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Langmuir 2006, 22, 410-418
Pore Anisotropy and Microporosity in Nanostructured Mesoporous Solids John Knowles,† Gerasimos Armatas,‡ Michael Hudson,*,† and Philippos Pomonis*,‡ School of Chemistry, UniVersity of Reading, Box 224, Whiteknights, Reading, RG6 6BD, Great Britain, and Department of Chemistry, UniVersity of Ioannina, Ioannina, 45110, Greece ReceiVed July 12, 2005. In Final Form: October 12, 2005 In this study, we carried out an investigation related to the determination of the anisotropy (b) of pores as well as the extent of microporosity (mic%) in various groups of nanostructured mesoporous materials. The mesoporous materials examined were fifteen samples belonging to the following groups of solids: MCM-48s, SBA-15s, SBA-16s, and mesoporous TiO2 anatases. The porosities of those materials were modified either during preparation or afterward by the addition of Cu(II) species and/or 3(5)-(2-pyridinyl) pyrazole (PyPzH) into the pores. The modification of porosity in each group took place to make possible the internal comparison of the b and mic% values within each group. The estimation of both the b and mic% parameters took place from the corresponding nitrogen adsorptiondesorption isotherms. The new proposed method is able to detect a percentage of microporosity as low as a few percent, which is impossible by any of the methods used currently, without the use of any reference sample or standard isotherms. A meaningful inverse relationship is apparent between the b and mic% values, indicating that large values of b correspond to small values of mic%.
1. Introduction The mesoporous materials are defined according to IUPAC1-3 as possessing pore openings/diameters Dp in the range 2 < Dp < 50 nm. By that it is usually meant that, if the majority of pores, or the maximum Dmax of the pore size distribution (PSD), falls within this region, the material is considered to be mesoporous. The majority of mesoporous materials, including the nanostructured ones such as MCM-41, MCM-48, and SBA-14-6 possess some microporosity, which is due to the fact that the nanostructure only rarely is developed in perfect order across the entire mass of the prepared material. This microporosity becomes clear in observations by transmission electron microscopy (TEM) where often only small fractions of the optical field show order, but these small regions are usually chosen for publication. Evidence * Corresponding authors. Department of Chemistry, University of Ioannina, Greece; phone: +302651098350, fax: +302651098795, e-mail:
[email protected]. (P.P.). Department of Chemistry, University of Reading, Box 224, Whiteknights, Reading RG6 6BD, GB; phone: +441183786717, fax: +441183786331, e-mail:
[email protected] (M.H.). † University of Reading. ‡ University of Ioannina. (1) (a) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Piertti, R. A.; Rouquerol, J.; Siemienniewska, T. Pure Appl. Chem. 1985, 57, 603; (b) Rouquerol, J.; Avnir, D.; Fairbridge, C. W.; Everett, D. H.; Haynes, J. M.; Pernicone, N.; Ramsay, D. J. F.; Sing, K. S. W.; Unger, K. K. Pure Appl. Chem. 1994, 66, 1739; (c) Sing, K. S. W.; Schuth, F. In Handbook of Porous Solids; Schuth, F., Sing, K. S. W., Weikamp, J., Eds.; Willey-VCH: Weinheim, Germany, 2002; Chapter 1.2. (2) Gregg, J. C.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London 1982. (3) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders and Porous Solids: Principles: Methodologies and Applications; Academic Press: London, 1999. (4) (a) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (b) Huo, Q.; Margolese, D. I.; Ciesla, U.; Feng, P.; Gier, T. E.; Sieger, P.; Leon, R.; Petroff, P. M.; Schuth, F.; Stucky, G. D. Nature 1994, 368, 317. (5) (a) Huo, Q.; Margolese, D. I.; Ciesla, U.; Demuth, D. K.; Feng, P.; Gier, T. E.; Sieger, P.; Firouzi, A.; Chmelka, B. F.; Schuth, F.; Stucky, G. D. Chem. Mater. 1994, 6, 1176. (b) Monnier, A.; Schuth, F.; Huo, Q.; Kumar, D.; Margolese, D.; Maxwell, R. S.; Stucky, G. D.; Krishnamurty, M.; Petroff, P.; Firouzi, A.; Janicke, M.; Chmelka, B. F. Science 1993, 261, 1299. (6) (a) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548. (b) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024.
