pubs.acs.org/Langmuir © 2009 American Chemical Society
Studies of Capillary Phase Transitions of Methane in Metal-Organic Frameworks by Gauge Cell Monte Carlo Simulation Qintian Ma, Qingyuan Yang, Chongli Zhong,* Jianguo Mi, and Dahuan Liu Lab of Computational Chemistry, Department of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China Received September 26, 2009. Revised Manuscript Received October 30, 2009 Capillary phase transitions of CH4 confined in a series of metal-organic frameworks (MOFs) were investigated in this work using gauge cell Monte Carlo simulations. The results show that capillary phase transitions can occur in MOFs, and the effects of temperature, pore size, and adsorption energy are very significant. Furthermore, this work shows the confinement can induce a shift in critical point for fluids confined in MOFs, leading to a decrease in critical temperature and an increase in critical density. The critical point shift is more obvious for MOFs with small pore size and large adsorption energy.
1. Introduction It has been generally recognized that fluids in confined space with dimensions in the order of a few molecular diameters, due to the strong surface-driven interactions, show anomalous physical properties to those of the bulk counterparts.1 Thus, knowledge of the phase behaviors of fluids confined in porous materials is not only of interest in the physical and surface sciences but also a prerequisite for the invention of nanoscale technologies and nanomaterials. Up to date, remarkable advances have been achieved in elucidating the specifics of vapor-liquid equilibria (VLE) and capillary phase transitions in various porous matrixes.2-6 Molecular modeling, mainly grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo (GEMC) simulations, has proved to be one of the most efficient methods for the description of these phase behaviors.7-9 However, previous investigation10 has shown that, at subcritical conditions, although GCMC simulation can obtain the hysteresis loop formed by the discontinuous adsorption and desorption branches of isotherms, it cannot be used to directly determine the equilibrium phase coexistences. Similarly, as pointed by Neimark and Vishnyakov,10 GEMC simulation suggested by Panagiotopoulos9 also bears its disadvantage that the coexistence point is sensitive to the initial configuration in the nanopores with strongly attractive walls. The gauge cell Monte Carlo (MC) simulation method, proposed by Neimark and co-worker,10 extends the capabilities of GCMC and GEMC methods, which is based on the construction of a continuous isothermal trajectory of the equilibrium states in the form of a van der Waals loop. The fascinating feature of this method is that the thermodynamically unstable states, which cannot be observed by experiments, are stabilized in simulations *Corresponding author: Tel þ86-10-64419862; e-mail
[email protected]. edu.cn. (1) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Rep. Prog. Phys. 1999, 62, 1573. (2) M€uller, E. A.; Rull, L. F.; Vega, L. F.; Gubbins, K. E. J. Phys. Chem. B 1996, 100, 1189. (3) Balbuena, P. B.; Gubbins, K. E. Langmuir 1993, 9, 1801. (4) Sokoleowska, Z.; Sokoleowski, S. J. Colloid Interface Sci. 2007, 316, 652. (5) Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, 7600. (6) Steele, W. A.; Bojan, M. J. Adv. Colloid Interface Sci. 1998, 76-77, 153. (7) Liu, J. C.; Monson, P. A. Langmuir 2005, 21, 10219. (8) Brovchenko, I.; Geiger, A.; Oleinikova, A. Phys. Chem. Chem. Phys. 2001, 3, 1567. (9) Panagiotopoulos, A. Z. Mol. Phys. 1987, 62, 701. (10) Neimark, A. V.; Vishnyakov, A. Phys. Rev. E 2000, 62, 4611.
