Assessing the Surface Area of Porous Solids - ACS Publications

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Assessing the Surface Area of Porous Solids: Limitations, Probe Molecules, and Methods Martijn F. de Lange,*,†,‡ Li-Chiang Lin,§ Jorge Gascon,‡ Thijs J. H. Vlugt,† and Freek Kapteijn*,‡ †

Engineering Thermodynamics, Process & Energy laboratory, Delft University of Technology, Leeghwaterstraat 39, 2628CB Delft, The Netherlands ‡ Catalysis Engineering, Chemical Engineering Department, Delft University of Technology, van der Maasweg 9, 2629HZ Delft, The Netherlands § William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, Ohio 43210, United States S Supporting Information *

ABSTRACT: In this modeling study, the uses of nitrogen (77.3 K), probe molecule of choice for decades, and argon, opted as alternative in the 2015 IUPAC report on adsorptive characterization, as probe molecules for geometric surface area determination are compared. Graphene sheets possessing slit-shaped pores with varying size (width) are chosen as model porous solids, and different methods for the determination of specific surface areas are investigated. The BET method, which is the most commonly applied analysis, is compared to the Langmuir and relatively recently proposed ESW (excess sorption work) method. We show that either using argon or nitrogen as adsorptive, the physical meaningfulness of adsorptionderived surface areas highly depends on the pore size. When less than two full layers of adsorbate molecules can be formed within slitlike pores of a graphitic material (Dpore < 5.8 Å for Ar/N2), adsorption-derived surface areas are about half that of the geometric surface area. Between two and four layers (6.8 < Dpore < 12.8 Å), adsorption surface areas can be significantly larger (up to 75%) than the geometric surface area because monolayer−multilayer formation and pore filling cannot be distinguished. For four or more layers of adsorbate molecules (Dpore > 12.8 Å), adsorption-derived surface areas are comparable to their geometrically accessible counterparts. Note that for the Langmuir method this only holds if pore-filling effects are excluded during determination. This occurs in activated carbon materials as well. In the literature, this indistinguishability issue has been largely overlooked, and erroneous claims of materials with extremely large surface areas have been made. Both the BET and Langmuir areas, for Dpore > 12.8 Å, correspond to geometric surface areas, whereas the ESW method yields significantly lower values. For the 6.8 Å < Dpore < 12.8 Å range, all methods erroneously overestimate the specific surface area. For the energetically homogeneous graphene sheets, differences between argon and nitrogen for the assessment of surface areas are minor.

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INTRODUCTION The most followed road to obtain textural information on porous material samples is via physisorption of gas molecules.1 This yields information on a material’s pore volume, pore size distribution, and, the focus of this work, its specific surface area,2 which is essential for the application of porous solids in catalysis, gas separation, storage, etc. Traditionally, nitrogen at its normal boiling point (77.3 K) has been the probe molecule of choice, for specific surface areas >5 m2 g−1, as previously advocated by the IUPAC.3,4 A major reason for such a recommendation can be attributed to the vast availability of liquid nitrogen.5 However, the quadrupole moment of nitrogen makes this adsorptive susceptible to surface inhomogeneities.5 Coulombic interactions may influence the arrangement of diatomic nitrogen on surfaces, which may in turn cause adsorption-derived properties to be erroneous.5 Hence, in the recent 2015 IUPAC report on adsorptive characterization, © 2016 American Chemical Society

argon (at 87.3 K) has been suggested as an alternative because of the absence of a quadrupole moment.5 This would make surface area quantification less dependent on surface chemistry.5 Previous studies that revolve around the comparison of argon and nitrogen have focused primarily on the differences in derived pore size distributions.5−8 Additional advantages of argon are that pore filling occurs at a higher relative pressures, making it easier to assess a material’s pore structure,5 and moreover narrower pores can be identified than by using nitrogen.6,8 The comparison of specific surface areas using either nitrogen or argon has been limited to zeolites with very narrow micropores ( 12.8 Å, the geometric and BET area are in good agreement, though SGEO is consistently ∼10% larger than SBET. This tends to corroborate with previous studies, especially with relatively large pore size metal−organic frameworks (MOFs).17,23,24 For Dpore < 5.8 Å, the BET areas are roughly half the geometric surface areas, avoiding the issues with “roll-up” overlap (by e.g. reducing geometric surface area probe molecule radius; see Figure S31). For these narrow pores, no more than one layer of adsorbate molecules can be formed between two neighboring sheets. In fact, for Dpore ∼ 3.24 Å, less than a full monolayer is formed (see Figure 4a−d). Note that the so-called pore size is the pore limiting size. As carbon atoms in these rigid stacked graphene sheets are shifted along the vertical direction only, the van der Waals radii of these atoms make larger spaces than 3.24 Å available for adsorbate molecules to adsorb in. The fact that only one layer of adsorbate molecules can be formed indicates that the contribution of each adsorbate molecule is divided over two sheets, thus reducing SBET by half. For 5.4 < Dpore < 5.8 Å, slightly more than one full adsorbate

