pubs.acs.org/Langmuir © 2009 American Chemical Society
Molecular Simulations of Water and Paracresol in MFI Zeolite - A Monte Carlo Study L. Narasimhan,† Pascal Boulet,*,† Bogdan Kuchta,† Oliver Schaef,† Renaud Denoyel,† and Philippe Brunet‡ † Laboratoire Chimie Provence, University of Provence Aix-Marseille I, II and III and UMR-CNRS 6264, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France, and ‡Universit e Aix-Marseille II, INSERM UMRS 608, H^ opital de la Conception, service de n ephrologie, 147 boulevard Baille, 13385 Marseille cedex 05, France
Received May 3, 2009. Revised Manuscript Received July 17, 2009 Paracresol is a protein-bound toxin that is not efficiently eliminated by the hemodialysis method. Monte Carlo simulations in grand-canonical (GCMC) and canonical ensembles were performed to investigate the adsorption of paracresol and water in silicalite-1 zeolite. GCMC simulations using a configurational-biased algorithm show that four paracresol molecules are adsorbed at the channel intersections per unit cell of silicalite-1. The adsorption isotherms of water with and without the presence of paracresol at the intersections were investigated. A cooperative phenomenon in the process of coadsorption has been observed: at very low chemical potential, paracresol facilitates the penetration of water into silicalite-1. This mechanism is interpreted in terms of the properties of the zeolite and paracresol molecules. A thermodynamic cycle is used to calculate the adsorption energy of paracresol in silicalite-1. The calculated adsorption energy reasonably agrees with the experimental data.
1. Introduction Nowadays, purification of blood for a patient’s chronic renal failure is being carried out mostly using polymer membranes. The impure blood contains many uremic toxins that are removed during the conventional dialysis method. Results from the literature show that hemodialysis is efficient at removing small toxins dissolved in water. For instance, 75% of urea, which is a waterdiluted toxin, is removed. Another example is creatinine (also a water-diluted toxin), for which 71% of the original serum concentration is removed.1 At the same time, the amount of proteinbound toxins removed by the conventional dialysis method is small. One such protein bound solute is paracresol (1,4-methylphenol), which results from the degradation of phenylalanine and tyrosine by intestinal bacteria.2,3 Its toxicity is responsible for the intoxication of patients, ultimately causing death because of its increased serum concentration during renal failure.4-8 From the experimental observations, paracresol (hereafter called as p-cresol) is by far better removed using adsorbent materials such as zeolites9 rather than by hemodialysis. Zeolites are microporous crystalline materials with well-defined porous structure. The shape selectivity of zeolite makes it a useful material device for various applications in many technological fields. Many studies report on the adsorption of hydrocarbons *Corresponding author. E-mail:
[email protected]. (1) Lesaffer, G.; De Smet, R; D’heuvaert, T; Belpairea, F.; Lameire, N.; Vanholder, R. Life Sci. 2001, 69, 2237. (2) De Smet, R.; Glorieux, G.; Hsu, C. Kidney Int. 1997, 52, S8. (3) Curtius, H. C.; Mettler, M. J. Chromatogr. 1976, 126, 596. (4) Abreo, K.; Sella, M.; Gautreaux, S.; De Smet, R.; Vogeleere, P.; Ringoir, S.; Vanholder, R. J. Am. Soc. Nephrol. 1997, 8, 935. (5) Niwa, T.; Maeda, K.; Ohki, T.; Saito, A. Clin. Chim. Acta 1981, 110, 51. (6) Vanholder, R.; De Smet, R.; Lesaffer, G. Nephrol. Dial. Transplant. 1999, 14, 2813. (7) Vanholder, R.; De Smet, R. J. Am. Soc. Nephrol. 1999, 10, 1815. (8) Lesaffer, G.; De Smet, R.; Lameire, N.; Dhondt, A. M.; Duym, P.; Vanholder, R. Nephrol. Dial. Transplant. 2000, 15, 50. (9) Berge-Lefranc, D.; Pizzala, H.; Paillaud, J. L.; Schaef, O.; Vagner, C.; Boulet, P.; Kuchta, B.; Denoyel, R. Adsorption 2008, 14, 377.
