Supporting information

Transcription

1 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 Supportng nformaton Separaton of -CH 4 Mxtures n the Mesoporous MIL-1(Cr) MOF: Expermental and modellng approaches Lomg Hamon, a Ncolas Heymans, b Phlp L. Llewellyn, c Vncent Gullerm, d Azz Ghouf, e Sébasten Vaesen, b Gullaume Maurn f Chrstan Serre, d Guy De Wereld,* b and Gerhard D. Prngruber* a a IFP Energes Nouvelles, Drecton Catalyse et Séparaton, Rond-pont de l'échangeur de Solaze, 6936 Solaze, France. E-mal:gerhard.prngruber@fpen.fr b Servce de Thermodynamque, Unversté de Mons, 2 Place du Parc, 7 Mons, Belgque. E-mal: guy.dewereld@umons.ac.be. c Laboratore Chme Provence, UMR CNRS 6264 Unverstés d'ax-marselle I, II & III, Centre de Sant- Jérôme, Marselle cedex 2, France. d Insttut Lavoser, UMR CNRS 818 Unversté de Versalles St Quentn en Yvelnes, 45 avenue des Etats-Uns, 7835 Versalles, France e Insttut de Physque de Rennes, CNRS-Unversty of Rennes 1, UMR 6251, 3542 Rennes, France. f Insttut Charles Gerhardt, UMR 5253 CNRS UM2 ENSCM, Unversté de Montpeller II, Place E. Batallon, 3495 Montpeller cedex 5, France. 1. Synthess and actvaton Fgure S1. XRPD dagram of MIL-1(Cr).

2 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry V a /cm 3 (STP) g -1 25,1,2,3,4 p/p Fgure S2. Ntrogen adsorpton sotherm of MIL-1(Cr). 2. Volumetrc apparatus For mxture adsorpton equlbrum measurements, we use an orgnal bult-n house devce (Fgure S3). Fgure S3: Mxture adsorpton volumetrc apparatus: (AdsC) adsorpton cell; (PT) pressure transmtter; (V1 and V2) three ways manual valves; (V3 to V8) manual valves; (T) Pt 1 temperature probes; (F) flter; (HS) n-stu heatng system; (VP) vacuum pump; (CP) crculaton pump; (R) ruler; (PR) pressure regulator; (GC) gas chromatograph; (Rr) refrgerated room. The prncple remans dentcal to the pure component adsorpton one. It allows the measurement of sobarc and sotherm mxture adsorpton equlbra n a range of pressures from 1 kpa to 1 kpa and for temperatures from 298 K to 353 K. In ths apparatus, a cylnder pston provdes a substtute of

3 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 the classc cell whch enables to change the total volume n order to fx pressure on a set pont value durng the adsorpton. A crculaton pump s used to homogenze the mxture and a gas chromatograph, coupled wth a thermal conductvty detector provded by Aglent (GC 685), allows the determnaton of the gas mole fracton of each component n the mxture. The pressure transmtter s provded by Endress-Hauser ( 1 kpa Cerabar PMP 731) wth an uncertanty of.1% of the full scale. Pror to each experment, the sample was outgassed at 523 K for 8 hours under vacuum (below 1-3 mbar). After that, the pure gases (provded by Praxar, Belgum) are ntroduced one by one n the nstallaton wthout gong through the adsorpton cell. When both equlbrum and homogenzaton are reached (checked by constant values of both pressure, temperature and composton obtaned usng a chromatography devce), we determne the gas composton by at least fve chromatographc analyses and the pressure, the temperature, and the volume values are recorded. Wth these measurements and the nstallaton volume, we can determne the mole number of each mxture component usng a mxture equaton of state. 1 In the second phase, the adsorpton cell s accessble va two three-ways valves. Durng the adsorpton, the pressure s mantaned on a set pont value by adaptng the nstallaton volume thanks to the cylnder pston. When the equlbrum s reached (checked by constant values of both temperature and volume), we wrte down the pressure and temperature values and determne gas composton by at least fve chromatographc analyses. Knowng the total nstallaton volume, we can calculate the mole number of each component n the gas phase after adsorpton thanks to a mxture equaton of state. 1 The dfference between the mole numbers n the gas phase before and after adsorpton allows to determne the adsorbed amounts. The adsorbent s then outgassed allowng to start agan the procedure wth a new composton of ntal mxture. 3. Expermental detals of the breakthrough curve measurements Fgure S4 shows a scheme of the setup used for the breakthrough experments at hgh pressure. Dfferent gas mxtures can be prepared by a set of mass flow controllers. The gas mxture s ether sent to the adsorpton column, whch s placed n an oven, or to a bypass lne. A backpressure regulator s placed downstream of the column and fxes the pressure n the column and by-pass lne. Downstream of the backpressure regulator, the column effluent s dluted wth helum and s then analyzed by a mass spectrometer. The dluton s necessary snce the response of the mass spectrometer s lnear only n a concentraton range of 15%. The dluton brngs the concentratons of the eluted gases down to ths range. Moreover, t keeps the total flow rate more or less constant, whch s a necessary condton for obtanng correct mass balances. Mass 44 s used for analyss of and mass 15 for the analyss of CH4 (mass 16 s avoded because contrbutes to the ntensty). The sgnals are normalzed by the ntensty of mass 4 (He), n order to correct for drfts n the mass spectrometer.