of mesoporosity can be obtained from X-ray diffraction (XRD) data, but, again, a considerable fraction of the material might be amorphous, disordered, or unstructured and thus not identified. A safer criterion for checking the existence of well-ordered mesoporosity is the shape of nitrogen adsorption-desorption isotherms and the appearance of the unmistakable sharp increase of adsorption at relative pressure (P/P0) ) 0.2-0.3. Even in such cases, many researchers in the field, on the basis of indirect evidence, suspect that a considerable fraction of porosity is due to micropores,7 and various attempts have been made to estimate the extent of microporosity.8 The established method of as-plots or t-plots for the estimation of microporosity2,3 in such cases provides erroneous evidence for zero microporosity, which must be due to the fact that these methods were proposed before the invention of MCM materials and are based on assumptions that do not apply to such materials.9 The as-plot or t-plot methods necessitate either the use of an additional adsorption isotherm from a sample without porosity but chemically similar to the porous one for comparison,2,3,10 or the use of the so-called standard isotherms, which correspond to a specific Value of the C parameter of the Brunauer-Emmett-Teller (BET) equation as proposed by Brunauer11 and by Lecloux and Pirard.12 Clearly, the first method has the drawback of additional experiments, while the second has the drawback of choosing a single specific value of C, which is not a constant.13,14 So it would be advantageous if there was a direct method for estimating the percentages of micro(7) (a) Sayari, A.; Liu, P.; Kruk, M.; Jaroniec, M. Chem. Mater. 1997, 9, 2499. (b) Kruk, M.; Jaroniec, M.; Ryoo, R.; Kim, J. M. Chem. Mater. 1999, 11, 2568. (8) Armatas, G. S.; Pomonis, P. J. Microporous Mesoporous Mater. 2004, 67, 167. (9) Armatas, G. S.; Petrakis, D. E.; Pomonis, P. J. Microporous Mesoporous Mater. 2005, 83, 251. (10) (a) Lippens, B. C.; de Boer, J. H. J. Catal. 1965, 4, 319; (b) Lippens, B. C.; Linsen, B. G.; de Boer, J. H. J. Catal. 1964, 3, 32. (11) (a) Brunauer, S.; Mikhail, R. Sh.; Bodor, E. E. J. Colloid Interface Sci. 1967, 24, 451. (b) Hanna, K. M.; Oder, I.; Brunauer, S.; Hagymassy, J.; Bodor, E. E. J. Colloid Interface Sci. 1973, 45, 27. (12) Lecloux, A.; Pirard, J. P. J. Colloid Interface Sci. 1979, 70, 265 (13) Pomonis, P. J.; Petrakis, D. E.; Ladavos, A. K.; Kolonia, K. M.; Armatas, G. S.; Sklari, S. D.; Dragani, P. C.; Zarlaha, A.; Stathopoulos, V. N.; Sdoukos, A. T. Microporous Mesoporous Mater. 2001, 69, 97. (14) Pomonis, P. J.; Petrakis, D. E.; Ladavos, A. K.; Kolonia, K. M.; Pantazis, C. C.; Giannakas, A. E.; Leontiou, A. A. Catal. Commun. 2005, 6, 93.