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using zeolites.10-16 Silicalite-1 zeolite (a pure siliceous zeolite with unit cell formula (SiO2)96) can be used as a catalyst for the cracking process in petrochemical industries where heavy alkanes (particularly branched alkanes) are adsorbed10,11 and converted into light alkanes, as well as in the separation of organic solvents.12-14 Sodium silicalite-1 is used as an ion exchanger for softening water and for hydrogen production in fuel cells15 by removing CO2 from the fuel processing unit. The adsorbed amount of sorbate molecules generally depends on the interactions between the molecule and the solid, the molecular configuration or size, and the capacity of the adsorbent at saturation. This work is devoted to the study of adsorption of p-cresol in silicalite-1 using numerical simulations. Molecular simulations have become an important tool in the study of adsorption and help us to understand the thermodynamic properties of the system on the molecular level. Additionally, computer simulations can help us to interpret experimental data because they give us a microscopic understanding of the structure-property relations. The necessity for understanding the zeolite-adsorbate interactions at the molecular scale is the reason for use of molecular simulation studies. Maginn et al.17 and Smit et al.18 have extensively studied the adsorption of linear and branched alkanes in silicalite-1. Snurr et al.19 simulated the adsorption of liquid (10) Flangien, M. E.; Bennett, M. J.; Grose, W. R.; Cohen, P. J.; Patton, L. R.; Kirchner, M. R.; Smith, V. J. Nature 1978, 271, 512. (11) Olson, H. D.; Kokotailo, T. G.; Lawton, L. S.; Meier, M. W. J. Phys. Chem. 1981, 85, 2238. (12) Creaser, D.; Wirawan, K. S. Microporous Mesoporous Mater. 2006, 91, 196. (13) Te Hennepe, C. J. H.; Bargeman, D.; Mulder, V. H. M.; Smolders, A. C. J. Membr. Sci. 1987, 35, 39. (14) Sano, T.; Yanagishita, H.; Kiyozumi, Y.; Mizukami, F.; Haraya, K. J. Membr. Sci. 1994, 95, 221. (15) Sano, T.; Yanagishita, H.; Hasegawa, M.; Kawakami, Y. J. Membr. Sci. 1995, 107, 193. (16) Fuchs, H. A.; Cheetham, K. A. J. Phys. Chem. B 2001, 105, 7375. (17) Maginn, J. E.; Macedonia, D. M. Mol. Phys. 1999, 96, 1375. (18) Smit, B.; Vlugt, H. J. T.; Krishna, R. J. Phys. Chem. B. 1999, 103, 1102. (19) Snurr, Q. R.; Chempath, S.; Denayer, M. F. J.; De Meyer, A. M. K.; Baron, V. G. Langmuir 2004, 20, 150.
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C5-C12 hydrocarbon mixtures in silicalite-1 using the configurational-biased grand canonical Monte Carlo (GCMC) method. It was found that long alkanes preferentially adsorb into straight channels, whereas the short ones adsorb in sinusoidal channels. Similarly, Fox et al.20 studied the vapor-liquid phase equilibria of alkanes in silicalite-1 over a wide range of temperatures. These authors found that, irrespective of temperature and pressure, linear alkanes prefer to adsorb in the channels rather than at the channel intersections, whereas cycloalkanes adsorb more favorably at the intersections. Theodorou et al.,21 who studied the adsorption of aromatic hydrocarbons in silicalite-1 using the biased insertion methods, clearly evidenced that the symmetry transformation of silicalite-1 (ortho=para) depends only on the loading of adsorbate molecules. The symmetry corresponds to ortho only if there are four molecules per unit cell locating themselves at the channels intersections. As the loading of adsorbate increases, the molecules tend to occupy straight and sinusoidal channels, leading to the symmetry transformation. Rees et al.22 performed dynamical studies on the diffusion of aromatic molecules in the MFI silicalite-1 over a wide range of temperatures and showed that benzene has low diffusivity inside the silicalite-1 channels, which is attributed to the entropy of the benzene molecule. Klemm et al.23 studied the adsorption of benzene and phenol on different type of H-exchangeable zeolites. The adsorption is more favorable into the NaAlZSM-5 than into silicalite-1 because of the high interaction between the sorbate molecules and the Na+ cations in the channel network of the zeolites. The work by Boutin et al.24 on the adsorption of p-xylene, m-xylene, and their mixtures in the NaY zeolite suggested that m-xylene has stronger binding capacity when compared to its isomeric p-xylene. Even in the mixture adsorption, irrespective of the concentration of the isomers in the mixtures, NaY zeolite exclusively prefers m-xylene for adsorption. The present work is focused on the adsorption of p-cresol and water in pure silicalite-1. As far as we know, the adsorption onto porous materials of this biological molecule has never been studied using simulation techniques. Note that, this work is not devoted to fully describe the system from a thermodynamic point of view. For example, simulations that aim at obtaining the vapor pressure25 of a liquid solution of p-cresol were not performed. This was derived using theoretical equations and experimental data (vide infra). The objective of this work is essentially to give insight into the mechanism of adsorption of p-cresol onto silicalite-1. The paper is divided as follows. We first present the methodology we used for our simulations, including the molecular models for adsorbates and zeolite. In a subsequent part, we present the results on the adsorption of water and p-cresol onto the silicalite-1 zeolite. On the basis of these results, we will propose a mechanism for the coadsorption of p-cresol and water onto the silicalite-1.