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by suppressing the density fluctuations, and the coexisting phases can be easily determined from the obtained continuous isotherms.11 Recently, this gauge cell method has been successfully used to investigate the capillary phase transitions and critical behaviors of fluids in materials with various pore shapes.12-16 Metal-organic frameworks (MOFs) are a new family of crystalline porous materials that are formed by the coordination of metal oxide clusters with multidentate organic linkers. The modular nature of MOFs allows for the facile, ordered incorporation of new functionalities into them, which makes these materials exhibit promising applications in various areas.17-19 Accompanied with the significant progress in experimental studies,20-24 many theoretical investigations have been carried out to study the adsorption,25-29 diffusion,30-33 and separation34-38 of gases (11) Vishnyakov, A.; Neimark, A. V. J. Phys. Chem. B 2001, 105, 7009. (12) Jorge, M.; Schumacher, C.; Seaton, N. A. Langmuir 2002, 18, 9296. (13) Jiang, J. W.; Sandler, S. I.; Smit, B. Nano Lett. 2004, 4, 241. (14) Jiang, J. W.; Sandler, S. I. Langmuir 2006, 22, 7391. (15) Neimark, A. V.; Vishnyakov, A. J. Phys. Chem. B 2006, 110, 9403. (16) Kowalczyk, P.; Holyst, R.; Tanaka, H.; Kaneko, K. J. Phys. Chem. B 2005, 109, 14659. (17) Li, J. R.; Kupper, R. J.; Zhou, H. C. Chem. Soc. Rev. 2009, 38, 1477. (18) Mueller, U.; Schubert, M.; Teich, F.; Puetter, H.; Schierle-Arndt, K.; Pastre, J. J. Mater. Chem. 2006, 16, 626. (19) Lee, J. Y.; Farha, O. K.; Roberts, J.; Scheidt, K. A.; Nguyen, S. T.; Hupp, J. T. Chem. Soc. Rev. 2009, 38, 1450. (20) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Science 2002, 295, 469. (21) Ma, S. Q.; Sun, D. F.; Simmons, J. M.; Collier, C. D.; Yuan, D. Q.; Zhou, H. C. J. Am. Chem. Soc. 2008, 130, 1012. (22) Demessence, A.; D’Alessandro, D. M.; Foo, M. L.; Long, J. R. J. Am. Chem. Soc. 2009, 131, 8784. (23) Llewellyn, P. L.; Bourrelly, S.; Serre, C.; Filinchuk, Y.; Ferey, G. Angew. Chem., Int. Ed. 2006, 45, 7751. (24) Tanaka, D.; Nakagawa, K.; Higuchi, M.; Horike, S.; Kubota, Y.; Kobayashi, T. C.; Takata, M.; Kitagawa, S. Angew. Chem., Int. Ed. 2008, 47, 3914. (25) Sagara, T.; Klassen, J.; Ganz, E. J. Chem. Phys. 2004, 121, 12543. (26) Han, S. S.; Gaddord, I. I. I. J. Am. Chem. Soc. 2007, 129, 8422. (27) Garberoglio, G.; Skoulidas, A. I.; Johnson, J. K. J. Phys. Chem. B 2005, 105, 13094. (28) Salles, F.; Ghoufi, A.; Maurin, G.; Bell, R. G.; Mellot-Draznieks, C.; Ferey, G. Angew. Chem., Int. Ed. 2008, 47, 8487. (29) D€uren, T.; Bae, Y. S.; Snurr, R. Q. Chem. Soc. Rev. 2009, 38, 1237. (30) Skoulidas, A. I.; Sholl, D. S. J. Phys. Chem. B 2005, 109, 15760. (31) Liu, J. C.; Lee, J. Y.; Pan, L.; Obermyer, R. T.; Simizu, S.; Zande, B.; Li, J.; Sankar, S. G.; Johnson, J. K. J. Phys. Chem. C 2008, 112, 2911. (32) Liu, B.; Yang, Q.; Xue, C.; Zhong, C.; Smit, B. Phys. Chem. Chem. Phys. 2008, 10, 3244. (33) Chmelik, C.; K€arger, J.; Wiebcke, M.; Caro, J.; van Baten, J. M.; Krishna, R. Microporous Mesoporous Mater. 2009, 117, 22. (34) Keskin, S.; Sholl, D. S. Ind. Eng. Chem. Res. 2009, 48, 914.