10.1021/la051887l CCC: $33.50 © 2006 American Chemical Society Published on Web 11/24/2005
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and mesoporosities in various mesoporous solids without the above drawbacks. Recently, we proposed such a methodology, which is based on self-consistent calculations for each particular adsorption-desorption isotherm for each solid.9 One of the purposes of the present paper is to check the applicability of that methodology in relation to various classes/groups of mesoporous solids. Another question about the porous solids is the anisotropy of their pores, that is, the dimensionless parameter
bi ) Di/Li
(1)
in which Di and Li are the diameter and length of each particular group i of pores filled by nitrogen at each particular relative pressure Pi() P/P0), respectively. Such a methodology was published recently.15 The relevant bibliography in this field is rather scarce, but Wheeler16 discussed a similar problem related to the anisotropy of intraparticle channels in a catalyst pellet.17,18 Recently Rigby discussed the subject of pore anisotropy from a different point of view.19 Clearly, the anisotropy of pores in a solid cannot have a single value, but must possess some kind of distribution. Therefore, a second aim of the present work is to calculate the pore anisotropy distribution (PAD) of the chosen mesoporous solids. It is expected that materials that have well-ordered porosity and long pores should show high values of pore anisotropy. It is also important to establish whether there is any possible effect of the extent of microporosity, mic%, on the PAD or the maximum of its value, bmax. To address those questions, 15 mesoporous materials /samples of variable porosity, which belong to four distinct groups/sets of solids, namely, MCM-48, SBA15, SBA-16, and mesoporous TiO2 anatase, were screened. The variation of porosities in a controllable way was achieved during the preparation of the solids of each group in order to have an internal comparison between the bi and mic% for each particular group. 2. Experimental Section 2.1 Preparation of the Porous Solids. The preparation of the mesoporous solids MCM-48 and Cu/MCM-48 took place as outlined by Schumacher et al.20 Briefly, hexadecyltrimethylammonium bromide (12 g) (CTAB; Acros) was dissolved in 250 mL of ethanol (British Drug House (BDH)) and 250 mL of distilled water. For Cu/MCM-48, 0.13 g of copper(II) nitrate trihydrate (BDH) was also added at this point. After the solution was stirred for 10 min, 60 mL of concentrated ammonium hydroxide (Fisher) was added, and the mixture was stirred for an additional 10 min. Then tetraethylorthosilicate (18.5 mL) (TEOS; Acros) was added under vigorous stirring, and the solution was stirred for an additional 2 h. The resulting mesophase was collected by filtration, dried overnight under ambient conditions, and calcined at 650 °C. For the solids MCM-48(100), we used the modified preparation outlined by Sun and Coppens using a postsynthetic treatment of the mesophase at 100 °C.21 A 9-g portion of the MCM-48 mesophase was taken prior to drying and dispersed in 20 mL of distilled water containing 0.2 g of CTAB within a Teflon liner. The pH was then adjusted to 8.5 using aqueous ammonia, and the suspension was stirred for 10 min under ambient (15) Pomonis, P. J.; Armatas, G. S. Langmuir 2004, 20, 6719. (16) (a) Wheeler, A. AdV. Catal. 1951, 3, 249. (b) Wheeler, A. Catalysis 1955, 2, 118. (17) Thomas, J. M.; Thomas, W. J. Introduction to the Principles of Heterogeneous Catalysis; Academic Press: London, 1967. (18) Thomas, J. M.; Thomas, W. J. Principles and Practice of Heterogeneous Catalysis; VCH: Weinheim, Germany, 1997. (19) Rigby, S. P.; Watt-Smith, M. J.; Fletcher, R. S. J. Catal. 2004, 227, 68. (20) Schumacher, K.; Grun, M.; Unger, K. K. Microporous Mesoporous Mater. 1999, 27, 201. (21) Sun, Ji-Hong; Coppens, M. O. J. Mater. Chem. 2002, 12, 3016.