2. Simulation Methods Models for Simulation. The initial structure of the silicalite-1 has been constructed according to International Zeolite Association (20) Fox, P. J.; Rooy, V.; Bates, P. S. Microporous Mesoporous Mater. 2004, 69, 9. (21) Theodorou, N. D.; Snurr, Q. R.; Bell, T. A. J. Phys. Chem. 1993, 97, 13742. (22) Rees, C. V. L.; Sun, L. Z.; Song, L. Microporous Mesoporous Mater. 2002, 55, 31. (23) Klemm, E.; Wang, J.; Emig, G. Microporous Mesoporous Mater. 1998, 26, 11. (24) Boutin, A.; Lachet, V.; Tavitian, B.; Fuchs, H. A. J. Phys. Chem. B. 1998, 102, 9224. (25) Ungerer, P.; Beauvais, C.; Delhommelle, J.; Boutin, A.; Rousseau, B.; Fuchs, A. H. J. Chem. Phys. 2000, 112, 5499.
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Table 1. Structural Data of Silicalite-1 (Orthorhombic, Pnma Symmetry Group) a (A˚) b (A˚)
c (A˚)
R=β=γ
straight channel sinusoidal channel pore size (A˚)a pore size (A˚)a
20.02 19.98 13.383 90 a Average value of the pore size.
5.45
5.30
(IZA) specifications,26,27 and the framework properties are listed in Table 1. The silicalite-1 used in the simulations is a completely rigid siliceous MFI zeolite with two intersecting channels. One is a straight channel, whereas the other channel is sinusoidal in shape. A single unit cell of silicalite is made up of 96 SiO2 units. Only the orthorhombic (Pnma) space group of silicalite-1 has been used in our simulations, as it is the stable state at human body temperature (310 K).28 The structure of the silicalite-1 is shown in Figure 1. All the Monte Carlo simulations were carried out using the simulation package “Towhee version 5.21”.29 The Amber30 force field for the adsorbate molecules (p-cresol and water) and the ClayFF31 one for the MFI zeolite were used in the simulations. The TIP3P model is embedded in the Amber force field for the parametrization of water molecules. Thus, water molecules were kept rigid in the simulations. Intramolecular energies arising from bonds, angles, and torsions were accounted for in the case of p-cresol molecules. The computation of these energy terms is compulsory for configurational-biased simulations. Force fields are used to calculate the potential energy of the system, which is the sum of bonded (bond stretching, angle, and torsions) and nonbonded (electrostatics and van der Waals) interactions. All the atoms in the system bear a point charge, which is used to calculate the Coulombic energy. The charges for p-cresol are obtained using density functional methods by fitting the electrostatic potential created by the electron density. The gradient corrected PBE functional32 were used with a triple-ζ basis set that included polarization functions on all the atoms. The calculations were performed with the Gaussian 03 package.33 Charges for water are from the TIP3P model, and charges for the silicalite-1 zeolite are +2.4 for silicon and -1.2 for oxygen atoms, respectively, which correspond to the charges recommended for use with the ClayFF force field. Table 2 gathers the charges used in the simulations. The zeolite and the sorbates do interact (26) International Zeolite Assosication, http://www.iza-structure.org/. (27) Baerlocher,Ch.; Meier, W. M.; Olson, D. H. In Atlas of Zeolite Framework Types, 5th ed.; Elsevier: Amsterdam, 2001. (28) Methivier, A.; Millot, B.; Jobic, H.; Clemencon, I.; Rebours, B. Langmuir 1999, 15, 2534. (29) Monte Carlo for Complex Chemical Systems (MCCCS) Towhee, Version 5.2.1.; http://towhee.sourceforge.net/. (30) Kollman, A. P.; Caldwell, W. J.; Fox, T.; Spellmeyer, C. D.; Ferguson, M. D.; Merz, M. K.; Gould, R. I; Bayly, I. C; Cieplak, P.; Cornell, D. W. J. Am. Chem. Soc. 1995, 117, 5179. (31) Cygan, T. R.; Liang, J. J.; Kalinichev, G. A. J. Phys. Chem. B 2004, 108, 1255. (32) Perdew, J. P.; Burke, K.; Ernzerhof, M. Chem. Phys. Lett. 1997, 78, 1396. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02Gaussian, Inc.: Wallingford, CT, 2004.
