Understanding The Solubility Of Gases In Alkyl- Imidazolium Based Ionic Liquids By A Molecular Modelling Approach.

Transcription

1 Understandng The Solublty Of Gases In Alkyl- Imdazolum Based Ionc Lquds By A Molecular Modellng Approach. Jord S. Andreu 1,2, Lourdes F. Vega 1,2 *, 1 Insttut de Cenca de Materals de Barcelona, Consejo Superor de Investgacones Centífcas, Campus de la UAB, Bellaterra, Barcelona, Span 2 MATGAS Research Center and Ar Products and Chemcals, Campus de la UAB, Bellaterra, Barcelona, Span E-mal: vegal@matgas.com; fax: Room temperature onc lquds (ILs) are currently recevng much attenton due to ther nterestng physco-chemcal propertes: neglgble vapor pressure, extremely wde range of compostons (whch allows the tunng of physcal propertes through desgn), etc. For these reasons, ILs are beng postulated as promsng alternatve solvents for a number of technologcal applcatons n the context of green processes. A careful characterzaton of them s needed pror they are put nto fnal use for a specfc applcaton; ths ncludes knowledge of the relatonshp between the structure and the propertes. Ths knowledge can be obtaned by expermental technques, smulatons and/or theoretcal approaches. A man advantage of a theory or equaton of state versus the other technques s the speed n whch these calculatons are performed, provded they are accurate enough to reproduce the expermental data. Ths work deals wth developng accurate molecular models for ILs and gases n the context of a molecular-based equaton of state, the soft-saft equaton, searchng for predctve tools for these systems. Introducton ILs are usually defned as organc salts that are lqud below 100ºC wth a set of physco-chemcal propertes whch make them sutable for several applcatons. These salts are typcally composed by an asymmetrc organc caton lke mdazolum, ammonum, pyrroldnum, pyrdnum, etc, and an organc or norganc anon such as chlorde, bromde, hexafluorophosphate, tetrafluoroborate, bs(trfluoromethylsulfonyl)mde and others. Snce they are salts, they tend to have extremely low vapor pressure (lmtng ther volatlty), good thermal stablty, low meltng pont, hgh onc conductvty and large electrochemcal wndow. The man feature of ILs s that ther propertes can be easly talored by the selecton of the anon and the caton. The number of potental ILs that can be syntheszed s huge and ther propertes can be tuned accordng to the desred applcatons. For ths reason, a good understandng about the dependence of ther physco-chemcal propertes on ther mcroscopc structure and theoretcal predctve tools s desred n order to enhance the desgn of new ILs for selected applcatons. Ther tunable and unque propertes make them a good alternatve to tradtonal solvents used n synthess and extracton, offerng the possblty to develop new processes. Specfcally, understandng CO 2 solublty n onc lquds has become an mportant ssue for several applcatons, lke supercrtcal flud extracton and gas separatons [1], [2]. As a frst step for the modelng work we have focused on three of the most studed famles of ILs found n lterature. These ILs are the [C n -mm][bf 4 ], the [C n -mm][pf 6 ] and