Published on Web 12/02/2009
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Figure 1. Unit cell crystal structures of the IRMOFs studied in this work: (a) IRMOF-16, (b) IRMOF-A4, (c) IRMOF-A5, (d) IRMOF-B3, (e) IRMOF-B4, (f) IRMOF-B5 (Zn, blue; O, red; C, gray; H, white). Table 1. Structural Properties for the IRMOFs Studied in This Work material
pore shape
unit cell (A˚)
dporeb (A˚)
Fcrys (g/cm3)
a = b = c = 42.981a 23.3c 0.21a IRMOF-16 cubica a = b = c = 51.699b 27.6b 0.14b IRMOF-A4 cubicb b b b a = b = c = 60.327 31.9 0.10b IRMOF-A5 cubic a = b = c = 42.981b 23.3b 0.28b IRMOF-B3 cubicb a = b = c = 51.699b 27.6b 0.16b IRMOF-B4 cubicb a = b = c = 60.327b 31.9b 0.13b IRMOF-B5 cubicb a 20 b c 41 Obtained from the XRD crystal data. Obtained in this work. Obtained by D€ uren et al.
and their mixtures in MOFs. Particularly, density functional theory (DFT) in three-dimensional nanoconfined space has recently been developed and applied for H2 adsorption in IRMOF-1 by Liu et al.39 as well as Siderius and Gelb,40 which is able to provide rich information on the equilibrium phase transition of fluid adsorption in MOFs. In this work, gauge cell MC simulation method was employed to systematically study the capillary phase transitions of CH4 in MOFs with mesopores, which is the main component of natural gas. To the best of our knowledge, this is the first work so far that the phase transition behaviors of fluids were studied in MOFs. The results obtained in this work not only can scientifically enrich the insights into the adsorption of gases in MOFs but also may contribute to technologically improve the design efficiency of MOFs for practical utilization in CH4 storage.
2. Models and Simulation Method 2.1. MOF Structures. In the present work, IRMOF-16 synthesized by Eddaoudi et al.20 was selected as a representative (35) Yang, Q.; Xue, C.; Zhong, C.; Chen, J.-F. AIChE J. 2007, 53, 2832. (36) Bae, Y.-S.; Farha, O. K.; Hupp, J. T.; Snurr, R. Q. J. Mater. Chem. 2009, 19, 2131. (37) Jiang, J. W.; Sandler, S. I. Langmuir 2006, 22, 5702. (38) Martı´ n-Calvo, A.; Garcı´ a-Perez, E.; Castillo, J. M.; Calero, S. Phys. Chem. Chem. Phys. 2008, 10, 7085. (39) Liu, Y.; Liu, H. L.; Hu, Y.; Jiang, J. W. J. Phys. Chem. B 2009, 113, 12326. (40) Siderius, D. W.; Gelb, L. D. Langmuir 2009, 25, 1296.
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Vfreeb (cm3/g)
porosityb (%)
4.55 6.84 9.49 3.38 6.14 7.43
93.4 95.6 96.7 94.6 95.8 96.9
of the highly porous MOFs with mesopores. The guest-free framework structure of IRMOF-16 with pore size of 23.3 A˚41 was constructed from its experimental single-crystal X-ray diffraction (XRD) data,20 and the unit cell crystal structure is shown in Figure 1a. In order to study the effect of pore size on the phase behavior of CH4 in MOFs, two new MOFs were designed by adding one and two benzene rings to the organic linkers of IRMOF-16, i.e., IRMOF-A4 and IRMOF-A5 as shown in Figure 1b,c. Furthermore, to study the effects of the strength of adsorbate-adsorbent interactions on the phase behaviors of CH4 in MOFs with similar pore sizes, three more MOFs were designed by substituting the organic linkers of IRMOFs-16, -A4, and -A5 with condensed benzene rings, i.e., IRMOFs-B3, -B4, and -B5, as shown in Figure 1d-f. Evidently, these six MOF materials shown in Figure 1 are very simple that consist of each oxide-centered Zn4O tetrahedron connected by six different aromatic dicarboxylate linkers with similar chemical compositions to form threedimensional porous cubic frameworks. The structural properties of these materials are summarized in Table 1. The pore shape, length, and crystal density of the unit cell of each MOF were measured using Materials Studio package,42 excepting for IRMOF-16 which were obtained from its XRD crystal data.20 (41) D€uren, T.; Millange, F.; Ferey, G.; Walton, K. S.; Snurr, R. Q. J. Phys. Chem. C 2007, 111, 15350. (42) Accelrys, Inc. Materials Studio, 3.0 V.; Accelrys Inc., San Diego, CA, 2003.