nor assumptions need to be made regarding isotherm shape or adsorption behavior. The excess sorption work function, Φ (in joules per gram adsorbent), is defined as Φ=q

vap ρSTP

Mi

Δμ (9)

The chemical potential of adsorption is subsequently written as Δμ = RT ln x

(10)

Plotting Φ as a function of q will yield at least one minimum in the excess sorption work function. One of these minima, in this work always the first (vide inf ra), corresponds to monolayer completion. The loading corresponding with this minimum in Φ (Φmin) is the ESW monolayer capacity, qESW. This loading can then simply be converted, like the BET and Langmuir area, to the ESW area via SESW =

vap qESW ρSTP NAAcs, i

Mi

(11)

Lastly, qESW can be used to normalize the ESW function to ϕ=

Δμ θESW = θESW ln x RT

(12)

Here φ (in units of RT) is a measure of degrees of freedom lost per mole of adsorbate, and θESW is the fractional coverage,13−16 defined as q θESW = qESW (13)

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RESULTS AND DISCUSSION In this section, first the applicability of the BET method as a function of slit pore size is elucidated. Next, the differences between argon and nitrogen as probe molecule are discussed, and finally the BET method is compared with the two other methods for surface area determination. BET Area versus Pore Size. The geometric surface areas of all graphene sheets are determined using both argon and nitrogen as probe molecule and depicted as a function of pore size (Figure 2). Clearly, for Dpore > 5−6 Å, the geometric surface areas of argon and nitrogen are similar. In this range, the minor differences in the probe molecule radii do not result in 12667

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multilayer adsorption and micropore f illing” for microporous materials,5 the report does not specify for which pore sizes this may occur, nor are there clear restrictions on the use of the BET method for microporous materials, yet. As shown in Figure 5a,c for both argon and nitrogen, monolayer−multilayer formation and pore filling are clearly distinguishable for Dpore ≥ 12.8 Å. This is also shown in the Rouquerol plots (see Figure 5b,d) as two distinct peaks are visible for each isotherm. For Dpore > 12.8 Å, evidently, applying the criterion that q(1 − x) should monotonically increase, which automatically disregards pore filling in the BET area determination and therefore results in comparable SBET and SGEO. For a pore size of 12.8 Å, the parts of the isotherm belonging to monolayer−multilayer formation and pore filling are not separated by a segment in the Rouquerol plot for which q(1 − x) decreases. Special care was taken to ensure that pore filling was not erroneously included in the BET area determination for this particular pore size, by manually omitting the second steep increase in the Rouquerol plot (see Figure 5b,d). This is also an indication that care must be taken to select the proper relative pressure window, even when all consistency criteria are being used. For Dpore < 12.8 Å, pore filling and monolayer−multilayer formation are increasingly harder to distinguish with decreasing pore size (see Figure 5a,c). The obtained BET areas for 5.8 < Dpore < 12.8 Å erroneously include pore filling to varying extent. For Dpore ∼ 10 Å, the deviation of SBET from SGEO is the largest as mentioned. At this pore size, about three layers of adsorbate molecules are formed (see Figure 6e−h), making the distinction between monolayer formation and pore filling the hardest. This can be explained as follows: During the formation of the third layer, adsorbate molecules are already located on both opposite sides of the graphene sheets. Addition of adsorbate molecules in between as a third layer gains attractive interactions with the adjacent molecules on the two graphene sheets that make up the pore, as can be seen from free energy profiles (Figure S32). Because of overlapping of adsorption potentials of adjacent atoms, the adsorbate molecules in this third layer are very strongly adsorbed as can be seen from the enthalpy of adsorption (see Figure S21c), which exhibits a step representing a stronger interaction after formation of the first layer at the two opposite graphene sheets. This is in fact opposite to what is assumed in