2 the [C n -mm][tf 2 N] famles. The approach we followed n ths work s the followng: frst of all, a molecular model for the ILs was developed and parameters ftted to avalable expermental data (densty versus temperature), provdng a correlaton of the molecular parameters wth the molecular weght of the ILs. Before fttng any bnary data, molecular parameters from the pure compounds were used to check f the model was able to capture the behavor of the mxture. Then, a unque energy bnary s used as a temperature ndependent fttng parameter n order to obtan quanttatve agreement wth expermental data of mxtures. The soft-saft EoS SAFT equatons are usually wrtten n terms of the resdual Helmholtz free energy. Each term n the equaton represents dfferent mcroscopc contrbutons to the total free energy of the flud. The equaton s wrtten as: res ref chan assoc a = a + a + a + a polar (1) where a res s the resdual Helmholtz free energy densty of the system. The superscrpts ref, chan, assoc and polar refer to the contrbutons from the reference term, the formaton of the chan, the assocaton, and the polar nteractons, respectvely, dependng on the system under study. In the soft-saft EoS, [3], [4], [5] the reference term s a Lennard-Jones (LJ) sphercal flud, whch accounts both for the repulsve and attractve nteractons of the monomers formng the chan. As n prevous works the accurate EoS of Johnson et al. [6] s used here. For the case of mxtures the same equaton s used by applyng the van der Waals one-flud theory, wth generalzed Lorentz-Berthelot mxng rules: σ + σ jj σ j = ηj (2) 2 j j ( ε ε ) 1/ 2 ε = ξ (3) jj here η and ξ are the sze and energy bnary adjustable parameters, respectvely. The equaton s used n a purely predctve manner from the pure component parameters when η and ξ are equal to unty, whle values dfferent from unty mean the use of one or two bnary parameters, takng nto account the dfferences n sze and/or energy of the segments formng the two compounds n the mxture. The chan and assocaton terms come from Werthem s theory [7]: a a chan = ρkbt assoc = ρk T B x ( 1 m ) ln g LJ α x X + α (4) α ln X M 2 2 (5) here ρ s the molecular densty, T s the temperature, m s the chan length, x s the molar fracton of component, k B the Boltzmann constant and g LJ s the radal dstrbuton functon

3 of a flud of LJ spheres at densty ρ = m mρ, evaluated at the bond length σ. M the number of assocatng stes of component, and X α the mole fracton of molecules of component non bonded at ste α, whch accounts for the contrbutons of all the assocatng stes n each spece. The leadng multpolar term for fluds of lnear symmetrcal molecules, lke carbon doxde, ntrogen, acetylene, etc., s the quadrupole-quadrupole potental. An expanson of the Helmholtz free energy densty n terms of the perturbed quadrupole-quadrupole potental wth the Padé approxmaton was proposed by Stell et al. [8]: a = a 2 1 a 1 a 3 2 (6) Expressons for a 2 and a 3, the second and thrd-order perturbaton terms, were derved for an arbtrary ntermolecular reference potental [9], [10] and nvolve the state varables, molecular parameters, and the ntegral for the reference flud. A detaled dervaton of these expressons s gven elsewhere [11]. Ths new term n the soft-saft EoS nvolves an addtonal molecular parameter, Q, the quadrupolar moment. The molecular model In order to use soft-saft for a partcular system, a molecular model of each compound should be chosen. The carbon doxde molecule was modeled as a LJ chan n whch explct quadrupolar nteractons were taken nto account. In ths case, the molecule was represented by fve molecular parameters: m, the chan length, σ, the segment sze, ε, the energy parameter of the segments makng the chan and those related to the quadrupolar nteractons: the quadrupolar moment Q and x p, defned as the fracton of segments n the chan that contan the quadrupole. The value for the quadrupole moment Q for ths molecule obtaned from the fttng s n agreement wth the ones present n lterature [12], [13]. Regardng the molecular parameter x p, t was fxed to 1/3 for carbon doxde, thus mmckng the molecule as three segments wth a quadrupole n one of them. Therefore, wth x p and Q fxed, only the usual m, σ and ε parameters need to be adjusted. Based on results obtaned from molecular dynamcs smulatons [14], [15], [16] showng the on parng of these systems, we have modeled these ILs as LJ chans wth one assocatng ste n each molecule [17]. Ths model mmcs the neutral pars (anon plus caton) as a sngle chan molecule wth ths assocaton ste descrbng the specfc nteractons because of the charges and the asymmetry. Followng a smlar approach, a model for the [C n -mm][tf 2 N] famly of ILs have been developed leadng also a good agreement wth the expermental results present n lterature. Results

