sponding value of the equilibrium constant is much less,31028 at 298 K in pure DMSO, in which the CIP configuration ~with a potential depth of 28.7kBT) is much morestable than the SSIP.7 These features do not get reproducby any of the solvent mixtures considered here. The preseof broad SSIP minima as well as a shallow barrierxDMSO50.21 allow for the possibilities for several low barier transitions40,41between various arrangements of the mecules of the solvent mixtures at different ion-pair sepations.

A rationale for the absence of the CIP in these mixtuhas been obtained by analyzing the solvent structuresdevelop around the ion pair in these solvents. We obserthat in all these solvent mixtures, the water molecules remstrongly bound to the ion pair at the SSIP minima, and omolecule of water tends to be close to the ion pair alonginterionic axis. In Fig. 4, we present a typical solvent cofiguration around the Na1 and Cl2 ions for xDMSO50.91 atr Na1 – Cl255.0 Å. It is noticed that a water molecule is closto the ion pair at a distance of about 3.0 Å from both tions. The strong bonding of the water molecules to formclosest solvation shell even at this lowest water containmixture (xDMSO50.91) dictates the formation of the SSIminima at a large ion–ion distance ofr Na1 – Cl2 near 5.0 Å.The contour plots of the O~water! density profiles aroundthe Na1 and Cl2 ions described in our earlier work42 atmixture compositions ofxDMSO50.21 and 0.35 also suppo

FIG. 4. A typical neighborhood of the Na1 – Cl2ion pair in a water–DMSOmixture of compositionxDMSO 50.91 for r Na1 – Cl255.0 Å. Notice the closeapproach of a water molecule.

TABLE IV. Characteristics of the Na1 – Cl2 PMF in water–DMSO mix-tures.

Firstminimum Depth

Firstmaximum Height

Secondminimum Depth

xDMSO ~Å! (kBT) ~Å! (kBT) ~Å! (kBT)

0.10 4.660.7 214.065.0 ¯ ¯ ¯ ¯

0.21 5.060.5 210.063.0 6.6 23.561.0 7.0 25.561.00.35 5.060.5 29.063.0 ¯ ¯ ¯ ¯

0.48 5.060.7 213.063.0 ¯ ¯ ¯ ¯

0.91 4.460.6 218.065.0 ¯ ¯ ¯ ¯


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the dominance of water molecules to form the SSIP miniat an ion-ion distance of 5.0 Å in all the mixed solvenconsidered here. The influence of DMSO to force thepair to form a CIP is further reduced because of the strintersolvent water–DMSO hydrogen bond which is mustronger than the water–water hydrogen bond.8 At the othertwo compositions ofxDMSO50.10 and 0.48 we have noticea similar trend. This description will be further quantifieda later section wherein we present the radial distributfunctions and the running coordination numbers betweenions and the solvent sites. We shall now test these PMusing the dynamical trajectories of the ion pair.

C. Dynamical trajectories of the Na 1 – Cl2 ION PAIR

A second confirmation of the nature of the potentialsmean force for the ion pair has been obtained by studyingdynamical trajectories of the ion pair initiated at various ioion separations. This is done by performing long MD simlations on the system by releasing the constraint on thepair at timet50, and then calculating the ion–ion separativector at each time step. For each of the mixture comptions we have selected several interionic separations~in therange of 2.6–9.0 Å! as the starting ion-ion distance and folowed each of the ion-pair trajectories for short times~5 ps!as well as for long times~20 ps!.

