Surface Area Determination of Porous Materials Using the Brunauer

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Surface Area Determination of Porous Materials Using the BrunauerEmmett-Teller (BET) Method: Limitations and Improvements Priya Sinha, Archit Datar, Chungsik Jeong, Xuepeng Deng, Yongchul G. Chung, and Li-Chiang Lin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02116 • Publication Date (Web): 17 Jul 2019 Downloaded from pubs.acs.org on July 19, 2019

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The Journal of Physical Chemistry

Surface Area Determination of Porous Materials Using the Brunauer-EmmettTeller (BET) Method: Limitations and Improvements

Priya Sinha†#, Archit Datar†#, Chungsik Jeong‡, Xuepeng Deng†, Yongchul G. Chung*‡, and LiChiang Lin*†

†

William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State

University, Columbus, Ohio 43210, United States ‡

School of Chemical and Biomolecular Engineering, Pusan National University, Busan 46241,

Korea (South) # These

authors contributed equally to this work

* Corresponding authors: Y.G. Chung ([email protected]) and L.-C. Lin ([email protected])

ACS Paragon Plus Environment

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Abstract: Surface areas of metal-organic frameworks (MOFs) have been commonly characterized using the Brunauer-Emmett-Teller (BET) method based on adsorption isotherms of non-reactive nitrogen or argon. Recently, some discrepancies between surface areas computed from the BET method and those from geometric methods were reported in the literature. In this study, we systematically evaluated the BET and geometric surface areas of over 200 geometrically diverse real MOFs as well as CNTs with varying pore sizes as model systems to achieve a comprehensive understanding of the limitations of the BET and geometric methods. We compared the BET and geometric surface areas to the true monolayer area which is determined by directly counting the number of molecules included in the monolayer of surface from molecular simulation snapshots. Furthermore, we found that the excess sorption work (ESW) method, or a combination of ESW and BET methods, can potentially help facilitate more accurate estimation of the surface area, particularly in cases where the structures show relatively less complex isotherms having distinct steps.


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1. Introduction Metal-organic frameworks (MOFs) are an emerging1,2 class of crystalline, porous compounds, formed by connecting metal clusters with organic linkers. This combination of inorganic clusters and organic linkers creates a highly ordered three-dimensional network of channels and cages, and leads to a variety of attractive properties, such as large surface area and lower heat capacity, for selective adsorption and transport of gas molecules.3 Moreover, MOFs are highly tunable; different combinations of metal clusters and linkers can create materials with varying pore geometries, topologies, and functionalities. Because of these reasons, MOFs have been investigated for applications in gas storage3–5 (methane storage6/hydrogen storage7), catalysis8,9, adsorption separations10–19, drug delivery20,21, purification22–24 and sensors.25 Surface area is one of the most important physical properties of a MOF, and the accurate determination of the surface area in MOF is important for applications in gas storage23 or separation processes.26–29 There are two common approaches for computing the surface areas of MOFs: 1) the isotherm-based approach, which relies on computing the monolayer coverage on the basis of the Brunauer-Emmett-Teller (BET) theory, and 2) the geometry-based approach, which uses a probe molecule to roll over individual atoms to compute the available surface area. The former method is commonly used in experimental characterization of surface areas because it only requires a knowledge of the adsorption isotherm which can be relatively easy to measure. The Brunauer-Emmett-Teller (BET) theory30–33, which was initially developed to describe multi-layer adsorption34 of gas molecules on a solid surface, is typically used for this purpose. The BET analysis35 is performed based on the adsorption isotherms of non-reactive gas molecules (such as nitrogen at 77 K or argon at 87 K) at a range of pressures that covers the monolayer coverage of molecules. The obtained isotherms are transformed into the linearized BET plot, where the monolayer loading can be determined. Note that the approach can also be used on the basis of adsorption isotherms obtained from molecular simulations. On the other hand, the geometry-based approach36 which requires precise knowledge of structural coordinates, are more commonly used by the computational characterization of MOFs because the method is computationally faster than computing the entire isotherms.


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One of the issues with the BET method, however, is the choice of the linear region from the linearized BET plot. Conventionally, the linear region in the BET analysis was chosen from a relative pressure range (P/P0) between 0.05 and 0.30, known as the BET standard pressure range33,34,37 with the assumption that the monolayer formation will occur in this pressure range. However, in 2007, Rouquerol and coworkers38 suggested that the standard range is not well suited for microporous adsorbents, as monolayer formation in such structures occurs at very low relative pressures (P/P0 < 0.05). Snurr and coworkers39 have also demonstrated that the standard BET pressure range is not applicable for the cases of microporous MOFs because the pores get filled with adsorbate molecules at pressures well below the standard BET range. To remediate this issue, Rouquerol and coworkers38 proposed four consistency criteria for choosing the appropriate BET pressure range. The first criterion states that the linear region should only be a range of P/P0 in which the value of v(1- P/P0) monotonically increases with P/P0, where 𝜈 is the adsorbate loading. According to the second criterion, the value of the BET fitted constant (C) should always be positive. The third criterion states that the value of the monolayer loading capacity should correspond to a value of P/P0 which falls within the selected linear region. The fourth criterion advocates that the value of P/P0 calculated from the BET theory (1/( 𝐶+1)) and P/P0 calculated from the third consistency rule be equal (with +/- 10% tolerance). The fulfillment of only the first and second consistency criteria were common practice previously, such as during the characterization of MOF-21040, NU-10041, NU-10942 and NU-11042. This led to an ambiguity in the selection of the region to compute the surface area resulting in reports of extremely high surface areas for some of these materials. For instance, Senkovska and Kaskel43 showed, during the development of DUT-32, that by only considering the first and second consistency criteria, they could claim a surface area higher than 10,000 m2/g. However, more recent works such as those by Senkovska and Kaskel43, Farha and coworkers,44 and Snurr and coworkers45 have used all of the four consistency criteria. This practice has also been recommended in the IUPAC report (2015).46 While those consistency criteria have been found useful in standardizing the surface area estimation using the BET method, Kapteijn and coworkers47, Nicholson and coworkers48, as well as Snurr and coworkers45 have suggested that the ability of the BET approach to accurately estimate the accessible surface area can be largely subject to the pore size and its distribution in a structure. In the work of Kapteijn and coworkers47, the authors studied nitrogen adsorption on


