Large ionic clusters in concentrated aqueous NaCl solutionLéo Degrève and Fernando Luıs B. da Silva Citation: The Journal of Chemical Physics 111, 5150 (1999); doi: 10.1063/1.479783 View online: http://dx.doi.org/10.1063/1.479783 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/111/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Fragile to strong crossover at the Widom line in supercooled aqueous solutions of NaCl J. Chem. Phys. 139, 204503 (2013); 10.1063/1.4832382 Effects of concentration on structure, dielectric, and dynamic properties of aqueous NaCl solutions using apolarizable model J. Chem. Phys. 132, 214505 (2010); 10.1063/1.3429253 Molecular dynamics simulations of aqueous NaCl and KCl solutions: Effects of ion concentration on the single-particle, pair, and collective dynamical properties of ions and water molecules J. Chem. Phys. 115, 3732 (2001); 10.1063/1.1387447 Dielectric response of concentrated NaCl aqueous solutions: Molecular dynamics simulations J. Chem. Phys. 115, 1448 (2001); 10.1063/1.1381055 Structure of concentrated aqueous NaCl solution: A Monte Carlo study J. Chem. Phys. 110, 3070 (1999); 10.1063/1.477903

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Large ionic clusters in concentrated aqueous NaCl solutionLeo Degrevea)

Grupo de Simulac¸ao Molecular, Depto. de Quı´mica, Faculdade de Filosofia, Cieˆncias e Letras de Ribeira˜oPreto, Universidade de Sa˜o Paulo, 14040–901 Ribeirao Preto, SP, Brasil

Fernando Luıs B. da SilvaGrupo de Simulac¸ao Molecular, Depto. de Quı´mica, Faculdade de Filosofia, Cieˆncias e Letras de Ribeira˜oPreto, Universidade de Sa˜o Paulo, 14040–901 Ribeirao Preto, SP, Brasil, and Physical Chemistry II—P.O. Box 124—Lund University, S-221 00 Lund, Sweden

~Received 29 May 1998; accepted 11 June 1999!

The stability of the local structure of aqueous 1.0 M NaCl solution at 293 K was investigated bymolecular dynamics simulations. The mean and maximum life-times of the ion pairs weredetermined to be 0.13, 0.14 and 0.27 ps for negatively charged, neutral and positively charged ionspairs, respectively. The stability of non-neutral ion pairs was studied from the structure of theanion–cation radial distribution function and other structural functions. We found that non-neutralions pairs are stabilized by at least one counter-ion forming in this way large ionic clusters thatinclude the hydration molecules. About 25% of the ions are included in neutral clusters formed bya minimum of four ions. The existence of these large clusters obfuscates the commonly acceptedchemical reaction scheme for the interconvention of ion pairs in aqueous solutions. ©1999American Institute of Physics.@S0021-9606~99!50134-7#

I. INTRODUCTION

The behavior of aqueous solutions in the bulk or at theinterfaces has receiving considerable attention for manyyears. It is clear that the understanding of these processes hasa wide range of technological applications and theoreticaldevelopments in liquid purification, homogeneous and non-homogeneous catalysis, transport, biophysical processes,chemical technology, petrochemistry, theory of chemical andphysical processes.1–9 One particular aspect of great interestis the interconversion of ion pairs in solution due to its directrelation with important chemical reactions.10,11 However,this mechanism remains poorly understood.10 The reactionscheme that is more accepted isA11B2 ~free ions!⇔A1iB2 ~solvent separated ion pair—SSIP! ⇔A1uB2

~contact ion pair—CIP! ⇔AB ~reaction product!, where thespecific role and nature of these ion pairs are stilluncertain.10,12 The so-called computer experiments, or simu-lation techniques, can by-pass experimental and theoreticaldifficulties and furnish a molecular level characterization forthese intermediate states and barriers separating them.3,10,12

They can also provide detailed information on the local con-centration in the neighborhood of molecules or macro-molecules at nonhomogeneous interfaces13–16 or aroundions in solutions using either the usual radial distributionfunction ~rdf!17,18 and/or multi-variable distributionfunctions.13–16,19–22

