Adsorption and Diffusion of Methanol, Glycerol, and Their Mixtures in a

Nov 16, 2011 - In this work, the GCMC simulations were performed using the MuSiC code. ..... (CCEI), an Energy Frontier Research Center funded by the ...
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Adsorption and Diffusion of Methanol, Glycerol, and Their Mixtures in a Metal Organic Framework Li Yang,†,‡ Stanley I. Sandler,*,‡ Dionisios G. Vlachos,‡ Changjun Peng,† Honglai Liu,† and Ying Hu† †

State Key Laboratory of Chemical Engineering and Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China ‡ Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, United States

bS Supporting Information ABSTRACT: Grand Canonical Monte Carlo (GCMC) simulation has been used to study the adsorption of methanol, glycerol, and their mixtures in the metal organic framework IRMOF-1, and canonical ensemble molecular dynamics simulation was used to study their diffusion in that adsorbent. In particular, we consider the adsorption of pure glycerol in IRMOF-1 at several different temperatures and the diffusion of pure glycerol in IRMOF-1 at infinite dilution. Then, we study the influence of the methanol as solvent and how different concentrations of methanol affect the behavior of glycerol in IRMOF-1. It is found that the glycerol is easily adsorbed into IRMOF-1, and a small concentration of adsorbed methanol promotes glycerol adsorption. The effect of methanol on the glycerol diffusivity depends on temperature and methanol concentration.

’ INTRODUCTION In recent years, the production of fuels and chemicals from plant biomass has become an increasingly important research area in energy-related catalysis. Glycerol is a product of biodiesel production.1 Due to the increasing use of biodiesel (as methyl esters) as fuel additives, one can expect an increasing production of glycerol and continued research on its conversion to other products or chemicals. Acrolein is the main product from the dehydration of glycerol, and zeolites are the main catalyst for these reactions. Jia et al.2 have reported the catalytic behavior of nanocrystalline HZSM-5 with a high Si/Al molar ratio (ca. 65) for the gas phase dehydration of aqueous glycerol. Chai et al.3 did similar research using a mesoporous SiO2 (SBA-15) and microporous molecular sieve materials (SAPO-34, Hβ and HZSM-5) as catalysts. Clacens et al.4 converted glycerol to polyglycerols using MCM-41 type mesoporous catalysts. While zeolites are the main catalysts mentioned above, nanoporous materials, in particular metal organic frameworks (MOFs), are being developed as new catalysts. MOFs contain two structural parts: diamond structures based on linking metal ions or metal clusters and linker structures of organic units. There are many papers and reviews on the use of MOFs as catalysts.5,6 Here, the adsorption and diffusion of methanol and glycerol in a MOF have been studied using computer simulation. The results provide basic information on the adsorption and diffusion of glycerol in MOF materials and the effect of the solvent methanol, which is often used in the transesterification reaction of converting triglycerides to biodiesel. The frequently used IRMOF-1 was chosen as a prototype for study here. In the following section, we describe the molecular models and simulation methods used. Next, the results of the Grand Canonical Monte Carlo (GCMC) and molecular dynamics r 2011 American Chemical Society

(MD) simulations are discussed, and this is followed by the conclusions.

’ MATERIALS MODELS AND SIMULATION METHODS Models and Potentials. IRMOF-1 is an isoreticular metal organic framework, also known as MOF-5.7,8 It has a lattice constant of 25.832 Å, a crystal density of 0.593 g/cm3, a free volume of 79.2%, and a surface area of 2833 m2/g.9 In our simulations, the atomic coordinates of the IRMOF-1 crystal were constructed from experimental crystallographic data. This MOF has straight channels with diameters of 15 Å and 12 Å. The universal force field (UFF)10 was used for Zn, C, O, and the H atoms in IRMOF-1 (listed in Table S1 of the Supporting Information).9,11 The charges of these atoms were from taken Babarao and Jiang11 (also listed in Table S1, Supporting Information) as they obtained results that compared well to experimental adsorption data using this force field. The effects of IRMOF-1 structure rigidity and flexibility on the diffusion of benzene has been considered elsewhere.12,13 The calculations and review of previous results in ref 13 found that the differences in the simulation results obtained for IRMOF-1 by including or neglecting flexibility and atomic vibrations in its structure were small in comparison to the uncertainties that result from the force field used. Consequently, in our simulations, the coordinates of the IRMOF-1 atoms were frozen, and atomic vibrations were not considered. (These effects of structural flexibility and atomic vibrations may be important when the diameter of the adsorbates is comparable Received: August 13, 2011 Accepted: November 16, 2011 Revised: November 16, 2011 Published: November 16, 2011 14084