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stacks of graphene sheets and found that the BET method significantly overestimates the surface area for a pore size of approximately 10 Å. For this pore size, the monolayer formation and porefilling (complete filling of the available space in a pore) become indistinguishable (i.e., simultaneously occur in the same pore) and cannot be differentiated on the basis of isotherm data. In this scenario, the BET method erroneously includes non-monolayer adsorbate molecules as monolayer loading, resulting in the overestimation of the surface area. In this work, we refer this as “pore indistinguishability”. Even when monolayer formation and pore-filling are distinguishable (i.e., monolayer formation and pore filling occur in different pressure regions), the BET method can overestimate surface areas as Snurr and coworkers45 observed for certain graphene slit pores. Snurr and co-workers concluded that the consistency rules do not always lead to the selection of the region corresponding to monolayer formation; the BET method may select a linear region which contains pore-filling (i.e., includes non-monolayer adsorbate molecules in the monolayer loading calculation). We note that Snurr and coworkers45 refer to the occurrence of including non-monolayer adsorbate molecules in the monolayer loading calculation as “porefilling contamination”. However, in this work, we refer the phenomenon as “pore-filling selection”, i.e., the one in which the monolayer and pore-filling regions are distinguishable, but the BET method selects a linear region that contains pore-filling for the calculation of monolayer loading. Therefore, pore-filling contamination, as defined by Snurr and co-workers, may be resulted from pore indistinguishability, pore-filling selection, a combination of both, or possibly other reasons. Overall, while the BET analysis is popular and has been found to be a useful method for characterizing porous materials, the reliability of the method in estimating the surface area of very large surface area materials with multimodal pore size distributions, such as MOFs, is still in debate. On the other hand, while the geometric method has been commonly regarded as a benchmark reference for surface areas, it may also be unable to represent the true available area for practical applications. It will, therefore, be useful to systematically test the applicability of current approaches for computing surface areas and suggest alternative or supplementary tools that can help more accurately determine the surface area of a material.


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With these objectives in mind, we performed a hierarchical and large-scale study on a set of over 200 MOFs with diverse geometrical features from the CoRE MOF (Computation-Ready, Experimental metal-organic framework) 2014 Database49 to probe the behavior of both the BET method and the geometric method, with a particular focus on the former. By employing molecular simulations, adsorption isotherms were computed for each of the structures for the BET analysis. The geometric areas of the MOFs can be determined based on their structural coordinates. To accurately assess these two methods with respect to the available surface area for practical applications, we further employed a new approach developed recently by Snurr and coworkers45 denoted as the true monolayer area hereafter. In this approach, molecular simulation snapshots from the isotherm calculations near saturation loading are analyzed, and every adsorbate molecule is categorized as being inside or out of the monolayer. The number of molecules inside the monolayer, referred to as “true monolayer loading”, are counted and the true monolayer area is accordingly determined. This area is believed to better represent the true area that is relevant to real applications. Furthermore, to better understand the aforementioned undesirable phenomena leading to the overestimation of the surface area by the BET method, we also used a series of single-walled carbon nanotubes (CNTs)50–52 of varying chiral indices, as our model porous solids. As noted above, the BET method relies on the accurate determination of monolayer loading from adsorption isotherm data alone, and the accurate determination of the surface area is subject to the choice of linear regions obtained from the adsorption isotherms. To aid in finding this loading, we also investigated the use of the excess sorption work (ESW) method.47,53 The ESW method54–56 is based on the thermodynamics of gaseous adsorption in porous solids and requires transforming the adsorption isotherm into the excess sorption work function as a function of loading, which helps in directly identifying the monolayer capacity by locating the first local minimum. We tested the applicability of the ESW method for computing the surface areas of MOFs. Furthermore, we propose a new approach combining the BET and ESW methods to help identify the correct BET linear region, which is critical in the accurate determination of the BET area, by choosing a linear region that includes the monolayer formation determined from the ESW method with the least deviation from the consistency criteria. We found that this combined method may offer a better estimation of the surface area in certain cases.


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2. Computational Methods A set of over 200 metal-organic frameworks (MOFs) with a wide range of pore sizes, based on largest cavity diameter (LCD), and geometric areas from the CoRE MOF 2014 Database49 was selected for this study. To determine their surface areas based on the BET method, argon adsorption isotherms at 87 K were computed by grand canonical Monte Carlo (GCMC) simulations using the open-source RASPA57 code. We note that argon at 87 K, for which the saturation pressure (𝑃0) is 1 bar, was used based on the latest recommendations of the IUPAC technical report46 as well as considerations of computational efficiency. In all the calculations, periodic boundary conditions were applied along all directions. The 6-12 Lennard-Jones (LJ) potentials were used to describe intermolecular interactions with parameters taken from the Universal Force Field (UFF)58 and from Reid et al.59 for framework atoms and argon, respectively. The LJ interaction parameters adopted in this work are summarized in Table S1 of the Supporting Information (SI). The Lorentz-Berthelot mixing rules were applied to calculate pairwise LJ parameters between dissimilar atoms. The LJ interactions were truncated at a cutoff radius of 12.8 Å. For each calculation, millions of Monte Carlo trial moves such as translation, reinsertion, and swap (insertion or deletion) were conducted to obtain statistically accurate uptakes. All framework atoms were kept fixed at their crystallographic positions throughout the simulations. The BET area calculations were then carried out by converting argon isotherms from the GCMC simulations into the BET plots. The linear regions were chosen such that they contained at least 4 points, had a high coefficient of determination (R2>0.998), satisfied the first two consistency criteria and as many of the third and fourth consistency criteria as possible. These regions were chosen by a tool which we have developed to systematically scan all possible linear regions and determine the one best suited for the BET method. More details about this tool can be found in SI section 3. The software has also been made available along with this manuscript. As will be discussed below, the linear region identified for most MOFs studied in this study satisfies all four consistency criteria, as shown in SI Figure S1. On the other hand, the geometric area was calculated using the Zeo++ software60 with argon as the probe molecule. In these calculations, a radius of 21/6𝜎 was used for each pairwise interaction between argon and the framework atoms, representing the minimum energy location of the potential. As introduced above, the true monolayer area was calculated by analyzing the molecular snapshots obtained from the GCMC simulations to count the number of gas molecules contacting the pore walls (i.e., the monolayer loading).


