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Recent advances in adsorption characterization of mesoporous molecular sieves
Studies in Surface Science and Catalysis 129 A. Sayari et al. (Editors) © 2000 Elsevier Science B.V. All rights reserved.
587
Recent advances in adsorption characterization of mesoporous molecular sieves Mietek Jaroniec,^ Michal Kruk^ and Abdelhamid Sayari^ ^ Department of Chemistry, Kent State University, Kent, Ohio 44242, USA ^ Department of Chemical Engineering and CERPIC, Universite Laval, Ste-Foy, Quebec, Canada G1K7P4 Recently developed approaches for adsorption characterization of mesoporous molecular sieves (MMS) are critically discussed with special emphasis on the methods for calculation of pore size distributions (PSDs). It is demonstrated that very similar mesopore size distributions can be evaluated using a properly calibrated classical procedure and a sophisticated hybrid method developed by combining density functional theory (DFT), experimental adsorption data and advanced deconvolution technique. The latter method allows for calculation of PSDs also in the micropore range. The deficiencies and limitations of approaches based on the condensation approximation, such as the Horvath-Kawazoe method, are discussed. A new approach for calculation of PSDs for hydrophobic porous solids is described. It is demonstrated that essentially the same PSDs can be obtained from nitrogen at 77 K and argon at 87 K, provided adsorption branches of isotherms are used in calculations. It is also shown that adsorption measurements for both calcined and assynthesized MMS samples provide useful information regarding possible changes in the structure upon calcination. Moreover, the external surface of particles of as-synthesized MCM-41 is shown to exhibit strongly hydrophobic properties, which suggests that it is covered with a relatively dense layer of electrostatically bonded surfactant ions.
1. INTRODUCTION A significant progress has recently been made in adsorption characterization of mesoporous adsorbents, especially in development of accurate, reliable and self-consistent methods to calculate PSDs of mesoporous molecular sieves [1-5] and other mesoporous or mesoporous-microporous adsorbents. Two different general strategies were employed in elaboration of these methods. The first one employed advanced statistical-mechanical approaches, such DFT, to generate model adsorption isotherms for well-defined pores, and subsequently used these isotherms to solve the integral equation for overall adsorption with respect to the PSD [6-9]. DFT calculations for homogeneous surfaces, which were performed in these studies, provided rather inaccurate predictions of low pressure adsorption on porous solids, such as silica [6,7,9], largely due to their strong surface heterogeneity [10,11]. To overcome this difficulty, one can resort to DFT calculations for heterogeneous surfaces [12]. However, similarity of low-pressure adsorption for different kinds of silicas [6,8-10], and
588 different types of silicate MMSs in particular [13,14], opened an opportunity of employing hybrid models, where adsorption isotherms for model pores are constructed using experimental low-pressure data for reference silicas and high-pressure data from DFT. Such hybrid models can be used for determination of PSDs, improving the numerical stability of calculations [6,8] and providing excellent fits to the experimental data in the entire pressure range [9]. The second fruitful approach to develop novel methods for pore size analysis directly employs well-defined MMSs as model porous solids, which eliminates the need of resorting to advanced computational approaches and provides an opportunity of elaboration and/or calibration of PSD calculation procedures from the first principles. Initially, Naono et al. [15] determined a relation between the capillary condensation pressure and the pore size as well as a stadstical film thickness curve (t-curve), both valid in a very narrow pressure range, using nitrogen adsorpfion data measured at 77 K for hexagonal MMSs. Subsequently, these relations were used in the Barrett-Joyner-Halenda (BJH) method [16] to calculate PSDs. The method of Naono et al. had serious limitations, including i) inaccurate calculation of pore sizes for model samples, ii) inaccurate determination of the t-curve, iii) very narrow pore size range, for which calculations can be performed and iv) lack of general relations suitable for computational purposes. Later, an approachft-eeft"omall these limitations was developed by Kruk, Jaroniec and Sayari [17-19] (this procedure will be referred to as the KJS approach). In the KJS procedure, the pore size of model MCM-41 silicas was determined using a reliable method based on a geometrical relation between the pore size, pore volume and Xray diffracfion (XRD) interplanar spacing in the honeycomb structure characteristic of MCM41 [10,20]. The t-curves in the model pores were calculated in a wide pressure range and their variation with the pore size was examined [17]. Relations between the capillary condensation/evaporation pressures and the pore size were examined and it was found that the capillary condensation pressure increased in a systematic way as the pore size increased, whereas the capillary evaporation pressure was dependent not only on the pore size, but also on the quality of samples and proximity of the lower limit of adsorption-desorption hysteresis [17]. Finally, the empirical relation between the capillary condensation pressure and the pore size as well as the t-curve were derived in order to provide an opportunity for calculating PSDs in the enfire mesopore range [17]. In such calculadons, well-known procedures, such as the BJH algorithm, can readily be employed [17], but one may also choose to use some more advanced computational methods, such as those based on an inversion of the integral equation for overall adsorption [6-9,21]. Originally, the KJS approach was applied to calculate PSDs for silicas with cylindrical pores using nitrogen adsorption data measured at 77 K [17]. The results reported therein were subsequently carefully verified and confirmed [22-24], The KJS procedure was also extended on PSD analysis using argon adsorption at 87 K [18] and generalized for mesoporous solids with hydrophobic surfaces [19]. An additional benefit of the KJS approach was determination of t-curves for different adsorptives (nitrogen, argon) and different kinds of solid surfaces (silica, alkylsilyl-modified silica). This provided reference adsorpfion data [18,19,24] suitable for comparative plot analysis, which can be used to determine the micropore volume, primary mesopore volume, external surface area and total surface area as well as to study the surface properties of porous materials [24-27]. In the current work, the aforementioned novel approaches for determination of PSDs will be discussed. A crifical comparison of the different methods for the PSD calculation will be presented in order to make some recommendations for practical applications. Advances in the analysis of surface properties of as-synthesized MMSs by means of comparafive methods will also be discussed.