conditions. The vessel was then sealed in a steel autoclave and placed in an oven at 100 °C for 48 h. The resulting mesophase was then treated the same way the MCM-48 sample was treated. The SBA-15 materials were prepared according to the procedure outlined by Zhao et al.22 The SBA-15(100) was prepared as follows: 4 g of P123 (BASF; triblock copolymer PEO20-PPO70-PEO20) was dissolved in 28 mL of distilled water and 122 g of 2 M HCl (aq) at 40 °C. Then, 9.2 mL of TEOS (Acros) was added, and the solution was heated at 40 °C for 1 day. The solution was then transferred to a Teflon bottle and placed in an oven at 40 °C for 2 days. The mesophase was recovered by filtration, washed with distilled water, and dried overnight under ambient conditions prior to calcination at 550 °C. The SBA-15(40) sample was obtained by taking an aliquot from the SBA-15(100) solution after the initial gelation period at 40 °C for 24 h. The SBA-16 samples were prepared according to the method outlined by van der Voort et al.23 In this case, 1 g of F127 (BASF, triblock copolymer PEO106-PPO70-PEO106) was dissolved in 150 g of 2 M HCl (aq) and 30 mL of distilled water at 38 °C. Then, 6 mL TEOS (Acros) was added and the solution was maintained at 38 °C for 24 h under vigorous stirring. The temperature was then elevated to 100 °C and maintained with stirring for an additional 48 h prior to filtration, drying, and calcinations at 450 °C. In the case of SBA-16(6.5), (10) and (20) 1,3,5-trimethylbenzene (TMB) was added as a porogen in different amounts in order to enable the formation of large-pore SBA-16 materials with different porosities. The samples are denoted as SBA-16/TMB(0), SBA-16/TMB(5.6), SBA-16/TMB(10), and SBA-16/TMB(20), where the number in the brackets refers to the TMB/F127 ratio used in the preparation. The TiO2-SESA-anatase materials (SESA denotes solvent evaporation self-assembly) were prepared via the procedure reported by Yang et al.24 In this case, 4 g of F127 (BASF) were dissolved in 40 g of absolute ethanol (BDH), and the solution was stirred for 10 min under ambient conditions. Then, 4.4 mL of TiCl4 (Aldrich) was added with care, and the resulting yellow solution was stirred for 30 min; the vessel was then placed in an oven at 40 °C for 7 days prior to calcination at 300 °C for 20 h. In the case of Cu/TiO2SESA-anatase, the addition of CuCl2 0.3H2O (0.0136 g, Aldrich) took place prior to the addition of TiCl4. The adsorption of 3(5)-(2-pyridinyl) pyrazole (PyPzH) within the mesostructures of MCM-48, Cu/MCM-48, and Cu/TiO2-SESAanatase was conducted by refluxing the mesoporous solids (∼1 g) with an ethanolic solution of PyPzH for 2 h (0.03 g in 50 mL). The solid was recovered by filtration, washed with cold ethanol, and then dried overnight at 60 °C. These materials are denoted as PyPzH/ MCM-48, PyPzH-Cu/MCM-48, and PyPzH-Cu/TiO2-SESA, respectively. The synthesis of PyPzH was conducted according to the procedure of Brunner and Scheck.25 The incorporation of copper(II) nitrate within the PyPzH/MCM48 material was conducted by the equilibration of an aqueous solution of copper(II) nitrate (0.02 g in 50 mL) under stirring for 30 min. The solid denoted as Cu-PyPzH/MCM-48 was recovered by filtration, washed with cold water, and then dried at 60 °C overnight. All the prepared materials with some of their properties are shown in Table 1. 2.2 N2 Adsorption-Desorption Porosimetry. Nitrogen sorption studies were conducted at 77 K using a Micromeritics Gemini III 2375 surface analyzer. All samples were outgassed at 150 °C for at least 12 h prior to analysis. 2.3 TEM Imaging. Transmission electron micrographs were obtained on a Philips CM20, operated under an acceleration field of 200 kV, with samples mounted upon holey carbon/copper support grids. (22) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024. (23) van der Voort, P.; Benjelloun, M.; Vansant, E. F. J. Phys. Chem. B 2002, 106, 9027. (24) Yang, P.; Zhao, D.; Margolese, D. I.; Chmelka, B. F.; Stucky, G. D. Chem. Mater. 1999, 11, 2813. (25) Brunner, H.; Scheck, T. Chem. Ber. 1992, 125, 701.
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Table 1. Specific Surface Areas Estimated from the Traditional BET Method (SBET) and from the I-Point Method (SI) and the Corresponding Vm and PI Values
samplea MCM-48 MCM-48(100) Cu/MCM-48 PyPzH-Cu/MCM-48 PyPzH/MCM-48 Cu-PyPzH/MCM-48 SBA-15(40) SBA-15(100) SBA-16/TMB(0) SBA-16/TMB(5.6) SBA-16/TMB(10) SBA-16/TMB(20) TiO2-SESA Cu/TiO2-SESA PyPzH-Cu/TiO2-SESA
C paraSI Vm ) V I SBET meter (I-point) {1 - (PI/P0)} 2 -1 2 -1 (m g ) BET (m g ) (cm2 g-1) PI/P0 1538 1451 1529 1143 1402 1303 419 675 692 725 747 634 262 197 148
25 42 29 24 28 34 -2680 93 -83 -124 -122 -95 127 113 65
1498 1775 1592 1060 1322 1244 432 659 793 814 835 734 258 194 284
344.0 407.5 365.6 243.4 303.5 285.5 99.1 151.4 182.0 186.8 191.6 168.4 59.1 44.5 65.2
0.32 0.35 0.35 0.29 0.29 0.29 0.17 0.24 0.09 0.10 0.09 0.09 0.26 0.33 0.34
a The precedent Cu indicates that Cu(II) was incorporated/adsorbed within the mesoporous solids. For PyPzH, this chemical species was adsorbed within the mesostructure.