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Table 2. LJ Potential Parameters for CH4 and MOFs Used in This Work atom/molecule
σ (A˚)
ε/kB (K)
CH4 MOF_Zn MOF_C MOF_H MOF_O
3.73 2.46 3.43 2.57 3.12
148.0 62.40 52.84 22.14 30.19
The pore sizes of these MOF materials were calculated using the method suggested by Bhattacharya and Gubbins.43 The total free volume Vfree of each material was estimated using the “Atoms Volume & Surfaces” calculation within the Materials Studio package,42 and porosity was obtained from the ratio of free volume Vfree to the total volume per unit cell. It should be noted that the free volume Vfree of each MOF material was estimated using a probe size of 0.0 A˚ to determine the absolute amount of volume not occupied by the framework atoms.44 2.2. Force Fields. In this work, a single site model with Lennard-Jones (LJ) interaction was used to describe a CH4 molecule, and the potential parameters were taken from the TraPPE force field,45 as listed in Table 2. For the MOFs studied here, an atomistic representation was used to model all of them. The CH4-adsorbent interactions were represented by the sitesite LJ potential, and the potential parameters for the framework atoms in MOFs were taken from the universal force field (UFF)46 as listed in Table 2. In our simulations, all the LJ cross-interaction parameters were determined by the Lorentz-Berthelot mixing rules. The above set of force field has been successfully used to study the adsorption37,47 and diffusion30,32 of CH4 in a various kinds of MOFs, including IRMOFs. As a result, further validation of the force fields was not performed in this work. 2.3. Simulation Method. The gauge cell MC simulation method10,12,15 was employed to study the capillary phase transitions of CH4 confined in the MOFs. In this method, two separate simulation boxes are adopted. One of the boxes is embedded within the pore of IRMOF material, and the other is a cubic gauge cell with limited capacity for bulk CH4. During the simulations, two simulation boxes were allowed to exchange molecules with one another so that chemical equilibrium were maintained in the system, but both of them had fixed volumes and were kept at the same constant temperature. By adjusting the total number of molecules in the system and the volume of gauge cell, we can suppress the density fluctuations inside the pore, from which a complete continuous isotherm can be sampled, including the stable, metastable, and unstable branches. In our simulations, one unit cell for each IRMOF was used, and the volume of gauge cell was adjusted to have on average about five molecules in the gauge cell.48 In our simulations, as done by others,38,49,50 all of the MOFs were treated as rigid frameworks, since the effects of the dynamics of MOFs become significant only when the guests are large and/or strong guest-host interactions exist in the system. The periodic boundary conditions were applied in all three dimensions of these two boxes in gauge cell simulations. A cutoff radius of 12.8 A˚ was applied to calculate all of the (43) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726. (44) Frost, H.; Snurr, R. Q. J. Phys. Chem. C 2007, 111, 18794. (45) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (46) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (47) Liu, B.; Yang, Q.; Xue, C.; Zhong, C.; Chen, B.; Smit, B. J. Phys. Chem. C 2008, 112, 9854. (48) Neimark, A. V.; Vishnyakov, A. J. Chem. Phys. 2005, 122, 234108. (49) Bae, Y. S.; Farha, O. K.; Spokoyny, A. M.; Mirkin, C. A.; Hupp, J. T.; Snurr, R. Q. Chem. Commun. 2008, 35, 4135. (50) Babarao, R.; Jiang, J. W.; Sandler, S. I. Langmuir 2009, 25, 5239.
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Figure 2. Isotherms of CH4 in the IRMOF-16 at 100, 120, 140, and 160 K. The open circles are from the gauge cell MC. The dashed lines are coexisting vapor and liquid phases. The regions of AVE and DLE are stable, those of VESV and LESL are metastable, and that of SVSL is unstable. At 100 and 160 K, the upper and lower triangles are the adsorption and desorption branches respectively from GCMC. At 100 K, the red and blue dot-dashed lines indicate capillary condensation and evaporation respectively from GCMC.