Recently, we presented an analysis of the structure of anelectrolyte solution at finite concentration, precisely aqueous1.0 M NaCl solution.3 One important point in that study wasthat the analysis focused on the ion pairs that were identifiedby the fact that two ions share at least two hydration mol-

ecules. The main idea was based on the fact that the numberof water molecules in the first solvation shells of these ionsare quite stable and close to six, i.e., 6.0060.27 for Na1 and5.7360.99 for Cl2.22 The fluctuations in these hydrationnumbers are small because ion–water energies are lowerthan the bulk energy.22 Another observation is that only fewexchanges between hydration molecules and the bulk areobserved.23 These stability conditions suggest that ion asso-ciation must occur keeping as far as possible the solvationshells. At least two cases of ion pairing can be identified. Thesimplest one is the case where there is the direct contactbetween the ions~this is the commonly accepted definition ofion association24–26!. The second one is detected when thesolvated water molecules are shared by two ions keepingthem close or making them approach each other. This willmaintain the stability of the structure.3 The consequence isthe stabilization of the clusters formed by two ions altogetherwith all their solvation molecules. In all ion association, theions must share some water molecules in their solvationshells: their number cannot be less than two excluding thecases of single nonassociating collisions. Therefore, the shar-ing of the minimum of two water molecules by two ions canbe a good criterion for the identification of an ionassociation.3 As a result, it was observed3 that the fractionsof associated ions were unexpectedly high, e.g., 0.46 for thecations and 0.32 for the anions. In particular, associationsbetween identical ions were largely observed. For instance,roughly 13% of the anions and 16% of the cations are asso-ciated in non-neutral pairs.3 These pairs were studied beforeby other authors in different ways mainly on primitivelymodeled solutions.27–29 However, apparently no informationon the stabilization process of charged pairs was obtained.Studies on nonprimitive models for electrolyte solutionswere also able to predict the stability of some ion pairs from

a!Author to whom correspondence should be addressed; electronic mail:leo@obelix.ffclrp.usp.br

JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 11 15 SEPTEMBER 1999

51500021-9606/99/111(11)/5150/7/$15.00 © 1999 American Institute of Physics

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mthe mean force potential, such as the Cl2–Cl2 pair,30 whilethe stability of Na1–Na1 pairs was not predicted. Conse-quently, the present question is to determine what is the sta-bilization mechanism of highly repulsive charged pairs andto determine if the stabilization process is mainly explainedby the solvent or ions properties.

II. METHOD

Systems constituted by 2117 water molecules and 40NaCl were submitted at 293 K to molecular dynamicssimulation.18,31,37The volume was adjusted to correspond toa density equal to 1.1402 kg/l so that the electrolyte concen-tration was 0.993 M. These conditions correspond to NaClsolutions under atmospheric pressure. Solvent moleculeswere described by the TIP4P water model33 and their inter-actions with the ions by a 6–12 plus Coulomb interactionpotential.34 Ion–ion interactions were modeled by theGROMOS force-field.38 Periodic boundary conditions andminimum image convention were adopted. The long-rangeelectrostatic energies were included through a Poisson–Boltzmann generalized reaction field32 with a spherical cut-off at 1.5 nm. The Newton movement equations were inte-grated by a time step of 1.0 fs and the total simulation timewas 0.2 ns. Quaternions36 and the Gear predictor–correctormethod37 were used.

Ion–ion rdf gion,ion8(r ), whereion could be both the an-ion and the cation andr is the interionic distance, were cal-culated in the usual way.18 As it will be seen, thegNa1,Cl2(r )function presents two very well defined peaks at short dis-tances. The first peakP1 is included in the range ofr 50.0 tor 5r min,1 and the second peakP2 in the range ofr min,1 tor min,2, wherer min,1 and r min,2 correspond to the positions ofthe first and secondgNa1,Cl2(r ) minima, respectively~it willbe noted thatr 5r min,150.34 nm andr min,250.58 nm). Theionic structures that are responsible for these peaks will beresolved from the fraction of ions present inP1 andP2 . Thisentity will denoteSion(n1

k ,n2k), where the subscription is the

reference anion, or cation, at the origin. The numbers ofcounter-ions of typek in P1 andP2 are given byn1

k andn2k ,

respectively. For instance, assuming that the Na1 is on the

center,SNa1(n1Cl2 ,n2

Cl2) records the frequency that the num-

ber of counter-ions Cl2 presents on peakP1(n1Cl2) and, si-

multaneously, inP2 (n2Cl2), appeared during the observation

time. TheSion(n1k ,n2

k) functions were not calculated from theradial distribution functions. Instead, they were calculated bydirect counting of the respective occurrence during the simu-lation process, after the proper equilibration of the system.