Figure 3. BET area of graphene sheets as a function of pore size, determined from simulated adsorption isotherms of argon (■) and nitrogen (●). Dashed lines indicate 95% confidence intervals and solid lines indicate the geometric surface area, SGEO (from Figure 2a).

layer can be formed due to rearrangement of the adsorptive, made possible by the larger pore size (see Figure 4e−h). For the region of 5.8 < Dpore < 12.8 Å, the BET area at first becomes larger than the geometric surface area as pore size increases and ultimately becomes nearly equal (SBET ∼ 0.9 SGEO) again. For Dpore ∼ 10 Å, SBET can be up to 75% larger than SGEO. In this range of pore sizes, monolayer−multilayer formation and pore filling cannot be distinguished. Here, monolayer formation means the adsorption of adsorbate molecules directly attached to the adsorbent surface, and multilayer formation constitutes the adsorption of molecules on previously adsorbed adsorbate molecules.5 Micropore filling is the complete filling of the available space in micropores.5 Strictly speaking, for mesopores filling up the available adsorbent space is denoted as capillary condensation,5 though for this work only narrow mesopores are studied and the terms capillary condensation and micropore filling can be used interchangedly (i.e., pore filling) herein. Although it is mentioned in the most recent IUPAC report that “it may be impossible to separate the processes of monolayer−

Figure 4. Side (a, c, e, g) and top (b, d, f, h) views of adsorbed argon (a, b, e, f) and nitrogen (c, d, g, h) for graphene sheets with a pore size of 3.24 (a−d) and 5.80 Å (e−h). These configurations were taken at a pressure to be the upper limit of the used relative pressure range, xul. Carbon atoms are depicted in cyan, argon in salmon, and nitrogen in dark blue. Representation in van der Waals radii. 12668

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Figure 5. Adsorption isotherms (a, c) and Rouquerol-plots (b, d) for argon (a, b) and nitrogen (c, d) in stacked graphene sheets with pore sizes of 9.91 (■), 10.88 (●), 12.85 (▲), 14.82 (▼), 16.80 (◀), and 21.76 Å (▶). m.m. and p.f. stand for monolayer−multilayer formation and pore filling, respectively.

the BET theory, where molecules in this layer have a smaller enthalpy of adsorption (in absolute value). Because of the strong interactions of the molecules adsorbed in this middle layer, the isotherm is very steep, especially for argon (see Figure S21a). This in turn causes that all adsorbate molecules are erroneously included in the determination of the BET area. The distinguishability issue, as mentioned, disappears at Dpore ≥ 12.8 Å, which corresponds to at least four layers of adsorbate molecules (see Figure 6i−l). This observation is logical, as during the formation of the two middle layers, the strong interactions with two already present adjacent molecules occur after monolayer−multilayer formation, and therefore the enthalpy of adsorption decreases after formation of the layers directly on the opposite graphene sheets before increasing due to pore filling (see Figure S24c). For Dpore ∼ 6.8 Å, SBET and SGEO are roughly equal, despite of the indistinguishability between monolayer−multilayer formation and pore filling. At this pore size, exactly two layers of adsorbate molecules are formed (see Figure 6a−d). Thus, even though all molecules are used for the determination, this leads to acceptable BET surface areas. To envisage whether previously described phenomena are also observed experimentally, a short literature survey was conducted. As the stacks of graphene sheets that are used here do not occur experimentally and as isolated graphene sheets or graphite are nonporous, we focused on activated carbon materials instead. These materials can be considered as irregularly stacked graphene domains, still comparable to our