589 2. RESULTS AND DISCUSSION 2.1. Accurate determination of the pore diameter for MMSs with honeycomb structures Application of MMSs as model adsorbents for development and verification of adsorption methods to calculate PSDs rests upon availability of reliable independent estimates of the MMS pore size. This fundamental problem was already solved for MCM-41 [1], silica with honeycomb arrays of approximately cylindrical pores. Taking advantage of its simple geometry, the following relation between the pore diameter, Wd, the primary mesopore volume, Vp, and the XRD (100) interplanar spacing, d, was derived [10, 20]: ^ PV. '"' .cd\ 1 + pFp J
(1)
where p is the density of the pore walls and c is a constant dependent on the pore geometry (1.213 for circular pores). In the original works employing the geometrical method based on Eq. 1, the density of the pore walls was either experimentally determined as 2.2 g cm'^ [20] or assumed to be equal to the latter value [10], which is typical for amorphous silica [28]. Later studies showed that this assumption is fully justified [29], especially as Eq. 1 is insensitive to small errors in the density evaluation [30]. Moreover, it was demonstrated that very similar MCM-41 primary mesopore volumes can be estimated using various adsorptives [29], and minor differences in the resulting Vp values do not have any appreciable effect on the pore size evaluation [29,30]. Eq. 1 was successfully applied in studies of non-silica MMSs [31] and generalized for the hexagonal pore geometry [30,32,33] Thus, the geometrical method promises to be applicable for a wide range of hexagonally ordered MMSs, including MCM41, FSM-16 [2], and SBA-15 [5]. Moreover, Eq. 1 can readily be modified to account for the presence of micropores in the walls of the hexagonal phase [34] and the presence of nonmesostructured impurity components [30]. It can be concluded that the geometrical method is suitable for evaluation of the pore diameters of model samples used for development, verification and calibration of adsorption methods of the mesopore size analysis [17] 2.2. KJS method to calculate pore size distributions from nitrogen adsorption data MCM-41 is currently the best model mesoporous adsorbent available, since it has simple pore geometry and can be synthesized in a wide range of pore sizes [17]. Nitrogen adsorption at 77 K is the most commonly used method for determination of the specific surface areas and mesopore size distributions of porous solids [25]. Therefore, the first successful work on verification and calibration of adsorption methods for mesopore size analysis using MMSs as the model materials was done for nitrogen adsorption on MCM-41 [17]. The originally obtained data describing the capillary condensation and evaporation pressures as functions of the cylindrical pore diameter (calculated using eq 1) are shown in Figure la, along with the results of later studies [13, 22, 23, 35-37]. This extensive data set covered the pore size range from 2 to 6.5 nm. To extend it on even larger pore sizes, the data reported in the literature for high-quality large-unit-cell MCM-41 [38] were used. For the latter, the pore size was evaluated using the reported unit-cell parameter (equal to 2-3"^^"^d) of 7.7 nm and an approximate primary mesopore volume (1.5 cm^ g'^) estimated from the reported total pore volume of 1.6 cm^ g'\ The capillary condensation and evaporation pressures for this sample were estimated from the reported nitrogen adsorption isotherm.
590 U. /
'
'
15
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/
0.3 0.2
'
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-'"^^
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OH
'
(a)
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'
/ r>0
-
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-
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'/
^ ^ J
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^
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-
Condensation Evaporation
-
Q
-
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— 1
3
4
5
6
Pore Diameter w^ (nm)
5
6
7
Pore Diameter w^ (nm)
Figure 1. (a) Experimental relations between the capillary condensation pressure and the pore diameter (hollow circles) and between the capillary evaporation pressure and the pore diameter (filled circles) for nitrogen adsorption at 77 K. The dashed line corresponds to the Kelvin equation with the statistical film thickness correction. The solid line corresponds to Eq. 2 derived using the KJS approach, (b) Relation between pore diameters calculated on the basis of Eq. 1 and the KJS-calibrated BJH algorithm using nitrogen adsorption data at 77 K. As can be seen in Figure la, nitrogen capillary condensation pressure in MCM-41 pores gradually increased as the pore size increased [ 17] and only minor random deviations from this general trend were observed. This indicates that adsorption branches of nitrogen isotherms are suitable for the pore size analysis [17]. In contrast, capillary evaporation pressure increased only slightly as the pore size increased from about 4.3 to 5.8 nm. This is related to the proximity of the lower limit of adsorption-desorption hysteresis [17] (relative pressure of about 0.4 for nitrogen at 77 K) [25] and to the fact that the quality of our model MCM-41 materials with pore sizes above 5 nm was in many cases somewhat lower than that of the samples with narrower pores. For pore sizes above 5.8 nm, the relation between the capillary evaporation pressure and the pore size also exhibited some scatter primarily related to differences in quality of the MCM-41 materials [17]. It can be concluded that the knowledge of capillary condensation pressure provides much more accurate information about the pore size than the knowledge of capillary evaporation pressure and thus adsorption branches of isotherms are more suitable for the pore size analysis than desorption branches. Since capillary condensation pressure was found to be a gradually increasing function of the pore size, it was possible to find an empirical equation for this relation (see Fig. la). This equation [17] was similar to the well-known Kelvin equation for cylindrical pores [25]: ip/p,)
[nm] = 0.416 [\og{pJp)]-'
(2)
where r is the pore radius as a function of the relative pressure (p/po), p is the equilibrium vapor pressure, po is the saturation vapor pressure and t is the statistical film thickness as a function of the relative pressure. The three terms in Eq. 2 are the Kelvin equation [25], the