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to the pore diameters.) The simulation box representing IRMOF-1 contained 8 (2  2  2) unit cells, and periodic boundary conditions were used in three dimensions to account for the crystalline periodicity. Methanol and glycerol were described by the TraPPE (transferable potentials for phase equilibria) united atom force field developed by the Siepmann group.1416 This force field is commonly used in the molecular simulation of phase behavior of small molecules. In the united atom TraPPE force field model, methanol is a three-site structure and glycerol has nine sites. The model parameters for the CH 3 , CH 2 , and CH groups and for the O and H atoms are listed in Table S2, Supporting Information.1416 Simulation Methodology. Grand Canonical Monte Carlo (GCMC)17,18 simulations at fixed temperature T, volume V, and adsorbate chemical potential μ were carried out for the adsorption of pure methanol, pure glycerol, and their mixtures in IRMOF-1. GCMC simulation allows one to directly relate the chemical potential in adsorbed and bulk phases, and so, it has been widely used for the simulation of adsorption. In this work, the GCMC simulations were performed using the MuSiC code.4,1923 A spherical cutoff length of 19.0 Å was used in all GCMC simulations for the intermolecular LJ (LennardJones potential) interactions without long-range corrections. The LorentzBerthelot combining rules were used to calculate the LJ cross parameters. The Coulombic interaction between the adsorbate and adsorbent was accounted for with the use of the Ewald sum technique, and the adsorbate Coulombic interaction was calculated directly using the atom-based pairwise summation method (Wolf and Zahn method)24 with the parameter α set to 0.1.24 The adsorbent molecules were fixed in the simulation box, while the adsorbate molecules moved freely with their bond lengths fixed; the internal rotational motions were described using the bending and torsion parameters listed in Table S3, Supporting Information.1416 The number of Monte Carlo trial moves used in a typical simulation was 6 million. The first half of these moves were used for equilibration, and the rest were used for calculating the ensemble averages. Four types of moves for the adsorbate molecules, namely, translation, rotation, insertion, and deletion, were randomly attempted. The ratio of frequencies for the four moves was 1:1:5:5, and the acceptance rates for the four types of moves were 0.5, 0.5, 0.05, and 0.05, respectively. The concentration of adsorbate c (mol/g) was calculated as follows cðmol=gÞ ¼

amount of adsorbate ðmolÞ adsorbent mass

ð1Þ

Molecular dynamics (MD) simulation17,18 at temperature T, volume V, and number of particles N (NVT ensemble) with a Nose-Hoover thermostat was carried out for the diffusivities of glycerol, methanol, and their mixtures in IRMOF-1. The initial configurations for the MD simulations came from the equilibrated GCMC simulations. In this work, MD simulations were performed using the LAMMPS code.25 A spherical cutoff length of 12 Å was used to evaluate the intermolecular LJ interactions without further long-range corrections. The LorentzBerthelot combining rules were used to calculate the LJ cross parameters. The intramolecular 14 pair interactions were described using the LJ potential attenuated by a factor of 0.5.21 The Coulombic interaction between the adsorbate and adsorbent was accounted using the PPPM method,26 which uses a particleparticle