model system. Generally, slit-shaped pores are assumed to be present in these materials.47−50 In Figure 7, the BET area determined using nitrogen adsorption as a function of pore size is shown.6,51−63 Unfortunately, insufficient studies were available to also investigate argon-based BET area. Clearly visible for these different materials, the specific surface area shows a notable maximum at intermediate pore sizes (9 < Dpore < 13 Å), comparable to our findings using graphene sheets (cf. Figure 3). This is again attributed to the indistinguishability between pore filling and monolayer−multilayer formation. In some studies, this phenomenon was overlooked, and thus these materials were erroneously claimed to have an “extremely high surface area”. This overestimation of BET area compared to geometric surface area was recently also found for several MOFs that (partially) contain pores in the 9 < Dpore < 13 Å range.28 Further, comparison of Figures 3 and 7 shows that for smaller pore sizes one can observe experimentally that indeed sharing of adsorbate molecules occurs between adjacent pore walls, lowering the BET area (for Dpore < 8 Å). As was also found for the theoretical case, the BET area here is lower for Dpore > 15 Å than for 9 < Dpore < 13 Å. There exist differences in BET trends between graphene sheets (Figure 3) and activated carbons (Figure 7) as well. In general, SBET is smaller for activated carbons than for stacked graphene sheets. This is likely because activated carbon materials consist of more irregularly stacked aromatic domains, and thus not all carbon atoms present in a sample contribute to the actual surface area. Also, activated carbon materials contain 12669

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Figure 6. Side (a, c, e, g, i, k) and top (b, d, f, h, j, l) views of adsorbed argon (a, b, e, f, i, j) and nitrogen (c, d, g, h, k, l) for graphene sheets with a pore size of 6.8 (a−d), 9.9 (e−h), and 12.8 Å (i−l). These configurations were taken at a pressure to be the upper limit of the used relative pressure range, xul. Carbon atoms depicted in cyan, argon in salmon, and nitrogen in dark blue. Representation in van der Waals radii.

obtained BET areas are roughly half that of the accessible surface. Between two and four layers, because of the indistinguishability between monolayer−multilayer formation and pore filling, obtained BET areas are overestimated. How this translates to porous materials with multiple different pore sizes and/or shapes is currently under investigation. However, it should be generally noted that for materials that contain pores smaller than 12 Å, one should treat obtained BET areas with caution, and claims of “extremely high surface areas” calculated from either argon or nitrogen adsorption should be accompanied by accurate pore size determination to be credible. For Dpore < 12 Å, we strongly advocate the use of (total) pore volume for material benchmarking, as indistinguishability issues do not apply for this property. To characterize materials with Dpore < 12 Å, one might desire to select a smaller probe molecule instead. To this end, we opt a simple equation to estimate adsorbate layer thickness, assuming that molecules are in a close packed configuration. The thickness of n layers of adsorbate molecules, tlay, can be estimated, using the Lennard-Jones well depth as an appropriate molecular radius, by

Figure 7. Reported, experimentally obtained, BET areas as a function of determined pore size for various experimental carbonaceous materials. Based on nitrogen adsorption only, data from Sircar et al.,51 Mochida et al.,52 Li et al.,53 Wiener et al.,54 Wang et al.,6 Shiratori et al.,55 Rejifu et al.,56 Almazan et al.,57 Morlay et al.,58 Kil et al.,59 Asakura et al.,60 Stoeckli et al.,61 Agarwal et al.,62 and Hu et al.63

tlay(n) = 21/6σ + (n − 1) 6

a varying degree of disorder, provoking a variance in BET areas for the same pore size. In addition, the pore sizes are determined differently by the various authors, creating a broader maximum for 9 Å < Dpore < 13 Å. Further, broadening may also occur due to the distribution of pore sizes present in the activated carbons (here average pore sizes were used). Clearly, one cannot obtain physically meaningful surface areas from either argon or nitrogen adsorption when dealing with materials that have pores that encompass less than four layers of adsorbate molecules (with the exception of exactly two layers). For less than two layers of adsorbate molecules,

21/6σ 3

(14)

Substituting appropriate LJ radii (σ) of argon and nitrogen yields a thickness of about 6.8, 9.8, and 12.9 Å for two, three, or four adsorbate layers both for argon and nitrogen, in line with corresponding graphene sheet pore sizes (vide supra). Using helium (σ ∼ 2.64 Å)40 or neon (σ ∼ 2.75 Å)64 would yield ∼10.2 and ∼10.6 Å thicknesses for four layers, respectively (see eq 14). This is, however, only a minor decrease in minimal pore sizes for physically sound BET area determination. With normal boiling points of 4.2 K for helium and 27 K for neon, it 12670