591 statistical film thickness correction [17,25] and an empirical correction [17]. The well-known problem of inaccuracy in determination of the t-curve, resulting from uncertainty in evaluation of the monolayer capacity [39], was eliminated using the t-curve calibration on larg e-pore MCM-41 [17]. The resulting t-curve (tabular data were reported in Ref 24) can be described by an empirical equation determined for relative pressure range of 0.1-0.95 [17]:
^A',.77/:(/^/'Po)[«^] = 0.1
60.65 0.03071 - \og{plp,)
(3)
The KJS Eq. 2 provides an excellent description of the relation between the capillary condensation pressure and the MCM-41 pore diameter (see Fig. la). An additional advantage of this relation is that it is approximately equivalent to the Kelvin equation iox larger mesopore sizes and thus is expected to be valid in the entire mesopore range, which makes it very useful for an accurate determination of the mesopore size distributions. As shown in Fig. lb, Eq. 2 was used to determine the pore diameter of 40 good-quality MCM-41 samples [13,17,22,23,35-37] and the results were in excellent agreement with those based on Eq. 1. The standard deviation of differences between these two estimates (Wd - WKJS) was only 0.10 nm, which is rather remarkable. On average, Wd was slightly larger than WKJS (about 0.06 nm), which indicates that it may be possible to further improve the agreement by adjusting the empirical correction in Eq. 2. However, because of the small magnitude of the observed differences, it is justified to use Eq. 2 in its present form and defer the final refinement until the quality of MCM-41 or structurally similar samples with both small (below 3 nm) and large (above 5 nm) pore sizes is improved and the range of accessible pore sizes is extended. 2.3. DFT-based method to calculate pore size distributions. As already discussed, DFT can be used to predict the capillary condensation and capillary evaporation pressures for pores with homogeneous surface and well-defined geometry. To generate model adsorption isotherms for heterogeneous pores, it is convenient to employ hybrid models based on both DFT data for homogeneous pores and experimental data for flat heterogeneous surfaces [6-9]. Such model adsorption isotherms can be used to calculate PSDs in mesopore [6-9] and micropore [9] ranges. This approach is particularly useful for pores of diameter below 2-3 nm (micropores and narrow mesopores), where an assumption about the common t-curve for pores of different sizes is less accurate, which in turn makes the methods based on such an assumption (even properly calibrated ones) less reliable [18]. In the case of PSD calculation on the basis of DFT or computer simulation data, one faces a fundamental problem, whether adsorption or desorption branches of isotherms should be used. The recent experimental studies clearly indicate that adsorption branches of isotherms provide much more information about the pore size and are more suitable for the mesopore size analysis [17, 18]. In addition, adsorption data can often be acquired starting from low pressures, providing information sufficient to determine both micropore and mesopore size distributions from a single adsorption isotherm [9]. Illustrative PSDs calculated using the DFT-based method [9] and the KJS-calibrated BJH method are compared in Figure 2a. Both of these PSDs have highly similar positions of their maxima, heights and widths of their peaks. The current version of the DFT method [9] somewhat overestimates the size of pores above 4 nm, but other than that, the two approaches considered provide similar PSDs in the mesopore range. As mentioned above, the DFT method considered is capable of providing better estimates of the micropore size distributions.
592 3.0 2.5 S o
2.0
—1
(a) KJS DFT HK-KJS HK-SF
O
• A
o
1.5
•
11 ( )l)
'C
1.0 C/3
o
1
0.5 0.0 JLmmMSm Pore Size (nm)
Pore Size (nm)
Figure 2. (a) PSDs for 3.88 nm MCM-41 [22] calculated from nitrogen adsorption data at 77 K using i) the KJS approach with the BJH algorithm, ii) the hybrid DFT method, iii) the HKbased method with the relation between pore size and condensation pressure described by Eq. 2, and iv) the HK-based Saito-Foley method, (b) Comparison of PSDs for octyldimethylsilylbonded MCM-41 calculated from nitrogen adsorption using the KJS-calibrated BJH algorithm with t-curves for reference ODMS-modified silica and unmodified silica. 2.4. Deficiencies of the Horvath-Kawazoe method and other similar procedures Recently, the Horvath-Kawazoe (HK) method for slit-like pores [40] and its later modifications for cylindrical pores, such as the Saito-Foley (SF) method [41] have been applied in calculations of the mesopore size distributions. These methods are based on the condensation approximation (CA), that is on the assumption that as pressure is increased, the pores of a given size are completely empty until the condensation pressure corresponding to their size is reached and they become completely filled with the adsorbate. This is a poor approximation even in the micropore range [42], and is even worse for mesoporous solids, since it attributes adsorption on the pore surface to the presence of non-existent pores smaller than those actually present (see Fig. 2a) [43]. It is easy to verify that the area under the HK PSD peak corresponding to actually existing pores does not provide their correct volume, so the HK-based PSD is not only excessively broad, but also provides underestimated volume of the actual pores. This is a fundamental problem with the HK-based methods. An additional problem is that the HK method for slit-like pores provides better estimates of the pore size of MCM-41 with cylindrical pores than the SF method for cylindrical pores. This shows the lack of consistency [32,43]. Since the HK-based methods use CA, one can replace the HK or SF relations between the pore size and pore filling pressure by the properly calibrated ones, which would lead to dramatic improvement of accuracy of the pore size determination [43] (see Fig. 2a). However, this will not eliminate the problem of artificial tailing of PSDs, since the latter results from the very nature of HK-based methods. 2.5. KJS method to calculate pore size distributions for hydrophobic porous solids As already discussed, one can use a series of MMSs (for instance MCM-41) of known pore sizes to determine a relation between the capillary condensation (or evaporation)