Figure 1. Pure methanol adsorption in IRMOF-1 at 300 K (9) and 600 K (2). The points are the simulation results, and the solid lines are a guide. Na is the absolute number of molecules absorbed, and f is fugacity of the absorbate; the dashed line is the fugacity of methanol at 300 K.

particlemesh solver to map atom charges to a 3d mesh, followed by 3d fast Fourier transforms to solve the Poisson equation on the mesh, and then an interpolation of the electric fields on the mesh points back to the atoms with the adsorbent fixed. The adsorbate molecules moved freely in the simulation box, and the molecule could bend and rotate; the intramolecular hydrogen bond was treated as rigid at a fixed distance using the SHAKE command of LAMMPS. The intramolecular parameters and computational methods are listed in Table S3, Supporting Information.1416 The motions of adsorbate molecule were computed using the rRESPA multitime scale integrator27 with 3 hierarchical levels, and the outer time step of motion was 1 fs. All the MD simulations were performed for a total 7 ns, with the first 6 ns used for equilibration and the last 1 ns used for calculating the ensemble average and diffusion coefficient. The tracer diffusivity was estimated from the mean-squared displacement using the Einstein relation28 * + 1 1 N 2 D ¼ lim jr k ðtÞ  r k ð0Þj ð2Þ t f ∞ 6t N k¼1

∑

where rk(t) is the position of the kth molecule at time t, and N is the number of molecules. To calculate diffusivities at finite concentrations and in mixtures, the adsorbateadsorbate interactions were turned on.

’ RESULTS AND DISCUSSION Adsorption of Pure Methanol in IRMOF-1. The results of the Grand Canonical Monte Carlo simulations for the adsorption of pure methanol in IRMOF-1 with increasing methanol fugacity are shown in Figure 1 for 300 and 600 K. Figure 1 shows the expected increased adsorption of methanol in IRMOF-1 with increasing fugacity. The saturated vapor pressure of methanol is 18.527 kPa at 300 K indicated by the dotted line in the figure which, at this low pressure, can be taken to be the fugacity at vaporliquid equilibrium. Consequently, the 300 K isotherm corresponds to the adsorption from a vapor (at subatmospheric 14085

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Figure 2. Pure glycerol adsorption in IRMOF-1 at 300 K (9) and 600 K (2). The symbols and lines have the same meaning as in Figure 1.

pressure) below vapor pressure and the adsorption from a liquid above 18.527 kPa. It is seen that the adsorption increases rapidly as the vapor pressure is approached, and then slowly as the methanol molecules saturate the pores. At 600 K, which is above the methanol critical temperature of 512.6 K, the adsorption behavior is slightly different. In this case, all the adsorption is from the vapor or gas, and the adsorption is very low at pressures below about 10 bar (1000 kPa) and increases less sharply with increasing pressure than at the lower temperature. At about 5000 bar, the system begins to approach saturation. At this high pressure, the saturation loading at 600 K is a little higher than that at 300 K. Adsorption of Pure Glycerol in IRMOF-1. Figure 2 shows the simulation results for the adsorption isotherms of pure glycerol in IRMOF-1 at 300 and 600 K. Glycerol was modeled using the Trappe united atom force field so that the molecule has 9 interaction sites. The vapor pressures are shown as dotted lines. At the lower temperature of 300 K, glycerol adsorption is mostly from the liquid except at pressures below the very low vapor pressure of 2.78  105 kPa at which there is little adsorption. At the higher temperature of 600 K, the vapor pressure is 257.07 kPa, glycerol adsorption in IRMOF-1 is from either the vapor or the liquid. Few glycerol molecules are adsorbed below 10 kPa, and above 10 kPa, the adsorption increases sharply as the fugacity increases. When the glycerol fugacity is higher than 257 kPa, adsorption is from the liquid and is approaching saturation. Adsorption of Methanol and Glycerol Mixtures in IRMOF-1. In catalytic chemistry, methanol is an important solvent for glycerol. We therefore studied the influence of methanol on glycerol adsorption in IRMOF-1 by simulation. We considered two different types of GCMC simulation. First, the numbers of methanol molecules were fixed in the simulation box, and only the glycerol molecules were allowed to exchange with the bulk phase in order to study the influence of methanol on glycerol adsorption. The second procedure employs a full GCMC mixture simulation in which both methanol and glycerol molecules were allowed to exchange with the bulk phase to study competitive adsorption. Figure 3 shows the adsorption isotherms of glycerol in IRMOF-1 at 300 K with the number of methanol molecules in the unit cell fixed at 0, 10 50, 200, and 500, respectively. Figure 4 shows the corresponding results at 600 K. In these simulations,