LJ interaction energies. The dependence of the fluid pressure on the chemical potential for CH4 was calculated in the gauge cell simulations. For each state point, simulation consisted of at least 1 105 steps per molecule to guarantee equilibration followed by at least 1105 steps per molecule to sample the desired thermodynamic properties. In addition, GCMC simulations were also utilized in the work to obtain the hysteresis loops formed by the discontinuous adsorption and desorption branches of isotherms. Details of GCMC simulations can be found elsewhere.32,35,51
3. Results and Discussion 3.1. Effect of Temperature on Capillary Phase Transitions. The isotherms of CH4 in IRMOF-16 at four temperatures 100, 120, 140, and 160 K are shown in Figure 2, in which μc is the dimensionless configurational chemical potential and F is the average CH4 density inside the free volume of MOF. At lower temperature 100 K, it can be found that the adsorption isotherm shows a sigmoidal van der Waals loop, which indicates the occurrence of first-order phase transition. Similar phenomena have also been observed in other materials with various pore shapes.10-16 The coexisting vapor-liquid phases were determined along the isotherm using a Maxwell equal area construction. Z
μSV μVE
Z Fa ðμ, TÞ dμ -
μSV μSL
Z Fs ðμ, TÞ dμ þ
μLE μSL
Fd ð μ, TÞ dμ ¼ 0
ð1Þ where VE and LE are vapor and liquid equilibrated phases at a saturation chemical potential and SV and SL are vapor and liquid spinodals. The stable (AVE and DLE), metastable (VESV and LESL), and unstable (SVSL) regions are shown in Figure 2. It can be found that the size of van der Waals loop obtained shrinks as the temperature increases from 100 to 120 K. At 140 K, the isotherm is almost vertical, which indicates the van der Waals loop almost disappearing. While at 160 K, the isotherm is monotonic with the increase of chemical potential, and the van der Waals loop vanishes. The characteristics of the isotherms for CH4 adsorption in Figure 2 indicate that there is a critical (51) Frenkel, D.; Smit, B. Understanding Molecular Simulations: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, CA, 2002.
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Figure 3. Contour plots of the COM probability densities of CH4 at 100 K (a-c) and 160 K (d-f) in planes through the Zn4O clusters in IRMOF-16 at different pressures (Zn, blue; O, red; C, gray; H, white).
temperature for the phase transition of CH4 in IRMOF-16, and the characteristics of the first-order phase transition occur only below this temperature. For comparison, the adsorption and desorption isotherms of CH4 in IRMOF-16 simulated with GCMC at 100 and 160 K are also depicted in Figure 2. Obviously, at 100 K the stable regions AVE and DLE and part of the metastable regions VSV and LSL generated by GCMC are consistent with those from gauge cell method. However, GCMC cannot access the unstable region SVSL. The GCMC adsorption branch terminates at point C, where the fluid underwent spontaneous capillary condensation. Similarly, the GCMC desorption branch ends at point B, where the fluid undergoes the spontaneous evaporation. At 160 K, the GCMC results show that the hysteresis loop disappears, which is in agreement with the gauge cell MC results. In order to further investigate the capillary phase transitions for CH4 confined in MOFs, the occupying situations of CH4 molecules in IRMOF-16 were investigated in detail to clarify the process of phase transitions at different temperatures. In this work, the center of mass (COM) probability distributions of CH4 in IRMOF-16 at 100 and 160 K were studied. As can be seen from Figure 3a-c, at the lowest density, the preferred location of CH4 molecules is near the metal clusters and phenyl linkers. With the increasing of density, the CH4 molecules start occupying part of the empty pores, followed by the saturation of these pores, and then, they start occupying the rest empty pores with increasing pressure. In addition, as can also be seen from Figure 3b, CH4 Langmuir 2010, 26(7), 5160–5166
molecules fill the pores of IRMOF-16 in the mode of alternative columns. At the moment, the underlying mechanism is still unclear, and this very interesting phenomenon should be further investigated in detail in the future. The COM probability densities of CH4 at 160 K are shown in Figure 3d-f. Similar to that at 100 K, at low pressure CH4 is preferably to be adsorbed near the metal clusters and phenyl linkers; however, with increasing pressure, CH4 molecules seem to distribute more uniformly in the material (Figure 3e) until the material is filled with CH4. Figure 3 shows that the microcosmic process of phase transition of CH4 confined in IRMOF-16 strongly depends on temperature. The phase transition of CH4 confined in IRMOF-16 is observed to be a first-order vapor-liquid transition at 100 K, whereas it exhibits a continuous process at 160 K. Comparison of the vapor-liquid coexistence curves for bulk CH452 and hysteresis phase diagrams for CH4 confined in IRMOF-16 is shown in Figure 4. In this work, the critical temperatures TC of the confined CH4 were estimated by fitting the coexisting data based on the usual power law. F ( µð1 -T=TC Þβ
ð2Þ
where β is the critical exponent of density order parameter. In Figure 4, it is evident that the phase diagram in the pore is largely (52) Smith, B. D.; Srivastava, R. Thermodynamic Data for Pure Compounds; Elsevier: Amsterdam, 1986.