The trajectories starting withr Na1 – Cl2 of 2.6 to 5.0 Å forall compositions settle at the broad SSIP minimum at60.8 Å in a very short time~within 1 ps! and after this initialperiod, the interionic distance remains near 5.060.8 Å forwell over 20 ps. Since these trajectories look similar beyo2 ps and the average interionic distance does not changemuch beyond 2 ps, we show only a few distinctive trajecries initiated at short interionic separations in Fig. 5. Onethem is for the mixed solvent withxDMSO50.10 and initiatedat r Na1 – Cl253.2 Å shown in Fig. 5~a!. The ion–pair quicklysettles at a distance of 4.660.5 Å. The trajectories for compositions withxDMSO50.21, 0.35 and 0.48 initiated at a ditance in the ranger Na1 – Cl252.6– 5.0 Å also settle at an average value ofr Na1 – Cl255.060.5 Å. The trajectories forxDMSO50.91 are shown in Figs. 5~b! and 5~c!. The trajectoryinitiated at r Na1 – Cl252.6 Å @Fig. 5~b!# settles atr Na1 – Cl2

54.260.7 Å and the trajectory initiated atr Na1 – Cl253.4 Å@Fig. 5~c!# settles atr Na1 – Cl254.660.7 Å. Although an ion–ion separation near 2.6 Å is expected to be a reasonsharp and long lived CIP configuration of the Na1 – Cl2 ionpair ~which actually is, in the presence of pure DMSO!,7 theconfiguration is not stable in any of these mixtures andresidence time of the ion pair in this region of the potenwell is much less (,1 ps). We have tested this finding witseveral equilibrated solvent configurations at this distanThe dynamical trajectories of Fig. 5 indicate that an ion pin these mixtures is a broad SSIP at a distance rang4.2–5.8 Å.

Figure 6 displays the long time~20 ps! trajectories of theNa1 – Cl2 ion pair which are initiated at longer ion–ioseparations of>7.0 Å, in the presence of the five solvemixtures. The diffusive nature of the ion pair trajectory in tpresence of the mixture withxDMSO50.10 is clearly seen in


a

ng

nes

fe

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i-

0

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Fig. 6~a!. The ion pair settles at the SSIP minimum near 5Å. The trajectory in Fig. 6~b! indicates that the ion pair in thepresence of the mixture withxDMSO50.21 spends a verylong time at the less stable second SSIP minimumatr Na1 – Cl257.0 Å. These results have been reconfirmed byps runs. The ion trajectories starting at shorter distances,r Na1 – Cl252.6, 3.2, 4.8, and 5.4 Å~not shown in the figures!also settle around the SSIP distance of 5.0 Å; but the tratories starting atr Na1 – Cl257.0 Å or at a larger interionicseparation settle at around 7.0 Å, the location of the secminimum in the ion–ion PMF in a mixture withxDMSO

50.21. All trajectories starting atr Na1 – Cl256.6 Å for thismixture have a finite nonzero probability of crossing to teither side of this;8 kBT barrier~from the minimum on theleft!. We have already reported the computation of the tramission coefficients~whose value is0.2660.10)across thisPMF barrier.42 The solvation structures of the ion pair in thpresence of this mixed solvent withxDMSO50.21 have alsobeen reported42 in this mixture composition. The ion pair axDMSO50.35 settles at the SSIP minimum near 5.060.6 Å@Fig. 6~c!# within 5 ps and tends to remain oscillatory btweenr Na1 – Cl254.5 Å and 5.3 Å. The solvent mixture withxDMSO50.48 causes the ion pair to settle at the SSIP mmum atr Na1 – Cl255.0 Å within about 8 ps@Fig. 6~d!#. In thiscomposition, the PMF is quite broad at the minimum acovers a range of 4.5–6.0 Å. Thus the ion pair showstendency to remain oscillatory between 5.0 and 6.0 Å. Ttrajectory starting at 7.0 Å in the presence of the mixed svent withxDMSO50.91 settles slowly at the stable SSIP minmum at around 4.460.7 Å @Fig. 6~e!#. Because of the presence of a flat deeply negative regionin the PMF in thepresence of this solvent mixture~with xDMSO50.91) at a

FIG. 5. Representative short time~5 ps! trajectories of the Na1 – Cl2 ionpair in water–DMSO mixed solvents of different compositions.~a! xDMSO

50.10 with starting r Na1 – Cl253.2 Å ~b! xDMSO 50.91 with startingr Na1 – Cl252.6 Å ~c! xDMSO 50.91 with startingr Na1 – Cl253.4 Å.