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Figure 3. Adsorption isotherms of glycerol in IRMOF-1 at 300 K with different numbers of added methanol molecules.

Figure 4. Adsorption isotherms of glycerol in IRMOF-1 at 600 K with different numbers of added methanol molecules.

all molecules had translational and rotational degrees of freedom, but the methanol molecules were not allowed to exchange with the bulk phase, while the glycerol molecules could. Since methanol molecules occupy some of the pore space, at saturation, the number of glycerol molecules is lower than that for pure glycerol. However, surprisingly, at low fugacities, the presence of methanol generally increases the extent of glycerol adsorption. This is especially evident at low glycerol fugacities and high methanol loadings. The reason might be that the adsorbed methanol molecules develop a hydrogen bond with the glycerol, as suggested by the observation that the glycerol loading increases (below saturation) with increasing methanol loading. Figures 5 and 6 show the competitive adsorption isotherms for mixtures of methanol and glycerol at 300 K. In the simulations, the liquid phase was assumed to be ideal, so that the vapor phase compositions in equilibrium with the liquid mole fractions were computed from vap vap xm Pm þ xg Pg ¼ P 14086

ð3Þ

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Figure 5. Extent of glycerol adsorption in IRMOF-1 at 300 K from methanolglycerol mixtures.

vap xm Pm ym ¼ P yg ¼

vap xg Pg P

Figure 6. Extent of methanol adsorption in IRMOF-1 at 300 K from methanolglycerol mixtures.

ð4Þ ð5Þ

where the symbols “m” and “g” label methanol and glycerol, respectively, x is mole fraction in liquid phase, y is mole fraction in gas phase, P is pressure, and the superscript vap indicates the vapor pressure. Since the total pressure is low, the fugacity of each component was taken to be its partial pressure. Both the methanol and glycerol molecules were allowed to exchange with the bulk phase. Figure 5 shows the glycerol adsorption as a function of glycerol mole fraction (bottom x axis) and vapor partial pressures (upper x axis). It is seen in this figure that the extent of glycerol adsorption, while low, first increases with decreasing methanol loading, similar to that in Figure 4, reaches a maximum, and then decreases with decreasing methanol concentration due to competitive adsorption. Another reason for the decrease is that the total pressure of the system decreases with increasing glycerol composition, decreasing to the glycerol vapor pressure for pure glycerol. Figure 6 is for methanol adsorption from the mixture. It shows that, at low mole fraction of glycerol, IRMOF-1 is saturated with methanol, and as expected, the methanol loading decreases as its partial pressure (fugacity) decreases with increasing mole fraction of glycerol. Diffusivity of Pure Glycerol at Infinite Dilution in IRMOF-1. The diffusivity of glycerol in a catalyst is an important property for diffusion controlled reactions. Diffusivity can be computed using molecular dynamics simulation. We used the LAMMPS software for simulation with the force fields described above, except that the simulation box contained at least 50 glycerol molecules that did not interact with each other, though they interacted with IRMOF-1. In this way, we could compute the glycerol diffusivity at infinite dilution but still have a sufficient number of molecules for good statistics. The mean square displacement as a function of time was obtained from changes of molecular position during the simulation. Figure S1

Figure 7. Glycerol diffusivity at infinite dilution in IRMOF-1 as a function of inverse temperature.