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Figure 4. Coexistence curves for the bulk CH4 and hysteresis phase diagrams for CH4 confined in IRMOF-16.
Figure 5. Isotherms of CH4 confined in IRMOF-16, IRMOF-A4, and IRMOF-A5 at 100 K.
suppressed when compared with that of the bulk fluid, and the critical temperature in the pore is also lower than that of the bulk fluid. These variations can be attributed to the strong fluid-material interactions. 3.2. Effect of Pore Size on Capillary Phase Transitions. To study the influence of pore size on the phase transition behavior of CH4 in MOFs, simulations were further performed on the adsorption of CH4 in the two designed MOFs with larger pore sizes, i.e., IRMOF-A4 and IRMOF-A5. Figure 5 shows the full adsorption isotherms in the IRMOFs-16, -A4, and -A5 at 100 K. The equations Δμ = μSV - μSL and F( = FL - FV were adopted to calculate the difference of spinodal shown in Figure 5. The calculation results show that the Δμ for CH4 confined in IRMOF-16, IRMOF-A4, and IRMOF-A5 are 0.358, 0.425, and 0.547, respectively, and F( are 0.168, 0.193, and 0.218 g/cm3, respectively. These results indicate that the van der Waals loops for CH4 in IRMOF materials shrink with the decreasing of their pore sizes. The saturation chemical potentials of CH4 confined in IRMOF-16, IRMOF-A4, and IRMOF-A5 are shown in Figure 6. All the saturation chemical potentials were calculated in gauge cell MC simulations. Figure 6 illustrates that both temperature and pore size have significant effects on the saturation chemical potentials of CH4 confined in MOFs, which increase monotonically with increasing temperature as well as pore size. In addition, pore with smaller size causes a lower saturated vapor pressure at the same temperature because of a critical point shift. According to the properties of phase equilibrium, the saturated vapor pressure becomes smaller with the decrease of temperature, leading to a lower saturation chemical potential. Similar 5164 DOI: 10.1021/la903643f
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Figure 6. Saturation chemical potentials of CH4 confined in IRMOF-16, IRMOF-A4, and IRMOF-A5.
Figure 7. Coexistence curves for the bulk CH4 and hysteresis phase diagrams for CH4 confined in IRMOF-16, IRMOF-A4, and IRMOF-A5.
observations were also found in the adsorption of linear alkanes in single-walled carbon nanotubes (SWNTs).14 Comparisons of vapor-liquid coexistence curve for bulk CH4 and hysteresis phase diagrams for CH4 confined in IRMOF-16, -A4, and -A5 are shown in Figure 7. Evidently, all the phase diagrams of CH4 confined in IRMOFs are strongly suppressed relative to the bulk state, and the shift in the hysteresis critical point is found to increase with decreasing pore size. These variations can be attributed to the fact that smaller pore size induces lower energies due to more overlap of interactions between adsorbates and adsorbents. Furthermore, the shift in the hysteresis critical point from IRMOF-A4 to IRMOF-16 is larger than from IRMOF-A5 to IRMOF-A4, attributed to the differences in the interaction energies between adsorbate molecules and these materials. 3.3. Effect of Adsorption Energy on Capillary Phase Transitions. It is useful to know how the capillary phase transition varies with the adsorption energy. Thus, we investigated the effects of the adsorption energies on the phase behaviors of CH4 in three pairs of IRMOFs: (a) IRMOF-16 and IRMOFB3; (b) IRMOF-A4 and IRMOF-B4; and (c) IRMOF-A5 and IRMOF-B5. The calculated results in these three pairs of IRMOFs at 100 K are shown in Figure 8a-c. As can be seen from Figure 8a, the adsorption energy of CH4 confined in IRMOF-B3 with more aromatic carbon atoms in the organic linkers is larger than that in IRMOF-16 at a given temperature. Similar observations are also found in Figure 8b,c for the other two pairs. In addition, Figure 8 also shows that the difference of Langmuir 2010, 26(7), 5160–5166
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Figure 8. Adsorption energy of CH4 confined in (a) IRMOF-16 and IRMOF-B3, (b) IRMOF-A4 and IRMOF-B4, and (c) IRMOF-A5 and IRMOF-B5 at 100 K.