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water MFI zeolite
Figure 1. Structure of the MFI zeolite. Four unit cells of MFI are shown. Color legend: silicon atoms in yellow; oxygen atoms in green.
through a pairwise additive potential. This is modeled using Lennard-Jones 12-6 potentials and is given by 2 !12 !6 3 σ σ ij ij 5 ð1Þ uðrij Þ ¼ 4εij 4 rij rij where i and j are atoms of the sorbate molecule and of the silicalite lattice, respectively, rij is the distance between these atoms, and σij and εij are the pair potential parameters. These parameters are calculated from atomic ones (σii and εii) using the standard Lorentz-Berthelot mixing rules:34,35 σij ¼ εij ¼
σ ii þ σ jj 2
ð2Þ
pffiffiffiffiffiffiffiffiffi εii εjj
ð3Þ
Part of the bonded energy term arises from the simple harmonic motion of the bond stretching and bond bending terms in the p-cresol molecule and is given by eqs 4 and 5: X kr ðr - req Þ2 ð4Þ Ebond stretching ¼ bonds
Ebond bending ¼
X
kθ ðθ - θeq Þ2
ð5Þ
angles
where req, θeq are the equilibrium bond lengths and equilibrium bond angles, respectively, and kr, kθ are the corresponding force constants. The torsional energy of the system is given in the Amber force field by a truncated Fourier series: Ebond torsion ¼
X Vn ½1 þ cosðnj þ γÞ 2 dihedrals
ring carbon methyl carbon carbon holding methyl group carbon holding hydroxyl group ring hydrogen methyl hydrogen hydrogen oxygen silicon oxygen
charges in unit of electrons -0.25 -0.30 0.20 0.35 0.20 0.10 0.40 -0.80 2.4 -1.2
Simulation Techniques. Monte Carlo36,37 simulations are particularly convenient for the calculation of thermodynamic properties at equilibrium such as the average number of particles ÆNæ adsorbed in a porous solid or heat of adsorption. They also provide us insight into the location of the sorbate molecule and the molecule distribution in adsorbent pores. In this study, all the simulations were performed at 310 K, unless otherwise specified. We used the GCMC-μVT method with a configurational-biased algorithm38,39 to adsorb p-cresol onto silicalite-1. The configurational-biased algorithm is used to have a better acceptance probability by inserting the molecule in a energetically favorable phase space. For more details on the configurational-biased algorithms, the reader should refer to refs 38-41. For the adsorption of the water molecules, simulations using grand-canonical ensemble were performed either in the presence or absence of p-cresol at the channel intersections of the silicalite-1 zeolite (which corresponds to the experimental location of the toxin in the zeolite). The direct coadsorption of both species could not be simulated for reasons that will become clear later. Subsequently, canonical Monte Carlo (NVT) simulations were used to monitor the energy profile of the system (p-cresol-water-zeolite). For better characterization of the interaction energy of adsorbate molecules with its environment, a single p-cresol molecule in one unit cell of silicalite-1 was modeled separately. Note that, for both ensembles, intramolecular relaxation of the p-cresol molecule was allowed. A single unit cell of silicalite-1 with periodic boundary conditions was used for the simulation of the adsorption of p-cresol. Each simulation was run for 2 million steps for attaining the equilibrium and also for the acquisition of data. A structural output was obtained for every 104 steps to have a prediction of the sorbate molecules locations. Adsorption of water molecules in silicalite-1 holding p-cresol were studied using 12 unit cells of zeolite. The whole adsorption isotherm was obtained using GCMC simulations. Simulations were performed for 1 million steps for equilibration and data acquisition. Similarly, the adsorption of water on pure silicalite-1 has been carried out using GCMC method with the same technical conditions as above.
3. Results and Discussions In this section, we start with a general discussion on the chemical potential of a liquid solution of p-cresol. Subsequently,
ð6Þ
where the value of Vn stands for rotational barrier heights, n stands for the periodicity, j is for dihedrals, and the γ is for phase. (34) Wood, W. W.; Parker, R. F. J. Chem. Phys. 1957, 27, 720. (35) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces; Clarendon Press: Oxford; 1987.