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There are differences between argon and nitrogen in applying the consistency criteria, in particular for the upper limit described in eq 5. As shown in Figure 9, the monolayer

might be difficult to determine a sufficiently large portion of the adsorption isotherm using commercially available volumetric adsorption equipment, even with the aid of current (commercially available) cryostats that can cool down to ∼50 K. From eq 14 and accompanying analysis it is clear that one should consider BET areas with great care and consideration, regardless of the chosen adsorptive for materials with Dpore < 10 Å. Argon versus Nitrogen. As apparent from the previous section, there are similarities between BET areas for both argon and nitrogen. Though, there are notable differences as well, even for the ideal and homogeneous pore systems we have investigated. A larger (maximum) erroneous increase in BET area is observed for argon than for nitrogen (see Figure 3). This is likely due to the less compact packing of diatomic nitrogen, as compared to monatomic argon in the 9 < Dpore < 13 Å pore range, as displayed by the radial distribution functions (see Figure S33). Besides this pore range, differences between BET areas are small. In Figure 8 the obtained BET C parameters,

Figure 9. Ratio of the pressure belonging to monolayer formation, pmono, calculated with eq 4, and the pressure belonging to the upper limit of the used relative pressure window, pul, as a function of pore size for argon (■) and nitrogen (●). Dashed line indicates unity (below this line, consistency criterion is satisfied).

capacity (see eq 4) corresponds to a relative pressure that is higher than the upper limit of the used relative pressure window for small pore sizes. For nitrogen this unwanted phenomenon occurs for Dpore ≤ 7 Å only, whereas for argon this occurs for a larger range of pore sizes (Dpore ≤ 10 Å). This is likely due to the fact that the step in the isotherm, caused by the combined monolayer formation and pore filling is more steep for argon (see Figures S1a−S18a), again because more compact packing of argon (see Figure S33). Note however that in this range indistinguishability between pore filling and monolayer−multilayer formation makes the BET area nonetheless erroneous. This also means that for nitrogen (7 < Dpore < 12.8 Å) and argon (10 < Dpore < 12.8 Å) there are thus pore sizes for which the consistency criteria are fulfilled, but the BET area is not physically sound. Indeed, fulfillment of the consistency criteria is not a guarantee for proper BET areas, as was mentioned earlier by Gómez-Gualdrón et al.17 The lower limit, as described in eq 5, did not pose any issues for either adsorptive and CBET was positive in all cases, making the upper limit the most strict consistency criterion to satisfy. BET versus Langmuir or ESW Area. In Figure 10 the surface areas determined with both the Langmuir and ESW method are shown for each stack of graphene sheets and compared to the geometric surface areas for the same materials (again from Figure 2b). Compared to the BET method, Langmuir areas are slightly larger over the entire pore size range, but especially for Dpore > 12.8 Å (Figure 10a). This is expected, as the Langmuir model tacitly assumes that all adsorbate molecules are used to build up a monolayer on the graphene surfaces. At this point it is important to note that for isotherms where pore filling can be distinguished from monolayer−multilayer formation, the pore filling part is omitted from the SLM determination. As the Langmuir methodology does not contain consistency criteria, the Rouquerol plot was borrowed for this purpose. Therefore, the Langmuir surface areas for Dpore > 12.8 Å are comparable to the geometric surface areas. If pore filling is not omitted from

Figure 8. BET C parameter for graphene sheets as a function of pore size, determined from simulated adsorption isotherms for argon (■) and nitrogen (●). Dashed lines indicate 95% confidence intervals. The inset shows a close-up.

corresponding to the surface areas in Figure 3, are shown for both adsorbate molecules. CBET is the largest when exactly one full layer of adsorbate molecules can be formed. Adsorbate molecules here are adsorbed on both sheets simultaneously, leading to a high enthalpy of adsorption (cf. Figures S1c−30c). For argon, at this maximum, CBET is about an order of magnitude larger than nitrogen. This results from the fact that the relative pressure range for narrow micropores (Dpore ∼ 5 Å) is orders of magnitude lower for argon than for nitrogen (cf. Figures S34−35 and 37). For these pore sizes, it is easier to experimentally determine a large part of the isotherm using nitrogen. For Dpore > 7 Å, this reverses and the lower limit of the relative pressure is higher for argon, making measurements easier for the latter. A local minimum in the C parameter occurs just before, and a local maximum occurs just after Dpore is large enough to encompass two layers of adsorbate molecules. At this local maximum in CBET, the C-parameter is larger for nitrogen than for argon, in line with the higher enthalpy of adsorption (cf. Figures S1c−30c). Further, the represented fractional loadings, qqm−1, of the BET fits remain similar for argon and nitrogen as well (Figure S38). 12671