593 pressure and the pore diameter for a given adsorptive. It is convenient to derive a description of such a relation, which expHcitly includes the t-curve (see Equation 2), since such a relation is expected to be valid for different porous materials with similar pore geometry when a proper t-curve is employed to account for differences in surface properties with respect to a given adsorbate. This in turn would open an opportunity to accurately determine PSDs of various mesoporous solids using a general relation between the pore size and capillary condensation (or evaporation) pressure for the particular pore geometry and a set of t-curves dependent on the composition (and consequently, surface properties) of porous materials. To verify this idea, MCM-41 silicas with chemically bonded octyldimethylsilyl (ODMS) ligands were studied, for which the pore size can be independently determined from the pore diameter of unmodified materials and the pore volume changes after modification [19]. The chemical bonding of ODMS groups renders surfaces which interact very weakly with nitrogen molecules [44] and this is likely to lower the statistical film thickness in comparison to that on the silica surface. The statistical film thickness in the pores of modified samples was indeed found to be significantly lower than that for the MCM-41 silicas [19]. The tcurves for the model modified materials were used to determine the reference t-curve for ODMS-modified silicas (reported in a tabular form in Ref 19), which is approximated in the pressure range from about 0.1 to 0.95 by the following equation [19]: 8.873 ^N,J7K,0DMsiP^ Po)[^^]
= ^''^
0.08004-log(/?//?o)
(4)
Along with Eq. 2, the t-curve for ODMS-modified silicas was used to determine PSDs of alkyldimethylsilyl-modified MCM-41 silicas employing the BJH algorithm. The resulting pore sizes were close to those obtained from the independent method mentioned above, which confirms that Eq. 2 with a proper t-curve is valid for materials with surface properties different from those of silica. The choice of the t-curve did not have a dramatic influence on the pore size evaluation (Fig. 2b), although the pore sizes determined using the t-curve for modified surfaces were somewhat lower as a result of the smaller t-curve correction. However, only when the proper t-curve was used, the total pore volumes and specific surface areas for the modified samples were correctly reproduced using the BJH method, whereas in the other case, they were grossly overestimated [19]. Moreover, the application of the proper t-curve largely eliminated the artificial tails on the PSDs (Fig. 2b). Eqs. 2 and 4 promise to be highly useful in characterization of a wide range of strongly hydrophobic solids, such as alkylsilyl-modified silicas (see Ref 44 and references therein). It needs to be kept in mind that not all organosilane-modified silicas have such weakly interacting surfaces and for instance aminopropylsilyl-modified silicas interact with nitrogen more similarly to the unmodified silica [44]. Anyway, the strongly hydrophobic surfaces abound in the field of both modified [44] and unmodified [23] MMSs. This can be illustrated on the example of an uncalcined MCM-41 (the calcined sample was described in Ref 35, Table 2, first entry). The uncalcined sample was macroporous and exhibited very weak adsorption at low pressures (see Figure 3a). As determined from the as-plot analysis [24-27] the low pressure data were similar to those of the ODMS-modified silicas and highly different from those for silicas, which manifested itself in minor deviations from linearity when the ODMS-modified reference adsorbent was used and considerable nonlinearity for the reference silica (see Figure 3b). This was already reported for MCM-41 materials prepared using surfactants of various chain lengths [23] and was attributed to the presence of
594 electrostatically bonded surfactant ions on the external surface of particles of these materials. This behavior may be general for a wide range of MMSs, at least those with direct ionic interactions between the template and inorganic framework. It also should be noted that the secondary porosity of the uncalcined sample under study closely resembled that of the calcined sample, which indicates that this porosity was a feature of particles of the material and did not result from partial collapse upon calcination, which may take place for some MMSs. Thus, examination of adsorption isotherms for both calcined and uncalcined MMSs may provide valuable insight into development of their secondary porosity. 90 OH
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0.001
0.010
0.100
00
o •
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00
ODMS ref Silica ref
80 T3
T3
<
O
B <
K i
60 40 -
<
20
0.0
c o
j ^
0.2
B < 1
1
[
0.4
0.6
0.8
0
1.0
0.0
0.2
0.4
Standard Adsorption a
Relative Pressure
Figure 3. (a) Nitrogen adsorption isotherm for uncalcined MCM-41. (b) Comparative plots for this sample calculated using reference data for ODMS-modified and unmodified silicas. 2.6. KJS method to calculate pore size distributions from argon adsorption data at 87 K Shown in Figure 4 are capillary condensation and capillary evaporation pressures as functions of the diameter of siliceous cylindrical pores for argon adsorption at 87 K [18]. These data were derived on the basis of the study of high-quality MCM-41 samples selected among those used in the case of nitrogen adsorption at 77 K [17,22,37]. As can be inferred from the comparison of Figs, la and 4a, adsorption behavior of argon at 87 K resembled that of nitrogen at 77 K. In general, the capillary condensation pressure gradually increased as the pore diameter increased, whereas the capillary evaporation pressure exhibited relatively smaller increase in the pressure range of the transition from the reversible adsorption behavior to adsorption-desorption hysteresis. Therefore, adsorption rather than desorption data were found to be suitable for the pore size analysis [18]. To facilitate the calculation of PSDs, the relation between the capillary condensation pressure and the pore diameter as well as the t-curve were derived [18] (tabulated t-curve data can be found in Ref 18): ip/ Po)[nm] = 0.3156[\og{p,/ p)Y
(5) + ^Ar.SlK ipl Po)'^ 0.438
^ArxiKipl Pa)[nm\ = 0.\
10.61 0.0561-log(p//;„)
(6)
595 Equation 5 is analogous to Eq. 2 discussed above. As illustrated in Figure 4b, the mesopore size distributions determined from nitrogen and argon adsorption data were essentially the same, when calculations were carried out for adsorption branches of isotherms using the corresponding KJS-calibrated relations (Eqs. 2 and 5) [18].
Pore Size w^ (mn)
Pore Size (nm)
Figure 4. (a) Capillary condensation/evaporation pressures as functions of the pore diameter for argon adsorption at 87 K. The solid line corresponds to Eq 5. See Fig. la for additional explanations, (b) PSDs calculated from nitrogen adsorption data at 77 K and argon adsorption data at 87 K using the BJH algorithm with the KJS relations (Eqs. 2 and 5, respectively).
3. ACKNOWLEDGMENTS The donors of the Petroleum Research Fund administered by the American Chemical Society are gratefully acknowledged for support of this research.
