Model Dependence of Solvent Separated Sodium Chloride Ion Pairs in Water-DMSO Mixtures

Transcription

1 Mdel Dependence f Slvent Separated Sdium Chlride In Pairs in Water-DMSO Mixtures A. Asthana, A.K. Chwdhury, A.K. Das, and B.L. Tembe Department f Chemistry, I.I.T. Bmbay, Pwai, Mumbai , India Abstract. Cnstrained mlecular dynamics simulatins have been used t investigate in pairing in water - DMSO mixtures. The ptentials f mean frce between the sdium - chlride in pair are cnstructed by estimating the mean frces between the in pair at varius interinic separatins and then integrating the mean frces. Tw cmpsitins f the slvent mixture with DMSO mle fractins f 0.21 and 0.35 are cnsidered. Tw mdel ptentials fr water and DMSO have been cnsidered. One f the main bservatins is that the cntact in pair which is dminantly present in bth the individual slvents is cnspicuusly absent in the mixture cmpsitins studied. While slvent separated in pairs dminate in all the mixture cmpsitins, there is a presence f a secnd slvent separated in pair in the water-dmso mixture f cmpsitin with mle fractin f DMSO = The ptentials f mean frce are verified by dynamical trajectries f the in pair. The dynamics f the slvatin shells has als been investigated in detail. 1 Intrductin In pairs play a very imprtant rle in a variety f chemical and bichemical reactins. The slvatin f ins and in pairs influences the nature f reactins in slutin media. 1-5 The cncept f tw in pair states, namely, the cntact in pair (CIP) and the slvent separated in pair (SSIP), was prpsed independently by Winstein 6 and by Fuss. 7 The general scheme fr any slvlysis reactin r any reactin that invlves participatin f slvent can be represented by CA C + A C + A C + + A (1) where the C + A represents the CIP and C + A represents the SSIP. The tw in pair states are characterized by the existence f well-defined barriers in the in-in ptential f mean frce (PMF) derived thrugh methds such as cnstrained MD simulatins. These in pairs als exist in mixed slvents and the transfrmatin f the CIP int SSIP r vice versa invlves the mtin ver an energy barrier between these tw sates. The first attempt t perfrm mdel calculatins f slvatins f alkali halides in DMSO was made by Gldenberg et al. 8 Energy calculatins were carried ut n a cluster f an in with 4, 5 and 6 mlecules f slvent and n in pairs with 14 DMSO mlecules respectively. Ten pint charges and nine plarizable bnds represented a DMSO mlecule. It was fund that calculated in slvatin energies were in quantitative agreement with experimental data. V.N. Alexandrv et al. (Eds.): ICCS 2006, Part III, LNCS 3993, pp , Springer-Verlag Berlin Heidelberg 2006