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Figure 10. Langmuir (a) and ESW (b) specific surface area of graphene sheets as a function of pore size, determined from simulated adsorption isotherms of argon (■) and nitrogen (●). For Langmuir (a), closed symbols indicate pore filling is omitted from consideration; open symbols purposely include pore filling. Dashed lines indicate 95% confidence intervals (in part a only), and solid lines indicate the geometric surface area, SGEO (from Figure 2a).

Figure 11. Ratios of BET and ESW area (a) and of Langmuir and ESW area (b), determined from simulated adsorption isotherms for argon (■) and nitrogen (●), supplemented with literature values (◆).13−16 Dashed lines indicate theoretical ratios, determined using eqs S6 and S9 respectively for (a) and (b). KLM is multiplied with p0 for dimensionless.

determination, the SLM erroneously becomes >8.000 m2 g−1 for large pore sizes (see Figure 10a). In fact, if volume filling is included, SLM increases roughly linearly with Dpore. This makes sense as with increasing Dpore, the available volume between adjacent graphene sheets increases as well and thus the total amount of adsorbate molecules (erroneously) included in SLM. The value of KLM, excluding volume filling when possible, shows the same dependency on pore size as CBET, having the largest magnitude when exactly one layer of adsorbate molecules is formed (cf. Figure 8 and Figure S39) and exhibits a second maximum when two layers are formed. The excess sorption work areas are over the whole range of pore sizes, smaller than the BET areas (cf. Figures 3 and 10b). The trends in normalized minimum energy, φmin (see Figure S40), show that at each pore size the adsorption is strongest when one full layer is formed, similar as for BET and Langmuir models. A second minimum in energy is found around two full layers of adsorbate molecules. Generally, the ESW area has the largest deviation from the geometric surface area over the investigated pore size range. Interestingly, the excess sorption work, Φ, shows two minima for Dpore > 12.8 Å (see Figure

S41). The first minimum corresponds to monolayer formation completion and the second to complete pore filling. For argon the first minimum is higher in energy than the second, for nitrogen the reverse is true (cf. Figures S41a and S41b). This means that the global minimum in the excess sorption work function does not necessarily correspond to monolayer formation, and thus care should be taken in distinguishing different phenomena when determining ESW areas properly, another clear drawback of the method. The accuracy in the ESW area does not depend on the quality of regression, but on the number of data points around the minimum in the excess sorption work function. This means that higher resolution isotherms are needed, at least around ESW monolayer formation, for accurate surface area estimation using ESW than for the BET and Langmuir models. The fact that the ESW method yields smaller surface areas than either the BET or the Langmuir method can be explained on a theoretical basis. One can simply determine SESW from either a BET or Langmuir isotherm (see section S-5 for details). From this one can obtain the ratios of either BET or Langmuir and ESW surface areas as a function of either CBET or KLM (see 12672

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counterparts, for the graphene sheets that have been investigated here. The corresponding pore sizes are 6.8, 9.8, and 12.9 Å for two, three, or four adsorbate layers of argon or nitrogen, meaning that for Dpore ≥ 13 Å physically sound surface areas are obtained, with either argon or nitrogen used as adsorptive. Fulfillment of the BET consistency criteria is thus not a guarantee for proper, physically sound BET areas. Though these findings are based on graphene sheets as model system, these trends are visible in activated carbon materials as well. In the literature, the indistinguishability issue in a pore size, Dpore, range between 9 and 13 Å have been largely missed and erroneous claims of materials with extremely large surface areas resulted. Both the BET and Langmuir areas, for Dpore > 13 Å, correspond to geometric surface areas, whereas the excess sorption work method yields significantly lower values (except for very narrow micropores). These findings have been corroborated with theoretical calculations for energetically homogeneous graphene sheets used as model pore systems in this study. Differences between argon and nitrogen for the assessment of surface areas are found to be minor and both can be used. For Dpore > 13 Å, argon has the advantage that the relative pressures used for the determination are higher than for nitrogen, slightly facilitating the experimental determination of the adsorption isotherm.