4 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 BPR vent BPR He MFC MFC MFC Column Oven MS CH 4 MFC He MFC dluton MFC = Mass Flow Controller BPR = Back Pressure Regulator MS = Mass Spectrometer Fgure S4. Scheme of the setup used for breakthrough experments. 4. Structural model and partal charges for framework of MIL-1(Cr) The accessble surface area (S acc ) s purely based on the geometrc topology of the adsorbent and calculated from a smple Monte Carlo ntegraton technque where the center of mass of the probe molecule wth hard sphere s rolled over the framework surface. 2 In ths method, a ntrogen-szed (3.6 Å) probe molecule s randomly nserted around each framework atom of the adsorbent and the fracton of the probe molecules wthout overlappng wth the other framework atoms s then used to calculate the accessble surface area. The LJ sze parameters of the framework atoms were the same as those used for the calculatons of the adsorpton propertes (DREIDING potental). The pore volume (V pore ) of the MIL-1(Cr) was obtaned accordng to the thermodynamc method proposed by Myers and Monson 3, the LJ parameters for Helum (ε/k B = 1.9 K, σ = 2.64 Å) beng taken from the work of Talu and Myers. 4

5 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 Fgure S5. Labels of the atoms for the MIL-1(Cr) framework. MIL 1(Cr) type Cc Co Ch Oc O3 Cr(1) Cr(2) Hc F q / u.e Table S1: Partal charges for all the atoms of the MIL-11(Cr) framework. The labels are descrbed n Fgure S5 7. Thermodynamc Smulatons The deal adsorbed soluton theory (IAST) was presented by Myers and Prausntz. 5a In ths model, the mxture adsorpton equlbrum s predcted on the bass of pure component sotherms only. The basc equaton for IAST has the followng form: p y x p (1) It descrbes the equlbrum between a perfect gas phase and an deal adsorbed phase. In ths equaton p s the mxture pressure, y and x are the gas phase and the adsorbed phase molar fractons for

6 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 component respectvely and p s the equlbrum gas phase pressure of the pure component correspondng to mxture temperature and spreadng pressure,.e. n the standard state. The standard state s defned by the equalty of the spreadng pressure for each component to the mxture spreadng pressure. The spreadng pressure of component can be calculated by the Gbbs adsorpton sotherm as follows: A RT q and p q p p dp p are related to pure component adsorpton sotherms. So, n order to solve smultaneously equatons (1) and (2) for determnng x for gven y and p, we need an expresson representng the sngle component sotherm. Dfferent classc expressons can be used. In ths work, the mult-stes Langmur equaton s chosen. Fnally, the total numbers of adsorbed moles s determned by: (2) 1 q t N q x p where N s the number of components n the mxture and q p (3) s the pure gas adsorbed quanttes at pressure p obtaned from sngle component sotherm. If the adsorbed phase s non deal (Real Adsorbed Soluton Theory, RAST), t s necessary to take nto account the non dealty of adsorbed phase by the mean of the actvty coeffcents, functons of spreadng pressure: p y x p, whch are In the equaton (4), the non dealty of gas phase s also taken nto account. Peng-Robnson equaton of state 6 s then used to determne fugacty coeffcent Moreover the total amount adsorbed ncludes also an excess term 5b 1 q t N ex p q x 1 (5) q All excess terms can be deduced from excess Gbbs free energy. So n order to apply RAST n a thermodynamc way, we use the followng form of excess Gbbs free energy gven by Spersten and Myers 5c whch takes account of the spreadng pressure dependence of the excess terms g Wth ex C 1T x1 x2 e 1 (6) A RT where A s the specfc surface area. (4) As we work wth sothermal data, the and 1 parameters are replaced by the parameter. Thus, the