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587
Recent advances in adsorption characterization of mesoporous molecular sieves Mietek Jaroniec,^ Michal Kruk^ and Abdelhamid Sayari^ ^ Department of Chemistry, Kent State University, Kent, Ohio 44242, USA ^ Department of Chemical Engineering and CERPIC, Universite Laval, Ste-Foy, Quebec, Canada G1K7P4 Recently developed approaches for adsorption characterization of mesoporous molecular sieves (MMS) are critically discussed with special emphasis on the methods for calculation of pore size distributions (PSDs). It is demonstrated that very similar mesopore size distributions can be evaluated using a properly calibrated classical procedure and a sophisticated hybrid method developed by combining density functional theory (DFT), experimental adsorption data and advanced deconvolution technique. The latter method allows for calculation of PSDs also in the micropore range. The deficiencies and limitations of approaches based on the condensation approximation, such as the Horvath-Kawazoe method, are discussed. A new approach for calculation of PSDs for hydrophobic porous solids is described. It is demonstrated that essentially the same PSDs can be obtained from nitrogen at 77 K and argon at 87 K, provided adsorption branches of isotherms are used in calculations. It is also shown that adsorption measurements for both calcined and assynthesized MMS samples provide useful information regarding possible changes in the structure upon calcination. Moreover, the external surface of particles of as-synthesized MCM-41 is shown to exhibit strongly hydrophobic properties, which suggests that it is covered with a relatively dense layer of electrostatically bonded surfactant ions.
1. INTRODUCTION A significant progress has recently been made in adsorption characterization of mesoporous adsorbents, especially in development of accurate, reliable and self-consistent methods to calculate PSDs of mesoporous molecular sieves [1-5] and other mesoporous or mesoporous-microporous adsorbents. Two different general strategies were employed in elaboration of these methods. The first one employed advanced statistical-mechanical approaches, such DFT, to generate model adsorption isotherms for well-defined pores, and subsequently used these isotherms to solve the integral equation for overall adsorption with respect to the PSD [6-9]. DFT calculations for homogeneous surfaces, which were performed in these studies, provided rather inaccurate predictions of low pressure adsorption on porous solids, such as silica [6,7,9], largely due to their strong surface heterogeneity [10,11]. To overcome this difficulty, one can resort to DFT calculations for heterogeneous surfaces [12]. However, similarity of low-pressure adsorption for different kinds of silicas [6,8-10], and
588 different types of silicate MMSs in particular [13,14], opened an opportunity of employing hybrid models, where adsorption isotherms for model pores are constructed using experimental low-pressure data for reference silicas and high-pressure data from DFT. Such hybrid models can be used for determination of PSDs, improving the numerical stability of calculations [6,8] and providing excellent fits to the experimental data in the entire pressure range [9]. The second fruitful approach to develop novel methods for pore size analysis directly employs well-defined MMSs as model porous solids, which eliminates the need of resorting to advanced computational approaches and provides an opportunity of elaboration and/or calibration of PSD calculation procedures from the first principles. Initially, Naono et al. [15] determined a relation between the capillary condensation pressure and the pore size as well as a stadstical film thickness curve (t-curve), both valid in a very narrow pressure range, using nitrogen adsorpfion data measured at 77 K for hexagonal MMSs. Subsequently, these relations were used in the Barrett-Joyner-Halenda (BJH) method [16] to calculate PSDs. The method of Naono et al. had serious limitations, including i) inaccurate calculation of pore sizes for model samples, ii) inaccurate determination of the t-curve, iii) very narrow pore size range, for which calculations can be performed and iv) lack of general relations suitable for computational purposes. Later, an approachft-eeft"omall these limitations was developed by Kruk, Jaroniec and Sayari [17-19] (this procedure will be referred to as the KJS approach). In the KJS procedure, the pore size of model MCM-41 silicas was determined using a reliable method based on a geometrical relation between the pore size, pore volume and Xray diffracfion (XRD) interplanar spacing in the honeycomb structure characteristic of MCM41 [10,20]. The t-curves in the model pores were calculated in a wide pressure range and their variation with the pore size was examined [17]. Relations between the capillary condensation/evaporation pressures and the pore size were examined and it was found that the capillary condensation pressure increased in a systematic way as the pore size increased, whereas the capillary evaporation pressure was dependent not only on the pore size, but also on the quality of samples and proximity of the lower limit of adsorption-desorption hysteresis [17]. Finally, the empirical relation between the capillary condensation pressure and the pore size as well as the t-curve were derived in order to provide an opportunity for calculating PSDs in the enfire mesopore range [17]. In such calculadons, well-known procedures, such as the BJH algorithm, can readily be employed [17], but one may also choose to use some more advanced computational methods, such as those based on an inversion of the integral equation for overall adsorption [6-9,21]. Originally, the KJS approach was applied to calculate PSDs for silicas with cylindrical pores using nitrogen adsorption data measured at 77 K [17]. The results reported therein were subsequently carefully verified and confirmed [22-24], The KJS procedure was also extended on PSD analysis using argon adsorption at 87 K [18] and generalized for mesoporous solids with hydrophobic surfaces [19]. An additional benefit of the KJS approach was determination of t-curves for different adsorptives (nitrogen, argon) and different kinds of solid surfaces (silica, alkylsilyl-modified silica). This provided reference adsorpfion data [18,19,24] suitable for comparative plot analysis, which can be used to determine the micropore volume, primary mesopore volume, external surface area and total surface area as well as to study the surface properties of porous materials [24-27]. In the current work, the aforementioned novel approaches for determination of PSDs will be discussed. A crifical comparison of the different methods for the PSD calculation will be presented in order to make some recommendations for practical applications. Advances in the analysis of surface properties of as-synthesized MMSs by means of comparafive methods will also be discussed.