The counter-ions present inn1k andn2

k are possibly dis-tributed in space according to the local energy minima, sothat we can define three partial radial distribution functionsgion

11 (r ), gion12 (r ) andgion

22 (r ), where the exponents 11, 12 and22 refer to the simultaneous presence of counter-ions inpeaksP1 and P1 , P1 and P2 , and in P2 and P2 , respec-tively. The distancer is the separation distance between thecounter-ions in the respective cases. It is convenient as wellto determine the distribution functions of the angleC formedby one counter-ion, the central ion and the second counter-ion: C ion

11 , C ion12 and C ion

22 . For example,CNa111 refers to the

angle formed by one Cl2, a central Na1 and a second Cl2,when both Cl2’s are inP1 . Analogously, if the anions are indifferent peaks, the corresponding function isCNa1

12 . Thepartial radial distribution functionsgion

11 (r ), gion12 (r ) and

gion22 (r ), together with the anglesC allow us to determine

accurately the most frequent interionic distances, and hencewill allow us to associate the respective configurations withthe features of the ion–ion radial distribution functions.

III. RESULTS

The mean total configurational energy was found to be217.460.1 kcal/mol. The configurational energy for the in-teractions between the water molecules was27.04760.07 kcal/mol, which is slightly above the configurationalenergy of the pure TIP4P water bulk phase (210.07kcal/mol30!. Ion–water energy was equal to24.2 kcal/mol.These results are similar to the Monte Carlo data formerlyobtained.3 The diffusion coefficients for Na1, Cl2 and watermolecules were determined as being equal to 1.23, 2.5 and4.6031029 m2 s21, respectively. These numbers are in goodagreement with the results obtained by the same ions modelsand rigid SPC water model.35 Some difference between ourresult for the diffusion coefficient and the value 2.9631029 m2 s21 for pure TIP4P water38 is observed while theconcordance with more recent data39 is good.

ThegCl2,Na1(r ) distribution function is displayed in Fig.1. It presents a first very well defined peak of 32.15 atr50.25 nm and a smooth second one of 2.5 atr 50.48 nm, atypical trait of strong long-range electrostatic attraction and ashort-range soft core repulsion. This data is similar to resultsobtained with SPC water and the same ion–ion interactionpotential reported in the literature.35 In Fig. 1, the number of

FIG. 1. The ionic radial distribution functions as a function of the separationdistancer between the ions:gCl2,Cl2(r ) ~dots!, gNa1,Cl2(r ) ~solid line! andgNa1,Na1(r ) ~dashed line!. The running integrals of these curves are alsorepresented.

5151J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 Large ionic clusters in aqueous solution

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cations–anions neighbors is also plotted. This graphic showsthat the firstgCl2,Na1(r ) peak corresponds to 0.41 ions sothat the fraction of ions in contact and consequently associ-ated in neutral pairs is 0.41. The secondgCl2,Na1(r ) peak andthe number of neighbors profile indicate the existence of astructure in ther 50.49 nm region too. The other rdfs,gCl2,Cl2(r ) andgNa1,Na1(r ), are also plotted in Fig. 1. Thesefunctions are badly defined such that the comparison withpublished data35 is not fruitful. However, in all cases thesefunctions present a first, but not so well defined peak corre-sponding to a mean of a 0.1 Cl2 ion near each Cl2 and 0.06in the Na1 case. More data are summarized in Table I.

The analysis of the stabilities or mean life-times beginswith the ion–ion rdfs. The characteristics of the various ion–ion rdf are fundamentally different; see Fig. 1. If we compareeithergCl2,Na1(r ) with gCl2,Cl2(r ) or with gNa1,Na1(r ), onlythe gCl2,Na1(r ) function presents two very well definedpeaks. This might indicate that a relatively long-range struc-ture of counter-ions exists around the central cation or anion.From data of Fig. 1, the values ofr min,1 and r min,2 are iden-tified as equal to 0.34 and 0.58 nm, respectively. The corre-spondingSion(n1

k ,n2k) data are reported in Table II. Both fre-

quencies SCl2(n1Na1

,n2Na1

) and SNa1(n1Cl2 ,n2

Cl2) are verysimilar showing roughly that 30% of the ions have no neigh-bor in eitherP1 or P2 , 44% one inP1 or P2 so that about