Figure 2. Nitrogen adsorption-desorption isotherms and the corresponding I-plots drawn according to eq 3. Each horizontal triplet contains similar groups of porous solids, either in pure form or modified with the addition of Cu and/or PyPzH.
Figure 1. Representative TEM images of (a,b,c) SBA-16(20) (b is a magnified image of the boxed area in a); (d,e) MCM-48(100) (e is a magnified image of the boxed area in d); (f) SBA-15(100); and (g) MCM-48.
3. Results Typical TEM images of the mesoporous solids SBA-16/TMB(20), MCM-48(100), SBA-15(100), and MCM-48 are shown in Figure 1. We observe that these materials show well-organized structures and pores in the nanometer range. In some of those photos, we can distinguish not only the openings but also the lengths of the pores. For the SBA-15(100) material (Figure 1F), the size of hexagonally arranged pores is around 5-6 nm. The last structure
is similar to the SBA-15(40) one (TEM not shown), which possesses smaller pores. The MCM-48 material (Figure 1G) exhibits pore channels, which are around 3 nm wide but are also at least 10 times as long. The MCM-48(100) solid (Figure 1E) has pores larger than those of the parent material MCM-48, but the continuous, uninterrupted channels cross the whole mass of the particle (isolated in Figure 1D) from one end to the other. The SBA-16/TMB(20) sample also shows ordered cubic structure (Figure 1A,B,C). The TiO2-SESA-based materials were poorly ordered solids, and no TEM photos are presented. The nitrogen adsorption-desorption isotherms for are shown in Figure 2. To make the comparison of the results more convenient, each horizontal triplet in Figure 2 contains similar groups of porous solids, either in pure form or modified with the addition of Cu and/or PyPzH. From the N2 adsorption-desorption isotherms, it was possible to estimate the specific surface areas SBET of the solids, as well as the values of the C parameter of the BET eq 2 using the traditional plots (P/P0)/V[1 - (P/P0)] vs (P/P0) in the range 0 < (P/P0) < 0.25 (plots not shown here; see Supporting Information BET plots).
(P/P0)/V[1 - (P/P0)] ) 1/CVm + (C - 1)(P/P0)/CVm (2) In some cases, the plots exhibited convex and/or concave shapes, and it was not easy to choose and draw a straight line because the estimate of C and Vm based on such a fit will be biased. In any case, and after several trials, a best-guess line was drawn, usually at the low-pressure end. The values of SBET and C found are collected in Table 1. In the same Figure 2, the I-plots of the BET equation were drawn according to the methodology discussed in references 13
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Figure 3. Comparison of the SBET values, estimated from the traditional treatment of the BET equation, with the SI values estimated from the I-plots. The dashed line is a guide for the eye. The correlation coefficient between the two sets of values is r ) 0.98, which is better than 99% confidence limits. The four points above the line in the middle correspond to the SBAs. All six points in the right upper part correspond to MCM-48’s. The point out of trend at the left lower part corresponds to PyPzH-Cu/TiO2-SESA.
and 14. Namely, the BET equation was rearranged in the form
V[1 - (P/P0)]/(P/P0) ) CVm - (C - 1)V[1 - (P/P0)] (3) Plots of the form V[1 - (P/P0)]/(P/P0) versus V[1 - (P/P0)] exhibit an inversion point, termed the I-point for short. The projection of this I-point on the horizontal V[1 - (P/P0)] axis corresponds exactly to the volume of monolayer Vm, from which the values of the specific surface area SI were calculated using the simple relation
SI(m2/g) ) 4.356Vm ) 4.356VI [1 - (PI/P0)]
(4)
in which VI and (PI/P0) are the volume and pressure corresponding to the I-point, respectively. Details about the above calculations are in the Appendix. The estimated values of SI(m2/g), Vm ) VI [1 - (PI/P0)], and (PI/P0) are all included in Table 1. A comparison of the SBET values, estimated from the traditional treatment via the BET equation, with the SI values, estimated from the I-plots of eq 3, are shown in Figure 3.