4 A needed step before applyng the equaton to mxtures s to obtan the molecular parameters of the pure compounds. We have used the molecular parameters for CO 2 obtaned n a prevous work [18]. Regardng the ILs, the chan length, sze and energy parameters were obtaned by fttng to avalable densty-temperature data. In order to keep the mnmum number of ftted parameters, we have decded, as a frst approxmaton, to use the assocaton parameters prevously used for the alkanols, thus avodng further fttng. Temperature [K] [C n -mm][tf2n] 3 3,2 3,4 3,6 3,8 4 4,2 Densty [mol/l] Fgure 1. Densty versus temperature dagram for the [C n -mm][tf 2 N] ILs famly: symbols are expermental data from dfferent authors (from n=2 crcles to n=6 astersks) and sold lnes are soft-saft calculatons correspondng to the pure compounds parameters n the fttng procedure. Followng prevous works [19], we were able to correlate the molecular parameters of the ILs wth ther molecular weght. These correlatons enable the equaton wth predctve power, as they provde the possblty to predct the behavor of heaver members of the seres, not ncluded n the fttng procedure. Ths s partcularly useful for the case of ILs, as t has been demonstrated than the toxcty of the ILs ncreases as the alkyl chan length ncreases, makng expermental measurements more dangerous [20]. Mxtures: solublty of CO 2 n onc lquds We present and dscuss here calculatons performed wth the aforementoned models wthn the soft-saft approach as appled to those famles of ILs wth CO 2, compared wth avalable expermental data. We frst studed the mxture [C 4 -mm][bf 4 ] + CO 2 at low pressures at four dfferent temperatures, between T=283K and T=348K. Fgure 2a depcts the solublty sotherms obtaned for these mxtures as compared to avalable expermental data [21]. Soft-SAFT calculatons presented here were done wth pure component parameters, and hence they are pure predctons. It s strkng to see the accuracy of these calculatons as compared to the expermental data, ndcatng that the smple model presented n the prevous secton s able to capture the solublty of these mxtures n quanttatve agreement wth expermental data. Wthn the same famly, predctve results for [C 2 -mm][bf 4 ] + CO 2, [C 4 -mm][bf 4 ] + CO 2 and [C 6 -mm][bf 4 ] + CO 2 mxtures at hgh pressures are obtaned wthn that model. The model s able to capture the sharp ncrease n pressure at a gven CO 2 composton, wthout any fttng. However, quanttatve predctons wth expermental data are not obtaned n ths case. Soft-SAFT s able to quanttatvely reproduce the behavor of these mxtures at hgh pressures wth a sngle temperature ndependent bnary parameter ξ=0.985 (very close to unty) for all members of the famly.

5 Pressure [MPa] 1.0 Pressure [MPa] CO 2 mole fracton CO 2 mole fracton Fgure 2. a) Solublty of CO 2 n the [C 4 -mm][bf 4 ] at four dfferent temperatures: T=283K (crcles), T=298K (squares), T=323K (damonds) and T=348K (trangles). Sold lnes are predctons wth soft-saft model wthout fttng. b) Solublty of CO 2 n the [C n -mm][pf 6 ] at low pressures. Symbols as n fgure 1a. In that case, the use of a bnary parameter ndependent of temperature s needed to ft the expermental data (ξ=0.970). As n the prevous case, the same methodology was appled to the systems [C n - mm][pf 6 ] + CO 2 and [C n -mm][tf 2 N]. Soft-SAFT results concernng CO 2 solublty sotherms n [C 4 -mm][pf 6 ] up to 2MPa and at four dfferent temperatures are shown n Fgure 2b. Contrary to what happens to the [C 4 -mm][bf 4 ] famly, the solublty of CO 2 estmated from the pure compounds parameters at low pressures s overestmated, as well as the solublty sotherms at hgh pressures. Agan, these devatons respect to the expermental data [22], [23], [24] were corrected by usng a sngle bnary parameter (ξ=0.970 n ths case) for all sotherms and for all compounds of the famly, showng excellent agreement wth expermental data. Fnally, taken advantage of the fact that the parameters of the equaton are ndependent of the thermodynamc condtons we present a comparson of the solublty of CO 2 n the three famles at the same condtons, for the same caton. As shown n Fgure 3 the solublty ncrease s [BF 4 ]<[PF 6 ]<[Tf 2 N]. [C 2 -mm][x]+co 2 80 Pressure [MPa] BF 4 anon PF 6 anon Tf2N anon Fgure 3. Predcted solublty of CO 2 n [C 2 -mm][bf 4 ], [C 2 -mm][pf 6 ] a [C 2 - mm][tf 2 N] usng the soft-saft model at T= K ,2 0,4 0,6 0,8 1 CO 2 mole fracton Conclusons