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atom type
(36) Metropolis, N.; Rosenbluth, W. A.; Rosenbluth, N. M.; Teller, H. A. J. Chem. Phys. 1953, 21, 1087. (37) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: Oxford; 1987. (38) Martin, G. M.; Siepmann, I. J. J. Phys. Chem. B 1998, 102, 2569. (39) Martin, G. M.; Siepmann, I. J. J. Phys. Chem. B 1999, 103, 4508. (40) De Pablo, J. J.; Bonnin, M.; Prausnitz, M. J. Fluid Phase Equilib. 1992, 73, 187. (41) Frenkel, D.; Mooji, M. A. C. G.; Smit, B. J. Phys.: Condens. Matter 1992, 4, 3053.
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Figure 2. Adsorption isotherm of p-cresol onto MFI at 310 K. ÆNæ is the mean number of p-cresol molecules adsorbed per unit cell of zeolite.
Figure 3. Adsorption site of p-cresol onto silicalite-1. p-Cresol is located at the intersection of the straight and sinusoidal channels. Color legend: silicon atoms in yellow; oxygen atoms in red; carbon atoms in cyan; hydrogen atoms in white.
the adsorption isotherm of p-cresol onto silicalite-1 is presented. Then adsorption of water on the silicalite-1 either in the presence or absence of p-cresol molecules is discussed in detail. Langmuir 2009, 25(19), 11598–11607
Chemical Potential of p-Cresol Liquid Solution. Let us start with a general thermodynamic analysis. The objective is to calculate the chemical potential of a dilute, aqueous solution of p-cresol in order to fix the thermodynamical reference state for DOI: 10.1021/la901579u
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determine this pressure using Clapeyron’s equation: dp Δvap H ¼ dT p RT 2
ð7Þ
although this equation assumes a constant value of the vaporization enthalpy over the whole range of temperature. However, once we know the heat capacities of liquid and gas p-cresol (Cp(l)(T) and Cp(g)(T)) and the vaporization enthalpy at a given temperature, it is possible to calculate the vaporization enthalpy at 310.15 K using a simple thermodynamic cycle that the reader can derive easily. The data for Cp(l)(T), Cp(g)(T), and ΔvapH(477.07 K) can be found in ref 42. We have Cp(l)(266.48 K) = 2323.7 J kg-1 K-1 and ΔvapH(477.07 K)=4.39 105 J kg-1. The data for Cp(g)(T) have been fitted on a polynomial function using data in ref 42, and we have obtained C pðgÞ ðTÞ ¼ 119:488 þ 3:89637T - 1:8794910 -3 T 2 þ 1:5642210 -6 T 3 Using the aformentioned thermodynamic cycle, we found ΔvapH(304.15 K) ≈ 5.893013 105 J kg-1. Note in passing that the temperature of 304.15 K is the mean value between 298.15 and 310.15 K, and the corresponding vaporization enthalpy will be used for integrating Clapeyron’s equation. In order to integrate Clapeyron’s equation (eq 7) we need to know the saturated vapor pressure at a temperature other than 310.15 K, which is our target temperature. For this, we used the following equation:43 lnðps;sat Þ ¼ lnðpl;sat Þ þ Figure 4. (a) Energy distribution of p-cresol in MFI at 310 K. (b) Energy distribution of p-cresol in MFI at 50 K.
