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Evaluation of the BET Method for Determining Surface Areas of MOFs and Zeolites that Contain Ultra-Micropores € ur Yazaydın, and Randall Q. Snurr* Youn-Sang Bae, A. Ozg€ Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208 Received April 21, 2009. Revised Manuscript Received March 10, 2010 The BET analysis is commonly used for determining surface areas of metal-organic frameworks (MOFs) and zeolites that contain “ultra-micropores” ( IRMOF-9 > MFI > BOG > FAU > LTA) coincides with the order of the smallest pore of each material (Table 2), which is related to the adsorption energy at low pressures. For both nitrogen and argon isotherms,
(18) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990, 94, 1508. (19) Emmett, P. H.; Brunauer, S. J. Am. Chem. Soc. 1937, 59, 1553. (20) Atkins, P. Physical Chemistry, 6th ed.; W. H. Freeman and Company: New York, 1997.
(21) Zagrafskaya, R. V.; Karnaukhov, A. P.; Fenelonov, V. B. React. Kinet. Catal. Lett. 1981, 16, 223. (22) Horniakova, J.; Kralik, M.; Kaszonyi, A.; Mravec, D. Microporous Mesoporous Mater. 2001, 46, 287. (23) Schuster, C.; H€olderich, W. F. Catal. Today 2000, 60, 193.
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3. Results and Discussion
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Figure 2. Simulated isotherms for nitrogen at 77 K and argon at 87 K in three MOFs and five zeolites: (a) Comparisons of nitrogen isotherms in MOR and FAU with experimental data, (b) MOF isotherms on a linear scale (same legends as (d)), (c) zeolite isotherms on a linear scale (same legends as (e)), (d) MOF isotherms on a log scale, (e) zeolite isotherms on a log scale.
the order of the adsorbed amounts at saturated pressure is as follows: IRMOF-9 > IRMOF-13 > IRMOF-11 > FAU > LTA > BOG > MOR > MFI. This correlates well with the crystal densities and void fractions of the materials (Table 2). Compared to zeolites, IRMOFs show much higher nitrogen and argon adsorption due to their low framework densities and large void fractions. The BET surface areas of all materials were calculated from the nitrogen and argon isotherms in Figure 2. The BET surface areas 5478 DOI: 10.1021/la100449z
were obtained from two different pressure ranges: (1) using the consistency criteria,7 and (2) using the standard pressure range (0.05 < P/P0 < 0.30). Examples of the application of these two criteria for the nitrogen isotherm in IRMOF-13 are shown in Figures 3 and 4. In addition, the analogous figures for all of the other cases (nitrogen and argon adsorption for all eight materials) are provided in the Supporting Information (Figures S2 to S16). For the consistency criteria, the low pressure and the high pressure regions are shown separately to demonstrate how the Langmuir 2010, 26(8), 5475–5483
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Figure 3. An example of the BET surface area calculation based on the consistency criteria for IRMOF-13 using N2 adsorption at 77 K. (a) A plot of v (P0 - P) vs P/P0 for determining the first consistency criterion. (b) The selected linear plot, which satisfies the second consistency criterion, and the resulting BET surface area based on this. (c) Low pressure data and the heat of adsorption as a function of reduced pressure (red dashed line and right-hand axis). Solid symbols indicate the selected BET linear region and empty symbols indicate the points not used in the linear plot. (d) High pressure data (same legends as (c)).