Figure 9. Isotherms of CH4 confined in (a) IRMOF-16 and IRMOF-B3, (b) IRMOF-A4 and IRMOF-B4, and (c) IRMOF-A5 and IRMOF-B5 at 100 K. Langmuir 2010, 26(7), 5160–5166
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Figure 10. Coexistence curve for the bulk CH4 and hysteresis phase diagrams for CH4 confined in IRMOFs: (a) IRMOF-16 and IRMOF-B3; (b) IRMOF-A4 and IRMOF-B4; (c) IRMOF-A5 and IRMOF-B5.
the adsorption energy between IRMOF-16 and IRMOF-B3 is larger than the other two pairs of IRMOFs, attributed to the smaller pore size of the former. The simulated isotherms for CH4 in the three pairs of IRMOFs at 100 K using the gauge cell MC method are shown in Figure 9. As can be seen from these figures, the van der Waals loops for CH4 in IRMOFs with condensed aromatic rings (IRMOF-B3, -B4, and -B5) are narrower than those in their corresponding counterparts. In addition, the hysteresis loop in IRMOF-B3 almost vanishes, indicating that the van der Waals loop shrinks with the increasing of adsorption energy as shown in Figure 8. Comparisons of the vapor-liquid coexistence curves for bulk CH4 and hysteresis phase diagrams for CH4 confined in the three pairs of IRMOFs ((a) IRMOF-16 and IRMOF-B3, (b) IRMOFA4 and IRMOF-B4, and (c) IRMOF-A5 and IRMOF-B5) are shown in Figures 10. In Figure 10a, CH4 confined in IRMOF-B3 shows lower critical temperature, higher critical density, and narrower coexistence curve than those for bulk CH4 as well as CH4 confined in IRMOF-16. Similar observations are also exhibited in Figure 10b,c. In addition, Figure 10a-c shows a critical point shift by adding more aromatic carbon atoms to the organic linkers, and the shift is more obvious in MOFs with smaller pore size. It can be explained as follows: the adsorption energy increases more significantly by the modification of MOFs with smaller size, leading to a larger shift of critical point. Therefore, this work demonstrates that modification of the organic linkers of MOFs with small pore size is a promising
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strategy to influencing the capillary phase transitions of fluids confined in them.
4. Conclusions The gauge cell MC simulations show that capillary phase transitions can occur in MOFs. Because of the geometry constraints and fluid-MOF interactions, the critical point of a fluid in confined space is shifted from the bulk phase to a lower critical temperature, a larger critical density, and a narrower coexistence curve. Temperature, pore size, and adsorption energy all have strong effects on the phase behaviors of fluids confined in MOFs; it is found that the critical temperature becomes lower, the critical density becomes higher, and the hysteresis loop becomes narrower with increasing temperature, decreasing pore size and increasing adsorption energy. The knowledge obtained in this work is helpful for understanding the adsorption behavior of gases in MOFs and provides useful information for guiding the future design of new MOFs with applications to the conditions dealing with phase transitions such as layering and freezing. Our future work will focus on a detailed understanding of the microscopic process of first-order phase transitions in MOFs. Acknowledgment. The authors thank Alexander V. Neimark and Jianwen Jiang for fruitful discussions. The financial support of the NSFC (Nos. 20725622, 20876006, 20821004, 20706002) is greatly appreciated.
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