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shorter ion-ion separation of near 4.5 Å, the long time tjectories approach shorter interionic separations. Thesejectories in Figs. 5 and 6 also show the presence of a brSSIP minimum in the distance range of 4.2–5.8 Å in all ficompositions and a second SSIP minimum atr Na1 – Cl2

57.0 Å for the composition withxDMSO50.21. As the molefraction of DMSO is increased up to 0.91, the SSIP mimum appears to become deeper and broader and shiftssmallerr Na1 – Cl2 distance confirming the pattern seen in F3. The well depth also appears to be the least whenxDMSO

50.35. As we increasexDMSObeyond 0.91 to unity we expect the CIP to eventually appear~the PMF is already largeand negative near 3.0 Å forxDMSO50.91), but simulationswith very few molecules of one component, especially adrogen bonding solvent such as water, are extremely tconsuming.

D. The ion-solvent radial distribution functions

In order to analyze the local solvation structures arouthe Na1 and Cl2 ions in the five mixed solvents, we havcomputed the ion-solvent pair distribution functions,gia(r ),and the running coordination numbersnia(r ). The ion-solvent pair distribution functiongia(r ) is the ratio of thelocal density of the solvent sitea at a distancer from the ioni and the bulk density (ra5Na /V)

FIG. 6. Representative long time~20 ps! trajectories of the Na1 – Cl2 ionpair in water–DMSO mixed solvents of different compositions. The startion-ion separation in each case is>7.0 Å. The mole fraction of DMSOxD

is shown on the graphs.


-ra-ad

-o a.

-e

d

gia~r !5V

Na•

Na~r !

4pr 2Dr, ~9!

whereNa is the number of theath solvent site in volumeVof the simulation shell andNa(r ) is the number of such sitein the spherical shell (r ,r 1Dr ) at a distancer from the ioni. The running coordination numbernia(r ) is the integratedintensity of thegia(r ) function up to the distancer

nia~r !54praE0

r

gia~s!s2ds. ~10!

The ion-solvent radial distribution functions have been cculated for all the solvent mixtures. For the sake of compason, the interionic separation has been chosen tor Na1 – Cl255.0– 5.4 Å for all the five mixed solvents. Figurepresents the ion-solvent radial distribution functions~RDFs!for the Na1 ion and Fig. 8 presents the ion-solvent RDFs fthe Cl2 ion. In both of these figures, the ion-solvent RDhave been shown by shifting them vertically with respectxDMSO.

From the plots in Fig. 7 we see that thNa1 – S~DMSO!, Na1 – O~DMSO!, Na1 – O ~water! andNa1 – H ~water! RDFs do not exhibit any change in the psition of the peak maxima, but the intensities of the peachange with the change in the solvent composition. TNa1 – CH3 ~DMSO! pair shows most pronounced variationin the peak position and peak height with the change incomposition. However, these variations are less intense~withintensities less than four units and these plots are notsented here!. We observe that the lowest DMSO containinmixture (xDMSO50.10) has the maximum height for thNa1 – S~DMSO!, Na1 – O~DMSO!, Na1 – CH3 ~DMSO!pairs. Once the solvation shell forms, it does not readallow the other DMSO molecules to come closer to the N1

ion. With the increase in the DMSO mole fraction the budensity increases, but the local DMSO density aroundNa1 ion does not increase correspondingly. Hence the pheight decreases. Turning to the solvation shell formedthe water molecules around the Na1 ion, we find that thelowest water containing mixture (xDMSO50.91) has themaximum height for the Na1 – O ~water! and Na1 – H ~wa-ter! pairs. The heights of the RDF maxima for these padecrease as the mole fraction of water increases. The ordincreasing water content in the solvent mixtures isxDMSO

50.91,0.48,0.35,0.21,0.10. Like before, with the in-crease in the water mole fraction the bulk water densitycreases, but the local water density around the Na1 ion doesnot increase proportionately. This makes the peak heightcrease with increasing water content in the mixtures. Itthus evident that the solvation shell around the Na1 ion con-sists of both water and DMSO molecules and the shell strture does not change in proportion to the changes insolvent composition.