2 162 A. Asthana et al. The first real MD simulatin f liquid DMSO represented by 216 rigid mlecules was perfrmed by Ra and Singh. 9 They determined relative differences in free energies f slvatin between tw different slutes, including Na +, K +, Cl and Br ins, in DMSO as well as in water and methanl. Their study shwed that strng in-diple interactin, and a well-defined c-rdinatin sphere f five DMSO is frmed arund Na + in in liquid DMSO. Cl in was fund t be surrunded by abut seven DMSO mlecules and there is n well-defined c-rdinatin. A detailed investigatin f the slvatin phenmena f sdium and chlride in pairs in liquid DMSO was undertaken by Madhusdanan and Tembe. 10 The ptential mean frce, the structure f slvatin shells arund the Na + - Cl pair and the dynamics f assciatin f Na + - Cl -, Na + - Na + and Cl - - Cl - pairs were studied by using the methd f cnstrained MD Neutrn diffractin and MD simulatin based n the data, generated frm the neutrn diffractin experiments, were perfrmed by Luzar et al t study the structure f water-dmso binary mixture. 14 The results shwed the DMSO xygen t be strngly hydrgen bnded, but the methyl grups were surrunded by lse hydrgen bnded cages f water mlecules. N evidence fr hydrphbic assciatin f DMSO was bserved. Chalaris and Samis 15 studied the dynamics f water-dmso mixtures using different effective ptential mdel fr bth water and DMSO. They used the SPC, SPC/E and TIPS2 mdels fr water and the P2 mdel fr DMSO. The SPC/E gave the gd results fr water self- diffusin cefficient at lw DMSO cncentratins. One f the recent MD simulatin study f DMSO-water mixtures cntaining either an inic r a neutral atmic slute was perfrmed by Chwdhury and Chandra. 16 The diffusin cefficients f bth inic and neutral slutes was fund ut using SPC/E ptential mdel fr water and 4-site P2 mdel f Luzar and Chandler fr representing the DMSO mlecules 14. In the next sectin, we utline the methdlgy used in the present study. This is fllwed by the results and discussins and cnclusins. 2 Methdlgy Simulatin studies have been carried ut n systems cnsisting f sdium and chlride ins in water-dmso mixtures. Psitins and velcities are calculated using the Verlet algrithm with a sufficiently small time step s that the cnstraints f the rigidity f the slvent mlecules are satisfied with little difficulty during the simulatins. 17 The simulatin study cnsiders bth the ins in ne cubic simulatin bx alng with slvent mlecules. T calculate the ptentials f mean frce between the ins, we first calculate the average frce between the ins using F ( r ) = F direct ( r ) + ΔF(r) (2) Where ΔF(r) is the cntributin t the mean frce frm the slvent and F direct ( r ) is the bare in-in ptential. The mean slvent frce ΔF(r) is btained by ensemble averaging the instantaneus slvent frce ΔF(r,t) between the ins. ΔF(r,t) = μ [ F + Na (r,t) / m Na + F Cl -(r,t) / m Cl -]. r (3) ΔF(r) = < ΔF(r,t)> (4) ^

3 Mdel Dependence f Slvent Separated Sdium Chlride In Pairs 163 ΔF(r) is calculated at varius fixed distances between the ins (in the range f 2.5 ^ t 8 A ). In Eq. (2) r is the unit vectr between the sdium and the chlride ins. The masses f the ins are dented by m Na + and m Cl - and μ is their reduced mass. Typically 20 t 50 ps f equilibratin is fllwed by prductin runs f 100 ps. The ptential f mean frce is btained by integrating the mean frce as r W(r) = - F ( r ) dr (5) r0 We need a suitable value f W(r) at r 0 t cmplete the integratin. This is dne by assuming that at a distance f r 0 = 8 A, W (r) is given by the frmula W (r) = q 1 q 2 / ε r (6) Where ε is the bulk dielectric cnstant. Its value is taken frm the experimental data at the apprpriate slvent mle fractin. The data is given in Table 1. Our results fr the SPC mdel f water and the P2 mdel f DMSO have been already reprted In the present article, we have used the SPC/E mdel f water and the P1 mdel f DMSO. While the parameters f the SPC/E mdel f water are rather clse t thse f the SPC mdel, the P1 mdel f DMSO differs cnsiderably frm the P2 mdel in that the charge n S in P1 is nearly fur times the charge f the P2 mdel and the methyl grups in P1 are uncharged. The energy parameter f methyl in P1 is als twice that f the P2 mdel. There are tw reasns fr chsing the new parameters. One is that the new mdel has been t give better values f the individual inic diffusin cefficients. The ther reasn is t find ut the mdel dependence f the secnd SSIP prpsed earlier. The interparticle ptentials are the usual Lennard Jnes plus the Culmb terms.the site-site in-slvent and slvent slvent ptential is represented as U αβ (r) = (A αβ /r 12 )-(C αβ /r 6 ) + (q α q β /r) (7) Where α and β dente a pair f interactin sites n different mlecules, r is the site separatin, q α is a pint charge lcated at siteα. The terms A αβ and C αβ are given by A αβ = 4ε αβ (σ αβ ) 12 (8) C αβ = 4ε αβ (σ αβ ) 6 (9) Here, ε αβ and σ αβ are the energy and the distance parameters in the Lennard-Jnes ptential. The crss interactins have been btained by using the Lrentz-Berthelt rules σ αβ = 1 2 (σ αα +σ ββ ) (10) ε αβ = (ε αα ε ββ ) 1/2 (11) These parameters f the ptentials used have been given in Table 1. Table 2 gives the details f the simulatin cells.