7 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 equaton 6 becomes: g ex x x 1 e C 1 2 (7) The bnary parameters are determned usng bnary expermental data. Wth a frst approxmaton of these parameters and the expermental values of pressure, temperature and gas composton, the partal sm amount adsorbed ( q ) s determned by the resoluton of RAST. Then, these quanttes are compared wth the expermental ones ( q followng objectve functon: exp sm q 2 exp ). The bnary parameters are determned by mnmzaton of the q (8) 7. Pure absolute expermental sotherms of and CH 4 on MIL-1(Cr) Adsorpton sotherm measurements were performed on a bult-n house apparatus based on a hghpressure magnetc suspenson balance marketed by Rubotherm. Ths system allows to separate the mcrobalance (resoluton: 1 µg) from the adsorpton chamber n whch can stand both hgh pressure and temperature, and corrosve operatng condtons. The magnetc system couples an electromagnet lnked to the balance wth a permanent magnet lnked to the crucble contanng the adsorbent. Moreover, t avods subcrtcal gases condensaton. Ths apparatus allows to perform experments n a wde range of temperatures ( K) and pressures (from vacuum to 15 bar). The related nformaton about the apparatus and the set-up have been descrbed n detals n our prevous studes. 7 Pror to each adsorpton measurement, the sample of MIL-1(Cr) was regenerated by heatng under secondary vacuum (1 5 mbar). Lke n volumetrc co-adsorpton measurements the sample was outgassed at 523 K for 16 hours under secondary vacuum. The sample mass varatons m meas (g) at dfferent pressures were measured when the thermodynamc equlbrum was reached. For our crteron, four of the fve last mass measurements (notced each 5 mn) were ncluded n 5 µg ntervally. The buoyancy effect of the gas phase on the adsorbent volume V ads was then corrected to determne the excess adsorbed amount, m ads m V (9) meas gas ads The gas phase densty was determned usng an approprate equaton of state (EOS). The adsorbent volume V ads s evaluated by drect helum buoyancy effect measurement accordng to the fact that helum does not adsorb at hgh pressure (range from 1 bar to 1 bar). Helum densty was calculated usng a modfed Benedct-Webb-Rubn EOS. 8 The pressures were measured wth two pressure transmtters (MKS Baratron up to bar for adsorpton measurement at low pressure and Endress- Hauser up to 1 bar). Maxmum measurement error on adsorpton sotherm measurement s evaluated to.5 % of adsorbed measured quanttes wth an nterval of confdence of 95%. The EOS used for

8 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry 212 buoyancy effect correcton s of Helmholtz type. 9 The expermental excess amounts have been converted nto the absolute values, usng the pore volumes measured for the sample ougassed at the correspondng temperature. 8. Langmur mult-stes model The sotherm parameters estmated by non-lnear regresson are obtaned by mnmzng the followng objectve functon: q 2 O. F. q (1) sm exp Those parameters are found n Table 2. In order to compare the correlaton results and the expermental data, the devaton parameter on the adsorbed amount s also provded n Table S2. It s calculated as follow: 1 D k k j1 Q exp j Q Q exp j sm j (11) Where k s the number of data, correlaton adsorbed amounts. exp Qj are the expermental adsorbed amounts and sm Qj are the q s (mmol/g) CH 4 b (1/kPa) q s (mmol/g) b (1/kPa) q s (mmol/g) b (1/kPa) q s (mmol/g) b (1/kPa) Table S2. Adsorpton sotherm parameters and devaton factors for and CH 4 on MIL-1 (Cr) at K.

9 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry Adsorbed amounts (mmol.g -1 ) CO2 Exp CO2 Langmur CH4 Exp CH4 Langmur Pressure (bar) Fgure S6. Expermental and Langmur ftted sotherms on MIL-1 (Cr) at 33K. 9. Expermental dfferental enthalpes of adsorpton of and CH 4 n MIL-1(Cr) ads h / kj mol n a / mmol g -1 Fgure S7. Dfferental enthalpes of adsorpton of carbon doxde and methane on MIL-1(Cr) at 33K. CH 4

10 Electronc Supplementary Materal (ESI) for Dalton Transactons Ths journal s The Royal Socety of Chemstry Comparson between the GCMC smulated absolute adsorpton sotherms for the pure and CH 4 on the MIL-1(Cr) and the expermental measurements. 18 Adsorbed amounts (mmol.g -1 ) Exp GCMC CH 4 Exp GCMC Pressure (bar) Fgure S8. Expermental and GCMC smulated sotherms on MIL-1(Cr) at 33K. References 1 O. Kunz, R. Klmeck, W. Wagner, M. Jaeschke, GERG Techncal Monographe 15, 27, Fortschr.-Ber. VDI, 6,VDI-Verlag, Düsseldorf. 2 T. Düren, F. Mllange, G. Férey, K. S. Walton and R. Q. Snurr, J. Phys. Chem. C, 27, 111, A. L. Myers, P. A. Monson, Langmur, 22, 18, O. Talu, A. L. Myers, AIChE J., 21, 47, (a) A.L. Myers and J.M. Prausntz, Journal of Amercan Insttute of Chemcal Engneers, 1965, 11, 121; (b) F.R. Spersten and A.L. Myers, Journal of Amercan Insttute of Chemcal Engneers, 21, 47, 1141; (c) O. Talu and A.L. Myers, AIChE Journal, 1988, 34, ; 6 D.Y. Peng, D.B. Robnson, Industral and Engneerng Chemstry Fundamentals,1976, 15, (a) G. De Wereld, M. Frere and R. Jadot, Meas. Sc. Technol., 1999, 1, 117; (b) Y. Belmabkhout, M. Frere and G. De Wereld, Meas. Sc. Technol., 24, 15, R. D. McCarty and V. D. Arp, Adv. Cryo. Eng., 199, 35, (a) U. Setzmann and W. Wagner, J. Phys. Chem. Ref. Data, 1991, 2, 16; (b) R. Span and W. Wagner, J. Phys. Chem. Ref. Data, 1996, 25, P.L. Llewellyn, S. Bourrelly, C. Serre, A. Vmont, M. Datur, L. Hamon, G. De Wereld, J.S. Chang, D.Y. Hong, Y.K. Hwang, S.H. Jhung and G Férey, Langmur, 28, 24, 7245.