4. Discussion This discussion is structured as follows: First, we shall make a comparative assessment between the SBET and the SI values shown in Figure 3. Second, we shall discuss the variation of the C parameter and the meaning of this variation in the whole range of relative pressure 0 < (P/P0) < 1. Third, we shall show how the variation of the C parameter, estimated from the I-plots in Figure 2, can be used to estimate the percentage of microporosity, mic%. Finally, we shall estimate the PAD of the pores, which is influenced by the method of preparation and/or doping for each particular group of solids, MCM-48, SBA-15, SBA-16, and TiO2-SESA. 4.1 Comparison between the SBET and the SI Values. From Figure 3, we observe that there is very good agreement between the SBET and the SI values, which are related with a correlation coefficient r ) 0.98, which is better than 99% confidence limits. There are some systematic exceptions with four SBA samples showing higher SI values (in the middle of Figure 3) while three
MCM-48 samples (all in the upper right part of the figure) show lower SI values. The sample MCM-48(100) (upper right part) and PyPzH-Cu/TiO2-SESA (lower left part) are obviously out of trend with higher SI values for reasons that are not understood for the moment. Using the traditional BET equation, we estimated the values of the C parameter cited in Table 1. For 5 out of the 15 samples, namely SBA-15(40), SBA-16/TMB(0), SBA-16/TMB(5.6), SBA-16/TMB(10), and SBA-16/TMB(20), the estimated C parameters were found to be negatiVe, which does not have a physical meaning. The most probable reason for this is the incorrect drawing of the plots (P/P0)/V[1 - (P/P0)] versus (P/ P0), which resulted in negatiVe intercepts i ) 1/CVm and necessarily larger Values of slopes s ) (C - 1)/CVm. What might be the relative error in the SBET resulting from such a drawing? If the absolute value of C is large, the error is rather small since C - 1 is almost equal to C, and, as a result, Vm ) 1/s. In other words, the large negative values of C do not systematically affect the SBET values when C is large. But if C is small, the mistake might become appreciable. To put it terms of a value, the relative mistake is around (1/C)%, as it can be easily calculated. So for C ) 1000, the mistake is around 0.1%, but for C ) 10 the error approaches 10%. So the remaining problem in this case is the negative value of C. Another problem is that the SBET and the SI values of the sample MCM-48(100) were found to be different, namely, 1451 and 1775 m2/g, respectively, whereas, for the PyPzH-Cu/TiO2SESA sample, the corresponding values were 148 (SBET) and 284 m2/g (SI). It is not clear which is the correct value for the moment, although, in the second case, the value 148 m2/g (SBET) seems more correct since the addition of PyPzH should result in a drop of surface area compared to the parent material TiO2SESA (SBET ) 262 m2/g) and the material Cu/TiO2-SESA (SBET ) 197 m2/g). For the rest of the materials, the correspondence between the SBET and the SI values is satisfactory. Nevertheless, the most critical reservation to the estimated constant values of C is that they are not constant, but they can vary as much as 6 orders of magnitude for fractional surface coverage θ between 0 < θ < 1.26 The determined values simply represent C as the values of θ tend to unity and V tends to Vm. 4.2 Variation of the C Parameter in the Range 0 < (P/P0) < 1 and Its Physical Meaning. The values of C can be determined in the range 0 < (P/P0) < 1 from the slopes of the I-plots (eq 3 and Figure 2) according to the relationships
Slope ) -(C - 1) ) 1 - C and C ) 1 - Slope
(5)
The values of C determined as a function of pressure (P/P0) are shown in Figure 4 in the form C ) f(P/P0). The C parameter initially has high values (1500-2000) at low-pressure ranges, which values subsequently reach the CBET value as the pressure increases and approaches the I-point. The explicit relationship for C is given by eq 6:2,3
C) [R1ν2/R2ν1] exp[(q1 - qL)/RT]
(6)
in which R1 and R2 are the condensation coefficients for the first and the second layers, respectively; ν1 and ν2 are the frequencies of oscillation of the molecules in the first and the second layers normal to the surface, respectively; q1 is the heat of adsorption in the first layer on the bare surface; and, finally, qL is the heat of condensation, which is equal for all the layers except the first. According to the above relation (eq 6), the high values of C, during the first stages of adsorption, should reflect the high values (26) Kemball, C.; Schneider, G. D. L. J. Am. Chem. Soc. 1950, 72, 5605.