our simulations on the adsorption of p-cresol onto silicalite-1. The chemical potential thus calculated is used to shift the chemical potential of the simulation accordingly. The derivation of the chemical potential is based on both theoretical equations (e.g., Clapeyron’s equation) and experimental data, and proceeds as follows. We wish to integrate the Clapeyron equation between 298.15 and 310.15 K to determine the vapor pressure of the liquid p-cresol at 310.15 K. For that, we first calculate the vaporization enthalpy at 304.15 K using experimental data and a thermodynamic cycle. In a second step, we determine the vapor pressure of liquid p-cresol at 298.15 K. From these data we calculate the vapor pressure of liquid p-cresol at 310.15 K, and it is then possible to calculate the chemical potential of a pure solution of liquid p-cresol in equilibrium with its gas phase. Finally, the chemical potential of the dilute, aqueous solution of p-cresol is obtained using the experimental Henry constant of the toxin. The full derivation is now presented. When a pure liquid is in equilibrium with its gas phase, the chemical potential of both phases equal each other, μ*(g) = μ*(l), where the “asterisk” symbolizes the pure component. The che* =kT ln(pΛ3/kT), mical potential of the ideal gas is given by μ(g) where k is the Boltzmann constant, T and p are the temperature and pressure, respectively, and Λ is the de Broglie length given by hNA/(2πMRT)1/2 (h: Planck’s constant; NA: Avogadro’s constant; M: molar mass of gas; R: ideal gas constant; T: temperature). For p-cresol, M=108.134 g mol-1 and Λ=9.533 10-12 m at 310.15 K. For a liquid-gas equilibrium, the pressure corresponds to the saturated vapor pressure that we note pl,sat. It is possible to 11602 DOI: 10.1021/la901579u
Δfus Sm Tm 1R T
ð8Þ
that links the saturated vapor of the solid to that of the liquid. Tm is the triple point temperature (307.4 K for p-cresol) and ΔfusSm is the molar entropy of fusion. The experimental value of ΔfusSm/R is 4.97,43,44 and that of ps,sat(298.15 K) is 0.15 mbar.45 Using eq 8, we then obtain pl,sat(298.15 K)=0.175 mbar. Putting all these data into eq 7 and integrating between 298.15 K and 310.15 K, we obtain 2.879 mbar for pl,sat(310.15 K). From the chemical * = potential formula for the ideal gas, we find (see above) μ(g) * =-60768 J mol-1. This chemical potential corresponds to that μ(l) of pure, liquid p-cresol. However, in experiment, p-cresol is adsorbed from dilute solution, which we can consider as an ideal, *þ dilute solution. In this case, using Henry’s law, we have μ(l)=μ(l) k ln(KHx/pl,sat), where KH and x are the Henry constant and the fraction of p-cresol in the liquid, respectively. The Henry constant can be determined from the equation " KH ¼ KH;ref
# -Δdissol Hm 1 1 T Tref T
ð9Þ
where ΔdissolHm is the molar enthalpy of dissolution. ΔdissolHm/R and KH,ref equal 7200 K and 12.83 mol m-3 Pa-1, respectively, at 298.15 K.46 Hence, we obtain KH(310.15 K)=32.66 mol m-3 Pa-1 (42) National Oceanic and atmospheric administration, Office of Response and Restoration (http://cameochemicals.noaa.gov/chemical/8467). (43) Coutsikos, P.; Voutsas, E.; Magoulas, K.; Tassios, D. P. Fluid Phase Equilib. 2003, 207, 263. (44) TRC Vapor Pressure Database, Physical and Chemical Properties Division, NIST, Boulder, CO (http://www.nist.gov/srd/nist87.htm). (45) The Good Scents Company, Canada (http://thegoodscentscompany.com/ data/rw1003851.html). (46) Parsons, G. H.; Rochester, C. H.; Rostron, A.; Sykes, P. C. J. Chem. Soc., Perkin Trans. 1972, 2, 136.
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Figure 5. (a) Orientational degrees of freedom of p-cresol molecule with respect to the Cartesian framework axes. The carbon atoms are those used as a reference for calculating the angles (see text). (b) Energy of p-cresol as a function of degrees of freedom.
from eq 9. From experiments9 it can be calculated that at maximum adsorption in the silicalite-1 zeolite the mole fraction of p-cresol amounts to about 1.17 10-5, hence, the chemical potential of the ideal, dilute solution of p-cresol is μ(l)=-95663 J mol-1. In other words, this is the chemical potential, at full loading, of the system of adsorbed p-cresol in the silicalite-1 zeolite. Adsorption of p-Cresol. Figure 2 depicts the adsorption isotherm of p-cresol in silicalite-1. It clearly shows that there are four molecules of p-cresol per unit cell of silicalite-1, which corresponds roughly to the experimentally obtained amount (0.65 mmol/g).9 Figure 3 shows that the adsorbed p-cresol molecules occupy the channel intersections only. The adsorbate molecules exhibit hydrogen bonding between the hydroxyl group of p-cresol and the oxygen of the silicalite-1 framework. The value of the chemical potential deserves an important digression here. It has been observed that a very high chemical potential has to be applied in our simulations in order for p-cresol to adsorb in the zeolite. This high value is caused by the use of the configurationalbiased algorithm, which is responsible for the strong distortion of Langmuir 2009, 25(19), 11598–11607
the p-cresol molecule (bond stretching, and angle and dihedral bends). The advantage is that p-cresol is more likely to adsorb in the confined zeolite environment, although at the expense of the internal energy, which is rising. To compensate the positive, internal energy, a high chemical potential has to be applied. This high value is unphysical and it is necessary to rescale it. This has been done on the basis of the thermodynamic calculations presented before. The simulated chemical potential around 190 kJ mol-1, that is, at full loading, effectively equals -95.7 kJ mol-1, the other chemical potential values being linearly shifted accordingly. The choice of the value of the chemical potential ( μ= 190 kJ mol-1) is approximate and we estimate the corresponding error to be around 5%. Figure 4a shows the adsorption energy profile of a single p-cresol molecule in silicalite-1 channels. From the energy distribution plot, it is seen that there is a broad distribution of energy starting from -90 kJ mol-1 to -5 kJ mol-1. To verify that only one site of adsorption of p-cresol is responsible for such a broad distribution, simulations at a lower temperature (50 K) were DOI: 10.1021/la901579u
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Figure 6. Adsorption isotherm of water in silicalite-1 with and without p-cresol adsorbed at the intersection of the straight and sinusoidal channels of the zeolite.