589 2. RESULTS AND DISCUSSION 2.1. Accurate determination of the pore diameter for MMSs with honeycomb structures Application of MMSs as model adsorbents for development and verification of adsorption methods to calculate PSDs rests upon availability of reliable independent estimates of the MMS pore size. This fundamental problem was already solved for MCM-41 [1], silica with honeycomb arrays of approximately cylindrical pores. Taking advantage of its simple geometry, the following relation between the pore diameter, Wd, the primary mesopore volume, Vp, and the XRD (100) interplanar spacing, d, was derived [10, 20]: ^ PV. '"' .cd\ 1 + pFp J
(1)
where p is the density of the pore walls and c is a constant dependent on the pore geometry (1.213 for circular pores). In the original works employing the geometrical method based on Eq. 1, the density of the pore walls was either experimentally determined as 2.2 g cm'^ [20] or assumed to be equal to the latter value [10], which is typical for amorphous silica [28]. Later studies showed that this assumption is fully justified [29], especially as Eq. 1 is insensitive to small errors in the density evaluation [30]. Moreover, it was demonstrated that very similar MCM-41 primary mesopore volumes can be estimated using various adsorptives [29], and minor differences in the resulting Vp values do not have any appreciable effect on the pore size evaluation [29,30]. Eq. 1 was successfully applied in studies of non-silica MMSs [31] and generalized for the hexagonal pore geometry [30,32,33] Thus, the geometrical method promises to be applicable for a wide range of hexagonally ordered MMSs, including MCM41, FSM-16 [2], and SBA-15 [5]. Moreover, Eq. 1 can readily be modified to account for the presence of micropores in the walls of the hexagonal phase [34] and the presence of nonmesostructured impurity components [30]. It can be concluded that the geometrical method is suitable for evaluation of the pore diameters of model samples used for development, verification and calibration of adsorption methods of the mesopore size analysis [17] 2.2. KJS method to calculate pore size distributions from nitrogen adsorption data MCM-41 is currently the best model mesoporous adsorbent available, since it has simple pore geometry and can be synthesized in a wide range of pore sizes [17]. Nitrogen adsorption at 77 K is the most commonly used method for determination of the specific surface areas and mesopore size distributions of porous solids [25]. Therefore, the first successful work on verification and calibration of adsorption methods for mesopore size analysis using MMSs as the model materials was done for nitrogen adsorption on MCM-41 [17]. The originally obtained data describing the capillary condensation and evaporation pressures as functions of the cylindrical pore diameter (calculated using eq 1) are shown in Figure la, along with the results of later studies [13, 22, 23, 35-37]. This extensive data set covered the pore size range from 2 to 6.5 nm. To extend it on even larger pore sizes, the data reported in the literature for high-quality large-unit-cell MCM-41 [38] were used. For the latter, the pore size was evaluated using the reported unit-cell parameter (equal to 2-3"^^"^d) of 7.7 nm and an approximate primary mesopore volume (1.5 cm^ g'^) estimated from the reported total pore volume of 1.6 cm^ g'\ The capillary condensation and evaporation pressures for this sample were estimated from the reported nitrogen adsorption isotherm.
590 U. /
'
'
15
/
0.4 -
/
0.3 0.2
'
_,__
-'"^^
•"
/^cAo • • *
0.5 -
C/3 C/5
OH
'
(a)
0.6 --1
'
/ r>0
-
^m o •
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1)
-
1^
'/
^ ^ J
J*.
^
/ /
-
Condensation Evaporation
-
Q
-
o
— 1
3
4
5
6
Pore Diameter w^ (nm)
5
6
7
Pore Diameter w^ (nm)
Figure 1. (a) Experimental relations between the capillary condensation pressure and the pore diameter (hollow circles) and between the capillary evaporation pressure and the pore diameter (filled circles) for nitrogen adsorption at 77 K. The dashed line corresponds to the Kelvin equation with the statistical film thickness correction. The solid line corresponds to Eq. 2 derived using the KJS approach, (b) Relation between pore diameters calculated on the basis of Eq. 1 and the KJS-calibrated BJH algorithm using nitrogen adsorption data at 77 K. As can be seen in Figure la, nitrogen capillary condensation pressure in MCM-41 pores gradually increased as the pore size increased [ 17] and only minor random deviations from this general trend were observed. This indicates that adsorption branches of nitrogen isotherms are suitable for the pore size analysis [17]. In contrast, capillary evaporation pressure increased only slightly as the pore size increased from about 4.3 to 5.8 nm. This is related to the proximity of the lower limit of adsorption-desorption hysteresis [17] (relative pressure of about 0.4 for nitrogen at 77 K) [25] and to the fact that the quality of our model MCM-41 materials with pore sizes above 5 nm was in many cases somewhat lower than that of the samples with narrower pores. For pore sizes above 5.8 nm, the relation between the capillary evaporation pressure and the pore size also exhibited some scatter primarily related to differences in quality of the MCM-41 materials [17]. It can be concluded that the knowledge of capillary condensation pressure provides much more accurate information about the pore size than the knowledge of capillary evaporation pressure and thus adsorption branches of isotherms are more suitable for the pore size analysis than desorption branches. Since capillary condensation pressure was found to be a gradually increasing function of the pore size, it was possible to find an empirical equation for this relation (see Fig. la). This equation [17] was similar to the well-known Kelvin equation for cylindrical pores [25]: ip/p,)
[nm] = 0.416 [\og{pJp)]-'
(2)
where r is the pore radius as a function of the relative pressure (p/po), p is the equilibrium vapor pressure, po is the saturation vapor pressure and t is the statistical film thickness as a function of the relative pressure. The three terms in Eq. 2 are the Kelvin equation [25], the
591 statistical film thickness correction [17,25] and an empirical correction [17]. The well-known problem of inaccuracy in determination of the t-curve, resulting from uncertainty in evaluation of the monolayer capacity [39], was eliminated using the t-curve calibration on larg e-pore MCM-41 [17]. The resulting t-curve (tabular data were reported in Ref 24) can be described by an empirical equation determined for relative pressure range of 0.1-0.95 [17]:
^A',.77/:(/^/'Po)[«^] = 0.1