We shall now discuss the ion-solvent RDFs for the C2

ion in the presence of the five mixed solvents. Thesedisplayed in the plots of Fig. 8. We see that tCl2 – S~DMSO! and Cl2 – CH3 ~DMSO! pairs do not exhibitthe formation of well defined DMSO coordination shellThis indicates the diffusiveness of the DMSO solvation sh

g



FIG. 7. The ion-solvent radial distribution functions for the Na1 ion in the presence of the mixed water–DMSO solvents withxDMSO50.10, 0.21, 0.35, 0.48and 0.91. For clarity, the functions for successive mole fractions~which are shown on the curves! are shifted vertically upwards.

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ange

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.

around the Cl2 ion. On the contrary, the Cl2 – O ~water! andCl2 – H ~water! pairs show the formation of wellcharacterized water solvation shells around this ion. TCl2 – H ~water! pair shows the formation of a second watshell which changes with the change in the solvent comsition. While the peak positions of the Cl2 – O ~water! andCl2 – H ~water! pairs do not change with mixture compostion, their intensities change significantly. As has beenserved in the case of Na1 ion, the intensity of the RDFmaximum is highest in the case of lowest water containmixture (xDMSO50.91), and the intensity decreases whmole fraction of water increases in the solvent. The explation for this is similar to that given for the Na1 ion. Watermolecules form the solvation shell around the Cl2 ion in thepresence of all five solvent mixtures considered here,this solvation shell does not undergo significant chan


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-

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ds

when the composition is altered. The bulk density of watethe mixed solvents increases fromxDMSO50.91,0.48,0.35,0.21,0.10, but the local density of water arounthe ion does not change appreciably because of the presof DMSO molecules, which form strongly hydrogen bondnetworks in the mixtures.9,10

Figure 9 presents the running coordination numbenia(r ) for the Na1 ion and Fig. 10 presents thenia(r ) for theCl2 ion. In both of these figures thenia(r ) functions arestacked vertically with respect toxDMSO. From theNa1 – S~DMSO! and Na1 – O~DMSO! nia(r )s we see thepresence of only one DMSO molecule near the Na1 ion atDMSO mole fraction xDMSO50.10, which rises to twoDMSO molecules atxDMSO50.48 and at the highest DMSOmole fraction of xDMSO50.91 this number is about 2.5Similarly the Na1 – O ~water! and Na1 – H ~water! nia(r )s

FIG. 8. The ion-solvent radial distribution functions for the Cl2 ion in the presence of the mixed water–DMSO solvents withxDMSO50.10, 0.21, 0.35, 0.48and 0.91. For clarity, the functions for successive mole fractions~which are shown on the curves! are shifted vertically upwards.



FIG. 9. The running coordination numbers around the Na1 ion in the presence of the mixed water–DMSO solvents withxDMSO50.10, 0.21, 0.35, 0.48 and0.91. For clarity, the functions for successive mole fractions~which are shown on the curves! are shifted vertically upwards.

ncn-

es

y

gol-

istione

ol-t

s

show the presence of four water molecules atxDMSO50.10which decreases to three water molecules atxDMSO50.48and to two water molecules atxDMSO50.91. We observe aconcomitant increase in the magnitude of thenia(r ) func-tions with the increase in the component mole fraction, sithesenia(r )s are always weighted with the bulk number desity of the solvent sitea @Eq. ~10!#. These observations suggest that the Na1 ion solvation shell is composed of fivmolecules~comprised of both DMSO and water molecule!in all the five solvent mixtures.