4 164 A. Asthana et al. Table 1. Site parameters fr mdels f water and DMSO ε ε Slvent Site q / e* q / e* / A σ / A (10J/ml) (10J/ml) SPC SPC SPC SPC/E SPC/E SPC/E Water O H RS/P2 RS/P2 RS/P2 P1 P1 P1 DMSO S O CH * e is the magnitude f the electrnic charge. σ Table 2. Details f the tw mixture cmpsitins shwing cmpsitins, number f slvent mlecules, bx lengths, densities and the dielectric cnstants 18,19 Cmpsitin x 1 x 2 N 1 N 2 L (Ǻ) ρ(kgl -1 ) Results and Discussin The mean frces between the ins fr the tw cmpsitins are shwn in Figs 1 and 2 fr cmpsitins 1 and 2 respectively. The direct frce is attractive and the slvent cntributin is repulsive in bth the cmpsitins. The ttal cntributin lies between 10 t 5 (kt/ Ǻ)in the distance range f 3.5 t 8 Ǻ. Bth these frces are integrated frm r 0 t r t get the ptential f mean frce (PMF). The asympttic frm f the PMF f the cntinuum mdel f the slvent mixture at r = r 0 is used during the integratin. The results fr the tw mixtures are shwn in Figs 3 and 4 respectively. Fig. 1. The in in frce F (r), the cntributin due t the slvent F ( r ) and the ttal frce between the in pair fr cmpsitin 1 (x DMSO = 0.21)

5 Mdel Dependence f Slvent Separated Sdium Chlride In Pairs 165 Fig. 2. The in in frce F ( r ), the cntributin due t the slvent F ( r ) and the ttal frce between the in pair fr cmpsitin 1 (x DMSO = 0.35) Fig. 3. Ptential f mean frce fr the sdium chlride in pair in cmpsitin 1(x DMSO = 0.21) Fig. 4. Ptential f mean frce fr the sdium chlride in pair in cmpsitin 2 (x DMSO = 0.35) Bth the PMFs shw the absence f a shrt range minimum arund 3 Ǻ crrespnding t the cntact in pair and the presence f a strng slvent-separated in pair (SSIP) in the range f 4.5 t 5.5 Ǻ with a well depth f arund 10 kt. The first cmpsitin (21 % DMSO) shws the presence f a secnd SSIP minimum near 7 Ǻ, althugh this minimum is nt separated frm the first SSIP minimum with a very

6 166 A. Asthana et al. clear barrier. The verificatin f these PMFs was dne by studying the in pair trajectries which are initiated at varius separatins. Figs 5 and 6 shw these in pair trajectries fr the mixtures. 12 r (NaCl) / Angstrms Ang 7 Ang t / ps Fig. 5. In pair trajectries initiated at 5and 7 Ǻ respectively fr mixture 2 (x DMSO = 0.21) r (NaCl) / Angstrms t / ps 3 Ang 4 Ang 5 Ang 7 Ang Fig. 6. In pair trajectries initiated at 3, 4, 5 and 7 Ǻ fr mixture 2 (x DMSO = 0.35) The trajectries are initiated with the in pair separatins f in the range f 3 t 7 Ǻ. The trajectries initiated at small in pair separatins f 3 Ǻ reach large in separatins ( f greater 4 Ǻ ) within a few ps. The in pair trajectries initiated at large in pair separatins diffuse very slwly indicating that the lng distance in pairs have a very significant stability in the slvent mixtures. One f the reasns fr this dminance f the slvent separated in pair is the strng interactin between water and DMSO and the cmpetitin f bth water and DMSO mlecules t get int the first slvatin shell f the in pair. 20 There appears t be a disruptin f the cntact in pair frmed in the pure slvents by the intrusin f the ther slvent mlecules in the first shell. The spread ut slvent separated in pair in the distance range f 4 t 6 Ǻ implies that there is a significant flux f mlecules frm the first shell t the bulk slvent and vice versa and this has been nticed in the simulatins. The diffusivity f