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Knowles et al. Table 2. Micropore Volumes Vmic as Calculated from the I-Plots in the Subregion of Relative Pressures Shown in the Last Column and the Specific Pore Volume Vp as Calculated by the Cranston and Inkley Method27 Vp (at P/ Vmic (cm3 g-1) P0 ) 0.98) (%) (cm3 g-1)
sample MCM-48 MCM-48(100) Cu/MCM-48 PyPzH-Cu/MCM-48 PyPzH/MCM-48 Cu-PyPzH/MCM-48 SBA-15(40) SBA-15(100) SBA-16/TMB(0) SBA-16/TMB(5.6) SBA-16/TMB(10) SBA-16/TMB(20) TiO2-SESA Cu/TiO2-SESA PyPzH-Cu/TiO2-SESA
0.068 (8) 0.079 (7) 0.125 (13) 0.049 (8) 0.070 (9) 0.074 (10) 0.034 (9) 0.057 (5) 0.063 (13) 0.063 (11) 0.059 (11) 0.051 (10) 0.006 (2) 0.006 (2) 0.016 (4)
0.88 1.08 1.00 0.60 0.75 0.71 0.40 1.08 0.50 0.55 0.56 0.53 0.38 0.28 0.39
subregion of pressure 5.1 × 10-3 - 4.5 × 10-2 5.1 × 10-3 - 4.5 × 10-2 5.2 × 10-3 - 4.5 × 10-2 5.1 × 10-3 - 4.5 × 10-2 5.1 × 10-3 - 4.5 × 10-2 5.1 × 10-3 - 4.5 × 10-2 5.1 × 10-3 - 4.5 × 10-2 5.0 × 10-3 - 3.5 × 10-2 5.0 × 10-3 - 3.5 × 10-2 5.0 × 10-3 - 3.5 × 10-2 5.0 × 10-3 - 3.5 × 10-2 5.0 × 10-3 - 3.5 × 10-2 5.3 × 10-3 - 5.5 × 10-2 5.3 × 10-3 - 5.5 × 10-2 5.1 × 10-3 - 5.4 × 10-2
Table 3. Mean Hydraulic Pore Diameter D h p, the Maximum of the PSD Dmax, the Pore Anisotropy b, and the Values of the Most Probable Length L of Pores
Figure 4. Variation of the C parameter as a function of the relative pressure (P/P0). The horizontal triplets are arranged in the same order as in Figure 1 and contain similar groups of porous solids to make the comparison of the results easier. The values of the CBET parameter correspond to the horizontal dashed lines.
of the condensation coefficient R1 in the first layer compared to the value of R2 as well as the high values of q1 compared to qL. As the adsorption proceeds, the case where R1 ) R2 is eventually reached. For ν1 ) ν2, which is a realistic approximation, as the pressure and the surface coverage increases, V tends to Vm. At this limit, eq 6 obtains the form
C ) exp[(q1 - qL)/RT]
(7)
For RT ) 0.6 kJ/mol at 77K and (q1 - qL) ) 2.0 kJ/mol, the value of C should be around C ) 20, whereas, for (q1 - qL) ) 3.7 kJ/mol, C ) 500. When q1 is larger than qL, even by 1-2 kJ/mol, there should be a positive value of C. The values of the CBET at this limit are indicated by the horizontal dashed lines in Figure 4. Exactly at the I-point, the values of C tend to infinity, and, after the I-point, they have small, negatiVe values.13,14 This can be explained if q1 < qL, as discussed in detail in the original references.13,14 In other words, after the I-point, the heat of condensation qL becomes larger than the heat of adsorption q1, and therefore liquefaction takes place within the pores. This fact is expressed in Figure 4. We suggest that, in the range 0 < (P/P0) < (PI/P0), the parameter Q ) RT ln C corresponds to the chemical potential of adsorption, which decays exponentially from very high values to its lower limit Q ) RT ln CBET. In the range (PI/P0) < (P/P0) < 1, the parameter Q ) RT ln C corresponds to the chemical potential of liquefaction, which is high immediately after the I-point but drops exponentially to zero as (P/P0) tends to unity. So we propose that the explanation for the variation of the C parameters (see Figure 4) is that it is composed of two
sample
D h p ) 4Vp/ SBET (nm)
Dmax (nm)
b
L) bxDmax (nm)
MCM-48 MCM-48(100) Cu/MCM-48 PyPzH-Cu/MCM-48 PyPzH/MCM-48 Cu-PyPzH/MCM-48 SBA-15(40) SBA-15(100) SBA-16/TMB(0) SBA-16/TMB(5.6) SBA-16/TMB(10) SBA-16/TMB(20) TiO2-SESA Cu/TiO2-SESA PyPzH-Cu/TiO2-SESA
2.3 3.0 2.6 2.1 2.1 2.2 3.8 6.4 2.9 3.0 3.0 3.3 5.8 5.7 10.5
1.90 2.06 1.93 1.86 1.54 1.65 3.90 7.42 4.50 7.98 7.98 9.22 (1.74, 5.34) (2.26, 4.10) (1.88, 4.54)
608 1562 607 100 102 13.2 211 1801 118 41 10.5 232 (4.5, 1.9) (0.5, 0.06) (0.05, 0.02)