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Further, to better correlate the structural features with the behavior of the BET method, we also performed a pore size analysis using an in-house script. The algorithm meshes the unit cell of the structure into grid points along the crystallographic a, b, and c directions. Then, excluding the van der Waals radius of each atom, the shortest distance (radius) of each grid point to the structure was computed. The largest cavity diameter (LCD) was then identified by searching for the maximum radius while the pore size distribution was obtained from the volumetric contributions of the pores of each size. In this work, the values of the van der Waals radii were taken to be the same as those used in the Zeo++ software.60 For consistency, we defined the pore diameter (𝑑) as the diameter excluding the van der Waals radii of the framework atoms. The pore diameter for a particular pore is, therefore, effectively equivalent to the LCD of the structure if it were entirely composed that type of pores. We also constructed a series of armchair type (i.e., the chiral indices, n = m) single-walled carbon nanotubes (CNTs) of varying diameters using TubeASP61 as model porous solids with surface curvatures. These CNTs had chiral indices ranging from CNT-5-5 to CNT-35-35 (nomenclature is CNT-n-m) with pore diameters ranging from approximately 3 Å to 44 Å (i.e., micropores to mesopores) where the van der Waals radius for carbon atoms, as considered in the Zeo++ software60, was 1.7 Å. The LJ parameters 𝜎 and 𝜖 for carbon atoms of CNTs were calculated using the same approach as Jiang and coworkers50. These CNTs were taken as open-ended and infinitely long along the tube axis. Tubes were placed parallel to each other and the minimum intertubular distance between proximate tubes in the simulation domain was greater than the cutoff radius of 12 Å. Thus, the molecules inside one tube exert no potential on those inside other tubes, and they also do not experience interactions from proximate tubes. Grand canonical Monte Carlo simulations were also performed to compute the adsorption of argon molecules inside the CNTs. In these calculations, the interstitial spaces between tubes were blocked and no adsorption was allowed. For studying the combination of pores in CNTs, the isotherm for a given combination of CNT-pairs was calculated by summing the weighted average of adsorption loading values in each type of CNTs in the pair, assuming that the two CNTs are independent of and sufficiently separated from each other to be considered as freely floating. We note that, while isolation of tubes might be rare in practice, we found that the intertubular distance between proximate tubes does not


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drastically alter their adsorption behavior (see SI Figure S4 for details). Although these model systems may unable to fully represent complex pore systems, they could serve as model systems to probe the behavior of the BET, ESW and BET + ESW methods. The geometric areas were computed in the same way as they were for the MOF study.

3. Results and Discussion 3.1 Characterization of over 200 metal-organic frameworks Figure 1(a) and 1(b) summarize comparisons of the BET and geometric surface areas with the true monolayer area for over 200 MOFs, while Figure 1(c) and Figure 1(d) correspondingly show the relative errors of the BET and geometric areas with respect to the true monolayer area. Note that we are referring to the true monolayer as the accessible surface area that is more relevant to practical adsorption applications, and use it as the gold standard for comparison with other surface areas. Our results indicate that, overall, there is good agreement in BET, geometric, and true monolayer areas. However, in many cases, the BET method significantly overestimates the true monolayer area. The geometric method, on the other hand, can notably underestimate the true monolayer area. In this section, we show the discrepancies between the areas determined by these methods and discuss the underlying reasons causing the differences. For clarity, we classify the MOFs into three regions based on the true monolayer area: (i) smaller than 1500 m2/g, (ii) between 1500 m2/g and 3500 m2/g and (iii) larger than 3500 m2/g. The observations for each region are discussed below.


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Figure 1: Comparisons of BET and geometric area with true monolayer area for over 200 MOFs. (a) BET area versus true monolayer area. (b) Geometric area versus true monolayer area (c) Deviation of the BET area from true monolayer area versus true monolayer area (d) Deviation of the geometric area from the true monolayer area versus the true monolayer area. In (a) and (b), the gray lines represent deviation from true monolayer area in steps of 20 %. For results shown in (c) and (d), each point is further color coded to represent the volume fraction of large micropores and mesopores (i.e., pore diameter > 10 Å) and micropores with a pore diameter less than 4 Å, respectively.

3.1.1. MOFs with true monolayer area smaller than 1500 m2/g For structures in this region, the BET areas generally agree with the true monolayer areas while the geometric areas severely underestimated the true monolayer areas, with errors as large as 75%, as shown in Figure 1(c) and (d) respectively (Detailed data can be found in Table S2 of the SI). It is also apparent from Figure 1 (d) that a large number of structures in this region have a high volumetric percentage of micropores with a pore diameter less than 4 Å which is comparable to


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the size of the probe molecule used in the geometric method (21/6𝜎𝐴𝑟 = 3.8 Å). Thus, the probe molecule may be unable to access these pores. However, as modelled in molecular simulations, as well as in reality, argon can, in fact, access these pores because the interactions between the argon molecules and the framework atoms do not have an infinitely large repulsion wall. As a result, the geometric method highly underestimates the surface area for these structures. Similar observations were made by Kapteijn and coworkers47 as well as by Snurr and coworkers45. While for most structures, the BET areas agree very well with the true monolayer areas, there are still a few structures for which the BET areas significantly overestimate the true monolayer areas. These structures contain a sizeable amount of large micropores and mesopores as shown in Figure 1(a) and highlighted in Table S2. The reason for the overestimation by the BET method will be discussed in subsequent sections.

3.1.2. MOFs with true monolayer area between 1500 m2/g and 3500 m2/g For structures in this region, both BET and geometric methods generally predict the true monolayer area fairly well, even though a few outliers still exist. Detailed data can be found in Table S3 of the SI. These outliers fall into two categories: (i) surface area overestimation by the BET method and (ii) surface area overestimation by the geometric method. In this region, as summarized in Table 1, the overestimation of the surface areas by BET method is non-negligible, and can be as large as 72%. This overestimation by the BET method can be attributed to two reasons related to pore-filling contamination: (i) pore indistinguishability and (ii) pore-filling selection. Here, for the former, the monolayer formation and pore-filling occur simultaneously in a pore and the two phenomena cannot be differentiated on the basis of isotherm data. As such, the monolayer coverage, which is used as an input for BET area calculation, is overestimated because the adsorbate molecules filling the pores are also counted as part of the molecules covering the MOF surface. According to Kapteijn and coworkers37, this occurs in pores where 3 layers of adsorbate molecules form during saturation, corresponding to pore diameters in the range of approximately 2-3 times 21/6𝜎, where 21/6𝜎 is the Lennard-Jones well-depth. Figure 2(a) shows the argon isotherm in JEJWEB, which contains a single step. Figure 2(b-d) shows density maps adsorbate molecules taken in molecular simulation snapshots projected onto the xy plane (This method of presentation is used in all of the density maps shown in this article). From a detailed investigation of the density maps of adsorbates obtained from simulation snapshots as shown in Figure 2(b-d),