The running coordination numbers for the Cl2 ion havebeen presented in Fig. 10. In thenia(r ) plots ofCl2 – S~DMSO! and Cl2 – CH3 ~DMSO! it is seen that the


e-

closest DMSO coordination shell around the Cl2 ion isformed by the CH3 groups, although the shell is not verwell characterized. We find that only atxDMSO50.91, thenia(r ) for the Cl2 – CH3 pair shows a significant bendinindicating the presence of 4–5 DMSO molecules in the svation shell. At the lower mole fractions of DMSO, thnumber could not be ascertained precisely since the solvashell is diffusive@absence of the horizontal portions in thnia(r ) plots#. The nia(r )s for the Cl2 – O ~water! andCl2 – H ~water! pairs indicate the presence of 5–6 water mecules at xDMSO50.10, about four water molecules axDMSO50.48 and 2–3 water molecules atxDMSO50.91.Hence the Cl2 ion solvation shell in the five solvent mixture

FIG. 10. The running coordination numbers around the Cl2 ion in the presence of the mixed water–DMSO solvents withxDMSO50.10, 0.21, 0.35, 0.48 and0.91. For clarity, the functions for successive mole fractions~which are shown on the curves! are shifted vertically upwards.


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is composed of 7–8 molecules~comprising of both DMSOand water molecules!.

E. Preferential solvation of the Na 1 – Cl2 ion pair

In order to examine the solvent preferences ofNa1 – Cl2 ion pair in the presence of the five mixed wateDMSO solvents, we have calculated the local mole fractioxD

loc of DMSO andxWloc of water in the ion solvation shells a

a function of the bulk solvent composition. These have bcalculated using the formula12

xDloc~xD!5

niD~xD!

niD~xD!1niW~xD!, ~11!

xWloc~xW!5

niW~xW!

niW~xW!1niD~xW!, ~12!

where niD(xD) is the coordination number of the DMSOsolvation shell of theith ion andniW(xD) is the coordinationnumber of the water solvation shell of theith ion at thesolvent compositionxD . The DMSO mole fraction isxD ([xDMSO) and the water mole fraction isxW ([xwater).Equations~11! and ~12! provide an opportunity to comparthe results with nuclear magnetic resonance~NMR! data ashas been done in the case of the solvation of Na1 – Cl2 in thepresence of water formamide mixtures.12 Since the S atom oDMSO and the O atom of water are located near the ceof mass of the corresponding solvent molecule, the coonation numbersniD and theniW are evaluated by integratinthe giS(DMSO)(r ) and giO(water)(r ) functions up to the firstminimum (r min). For the Na1 – S~DMSO!, Na1 O ~water!,Cl2 – S~DMSO! and Cl2 – O ~water! pairs ther min values are4.2, 2.8, 6.4, and 4.0 Å, respectively. Figure 11 showsplots of thexD

loc andxWloc functions for the Na1 and the Cl2

ions. From the plots ofxDloc andxW

loc for the Na1 ion we findthat the Na1 ion is preferentially solvated by water in thmixed solvents with DMSO mole fractionxDMSO > 0.21.The solvation of the Cl2 ion is preferred by DMSO in thesolvent compositions withxDMSO50.10 and 0.21.

IV. CONCLUSIONS

Constrained MD simulations have been performedthe Na1 – Cl2 ion pair in the presence of five selected wateDMSO mixtures with the mole fraction of DMSO,xDMSO

50.10, 0.21, 0.35, 0.48 and 0.91. The derived potentialsmean force for the ion pair do not show the existence ostable contact ion pair in any of the mixtures. The preseof the pervasive solvent separated ion pairs in all these cpositions has been demonstrated from the nature ofPMFs. The derived PMFs have been tested by doing auiary MD simulations on the ion pair and generating the dnamical ion-ion trajectories of the pair. This was donereleasing the constraint on the ion pair at timet50, andtrailing the ions for a considerably long time (.20 ps).Interestingly, the Na1 – Cl2 ion pair in pure water is seen texist both as a CIP and as a SSIP, with the SSIP configtion a little more stable than the CIP.5 The ion pair in pure


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DMSO also exists in both the configurations, but the Cconfiguration in DMSO is much more stable than the SSconfiguration.7