25% of the ions are embedded in clusters of three or moreions. The frequency of these clusters is so large that we canstudy their structure by means of the partial radial distribu-tion functionsgion

11 (r ), gion12 (r ) and gion

22 (r ) @see Figs. 2~a!–~c!#, and from the anglesC ion

11 , C ion12 and C ion

22 @see Figs.3~a!–~c!#. In Fig. 2~a!, one sharp peak is present ingNa1

11 (r )and two peaks ingCl2

11 (r ) at the same distance as those foundat thegCl2,Cl2(r ) andgNa1,Na1(r ) peaks~see Fig. 1!. Despitesome fluctuations, a similar behavior is observed in Fig. 2~b!.Figure 2~c! shows a double behavior taking into account theelectrostatic repulsion at a large distance and the formationof ion pairs at short distances. Comparing the positions of thepeaks in Fig. 1 and in Figs. 2~a!–~c!, the identification of thenature of the peaks, or bumps, comes out with no efforts.The first peak ofgCl2,Cl2(r ) at 0.43 nm appears at least par-tially as a consequence of the first peaks presented at thethree partial distributions,gNa1

11 (r ), gNa112 (r ) and gNa1

22 (r ),while the second peak is related to the second one found atgNa1

12 (r ) and gNa122 (r ). Similar identifications can be made

betweengNa1,Na1(r ) andgCl211 (r ), gCl2

12 (r ) andgCl222 (r ). The

correlations between the peaks and their positions are exactlyone to one. This is an obvious influence of the solvent as aquite important factor on the determination of the peak po-sitions, i.e., the structure of the medium is largely defined bythe solvation structures of the ion pairs. The remark includesthe cation–anion pairs that are the starting point of thepresent analyses. A comparison between the three partial rdffor the anion and for the cation reveals one characteristicdifference. In the anion case as the reference ion, the cation–cation distribution presents two peaks that must be associ-ated with the high stability of the cationic pairs. This ex-plains the high stability of the first cationic hydration shellby the presence of one anion turning the cluster energeticallystable.

The same structural properties are obtained for theCfunctions as well; see Figs. 3~a!–~c!. These figures also showthe same tendency to increase the interionic distance betweenco-ions implying definite angles that correspond to the peaksobserved in Figs. 2~a!–~c!. A detailed analysis of the corre-lations between the anglesC and the partial and total radialdistribution functions can now be made. The position of thefirst gCl2,Na1(r ) maxima in Fig. 1 arer max,150.25 nm andr max,250.48 nm, while the peaks ingCl2,Cl2(r ) are observedat 0.43 and 0.51 nm; see Fig. 1. Yet ingNa1,Na1(r ), the peaksare found at 0.35, 0.44 and 0.61 nm. From these sets of probedistances and together with the coordinates of the observedpeaks in Fig. 2~a!–~c!, the values of the maxima ofC ion

11 ,C ion

12 andC ion22 observed in the Figs. 3~a!–~c! are recovered.

A consistency check together with a yet more completecomparison between the partial and the full ion–ion rdfs cannow be made comparing the sums of the partial rdf with thefull rdf. In Fig. 4~a!, gNa1,Na1(r ) is compared withgCl2

11 (r )1gCl2

12 (r )1gCl222 (r ) and in Fig. 4~b! gCl2,Cl2(r ) with

gNa111 (r )1gNa1

12 (r )1gNa122 (r ). The gNa1,Na1(r ) is extremely

well reproduced mainly at short distances so that all theNa12Na1 pairs are associated with counter-ions. At shortdistances, i.e., when both counter-ions pertain toP1 and/or

TABLE I. Positions (nm) and intensities of the first two extrema of theradial distribution functions and the corresponding value of the coordinationnumber calculated until the corresponding minimum,n(r min).

r max g(r max) r min g(r min) n(r min)

gCl2,Cl2(r )

0.43 1.15 0.47 0.83 0.100.51 1.41 0.63 0.78 0.47

gNa1,Cl2(r )

0.25 32.15 0.34 0.83 0.410.48 2.50 0.58 0.95 1.05

gNa1Na1(r )

0.35 1.39 0.39 0.59 0.060.44 0.88 0.49 0.32 0.15

TABLE II. The frequenciesSCl2(n1Na1

,n2Na1

) andSNa1(n1Cl2,n2

Cl2). See thetext for details.