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we can clearly see that the pore-filling occurs before the monolayer formation is completed, indicating that the pore gets filled up simultaneously with the formation of the monolayer. Surface area overestimation by the BET method due to pore indistinguishability requires that the structure have pores of the right size. While it may be prevalent in many structures, it contributes to the overestimation of the surface area by the BET method most significantly when the structure has homogeneous pores. We observed this phenomenon most clearly for two structures in Table 1 (i.e., JEJWEB and VEBHUG) as they demonstrated homogeneous pore sizes, while other structures instead featured other pore filling contamination issues, such as pore-filling selection, which are discussed in subsequent sections. Table 1: Surface area overestimation cases by the BET method for structures having true monolayer areas between 1500 m2/g and 3500 m2/g. The column PSD shows the pore size distribution of the mesopores (Meso (M), pore diameter  20 Å), large micropores (Large (L), 20 Å> pore diameter  10 Å) and small micropores (Small (S), pore diameter < 10 Å). For columns BET and Geometric, the numbers in parenthesis indicate the percentage deviation from the true monolayer area. The column BET criteria indicates the fulfillment of the 3rd and 4th consistency criteria. Structure ID GUPBEZ02 CIGXIA cm901983a GULVUF SUNLET VETSOE RAVWUI VEBHUG LURRIA JEJWEB

True monolayer

LCD

PSD (%)

BET

BET criteria

Geometric

(m2/g)

(Å)

M/ L/ S

(m2/g)

3rd, 4th

(m2/g)

1579 1767 2044 2146 2405 2480 2893 3042 3352 3406

23.4 28.5 27.6 15.7 14.5 20.5 35.8 17.3 22.3 10.8

23/ 64/ 14 61/ 22/ 18 56/ 30/ 14 0/ 45/ 55 0/ 66/ 34 25/ 46/ 29 98/ 2/ 0 0/ 92/ 8 22/ 65/ 13 0/ 49/ 51

2070 (31) 2375 (34) 2935 (43) 2674 (24) 2900 (20) 3481 (40) 3537 (22) 4296 (41) 5776 (72) 4127 (21)

no, no yes, yes yes, yes yes, yes yes, yes yes, yes yes, yes yes, yes no, yes yes, yes

1741 (10) 1918 (8) 2093 (2) 2252 (4) 2367 (-1) 2520 (1) 2882 (0) 3781 (24) 4563 (36) 4009 (17)


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Figure 2: Pore indistinguishability identified in JEJWEB. (a) Adsorption isotherm with ochre region representing the BET region identified by the consistency criteria. (b) Loading density map at 100 Pa. (c) Loading density map at 1500 Pa, within the pressure region chosen by the consistency criteria for the monolayer formation. (d) Loading density map at 7500 Pa. In (b), (c) and (d), the loading density is the number of the adsorbate molecules per area (Å2). The green circles represent the pore. The framework is shown by a ball and stick model and the framework atoms are shown in gray for clarity. Regarding surface area overestimation by the geometric method observed in this region, we found that it tends to occur for structures containing small slit-like confined channels with a pore diameter roughly between 3.5 and 7 Å. The BET and true monolayer areas are comparable in these structures while the geometric area is significantly higher than the true monolayer area, suggesting that the geometric method may not accurately estimate the surface area in these structures. In these structures, two layers of adsorbate molecules cannot be actually formed, whereas the geometric method predicts two layers of adsorption due to its ignorance of the inaccessible space caused by the presence of gas molecules adsorbed on the adjacent layer that, in reality, prevents the formation


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of two layers. This phenomenon is also observed in structures in Section 3.1.3 below and an example is discussed there. Table 2: Surface area overestimation cases by the geometric method for structures having true monolayer area between 1500 m2/g and 3500 m2/g. The column PSD shows the pore size distribution of the mesopores (Meso (M), pore diameter  20 Å), large micropores (Large (L), 20 Å> pore diameter  10 Å) and small micropores (Small (S), pore diameter < 10 Å). For columns BET and geometric, the figures in brackets indicate the percentage deviation from the true monolayer area. The column BET criteria indicates the fulfillment of the 3rd and 4th consistency criteria. The 1st and 2nd criteria are always fulfilled in this study. True monolayer

LCD

PSD (%)

BET

BET criteria

Geometric

(m2/g)

(Å)

M/ L/ S

(m2/g)

3rd, 4th

(m2/g)

ETEJIX01

1560

6.5

0/ 0/ 100

1428 (-8)

yes, yes

1900 (21)

PUDSUD

1606

6.8

0/ 0/ 100

1475 (-8)

yes, yes

1955 (21)

VIRVEY

1762

7.1

0/ 0/ 100

1743 (-1)

yes, yes

2145 (21)

cg2007167

1892

6.2

0/ 0/ 100

1637 (-13)

yes, yes

2305 (21)

FOTNIN

2343

33.3

88/ 4/ 8

2312 (-1)

yes, yes

2962 (26)

KEFBII

2466

11.8

0/ 31/ 69

2515 (1)

yes, yes

3005 (21)

QUBZIX

2643

7.5

0/ 0/ 100

2584 (-2)

yes, yes

3324 (25)

OWITAQ

2886

7.1

0/ 0/ 100

2798 (-3)

yes, yes

4770 (65)

OWITOE

2905

7.1

0/ 0/ 100

2958 (1)

no, no

4838 (66)

VEBHUG

3042

17.3

0/ 92/ 8

4296 (41)

yes, yes

3781 (24)

HOJLID

3224

7.9

0/ 0/ 100

2937 (-8)

yes, yes

4415 (36)

CEKHIL

3330

8.6

0/ 0/ 100

3281 (-1)

yes, yes

4245 (27)

LURRIA

3352

22.3

22/ 65/ 13

5776 (72)

no, yes

4563 (36)

Structure ID

3.1.3. MOFs with true monolayer area larger than 3500 m2/g MOFs in this range are particularly important for gas storage purposes due to the strong correlation between the surface area and gas uptake.62 Figure 1(c) shows that most of the structures in this region have a combination of large micropores and mesopores due to which the BET method significantly overestimates the surface areas in these structures while the geometric method yields largely comparable areas to the true monolayer area (Detailed data can be found in Table S4 of the


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SI). This observation is in agreement with a previous study by Snurr and coworkers.45 However, there are still a few structures as shown in Table 3 for which the geometric method overestimates the surface area (> 20%). The discrepancies are, as discussed in Section 3.1.2, due to the formation of a narrow-slit region between proximate framework atoms in a part of the structure where only a single layer of adsorption is allowed. An illustrative example using SUKYON is given in Figure 3. Similar to the slit created by two graphene layers as reported by Kapteijn and coworkers47, those parallel-oriented organic linkers in SUKYON also analogously result in a region for single-layer adsorption and consequently lead to an erroneous geometry-based estimate in surface area. We note that, for MOFs in this region, the calculated geometric area is generally larger than the true monolayer area. This may be due to the relative inefficient packing of argon molecules near the surface for MOFs with larger porosity, as also pointed out by Snurr and coworkers.45 Table 3: Surface area overestimation cases by the geometric method for structures with true monolayer area greater than 3500 m2/g. The column PSD shows the pore size distribution of the mesopores (Meso (M), pore diameter  20 Å), large micropores (Large (L), 20 Å> pore diameter  10 Å) and small micropores (Small (S), pore diameter < 10 Å). For columns BET and Geometric, the numbers in parenthesis indicate the percentage deviation from the true monolayer area. The column BET criteria indicates the fulfillment of the 3rd and 4th consistency criteria. Structure ID XUTQEI GAGZEV BIBXOB SUKYON EFAYEQ HABQUY BAZGAM WIYMOG