carried out. The results are depicted in Figure 4b. It clearly confirms that there is only one energetically stable state for the adsorption of p-cresol. The widths of the energy profile are attributed to the different orientations of the p-cresol molecule inside the pore volume. The fluctuations of orientational degree of freedom of p-cresol molecule have been analyzed to help us to estimate the best possible orientation of the sorbate molecule in the silicalite-1 zeolite. Orientations of any sorbate molecule have been defined by three independent angles, namely, Θ, Φ, and Ω (see Figure 5a). Two carbon atoms of the benzene ring are taken as a reference for calculating the relative orientation of the molecule with respect to the Cartesian framework axes. These two atoms are those that are located in para position to each other on the molecule ring and that bear the methyl and hydroxyl groups. The plot of the energy of the sorbate molecules with respect to the three angles Θ, Φ, and Ω is presented in Figure 5b. It depicts that p-cresol molecule is allowed to have only constrained orientation in silicalite-1 channels. The values of Θ and Φ are confined to a cloud of points that are symmetric around 75 and 250, respectively. In the case of Ω, the points are also symmetric around 75, but the distribution is slightly broader than for the other degrees of freedom. In conclusion, the molecule is very constrained in its adsorption site. The only true degree of freedrom corresponds to the rotation around its benzyl rotational axis, which links the methyl and hydroxyl groups. Adsorption Phenomena of p-Cresol and Water. Strictly speaking, the simulation of the coadsorption of both p-cresol and water molecules cannot be performed. In effect, the chemical potential of both species are too different from each other to permit coadsorption through GCMC simulations. Therefore, we proceeded as follows: The four p-cresol molecules were placed at their adsorption sites on the silicalite-1 framework, namely, at the channel intersections. Then, GCMC simulations were performed to adsorb water molecules and to simulate the corresponding adsorption isotherm. Comparisons are also presented with the adsorption isotherm of water simulated in the absence of p-cresol. The adsorption isotherms of water in silicalite-1 with and without the presence of p-cresol are shown in Figure 6. They show that the amount of water molecules adsorbed in the absence of p-cresol is almost twice the amount of water molecules that adsorbs when there is p-cresol inside the silicalite-1. In the case of the water adsorption without p-cresol in the silicalite-1, it is observed in Figure 6 that, at very low chemical potential (-38 kJ mol-1), no water is adsorbed initially. This is consistent 11604 DOI: 10.1021/la901579u
Narasimhan et al.