7 Mdel Dependence f Slvent Separated Sdium Chlride In Pairs 167 the trajectries in the present case 21 is similar t ur previus wrk 18, 19 and we are investigating these aspects in greater detail. 4 Cnclusins The present results fr the PMFs have a clse similarity t the findings f the earlier mdel calculatins. 18 There is a striking absence f cntact ins pairs and a dminance f slvent separated ins pairs. These are cnfirmed by detailed dynamical trajectries. While the parameters f the SPC/E mdel f water are rather clse t thse f the SPC mdel, the P1 mdel f DMSO differs cnsiderably frm the P2 mdel with respect t the charge n S and the size f the methyl grups. We are investigating the details f this clustering as well as the lng time trajectries f the in pairs. We may find larger deviatins in the PMFs between the tw mdels fr cmpsitins wherein the mle fractins f DMSO are larger. These studies are under way. References 1. Hubbard, J., Wlynes, P.: The Chemical Physics f Slvatin, Part C: (Ed) Dgnadze, R.R., Kalman, E.,Krnyshev, A. A., Ulstrup, J., Elsevier, New Yrk (1988) 2. Buchner, R.:Dielectric Spectrscpy f Slutins, in: (eds) Samis, J,. Durv, V.A. Nvel Appraches t the Structure and Dynamics f Liquids: Experiments, Theries and Simulatins, NATO Science Ser. II: Mathematics, Physics and Chemistry, Vl. 133, pp , Kluwer, Drdrecht (2004) 3. Bester-Rgac, M., Neueder, R., Barthel, J.: J. Slutin Chem. 28 (1999) Tngraar, A., Rde, B. M.: Phys.Chem.ChemPhys., 6 (2004) Schwenk, C. F., Hfer, T. S., Rde, B. M.: J. Phys. Chem.A 108 (2004) Winstein, S., Clippinger, E., Fainber, A. H., Rbinsn, G.C.: J. Am. Chem. Sc. 26 (1954) Sadek, H., Fuuss, R.: J. Am. Chem. Sc., 76 (1954) Gldenberg, M.S., Kruus, P., Luk, S. F. K.: Can. J. Chem. 53 ( 1975) Ra, B. G., Singh, U. C.: J. Am. Chem.Sc. 112 (1990) Madhusdanan, M.; Tembe, B.L.: J. Phys.Chem. 98 (1994) Guardia, E., Rey, R., Padr, J. A.: Chem. Phys. 155 (1991) Sesse, G.;Guardia, E., Padr, J. A.: J. Chem. Phys. 99 (1995) Das, A. K., Madhusdanan, M., Tembe, B. L.: J. Phys. Chem. A101 (1997), Luzar, A., Chandler, D.: J. Chem. Phys 98 (1993) Chalaris, M., Samis, J.: J. Ml. Liq., 98 (2002) Chwdhury, S.; Chandra, A.: J. Chem. Phys. 119 (2003) Allen, M. P., Tildesley D. J.: Cmputer Simulatin f Liquids, Oxfrd University Press (1987) 18. Das, A. K., Tembe, B. L.: J. Chem. Phys. 111 (1999) Das, A. K.: Simulatin Studies n the Sdium Chlride In Pair in DMSO and Water- DMSO Mixtures, Ph.D Thesis, IIT Bmbay ( 1998) 20. Das, U.: Mlecular dynamics study f the slvatin f ins in water-dmso Mixtures, M.Sc. Thesis, Department f Chemistry, IIT Bmbay, Asthana, A.: Dynamics f ins and mlecules in slvent mixtures like Water-DMSO, M.Sc. Thesis, Department f Chemistry, IIT Bmbay, 2005