True monolayer

LCD

PSD (%)

BET

BET criteria

Geometric

(m2/g)

(Å)

M/ L/ S

(m2/g)

3rd , 4th

(m2/g)

3547 3958 3989 4047 4195 4216 5099 5102

15.0 28.6 19.5 10.5 11.0 25.7 42.4 11.9

0/ 46/ 54 35/ 57/ 8 0/ 68/ 32 0/ 15/ 85 0/ 21/ 79 24/ 67/ 9 88/ 10/ 2 0/ 20/ 80

4132 (16) 7147 (80) 5184 (29) 3888 (-3) 4540 (8) 7525 (78) 7239 (41) 5115 (0)

yes, yes yes, yes yes, yes yes, yes yes, yes yes, yes yes, yes yes, yes

4288 (20) 5765 (45) 4930 (23) 4991 (23) 5074 (20) 5742 (36) 6613 (29) 6722 (31)


15


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Figure 3: Formation of a narrow slit for single-layer adsorption in SUKYON. This figure shows the density map of SUKYON at 1500 Pa, a pressure which lies in the linear region chosen by the BET method. The loading density is the number of the adsorbate molecules per area (Å2). The green rectangles show slit-like pores (𝑑 ≈ 6.2 Å) in which probe molecules form a single sheet. The framework is shown by a ball and stick model and the framework atoms are shown in gray for clarity. More importantly, in this region, significant overestimation of the surface area by the BET method commonly occurs which can be attributed to the pore-filling selection. Figure 4 illustrates the adsorption isotherm and the corresponding density maps of molecular simulation snapshots of SEMNIJ at three different pressures. In the density maps shown in Figure 4(b-d), the green circles denote smaller pores while the purple circle indicates the larger pores. At the pressure region chosen by the BET method, Figure 4(c) evidently shows that smaller pores are already condensed. As a result, this extra adsorbate loading which is erroneously counted as monolayer loading is the primary cause of pore-filling selection. As noted above, this has been found to be a common scenario in this region which causes surface area overestimation due to the BET method.


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Figure 4: Pore-filling selection in SEMNIJ. (a) Adsorption isotherm with ochre region representing the BET region. (b) Loading density map at 4000 Pa. (c) Loading density map at 9000 Pa. (d) Loading density map at 90000 Pa. In (b), (c) and (d), the loading density is the number of adsorbate molecules per area (Å2). The green circles depict the smaller pores (𝑑 ≈ 14.6 Å and 𝑑 ≈ 16.6 Å) and the blue circle depicts the larger pores (𝑑 ≈ 28.6 Å). The framework is shown by a ball and stick model and the framework atoms are shown in gray for clarity. Through our large-scale MOF study, we have demonstrated that while the BET and geometric methods are generally applicable for estimating the true monolayer surface area of a MOF, they have their limitations in characterizing porous materials with complex pore geometry and size. We have shown that the geometric method can highly underestimate the surface area, particularly in the case of microporous materials with a high volumetric percentage of pores with diameters less than 4 Å due to inaccessibility of probe molecules to certain pores. However, the geometric method overestimates the surface area for slit-like pores with diameters between 3.5 and 7 Å due to the fact that it counts two layers of adsorbates whereas, in reality, two layers of adsorbates cannot be formed due to the inaccessible space created by adsorbate molecules. The BET method, on the


17


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other hand, can significantly overestimate the surface area due to pore-filling contamination issues such as pore indistinguishability or pore-filling selection. The results agree with the conclusions from the previous investigation by Snurr and coworkers45, where the authors emphasized that caution needs to be exercised while applying the BET method for MOFs with large surface areas, especially for those that may have heterogeneous pore structures.

3.2. Study of a series of single-walled CNTs From our large-scale computational screening, it is clear that the presence of different sized pores within a single structure (i.e., structures with hierarchical pore structures) limits the applicability of BET method to accurately estimate the true monolayer area. In order to systematically evaluate the limitations of the BET method for hierarchical pore structures, we studied a system of CNTs containing cylindrical pores with varying sizes as model porous solids. Specifically, we computed BET and geometric areas for a series of single CNTs varying in chiral indices (CNT-5-5 to CNT35-35 (𝑑 from ~ 3 to 44 Å)), and a summary of the BET as well as geometric areas for these systems can be seen in Figure 5(a). To explore structures having combinations of pores with different sizes, systematic combinations of one CNT with all other CNTs were also investigated. For simplicity, we picked CNT-15-15 (d = 16.9 Å) as the base porous solid because it displayed the largest overestimation of the surface area by the BET method and studied its combination with each of the other CNTs. A summary of these areas is shown in Figure 5(b).


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Figure 5: Comparisons of surface areas computed by various methods for CNTs (a) Selected single CNTs (b) Selected combinations of CNTs with CNT-15-15 (d = 16.9 Å). The full figure (Figure S5 in the SI) that contains all of the CNTs studied in this work can be found in the SI and the corresponding data can be found in Tables S5 and S6 in the SI. By comparing the geometric and BET areas to the true monolayer areas for single CNTs, many discrepancies observed in MOFs can also be identified. In structures with small pores, as shown in SI Figure S6, for CNT-5-5 (d = 3.4 Å), we can find the inaccessibility issue as discussed in Section 3.1.1. The pore diameter of 3.4 Å for CNT-5-5 is smaller than 21/6𝜎, where 21/6𝜎 is the Lennard-Jones potential well depth between argon molecules and carbon atoms as well as the size of the probe used in the geometric method. This precludes the rigid probe molecule from being


19


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able to enter the pore, resulting in zero geometric area. In the case of CNT-11-11 (shown in SI Figure S7) with d = 11.5 Å, we also observe a surface area overestimation by the BET method due to pore indistinguishability. Furthermore, in the cases of CNT-12-12 to CNT-17-17 (𝑑 between 12.9 Å and 19.7 Å), overestimation issues caused by pore-filling selection are found. In these cases, unlike the pore indistinguishably issue where the monolayer and the pore-filling occur simultaneously, the BET analysis chooses the wrong linear region as the monolayer region, as illustrated in Figure 6 using CNT-15-15 (d = 16.9 Å) which showed the highest surface area overestimation by the BET method with respect to the true monolayer area. The pore in CNT-1515 (d = 16.9 Å) is sufficiently large to accommodate 3 layers of adsorbate molecules. Following the BET consistency criteria results in a selection of a monolayer region that already has the first layer completed filled up, where the second and third layers have also been formed.