6 We have shown the capablty of soft-saft to reproduce the solublty of CO 2 n dfferent famles of ILs n a wde range of temperatures and pressures wth a smple model for the IL. The key of the model s to mmc the strong par nteracton between the anon and the caton as a specfc assocatng ste n an end of the LJ chan whch represents the IL. Only fve parameters were needed to model the ILs. The model was able to capture the sharp rse n pressure as the solublty of CO 2 ncreases from pure component parameters, wthout the need of any specfc assumpton regardng the nteracton of the ILs wth CO 2. Further more, the equaton can be used for comparatve purposes of dfferent compounds, searchng for trends wthn dfferent famles. Acknowledgments. Several helpful dscussons wth C. Rey-Castro and F. Llovell are gratefully acknowledged. Fnancal support has been provded by the Spansh Government, (project CTQ /PPQ), the Catalan Government (2005SGR-00288), and Ar Products and Chemcals. J.S.A. acknowledges a grant from MATGAS 2000 AIE. References: [1] [2] Blanchard, L.A., Brennecke, J.F., Ind. Eng. Chem. Res., 40, 2001, p Baltus, R.E., Counce, R.M., Culbertson, B.H., Luo, H., DePaol, D.W., Da, S., Duckworth, D.C., Sep. Sc. Technol., 40, 2005, p [3] Blas, F.J., Vega, L.F., Mol. Phys., 92, 1997, p [4] Pàmes, J.C., Vega, L.F., Ind. Eng. Chem. Res., 40, 2001, p [5] Blas, F.J., Vega, L.F., Ind. Eng. Chem. Res., 37, 1998, p [6] [7] [8] [9] [10] Johnson, J., Zollweg, J., Gubbns, K.E., Mol. Phys., 78, 1993, p Werthem, M.S., J. Stat. Phys., 35, 19, Ibd., 42, , p. 459, 477. Stell, G., Rasaah, J.C., Narang, H., Mol. Phys., 27, 1974, p Two, C.H., Gubbns, K.E., Gray C.G., Mol. Phys, 29, 1975, p Two, C.H., PhD Dssertaton, Unversty of Florda,1976. [11] Gubbns, K.E., Two, C.H., Chem. Eng, Sc., 33, 1978, p [12] Vrabec, J., Stoll, J., Hasse, H., J. Phys. Chem. B, 105, 2001, p [13] [14] Vrbancch, J., Rtche, G.L.D., J. Chem. Soc. Faraday II, 76, 1980, p Urahata, S.R., Rbero, M.C.C., J. Chem. Phys, 120 (4), 2004, p [15] Morrow, T.I., Magnn, E.J., J. Chem. Phys. B., 106, 2002, p [16] Del Pópolo, M.G., Voth, G.A., J. Phys. Chem. B., 108, 2004, p [17] [18] Andreu, J.S., Vega, L.F., J. Phys. Chem C., 111, 2007, p , Das, A.M.A., Carrer, H., Dardon, J.L., Pàmes, J.C., Vega, L.F., Coutnho, J.A.P., Marrucho, I.M., Ind. Eng. Chem. Res., 45, 2006, p [19] Pàmes, J.C., Vega, L.F., Ind. Eng. Chem. Res., 40, 2001, p [20] Ranke, J., Mölter, K., Stock, F., Bottn-Weber, U., Poczobutt, J., Hoffmann, J., Ondruschka, B., Flser, J., Jastorff, B., Ecotoxcol. Envron. Saf, 58, 2004, p [21] Shflett, M.B., Yokozek, A., Ind. Eng. Chem. Res., 44, 2005, p [22] NIST Chemstry Webbook, [23] Sharat, A., Peters, C.J., J. Supercrt. Fluds, 30, 2004, p [24] Sharat, A., Gutkowsk, K., Peters, C.J., AIChE, 51, 2005, p