with the hydrophobic nature of the silicalite-1 zeolite. However, when the chemical potential of the water is increased, there is slight adsorption of water and when the chemical potential reaches about -21 kJ mol-1, water molecules start to adsorb strongly in the silicalite-1 filling the entire straight and sinusoidal channels. Similar results were obtained by Puibasset et al.47 and Desbians et al.48 when examining the water adsorption in silicalite-1 zeolite. By examining the structures, we can infer that this is due to the fact that at higher chemical potentials, the water molecules inside the silicalite-1 channels tend to form mostly dimer and trimer clusters of water molecules. The silicalite-1 framework is completely saturated with the water molecules for chemical potentials above -4.2 kJ mol-1 indicating that cluster formation favors the adsorption of water by means of hydrogenbond interactions. At the same time, the amount of water molecules adsorbed when the p-cresol molecules are present at the intersection of the straight and the sinusoidal channels is almost half of the number of water molecules that are adsorbed when there is no p-cresol (see Figure 6). It is because p-cresol molecules occupy adsorption sites that are normally occupied by the water molecules in the silicalite-1 channels. The presence of the p-cresol does not prevent the adsorption of water, but it modifies the mechanism of adsorption. We observe that the presence of p-cresol inside the silicalite-1 initiates the adsorption of water at a lower chemical potential than in the absence of p-cresol. Silicalite-1 without p-cresol starts adsorbing water significantly when the chemical potential is around -24 kJ mol-1, whereas, in the presence of p-cresol, significant adsorption of water starts well below this chemical potential (-31 kJ mol-1). At low chemical potentials, the adsorbed water molecules are located at the silicalite-1 intersections, in close proximity with the p-cresol molecules. The analysis of the distances between molecules shows that this behavior is due to the formation of hydrogen bonding between the p-cresol and water molecules. As the chemical potential of water increases, the hydrogen bonding between the water and p-cresol molecules is strengthened, enabling water adsorption and thereby overcoming the hydrophobic nature of silicalite-1. When the chemical potential is around -22 kJ mol-1, there is a strong adsorption of water inside the silicalite-1 which reaches a plateau when the chemical potential is about -8 kJ mol-1 (see Figure 6). It is seen in Figure 6 that there is small step along the adsorption isotherm when the chemical potential is between -13.7 kJ mol-1 and -12.5 kJ mol-1. This step is attributed to the change in interactions between the adsorbate-adsorbate (p-cresol-water and water-water) and the adsorbate-adsorbent (water-silicalite-1 and p-cresol-silicalite-1). To explain these features, all simulated configurations along the adsorption isotherm of water in silicalite-1 in the presence of p-cresol were analyzed in detail. The results are depicted in Figure 7. It should be first mentioned that interactions between p-cresol molecules are negligible. When the chemical potential of water is increased (from -36 kJ mol-1 to -24 kJ mol-1), a strong increase of the strength of the interaction between water and p-cresol is observed (approximately 6-7 kJ mol-1, see Figure 7b). This is a sign of initial water adsorption at low chemical potential. As the chemical potential of water is further increased (from -24 kJ mol-1 to -20 kJ mol-1) the mean interaction strength between the p-cresol molecules and the silicalite-1 framework is decreased from about -64.5 kJ mol-1 to -63.5 kJ mol-1 (Figure 7a). More importantly, the strength of interactions between water and its surrounding partners (47) Puibasset, J.; Pellenq, M. J. R. J. Phys. Chem. B 2008, 112, 6390. (48) Desbiens, N.; Boutin, A. J. Phys. Chem. B 2005, 109, 24071.
Langmuir 2009, 25(19), 11598–11607
Narasimhan et al.
Article
Figure 7. (a) Variation of the interaction energies between p-cresol and silicalite along the adsorption isotherm. (b) Variation of the interaction energies between p-cresol and water along the adsorption isotherm. (c) Variation of the interaction energies between water and silicalite along the adsorption isotherm. (d) Variation of the interaction energies between water and water along the adsorption isotherm.
(p-cresol and silicalite-1) also decrease by about 1-2 kJ mol-1 and 1.0 kJ mol-1, respectively (see Figure 7b,c). To counterbalance this behavior, we observe increasing interaction strength between water molecules responsible for the formation of dimers and trimers. It is evident from Figure 7d that there is a strong interaction among water molecules leading to the formation of water clusters as depicted in Figure 8a. Between μ=-20 kJ mol-1 and μ=-13 kJ mol-1, since there is a growing formation of water clusters, the interaction between the p-cresol and the silicalite framework remains almost the same (Figure 7a), whereas the strength of interactions between water and the silicalite-1 zeolite still decreases (Figure 7c). It is noticeable that, the strength of the interactions between water molecules and silicalite-1 monotonically decreases along the adsorption isotherm. This can probably be related to the hydrophilic and hydrophobic nature of water and silicalite-1, respectively. Indeed, as the number of water molecules increases, there are more and more opportunities for water molecules to interact with surrounding water molecules and to move away from the hydrophobic zeolite. In Figure 8a,b we can see the difference between the few isolated water molecules adsorbed at μ=-26.8 kJ mol-1 and the dimer and trimer clusters formed at a higher chemical potential (μ = -20.33 kJ mol-1). Across the small step in the adsorption isotherm (-13< μ