Figure 6: Pore-filling selection in CNT-15-15 (d = 16.9 Å). (a) Adsorption isotherm with ochre region representing the BET region (b) Loading density map at 9.75 Pa. (c) Loading density map at 40 Pa. (d) Loading density map at 2500 Pa. In (b), (c) and (d), the loading density is the number of adsorbate molecules per area (Å2). Framework atoms are shown by a ball and stick model in gray for clarity.


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As seen in our MOF study as well as other studies45,47,63 the BET method tends to overestimate the true monolayer surface area for structures possessing pores with distinct pore size combinations. Interestingly, our results of mixture CNTs also show, as can be seen in Figure 5(b), that the BET method indeed consistently overestimated the surface area while the true monolayer and geometric areas were comparable. Overall, we generally observed surface area overestimation due to two pore filling-related issues: those occurring in a uniform pore and the one occurring in heterogeneous pores. In the former, as shown with reference to CNT-15-15 (d = 16.9 Å) in Figure 6, there are two potential regions. One corresponds to the monolayer loading while the other to pore filling in the same pore. On the other hand, in the latter, for a combination of CNT-15-15 (d = 16.9 Å) and other CNTs (e.g., see SI Figure S8 for an illustrative example of CNT-15-15 and CNT-22-22), the monolayer loading of the larger pore overlaps with pore filling in the smaller pore. This type of pore-filling selection typically occurs when a structure contains large micropores and mesopores.

3.3. Improvements in surface area characterization 3.3.1. ESW method It is clear now that the determination of surface area of a structure using the BET method may not always be reliable. As an alternative, the excess sorption work (ESW) method can be used to locate the monolayer formation and compute the surface area of materials on the basis of adsorption isotherm data. The ESW method was originally proposed by Adolphs and Setzer53 in 1996 with the aim of directly determining the monolayer loading from an adsorption isotherm without having to resort to models. In the ESW method, the adsorption isotherm is first transformed into a plot of excess sorption work versus loading through Equation 1. 𝜙 = 𝜈𝑅𝑇ln 𝑃/𝑃0

(1)

where 𝜙 is the excess sorption work, 𝜈 is the adsorption loading, R is the universal gas constant, T is the temperature, and 𝑃/𝑃0 is the relative pressure. The surface area can be then computed by identifying the first minimum from the ESW plot as the monolayer loading and then multiplying it with the cross-sectional area of the adsorbate molecules (for argon, Across=0.142


21


Page 22 of 38

nm2/molecule47). Figure 7 illustrates the use of the ESW method. The isotherm in Figure 7(a) was transformed into the ESW plot as shown in Figure 7(b). The first ESW minimum was identified with the loading corresponding to the relative pressure P1, and the area was computed from the ESW loading. To demonstrate the effectiveness of the ESW method, we first applied it to our CNT model systems of CNTs and compared the results with true monolayer loading. Interestingly, as shown in Figure 5(a), the ESW areas for single CNTs with varying sizes are comparable to the true monolayer areas as well as geometric areas. As shown in Figure 7 for CNT-15-15 (d = 16.9 Å), the monolayer loading chosen by the ESW method indeed does not include non-monolayer adsorbate molecules (i.e., corresponding to the loading density shown in Figure 6(c)), unlike the BET method, even though the BET region (ochre in Figure 6(d)) satisfies all four consistency criteria. The results illustrate that the ESW method can be used to correctly identify the monolayer formation and estimate the true monolayer area. Moreover, Figure 5(b) shows that the ESW method works well for correctly predicting the surface area for the combination of CNT pores, and an illustrative example can be seen in Figure S8 for the mixture of CNT-15-15 (d = 16.9 Å) and CNT-22-22 (d = 26.4 Å).

Figure 7: Illustration of the ESW and BET + ESW methods on CNT-15-15 (𝑑 = 16.9 Å). (a) Adsorption isotherm (b) ESW plot. Ochre represents the BET region while green represents the BET + ESW region. Relative pressure P2 = 0.0004 (pressure = 40 Pa) corresponds to the first ESW minimum and the pressure shown in Figure 6: Pore-filling selection in CNT-15-15 (d = 16.9 Å).


22

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(a) Adsorption isotherm with ochre region representing the BET region (b) Loading density map at 9.75 Pa. (c) Loading density map at 40 Pa. (d) Loading density map at 2500 Pa. In (b), (c) and (d), the loading density is the number of adsorbate molecules per area (Å2). Framework atoms are shown by a ball and stick model in gray for clarity.(c) while relative pressure P3 = 0.025 (pressure = 2500 Pa) corresponds to the pressure shown in Figure 6: Pore-filling selection in CNT-15-15 (d = 16.9 Å). (a) Adsorption isotherm with ochre region representing the BET region (b) Loading density map at 9.75 Pa. (c) Loading density map at 40 Pa. (d) Loading density map at 2500 Pa. In (b), (c) and (d), the loading density is the number of adsorbate molecules per area (Å2). Framework atoms are shown by a ball and stick model in gray for clarity.(d).

3.3.2. BET + ESW method Although the area predicted by BET method may be unreliable for certain types of structures, it has been widely adopted by the adsorption community to characterize porous materials. Given that the ESW method can locate the monolayer formation region for the model CNT system, we propose to incorporate the ESW method in the surface area determination using the BET method and call it the BET + ESW method. We propose that the BET linear region be chosen such that it includes the relative pressure point corresponding to the first minimum from the ESW plot as shown in Figure 7, while also satisfying the first and second consistency criteria for BET analysis. The motivation behind proposing this method was that, in some cases, especially those of large surface area structures, there are multiple regions that satisfy the 1st and 2nd criteria and have a high R2 value (R2 > 0.999) while some additionally satisfy either one or both of the 3rd and 4th criteria. Following the currently used BET method, one would select a linear region that satisfies as many criteria as possible (i.e., all four criteria). However, as shown above, this resulting region can erroneously include pore filling, thus highly overestimating the surface area. Choosing a linear region that doesn’t fulfill all four criteria (i.e., only the 1st and 2nd criteria) may possibly yield a more reasonable area prediction. However, the main challenge remains to decide which linear region to choose. A similar scenario can also occur when we have several regions satisfying only the 1st and 2nd criteria but not the 3rd and 4th criteria. Incorporating the ESW method into the determination of the linear region can help make this choice. Overall, the BET + ESW method