SCl2(n1Na1

,n2Na1

)

n2Na1

50 n2Na1

51 n2Na1

52 n2Na1

53

n1Na1

50 0.302 0.255 0.079 0.006

n1Na1

51 0.179 0.114 0.015 0.002

n1Na1

52 0.046 0.004 0.000 0.000

SNa1(n1Cl2 ,n2

Cl2)

n2Cl250 n2

Cl251 n2Cl252 n2

Cl253 n2Cl254

n1Cl250 0.296 0.257 0.069 0.009 0.001

n1Cl251 0.203 0.109 0.015 0.003 0.000

n1Cl252 0.004 0.004 0.000 0.000 0.000

5152 J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 L. Degreve and F. L. B. da Silva

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P2 , the full rdf are always smaller than the sum of the partialrdf. This is evidence that the same two ions give more thanone contribution to the partial rdf. This is possible only if thesame two counter-ions are found inP1 and/or P2 of twodifferent central ions. Consequently not only the Na12Na1

pairs are associated with counter-ions but the Cl22Cl2 pairsare too. The fact that the full rdf is always smaller than thesum of the partial rdf at short distance is the consequence ofthe existence of clusters formed by four ions, two pairs ofcounter-ions. The quantity of these large clusters can be de-duced from the running integrals of the full rdf and from thesums of the partial rdf shown in Fig. 5. Running integralscalculated until the same minima positions as the minima ofgNa1,Na1(r ) and gCl2,Cl2(r ) are found to be 0.09 and 0.15,respectively. These values are exactly 50% larger than the

values in Table I, i.e., half of the ion pairs are associated totwo counter-ions. The ratios of the running integrals on thesums of the partial and on the full rdf show peaks that areconsequence of structural fluctuations at short distances; seeFig. 6. More important is the stabilization of these ratios near2.0 for the Na12Na1 and 3.5 for Cl22Cl2 pairs in bothcases for interionic distances at about 0.03 nm, before thefirst peaks of their respective distributions. These numbersindicate the existence of larger clusters.

The mean life-times of the ion pairs were determineddirectly from the generated trajectory, see Table III, wherethey are listed together with the longest observed life-time.They were determined ast f2t i . The initial timet i is definedby the moment of the first identification of the pair forma-tion, when the first solvation shells of two ions begin to share

FIG. 2. Partial radial distribution functions as a function of the interionicseparation distancer . See the text for details.~a! gNa1

11 (r ) ~solid curve! andgCl2

11 (r ) ~dots!; ~b! gNa112 (r ) ~solid curve! and gCl2

12 (r ) ~dots!; ~c! gNa122 (r )

~solid curve! andgCl222 (r ) ~dots!.

5153J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 Large ionic clusters in aqueous solution

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two water molecules. The final timet f is the last time imme-diately before the same two ions discontinue the sharing ofany two water molecules in their first solvation shells. Nosort of time correlation function or ‘‘survival function’’40

was adopted. Consequently, fluctuations in the sharing ofsolvent molecules, resulting in the discontinuity of the exis-tence of the ion pair, imply the limit of its life-time. It shouldbe noticed from the data in Table III that there is a raise onthe mean life and longest life-times from the Cl22Cl2 pairsto the Na12Cl2 and Na12Na1 pairs. The positive pairs areuncommonly stable comparing with the neutral pairs. Al-though they have both a mean life-time and a maximumlife-time of almost twice the neutral pairs, their relative fre-quency ~number of detected pairs! is ca. 10% of what isfound for the neutral pairs. The last ones are surely

predominant.3 The numbers of detected pairs are of the sameorder as the numbers of ions in the first rdf peaks.

IV. DISCUSSION

In a former study,3 the existence of ion pairs was con-firmed. The pairs can be charged or not. The structure ofthese pairs is determined by the solvent because the hydra-tion energies are so attractive that the pairs were able to beformed and to maintain some degree of stability. An impor-tant point was that the ions in these pairs must share somehydration molecules. In the case of the non-neutral pairs, thehighly repulsive electrostatic interactions must prohibit theapproach of the ions, at first sight. This is not the case, sincethe ions can approach one another; see Fig. 1. Together with

FIG. 3. Distribution functions of the angle formed by one counter-ion, acentral ion and a second counter-ion,C, in arbitrary units.C is given indegrees. See the text for details.~a! CNa1

11 ~solid curve! andCCl211 ~dots!; ~b!