BET linear range was chosen. Most of the figures show three regions in the BET plots as follows: (1) an initial short convex curve at low P, (2) a linear region at medium P, (3) a concave curve at high P. In the case of the standard BET analysis, four data points were used for each linear regression. All of the figures using the standard BET range clearly show that the data do not, in fact, fall on a straight line in this region but include the concave part of the curve. Figure 5 compares the surface areas from different methods. Figure 5a shows the BET surface areas calculated from nitrogen isotherms at 77 K and the accessible surface areas calculated from the crystal structures based on a nitrogen-sized probe, as well as experimental results from the literature. The BET surface areas calculated based on the consistency criteria (red) agree well with the accessible surface areas (black) within a 10% error margin except MOR (23.9%). This is an interesting result because the BET surface area and the accessible surface area are obtained from completely different routes. Moreover, the reasonably good agreement between the BET and the accessible surface areas is surprising, since all of the (24) Wong-Foy, A. G.; Matzger, A. J.; Yaghi, O. M. J. Am. Chem. Soc. 2006, 128, 3494. (25) Rowsell, J. L. C.; Yaghi, O. M. J. Am. Chem. Soc. 2006, 128, 1304. (26) Turov, V. V.; Brei, V. V.; Khomenko, K. N.; Leboda, R. Microporous Mesoporous Mater. 1998, 23, 189.
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MOFs and zeolites in this study except LTA and FAU have ultramicropores. The disagreement observed for MOR may come from the presence of the side pockets and is discussed in greater detail below. It is sometimes reported that the surface occupied by a nitrogen molecule is less than 16.2 A˚2 for microporous materials,27 but even though we used the traditional value of 16.2 A˚2, the BET surface areas based on the consistency criteria (red) match well with the geometrical surface areas (black). However, when the BET surface areas were calculated from the standard pressure region (green), they underestimated the geometrical surface areas (black). These results indicate that the BET surface areas of microporous materials should not be calculated based on the standard method but based on the consistency criteria. Another point in Figure 5a is that the BET surface areas reported in the literature from experimental nitrogen isotherms are much smaller than the accessible surface areas from the crystal structures. This may come from (1) defects in the real materials or (2) calculation of the BET surface areas from the standard pressure range. Interestingly, for all materials except IRMOF11, the experimental BET surface areas reported in the literature (yellow) agree well with the BET surface areas obtained from the (27) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982.
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Bae et al. Table 3. Selected Linear Ranges (P/P0) for BET Analysis Based on the Consistency Criteria
IRMOF-9 IRMOF-11 IRMOF-13 MFI MOR BOG LTA FAU
Figure 4. An example of the BET surface area calculation based on the standard pressure region for IRMOF-13 using N2 adsorption at 77 K.
Figure 5. Comparisons of surface areas from different methods: (a) accessible surface areas based on N2 probe, BET surface areas from GCMC N2 isotherms at 77 K, and BET surface areas from experimental N2 isotherms at 77 K (i, pressure range not reported; ii, 0.02 < P/P0 < 0.1; iii, 0.02 < P/P0 < 0.3; iv, 0.05 < P/P0 < 0.35),22-26 (b) same as (a) except using Ar probe and GCMC Ar isotherms at 87 K.
standard pressure range of the simulated isotherms (green). This may be because the experimental values were calculated using pressures closer to the standard BET pressure range. From the experimental reports, we know that the BET areas of IRMOF-13 and MOR were calculated using pressure ranges close to the standard BET range. In addition, the experimental BET areas of IRMOF-9, MFI, and FAU were reported without any information about the pressure range, but we can speculate they were calculated using the standard pressure range. For IRMOF-11, however, the experimental surface area is close to the accessible surface area because it was calculated from a lower pressure range 5480 DOI: 10.1021/la100449z
nitrogen isotherm at 77 K
argon isotherm at 87 K
0.0001-0.0499 0.00005-0.01 0.00005-0.01 0.00005-0.01 0.00005-0.005 0.0001-0.01 0.00001-0.0499 0.00005-0.01
0.0005-0.0499 0.0005-0.01 0.0001-0.01 0.0005-0.01 0.0005-0.0499 0.005-0.0499 0.005-0.0499 0.01-0.0499
(0.02 < P/P0 < 0.1) than the standard range. It is possible that the experimental BET area of IRMOF-11 might have matched even better with the geometric accessible surface area if it had been calculated based on the exact consistency criteria. These results demonstrate that the BET theory can be applied to experimental nitrogen isotherms for characterizing MOFs and zeolites that contain ultra-micropores (