23


Page 24 of 38

ensures that the region we choose includes monolayer formation located by the ESW method, thus providing a reasonable theoretical basis in estimating the true monolayer surface area. To illustrate the application and effectiveness of the BET + ESW method, we again use the example of CNT-15-15 (d = 16.9 Å, shown in Figure 7). CNT-15-15 (d = 16.9 Å) can accommodate three layers of adsorbate on the surface, and this corresponds to at least two potential linear regions: the first linear region which fulfills the first and second criteria, and the second linear region which fulfills all four criteria. In such scenarios, the second linear region was chosen by the BET method in order to fulfill all the consistency criteria as highlighted in the ochre region in Figure 7(a), but it incorrectly includes pore filling in the monolayer formation region, i.e. porefilling selection, resulting in surface area overestimation by the BET method (Figure 6). By incorporating the monolayer information from the ESW method, the monolayer region can now be correctly selected (i.e., green region in Figure 7(a)) and yield a correct estimate of the surface area as compared to the true monolayer one. Overall, on comparing the BET areas with the corresponding BET + ESW areas (Figure 5(a)), it is evident that the overestimation issue for single CNTs has been significantly reduced. The same conclusion can be seen in Figure 5(b) for the CNT mixture, where incorporating the ESW minimum criterion leads us to identify the correct BET linear region. While CNT-15-15 (d = 16.9 Å) was a case of homogeneous pore structures, we also observe the same result for heterogeneous pore configurations, for example, a mixture of CNT15-15 (d = 16.9 Å) and CNT-22-22 (d = 26.4 Å) as shown in SI Figure S8. Again, the BET method selects a linear region satisfying all four consistency criteria, but overpredicts the true monolayer area due to pore-filling selection. Using the BET + ESW method, however, the agreement between calculated area and true monolayer surface area is excellent by selecting a linear region satisfying only the first and second criteria but including the ESW minimum. Thus far, we have shown that the ESW and BET + ESW are both promising methods for better estimating the true monolayer surface area in systems like CNTs. An automatic tool has been made available along with this study for computing these areas, and details can be found in the SI section 3. However, we note that in cases where there is surface area overestimation due to pore indistinguishability, i.e. monolayer filling and pore-filling occur simultaneously, (for instance in single CNT-11-11 (d = 11.5 Å)), neither ESW nor BET + ESW methods can reduce the error. In


24

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this case, as shown in SI Figure S9, the ESW plot shows a single minimum that corresponds to the simultaneous formation of monolayer and pore-filling, and therefore neither the ESW nor the BET + ESW methods can correctly estimate the monolayer surface area.

3.3.3. Application of improvement methods to the MOF study We have further applied the ESW and the BET + ESW methods to selected MOFs in this study. Figure 8 shows the comparison of BET and ESW areas for MOF structures having surface area overestimation by the BET method of greater than 30%. A significant improvement can be seen when the ESW method is used. For instance, in structures such as ADATAK, BAZGEQ, DAWMUL, ja809985t, QIYDIN, RAYMOV, the overestimation error was brought down from 31%, 85%, 31%, 56%, 37%, 32% respectively to less than 20% using the ESW method alone. However, there are structures for which the ESW areas are comparable to the BET areas. For instance, for structures such as HABQUY, SEMNIJ, XUKYEI which feature multilayer adsorption in the structures before the monolayer is fully formed (i.e., the pore indistinguishability) as illustrated in SI Figure S10. We note that, while the ESW method generally provides a better estimate of the area in high surface area materials, it tends to moderately underestimate the area for structures with a relatively smaller surface area as shown in Figure S11. In some cases, the ESW method substantially underestimates the area because of the presence of a pore with a rather small diameter occupying a large volume fraction. This leads to a minimum on the ESW plot which is picked up as the first minimum. However, at this point, the larger pore doesn’t have monolayer filling leading to the predicted area being underestimated. Thus, caution needs to be exercised during the application of the ESW method. Nonetheless, ESW does appear to be a promising approach in the estimate of the true monolayer area.


25


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Figure 8: Comparison of the areas computed by using the BET and ESW methods for MOFs with surface area overestimation by the BET method greater than 30%. These structures shown in the figure are sorted based on the absolute value of error using the ESW method. Detailed data can be found in Table S7 in the SI. The BET + ESW method can also be effective as it can improve the estimation of the true monolayer surface area. As mentioned in Sec 3.3.2, by incorporating the ESW method, we can choose a linear region that avoids the inclusion of non-monolayer adsorbate molecules in the calculation of monolayer loading, irrespective of the fulfillment of the consistency criteria. The application of the BET + ESW method in MOFs is illustrated using the example of ICAQIO, as shown in Error! Reference source not found. Figure 9 and for other MOFs as shown in Table 4 and in Figures S12-S15 in the SI. As can be seen from these figures, similar to that discussed for CNTs, there exist two distinct minima in the ESW plot, and the linear region identified by fulfilling all four consistency criteria tends to be close to the second minimum in the ESW plot (i.e., larger loading where pore-filling is erroneously included as highlighted in Figure 9(d)). In cases such as cm901983a and ICAQIO, the BET method overestimates the true monolayer area by 44% and


26

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25%, respectively, whereas the BET + ESW method is able to bring the error down to 9% and 4%, respectively. On the other hand, in cases such as CUSYAR, GAGZEV, and SEMNEF, the BET + ESW method doesn’t improve the estimation of the true monolayer area, but yields the same estimate as that made by the BET method alone. This occurs because, the isotherm, which represents a multimodal pore size distribution, is complicated and does not show a clear first minimum corresponding to the monolayer formation. However, we note that, in OKUSOE, a distinct first minimum exists, but it corresponds to a pore size which is so small that it condenses before the monolayer filling of the larger pore is completed. This results in a significant underestimation of the surface area. In the case of NIHWIN, we are unable to find a region that satisfies all of the BET as well as the ESW condition, thus not providing an estimate of the BET + ESW area. Overall, while the BET + ESW method cannot provide improvements to all BET overestimation cases, it is particularly useful for structures with step-wise isotherms which correspond to distinct minima in the ESW plot; that is, isotherms that contain steps distinguishing monolayer and multi-layer adsorption. Thus, we recommend that the BET + ESW method not be used as a stand-alone method, but instead be used as a supplement to the BET method — a “second line of defense” against overestimation — for structures with the aforementioned adsorption characteristics. As shown above, the BET + ESW method works very well for CNT model systems with rather simple pore features and step-wise isotherms. On the other hand, based on our study of the application of this method to MOFs, we found that only a portion of MOFs display such isotherms. In our study, we had 36 structures where the BET method overestimated the surface area by over 20%. Of these, the BET + ESW method was able to reduce the deviation for 11 structures and 7 of them are within 20% of the true monolayer area. While the applicability of BET + ESW method may appear to remain fairly limited for MOFs, a further study should be able to help extend its applicability, e.g., exploring methods other than ESW to help better locate the monolayer region. It can then be subsequently integrated with the BET method, using the same idea as in the proposed BET+ESW method. Table 4: Comparison between the true monolayer area and the BET and BET + ESW areas for some selected MOF structures. The column PSD shows the pore size distribution (PSD) of the mesopores (Meso (M), pore diameter  20 Å), large micropores (Large (L), 20 Å> pore diameter  10 Å) and small micropores (Small (S), pore diameter < 10 Å). For columns BET and BET +