(Supporting Information) shows the mean square displacement of glycerol molecules at infinite dilution in IRMOF-1 at 350 K. The diffusivity was then calculated using eq 2, and the results are shown in Figure S2 (Supporting Information) expressed as the diffusivity of glycerol in IRMOF-1 at infinite dilution D(0) as a function of simulation time. The diffusivity of glycerol at this temperature is the ensemble average of the last 1 ns of simulation (from 6 to 7 ns). This simulation procedure was repeated at other temperatures. Figure 7 shows the diffusivities as a function of the inverse temperature. In nanoporous materials, steric effects and interaction with the adsorbent surface are considered to dominate, and diffusion is normally interpreted as an activated process. Thus, the temperature dependence of the diffusivity can be described by the Arrhenius relation28   Ea Dð0Þ ¼ Df exp ð6Þ RT 14087

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Figure 8. Self-diffusivities of glycerol in IRMOF-1 as a function of glycerol concentration at 300 K (9) and 600 K (2).

where Df is the prefactor, Ea is the activation energy, and R is the gas constant. By fitting the simulated D(0) at various temperatures using eq 6, values for Df and Ea can be obtained. In Figure 7, the points are simulation results and the line is the Arrhenius fit to the simulation data. We found the prefactor Df to be 1.33  106 m2/s and the activation energy Ea to be 19.84 kJ/mol, considerably less than its heat of vaporization of about 92 kJ/mol. Diffusivities of Methanol and Glycerol at Finite Concentrations in IRMOF-1. In the case of mixtures, molecular dynamic simulations were done with solutesolute and solutesolvent interactions turned on so that the effect of concentration on diffusivity could be studied. Figure S3 (Supporting Information) shows the mean square displacement of pure glycerol in IRMOF1 at 600 K as a function of simulation time at a concentration of 2.03 mmol/g. The diffusivity was then calculated as shown in Figure S4, Supporting Information. Calculations were repeated at other adsorbed glycerol concentrations at 300 and 600 K. Figure 8 shows the self-diffusivity of glycerol in IRMOF-1 at 300 and 600 K as a function of glycerol concentration. The results of these simulations with glycerol glycerol interactions turned on show a small decrease in the glycerol diffusivity with increasing amounts of glycerol adsorbed, as expected from molecular interactions. Simulations were also done for the diffusion of methanol and glycerol in IRMOF-1 in mixtures at finite concentrations and as expected, the diffusivity of each species is affected by the presence of the other species. Figures 9 (300 K) and 10 (600 K) show the diffusivity of pure glycerol and glycerol at fixed methanol concentrations of 0.93 mmol/g (46 methanol molecules in 2  2  2 cells) and 9.56 mmol/g (471 methanol molecules in 2  2  2 cells) as a function of glycerol concentration. The diffusivity of methanol is also shown as a function of glycerol concentration at the two methanol loadings. The results show that there is little effect of methanol on the glycerol diffusivity at the low concentration of methanol; however, at the higher methanol concentration, the glycerol diffusivity is higher than the self-diffusivity of pure glycerol. That is, the presence of methanol enhances the diffusion of glycerol in IRMOF-1. At both temperatures, the methanol diffusivity decreases rapidly with increasing glycerol concentration. Figure 9 shows that the glycerol diffusivity at a higher concentration of methanol is greater

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Figure 9. Diffusivity of glycerol as pure (b, solid line) and with 0.93 mmol/g (9, solid line) and 9.56 mmol/g (2, solid line) methanol. Also, the methanol diffusivity at 0.93 mmol/g (9, dashed line) and 9.56 mmol/g (2, dashed line), methanol concentrations a function of glycerol concentration. All the results are for diffusion in IRMOF-1 at 300 K.