60.65 0.03071 - \og{plp,)
(3)
The KJS Eq. 2 provides an excellent description of the relation between the capillary condensation pressure and the MCM-41 pore diameter (see Fig. la). An additional advantage of this relation is that it is approximately equivalent to the Kelvin equation iox larger mesopore sizes and thus is expected to be valid in the entire mesopore range, which makes it very useful for an accurate determination of the mesopore size distributions. As shown in Fig. lb, Eq. 2 was used to determine the pore diameter of 40 good-quality MCM-41 samples [13,17,22,23,35-37] and the results were in excellent agreement with those based on Eq. 1. The standard deviation of differences between these two estimates (Wd - WKJS) was only 0.10 nm, which is rather remarkable. On average, Wd was slightly larger than WKJS (about 0.06 nm), which indicates that it may be possible to further improve the agreement by adjusting the empirical correction in Eq. 2. However, because of the small magnitude of the observed differences, it is justified to use Eq. 2 in its present form and defer the final refinement until the quality of MCM-41 or structurally similar samples with both small (below 3 nm) and large (above 5 nm) pore sizes is improved and the range of accessible pore sizes is extended. 2.3. DFT-based method to calculate pore size distributions. As already discussed, DFT can be used to predict the capillary condensation and capillary evaporation pressures for pores with homogeneous surface and well-defined geometry. To generate model adsorption isotherms for heterogeneous pores, it is convenient to employ hybrid models based on both DFT data for homogeneous pores and experimental data for flat heterogeneous surfaces [6-9]. Such model adsorption isotherms can be used to calculate PSDs in mesopore [6-9] and micropore [9] ranges. This approach is particularly useful for pores of diameter below 2-3 nm (micropores and narrow mesopores), where an assumption about the common t-curve for pores of different sizes is less accurate, which in turn makes the methods based on such an assumption (even properly calibrated ones) less reliable [18]. In the case of PSD calculation on the basis of DFT or computer simulation data, one faces a fundamental problem, whether adsorption or desorption branches of isotherms should be used. The recent experimental studies clearly indicate that adsorption branches of isotherms provide much more information about the pore size and are more suitable for the mesopore size analysis [17, 18]. In addition, adsorption data can often be acquired starting from low pressures, providing information sufficient to determine both micropore and mesopore size distributions from a single adsorption isotherm [9]. Illustrative PSDs calculated using the DFT-based method [9] and the KJS-calibrated BJH method are compared in Figure 2a. Both of these PSDs have highly similar positions of their maxima, heights and widths of their peaks. The current version of the DFT method [9] somewhat overestimates the size of pores above 4 nm, but other than that, the two approaches considered provide similar PSDs in the mesopore range. As mentioned above, the DFT method considered is capable of providing better estimates of the micropore size distributions.
592 3.0 2.5 S o
2.0
—1
(a) KJS DFT HK-KJS HK-SF
O
• A
o
1.5
•
11 ( )l)
'C
1.0 C/3
o
1
0.5 0.0 JLmmMSm Pore Size (nm)
Pore Size (nm)
Figure 2. (a) PSDs for 3.88 nm MCM-41 [22] calculated from nitrogen adsorption data at 77 K using i) the KJS approach with the BJH algorithm, ii) the hybrid DFT method, iii) the HKbased method with the relation between pore size and condensation pressure described by Eq. 2, and iv) the HK-based Saito-Foley method, (b) Comparison of PSDs for octyldimethylsilylbonded MCM-41 calculated from nitrogen adsorption using the KJS-calibrated BJH algorithm with t-curves for reference ODMS-modified silica and unmodified silica. 2.4. Deficiencies of the Horvath-Kawazoe method and other similar procedures Recently, the Horvath-Kawazoe (HK) method for slit-like pores [40] and its later modifications for cylindrical pores, such as the Saito-Foley (SF) method [41] have been applied in calculations of the mesopore size distributions. These methods are based on the condensation approximation (CA), that is on the assumption that as pressure is increased, the pores of a given size are completely empty until the condensation pressure corresponding to their size is reached and they become completely filled with the adsorbate. This is a poor approximation even in the micropore range [42], and is even worse for mesoporous solids, since it attributes adsorption on the pore surface to the presence of non-existent pores smaller than those actually present (see Fig. 2a) [43]. It is easy to verify that the area under the HK PSD peak corresponding to actually existing pores does not provide their correct volume, so the HK-based PSD is not only excessively broad, but also provides underestimated volume of the actual pores. This is a fundamental problem with the HK-based methods. An additional problem is that the HK method for slit-like pores provides better estimates of the pore size of MCM-41 with cylindrical pores than the SF method for cylindrical pores. This shows the lack of consistency [32,43]. Since the HK-based methods use CA, one can replace the HK or SF relations between the pore size and pore filling pressure by the properly calibrated ones, which would lead to dramatic improvement of accuracy of the pore size determination [43] (see Fig. 2a). However, this will not eliminate the problem of artificial tailing of PSDs, since the latter results from the very nature of HK-based methods. 2.5. KJS method to calculate pore size distributions for hydrophobic porous solids As already discussed, one can use a series of MMSs (for instance MCM-41) of known pore sizes to determine a relation between the capillary condensation (or evaporation)