27


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ESW, the figures in brackets indicate the percentage deviation from the true monolayer area. The columns BET and BET+ESW criteria indicate the fulfillment of the 3rd and 4th consistency criteria. A visual representation can be found in SI Figure S16. Name

Common name

True mono

LCD

PSD (%)

BET

BET 3rd,

Geometric

BET+ESW

BET+ESW

(m2/g)

(Å)

M/L/S

(m2/g)

4th

(m2/g)

(m2/g)

3rd, 4th

BUFPAU

-

1294

17.5

0/ 67/ 33

1687 (30)

yes, yes

1369 (5)

1180 (-8)

no, no

CIGXIA

MIL-100 (Fe)

1767

28.5

61/ 22/ 18

2375 (34)

yes, yes

1918 (8)

2075 (17)

no, no

cm901983a

MIL-100 (Al)

2044

27.6

56/ 30/ 14

2935 (43)

yes, yes

2093 (2)

2231 (9)

no, yes

GULVUF

-

2146

15.7

0/ 45/ 55

2674 (24)

yes, yes

2252 (4)

1934 (-9)

no, no

VETSOE

POST-65 (Mn)

2480

20.5

25/ 46/ 29

3481 (40)

yes, yes

2520 (1)

1923 (-22)

no, no

JEJWEB

-

3406

10.8

0/ 49/ 51

4127 (21)

yes, yes

4009 (17)

4083 (19)

no, yes

ja809985t

UMCM-2

3815

22.7

45/ 36/ 19

5946 (55)

no, yes

4380 (14)

4869 (27)

no, no

GAGZEV

NU-100

3958

28.6

35/57/8

7148 (80)

yes, yes

5765 (46)

7170 (81)

yes, yes

BAZGEQ

MOF-388

4150

27.0

45/ 39/ 15

7684 (85)

no, no

4589 (10)

6476 (56)

no, no

ICAQIO

DUT-23 (Co)

4403

20.2

25/ 44/ 31

5495 (24)

yes, yes

4682 (6)

4544 (3)

no, no

OKUSOE

DUT-49

4574

24.3

41/43/16

4682 (2)

no, no

4964 (9)

1944 (-57)

no, no

CUSYAR

MOF-210

5257

27.8

41/49/10

8203 (56)

yes, yes

5715 (9)

8203 (56)

yes, yes

NIHWIN

DUT-60

5574

32.3

69/27/4

8254 (48)

no, no

6144 (10)

-

-

SEMNEF

NU-109

5783

30.8

38/55/7

9120 (58)

no, yes

5952 (3)

9120 (57)

no, yes


28

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Figure 9: Improvement in area estimation of ICAQIO with the BET + ESW method. The ochre region corresponds to the region selected by the BET method while the green region corresponds to the one selected by the BET + ESW method. (a) Adsorption isotherm (b) The corresponding ESW plot (c) Loading density map at 500 Pa. (d) Loading density map at 3000 Pa. In (c) and (d), the loading density is the number of adsorbate molecules per area (Å2). The green circles indicate the pores that get filled up at a pressure within the BET-chosen region. Framework atoms are shown as a ball and stick model in gray for clarity.


29


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4. Conclusions In this work, we investigated a diverse set of MOFs and CNT systems to understand the behavior of methods such as BET, ESW, the proposed ESW+BET, and geometric method by comparing them to the true monolayer area method which uses molecular configurations obtained from simulations. Overall, we found that: i) the geometric method can accurately predict the surface area for structures that do not contain very small pores that are inaccessible to the probe molecule or slit-like pores where only a single layer of adsorbates forms; and ii) the BET method is indeed a useful surface area analysis tool, and in general, provides a fair estimate of the true monolayer surface area using the linear region chosen by applying all the four consistency rules. However, the consistency rules do not always help in locating the correct monolayer formation region, in particular for MOFs with large surface areas that are of particular interest to storage and other applications. This limits the reliability of the BET method in estimating the surface areas of high surface area MOFs with multimodal pores due to overestimation of the BET areas. To facilitate reliable characterization of surface areas, we found that, compared to the BET method, the ESW method can generally reduce the deviation with the true monolayer area, particularly for high surface area materials. Furthermore, considering the popularity of BET method, we also propose the so-called BET + ESW method to help locate the correct BET linear region, which can serve as a supplemental method to the BET approach. This new approach can be applied to structures having isotherms with distinct steps corresponding to monolayer and multilayer loading, and we have shown that it can yield improved predictions of the surface area. Although further studies are still needed to extend the applicability of the ESW and BET+ESW methods for the estimation of surface area for porous materials, the outcomes of this study have shown that these methods could be potentially promising to facilitate a more meaningful determination of surface areas of porous materials. The code to compute the BET, ESW, ESW+BET, and the BET areas has been made available along with this work.


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXXX. Force field parameters, satisfaction of the BET consistency criteria for MOFs, details of the calculations for BET, ESW and BET + ESW areas, additional data for analysis of MOFs, additional data for analysis of CNTs, and results of the ESW and BET + ESW methods applied to MOFs. A script to estimate surface areas of materials from their isotherms (SESAMI) is also included as part of the supporting information.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Y.G. Chung) *E-mail: [email protected] (L.-C. Lin)

Author Contributions The study was developed and completed through contributions by all authors.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS Y.G.C thanks the financial support from the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (NRF-2016R1D1A1B03934484) and the computational time provided by KISTI (KSC-2018-CHA-0075) for initial phase of the work. The authors gratefully acknowledge the Ohio Supercomputer Center (OSC)64 for providing computational resources.


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Table of Content (TOC) Graphic


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Surface Area Determination of Porous Materials Using the Brunauer

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