Figure 10. Diffusivity of glycerol as pure (b, solid line) and with 0.93 mmol/g (9, solid line) and 9.56 mmol/g (2, solid line) methanol. Also, the methanol diffusivity at 0.93 mmol/g (9, dashed line) and 9.56 mmol/g (2, dashed line), methanol concentrations a function of glycerol concentration. All the results are for diffusion in IRMOF-1 at 600 K.

than that at a lower methanol concentration at 300 K, presumably because the small number of methanol molecules interact strongly with the IRMOF-1 structure at low temperature. However, as shown in Figure 10 at 600 K, the diffusivity of methanol at the higher concentration is lower than that at lower concentrations, indicating that interactions of the methanol with the IRMOF-1 structure are less important at higher temperature.

’ CONCLUSIONS The purpose of this research is to understand the adsorption and diffusion of glycerol and methanol that may occur in biofuels/biochemicals processing in a representative nanoporous catalysis cycle. In particular, we used molecular simulation to study the behavior of methanol and glycerol in IRMOF-1 as the 14088

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Industrial & Engineering Chemistry Research prototype for catalytic materials. We found that pure glycerol is easily adsorbed and quickly reaches saturation in IRMOF-1 with increasing the fugacity at room temperature. Methanol is also adsorbed, and the adsorption saturates near the methanol vapor pressure. Interesting, the mixture simulations indicate that the presence of a small number of methanol molecules promotes the adsorption of glycerol. The diffusivity of glycerol at infinite dilution and at finite glycerol concentrations was studied as a function of methanol concentration. At 300 K, low methanol concentration does not affect the diffusivity of glycerol in IRMOF-1. Higher methanol concentrations enhance the glycerol diffusivity at low glycerol concentrations. The behavior of the methanol diffusivity is more complicated because of the interplay between interactions with the IRMOF-1 framework and intermolecular steric interference.

’ ASSOCIATED CONTENT

bS

Supporting Information. The force fields and charges parameters for IRMOF-1, methanol, and glycerol. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Financial support for this work was provided by the National Natural Science Foundation of China (No. 20876041, 20736002), National Basic Research Program of China (2009CB219902), Program for Changjiang Scholars and Innovative Research Team in University of China (Grant IRT0721), and the 111 Project (Grant B08021) of China. This material is also based upon work supported as part of the Catalysis Center for Energy Innovation (CCEI), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0001004. The effort of S. I.S. is funded by both NSF Grant GOALI-0853685 and the CCEI, and the effort of D.G.V. is funded by the CCEI. Computational support for this work was provided by Teragrid Project (TG-CTS080045N) and the Texas Advanced Computing Center (TACC). ’ REFERENCES (1) Behr, A.; Eilting, J.; Irawadi, K.; Leschinski, J.; Lindner, F. Improved Utilisation of Renewable Resources: New Important Derivatives of Glycerol. Green Chem. 2008, 10, 13. (2) Jia, C. J.; Liu, Y.; Schmidt, W.; Lu, A. H.; Schuth, F. Small-sized HZSM-5 Zeolite as Highly Active Catalyst for Gas Phase Dehydration of Glycerol to Acrolein. J. Catal. 2010, 269, 71. (3) Chai, S. H.; Wang, H. P.; Liang, Y.; Xu, B. Q. Sustainable Production of Acrolein: Investigation of Solid Acid-Base Catalysts for Gas-Phase Dehydration of Glycerol. Green Chem. 2007, 9, 1130. (4) Clacens, J. M.; Pouilloux, Y.; Barrault, J. Selective Etherification of Glycerol to Polyglycerols over Impregnated Basic MCM-41 Type Mesoporous Catalysts. Appl. Catal., A: Gen. 2002, 227, 181. (5) Czaja, A. U.; Trukhan, N.; Muller, U. Industrial Applications of Metal-Organic Frameworks. Chem. Soc. Rev. 2009, 38, 1284. (6) Lee, J.; Farha, O. K.; Roberts, J.; Scheidt, K. A.; Nguyen, S. T.; Hupp, J. T. Metal-Organic Framework Materials as Catalysts. Chem. Soc. Rev. 2009, 38, 1450.

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