593 pressure and the pore diameter for a given adsorptive. It is convenient to derive a description of such a relation, which expHcitly includes the t-curve (see Equation 2), since such a relation is expected to be valid for different porous materials with similar pore geometry when a proper t-curve is employed to account for differences in surface properties with respect to a given adsorbate. This in turn would open an opportunity to accurately determine PSDs of various mesoporous solids using a general relation between the pore size and capillary condensation (or evaporation) pressure for the particular pore geometry and a set of t-curves dependent on the composition (and consequently, surface properties) of porous materials. To verify this idea, MCM-41 silicas with chemically bonded octyldimethylsilyl (ODMS) ligands were studied, for which the pore size can be independently determined from the pore diameter of unmodified materials and the pore volume changes after modification [19]. The chemical bonding of ODMS groups renders surfaces which interact very weakly with nitrogen molecules [44] and this is likely to lower the statistical film thickness in comparison to that on the silica surface. The statistical film thickness in the pores of modified samples was indeed found to be significantly lower than that for the MCM-41 silicas [19]. The tcurves for the model modified materials were used to determine the reference t-curve for ODMS-modified silicas (reported in a tabular form in Ref 19), which is approximated in the pressure range from about 0.1 to 0.95 by the following equation [19]: 8.873 ^N,J7K,0DMsiP^ Po)[^^]
= ^''^
0.08004-log(/?//?o)
(4)
Along with Eq. 2, the t-curve for ODMS-modified silicas was used to determine PSDs of alkyldimethylsilyl-modified MCM-41 silicas employing the BJH algorithm. The resulting pore sizes were close to those obtained from the independent method mentioned above, which confirms that Eq. 2 with a proper t-curve is valid for materials with surface properties different from those of silica. The choice of the t-curve did not have a dramatic influence on the pore size evaluation (Fig. 2b), although the pore sizes determined using the t-curve for modified surfaces were somewhat lower as a result of the smaller t-curve correction. However, only when the proper t-curve was used, the total pore volumes and specific surface areas for the modified samples were correctly reproduced using the BJH method, whereas in the other case, they were grossly overestimated [19]. Moreover, the application of the proper t-curve largely eliminated the artificial tails on the PSDs (Fig. 2b). Eqs. 2 and 4 promise to be highly useful in characterization of a wide range of strongly hydrophobic solids, such as alkylsilyl-modified silicas (see Ref 44 and references therein). It needs to be kept in mind that not all organosilane-modified silicas have such weakly interacting surfaces and for instance aminopropylsilyl-modified silicas interact with nitrogen more similarly to the unmodified silica [44]. Anyway, the strongly hydrophobic surfaces abound in the field of both modified [44] and unmodified [23] MMSs. This can be illustrated on the example of an uncalcined MCM-41 (the calcined sample was described in Ref 35, Table 2, first entry). The uncalcined sample was macroporous and exhibited very weak adsorption at low pressures (see Figure 3a). As determined from the as-plot analysis [24-27] the low pressure data were similar to those of the ODMS-modified silicas and highly different from those for silicas, which manifested itself in minor deviations from linearity when the ODMS-modified reference adsorbent was used and considerable nonlinearity for the reference silica (see Figure 3b). This was already reported for MCM-41 materials prepared using surfactants of various chain lengths [23] and was attributed to the presence of
594 electrostatically bonded surfactant ions on the external surface of particles of these materials. This behavior may be general for a wide range of MMSs, at least those with direct ionic interactions between the template and inorganic framework. It also should be noted that the secondary porosity of the uncalcined sample under study closely resembled that of the calcined sample, which indicates that this porosity was a feature of particles of the material and did not result from partial collapse upon calcination, which may take place for some MMSs. Thus, examination of adsorption isotherms for both calcined and uncalcined MMSs may provide valuable insight into development of their secondary porosity. 90 OH
H
0.001
0.010
0.100
00
o •
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00
ODMS ref Silica ref
80 T3
T3
<
O
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K i
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<
20
0.0
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j ^
0.2
B < 1
1
[
0.4
0.6
0.8
0
1.0
0.0
0.2
0.4
Standard Adsorption a
Relative Pressure
Figure 3. (a) Nitrogen adsorption isotherm for uncalcined MCM-41. (b) Comparative plots for this sample calculated using reference data for ODMS-modified and unmodified silicas. 2.6. KJS method to calculate pore size distributions from argon adsorption data at 87 K Shown in Figure 4 are capillary condensation and capillary evaporation pressures as functions of the diameter of siliceous cylindrical pores for argon adsorption at 87 K [18]. These data were derived on the basis of the study of high-quality MCM-41 samples selected among those used in the case of nitrogen adsorption at 77 K [17,22,37]. As can be inferred from the comparison of Figs, la and 4a, adsorption behavior of argon at 87 K resembled that of nitrogen at 77 K. In general, the capillary condensation pressure gradually increased as the pore diameter increased, whereas the capillary evaporation pressure exhibited relatively smaller increase in the pressure range of the transition from the reversible adsorption behavior to adsorption-desorption hysteresis. Therefore, adsorption rather than desorption data were found to be suitable for the pore size analysis [18]. To facilitate the calculation of PSDs, the relation between the capillary condensation pressure and the pore diameter as well as the t-curve were derived [18] (tabulated t-curve data can be found in Ref 18): ip/ Po)[nm] = 0.3156[\og{p,/ p)Y
(5) + ^Ar.SlK ipl Po)'^ 0.438
^ArxiKipl Pa)[nm\ = 0.\
10.61 0.0561-log(p//;„)
(6)
595 Equation 5 is analogous to Eq. 2 discussed above. As illustrated in Figure 4b, the mesopore size distributions determined from nitrogen and argon adsorption data were essentially the same, when calculations were carried out for adsorption branches of isotherms using the corresponding KJS-calibrated relations (Eqs. 2 and 5) [18].
Pore Size w^ (mn)
Pore Size (nm)
Figure 4. (a) Capillary condensation/evaporation pressures as functions of the pore diameter for argon adsorption at 87 K. The solid line corresponds to Eq 5. See Fig. la for additional explanations, (b) PSDs calculated from nitrogen adsorption data at 77 K and argon adsorption data at 87 K using the BJH algorithm with the KJS relations (Eqs. 2 and 5, respectively).
3. ACKNOWLEDGMENTS The donors of the Petroleum Research Fund administered by the American Chemical Society are gratefully acknowledged for support of this research.
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