The solvent composition withxDMSO50.10 has shown asingle well-defined SSIP minimum atr Na1 – Cl254.6 Å. Themixture with xDMSO50.21 shows two well-defined SSIPminima atr Na1 – Cl255.0 and 7.0 Å. These SSIPs are seprated by an activation barrier atr Na1 – Cl256.6 Å. We haveanalyzed the solvation of the individual ions at these ion–separations in an earlier paper and also calculated the trmission coefficients across the PMF barrier in this mixtucomposition.42 The mixed solvent withxDMSO50.35 exhibitsthe presence of only one SSIP atr Na1 – Cl255.0 Å. Thefourth solvent mixture withxDMSO50.48 shows the presencof a SSIP well covering the range ofr Na1 – Cl254.4– 5.1 Å.The composition with higher DMSO content (xDMSO

50.91) shows the presence an SSIP atr Na1 – Cl254.4 Å, butthe PMF has become significantly negative nearr Na1 – Cl2

53.0 Å.The ion-solvent radial distribution functions for th

Na1 – Cl2 ion pair in the presence of the five mixed wateDMSO solvents emphasize the formation of solvation sharound each ion comprising of molecules of both the coponents of the solvent mixture. In all the five mixtures tlocal solvation shells around the ions are strong and doshow any changes in the RDF peak positions with the chain the mixture composition. With respect to the changeintensities of the RDF peaks, the lowest DMSO containmixture (xDMSO50.10) has the maximum height for thNa1 – S~DMSO!, Na1 – O~DMSO! and Na1 – CH3 ~DMSO!pairs. Similarly, the lowest water containing mixtu(xDMSO50.91) has the maximum height for the Na1 –O ~wa-ter! and Na1 – H ~water! pairs. These are attributed to the fathat the local density of the solvent site around thechanges very slowly in comparison with the bulk densitythe solvent. Similar arguments hold good for the decreas

FIG. 11. The local mole fractionsxDloc of DMSO andxW

loc of water in the Na1

and Cl2 ion solvation shells as functions of solvent composition (xD or xW).


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the peak heights in the Cl2 –O ~water! and Cl2 –H ~water!RDFs with increasing water content. The RDFs of tCl2 – S~DMSO! and Cl2 – CH3 ~DMSO! pairs do not showthe formation of well-defined DMSO coordination shearound this ion.

The plots of the running coordination numbers show tthe Na1 ion has a total of five solvent molecules and the C2

ion has a total of 7–8 solvent molecules in the respecsolvation shells. The numbers of each component solvmolecules vary as the solvent composition changes. Forample, atxDMSO50.10, one DMSO and four water moleculeconstitute the Na1 ion solvation shell. AtxDMSO50.91, threeDMSO and two water molecules solvate the Na1 ion. Simi-larly, at xDMSO50.10, the solvation shell of the Cl2 ion hasone DMSO and 5–6 water molecules. AtxDMSO50.91, thision is solvated by four DMSO and 2–3 water molecules.

In order to determine the solvent preferences of the N1

and Cl2 ions in the mixed solvents, we have calculatedlocal mole fractions around each ion. It is found that the N1

ion prefers to be solvated by water in the mixed solvewith DMSO mole fractionxDMSO>0.21. The Cl2 ion ispreferred by the DMSO component in the mixtures wxDMSO50.10 and 0.21.

It would be of great interest to investigate the transtional diffusion of the Na1 and Cl2 ions in the presence othese strongly nonideal solvent mixtures. The influencethe solvation shell~where both the component solvent moecules are present! on the individual ionic mobilities is alsoworth investigating. Such studies in the presence of neideal solvent mixtures~like water–formamide!12 are beinginvestigated by other groups. The dependence of the reon the choice of the models used for the site–site potenalso needs to be assessed in detail.

ACKNOWLEDGMENTS

We gratefully acknowledge the computational suppprovided by the Department of Science and TechnoloGovernment of India, for this work. We also thank the reeree for a critical reading of the manuscript and valuasuggestions.

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molecular dynamics simulations of sodium chloride …...properties.15,16 with respect to the...

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