CNa112 ~solid curve! andCCl2

12 ~dots!; ~c! CNa122 ~solid curve! andCCl2

22 ~dots!.

5154 J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 L. Degreve and F. L. B. da Silva

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this fact, it is relevant to point out that these pairs weredetected too by direct and independent inspection into thetrajectories. The present results furnish the simple explana-tion that ion pairs can exist and that they exist in the pres-ence of at least one counter-ion and probably two counter-ions. The resulting electrostatic energy is clearly attractive.Many consequences are immediately identified, e.g., ions inaqueous solution are not only associated in pairs, but incharged triplets and larger clusters. The running integrals ofthe full and sums of the partial rdf suggest strongly thatmany neutral clusters are formed by two anions and twocations. A rough estimation of the fraction of ions associated

in these clusters, calculated from the fraction of non-neutralpairs, results in more than 0.25. The second consequence isthat an important component of the electrolyte diffusion andself-diffusion is determined by the diffusion of large clusterscontaining at least three ions and a high number of solventmolecules~speculatively about 12 to 14!. In order to deter-mine this physical property, it is probably advisable to studysuch aggregates center of mass displacement. A third conse-

FIG. 4. A comparison of the full and partial sums of rdf:~a! gNa1,Na1(r )~solid line!, gCl2

11 (r )1gCl212 (r )1gCl2

22 (r ) ~dashed line!; ~b! gCl2,Cl2(r ) ~solidline!, gNa1

11 (r )1gNa112 (r )1gNa1

22 (r ) ~dashed line!.

FIG. 5. Running integrals ofgCl2,Cl2(r ) ~circle!, gCl211 (r )1gCl2

12 (r )1gCl2

22 (r ) ~dashed line!, gNa1,Na1(r ) ~cross! gNa111 (r )1gNa1

12 (r )1gNa122 (r )

~solid line!.

FIG. 6. Ratio of the running integral ongCl2,Cl2(r ) divided by the runningintegral ongNa1

11 (r )1gNa112 (r )1gNa1

22 (r ) ~solid curve!. The same plot for theNa1,Na1 pairs is shown as dashed lines.

5155J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 Large ionic clusters in aqueous solution

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quence is that no structure involving only ions can be ex-pected. This is because their relative positions in the threedimensional space are governed by the scheme of ionic hy-dration. The slow diffusion of the ions always observed inexperiments41 and in simulations of aqueous electrolyte sys-tems is easily explained by the existence of these large clus-ters.

Some question remains yet unanswered such as the ex-tension, the kinetics of formation/destruction of the clusters;what is the fraction of the ions associated in these large clus-ters? What are the consequences of the existence of the clus-ters on the kinetics and mechanisms of the ionic reactions?How is the behavior of the clusters in external fields? This iscurrently under investigation and our results will be pre-sented in a forthcoming paper.

V. CONCLUSION

The structure and properties of the aqueous NaCl is gov-erned by the solvent properties. The fact that the tetrahedralstructure of water is maintained~due to the high energeticcost to be broken! together with the fact that the interionicinteractions are not able to by-pass this cost, result in theextremely good solvent properties of water regarding ionicsolutes. These observations are direct and indirect conse-quences of the high water polarity. The 1 M NaCl solution isvery similar to a coloidal dispersion of entities formed byclusters of solvated and associated ions. The neutral andcharged ionic clusters are energetically stable and contain atleast three ions. Clusters formed by two anions and two cat-ions are frequent and include a quarter of the all the ions.This explains the ambiguity between the number of identi-fied paired ions and free ions. The existence of large solvatedion clusters obfuscates the apparently simplicity of the men-tioned chemical reaction by the increasing of a new ion~thecounter-ion! in the picture of SSIP and CIP pair schemes.

ACKNOWLEDGMENTS

This work was supported in part by the Conselho Nacio-nal de Desenvolvimento Cientı´fico e Tecnolo´gico and by theFundac¸ao de Amparo a` Pesquisa do Estado de Sa˜o Paulo.

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TABLE III. Life-times of the ion pairs (ps).

Mean life-time Relative frequency Maximum life-time

Cl2/Cl2 0.13 0.193 1.41Na1/Cl2 0.14 0.728 3.83Na1/Na1 0.27 0.079 6.63

5156 J. Chem. Phys., Vol. 111, No. 11, 15 September 1999 L. Degreve and F. L. B. da Silva

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