eqs S6 and S9, respectively). This is shown in Figure 11 and compared with the same ratios determined from analyzing the simulated adsorption isotherms (from Figures 3 and 10). For both SBET/SESW and SLM/SESW, the theoretical results and those based on simulations are in agreement. Deviations from theoretical predictions can be explained by the finite resolution of data points near the formation of ESW monolayer and a small correlation between the two fitting parameters used for the BET and Langmuir method.45 Closer inspection shows that the BET area will be larger than the ESW area when CBET > 5− 7 (see Figure 11a). Such small CBET values correspond to very large meso- or macropores. The Langmuir area will always be larger than that determined with the ESW method, regardless of pore size (Figure 11b). With decreasing values of KLM or CBET, corresponding to increasing pore size, SLM will be increasingly larger than SBET. The difference in Langmuir and BET area diminishes with increasing values KLM or CBET, i.e., with decreasing pore size. This corroborates with comparison of Figures 3 and 10a and makes perfect sense as with decreasing pore size, the number of layers that can be formed decreases. The highest values obtained for both p0KLM and CBET (∼107) correspond to formation of one single adsorbate layer (see Figure 8 and Figure S37), for which very similar monolayer capacities should be obtained when using BET or Langmuir. The areas determined by the three investigated methods BET, Langmuir, and ESWshow similar deviations from geometric surface areas for 9 < Dpore < 13 Å for slit-shaped pores, when using either argon or nitrogen as the adsorbate, corresponding to the aforementioned distinguishability issue between pore filling and monolayer−multilayer formation (cf. Figures 3 and 10). This strengthens the findings that while assessing materials with pores in this range, specific surface areas determined from adsorption isotherms should be investigated with great care. In fact, we strongly advise here to compare materials based on pore volumes if possible, for which this issue is absent. Though results are based on homogeneous slit pores, the underlying phenomena that give rise to deviation in obtained surface areas occur in materials containing a distribution of pores sizes as well. Albeit that the identified trends, as a function of pore size, will most likely appear more convoluted in this case. Material scientists thus should take into account the dominant pore sizes present in a sample, before determining its specific surface areas using adsorption.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03531. Simulated isotherms, Rouquerol plots and enthalpies of adsorption, effect of probe radius on geometric surface area, additional information on BET fits, and comparison with Langmuir and ESW methods and additional calculation details (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (M.F.d.L.). *E-mail [email protected] (F.K.). ORCID

Freek Kapteijn: 0000-0003-0575-7953

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Funding

CONCLUSIONS When less than two full layers of adsorbate molecules can be formed within slitlike pores of a graphitic material, adsorptionderived specific surface areas are about half that of the geometric surface area. Between two and four layers, adsorption surface areas can be significantly higher (up to ∼75%) than the geometric surface area. This is because monolayer−multilayer formation and pore filling occur at the same time and cannot be distinguished. The main reason behind is the strong interactions of the adsorptive molecules in the intermediate layer, causing a very rapid filling of the pores before completion of monolayer adsorption on either sides of the pore wall. This phenomenon also occurs for pore sizes of exactly two layers of adsorbate molecules, though this does not lead to overestimation of adsorption-derived surface areas in this specific case. For four or more layers of adsorbate molecules, indistinguishability issues diminish and adsorption-derived surface areas are comparable to their geometrically accessible

This work was sponsored by NWO Exacte Wetenschappen (Physical Sciences) for the use of supercomputer facilities, with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (Netherlands Organisation for Scientific Research, NWO). The authors are also grateful to Ohio Supercomputer Center65 for computational resources. M.F.d.L. acknowledges financial support for this research from ADEM, “A green Deal in Energy Materials” of the Ministry of Economic Affairs of The Netherlands. T.J.H.V. acknowledges NWO-CW for a VICI grant. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders & Porous Solids; Academic Press: London, 1999. (2) Schüth, F.; Sing, K. S. W.; Weitkamp, J. Handbook of Porous Solids; Wiley-VCH: 2002. 12673

DOI: 10.1021/acs.langmuir.6b03531 Langmuir 2016, 32, 12664−12675

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DOI: 10.1021/acs.langmuir.6b03531 Langmuir 2016, 32, 12664−12675