1155 3218 1172 186 157 22 823 13363 531 327 84 2139 (8, 10) (1.1, 0.3) ( C > 100/, /100 > C > 40/, /40 > C > 30/, and /30 > C > 20/,8 and similar proposals are found in ref 11. Clearly C
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is not a constant at all, as explained above (see also Figure 4), and only as the I-point is approached does its value tend to the constant C value estimated from the traditional BET treatment. If a standard isotherm is not used, then an adsorption isotherm of a “reference sample”, which is chemically similar to the one under test but without porosity, is required. Then,
ssa(test) ssa(reference)
)
b(test) b(reference)
)
V0.4(test) V0.4(reference)
(8)
where ssa is the specific surface area; V0.4 is the N2 volume adsorbed at (P/P0) ) 0.4, where the formation of monolayer is completed under any circumstances; and b ) Vm/σ, where σ ) 3.54 Å is the thickness of a single monolayer of N2.10 The notations “test” and “reference” indicate data obtain from the sample under testing and the reference sample, respectively. It would be advantageous to separate and estimate the extent of microporosity from the mesoporosity without resorting to the use of any standard isotherm or any reference sample or any pre-fixed pressure for the formation of the monolayer of nitrogen molecules. We have examined the mesoporous samples dealt with in this work using the standard t-plots methodology (data not shown here; see Supporting Information t-plots). The results did not show any apparent consistency, providing negative micropore volume in some cases (MCM-48, MCM-48(100) and PyPzHCu/TiO2-SESA samples), while, for the SBA-16/TMB(0), SBA16/TMB(5.6), SBA-16/TMB(10), and SBA-16/TMB(20) solids, the standard t-plots had the downward shape expected from mainly microporous materials, although the samples are clearly mesoporous in TEM (Figure 1). Such uncertain results could be due to the difficulty of correctly drawing the t-plots. So a method proposed recently9 for the determination of microporosity based on the variation of C will be used. From the plots C ) f(P/P0), it is possible to calculate the plots C ) f(V/Vm) and estimate the slopes dC/d(V/Vm) ) f(V/Vm) or the equivalents dC/d(n/nm) ) f(n/nm). Such plots are shown in Figure 5. The graphs dC/d(n/nm) ) f(n/nm) have a zero gradient at very low values of pressure where the fraction (n/nm) is low. Then, as the pressure and the adsorbed fraction (n/nm) increases, the slope becomes positive, but, at higher pressures, it becomes zero again. Armatas et al.9 showed both experimentally and theoretically that the Variation of C as a function of the fraction of the monolayer (n/nm) was only altered in the microporous region, since, in this range, the chemical potential of adsorption, which is an extensiVe physicochemical property, relates to the formation of a monolayer. On the contrary, in the range of mesoporosity, this Variation is nullified since the C parameter and the corresponding chemical potential both reflect the process of liquefaction, which is an intensiVe physicochemical property. The volume of the micropores can be estimated from the volume of nitrogen adsorbed in the pressure range in which the second derivative d2C/d(n/nm)2 is not nullified. The second derivative was chosen to be “zero” when it obtained values less than 1% of its maximum. The maxima had values around e5, so zeroing was assumed at e3. Then, about 97-98% of the corresponding area is covered by the integration. The corresponding results are in Table 2. The specific pore volume Vp in Table 2 was calculated by the method of Cranston and Inkley27 using the adsorption branch of the isotherm to avoid any effects generated by hysteresis. There was some microporosity that in all cases was less than 10%. The samples based on TiO2-SESA showed almost no microporosity, whereas the MCM-48-based materials showed a (27) Cranston, R. W.; Inkley, F. A. AdV. Catal. 1957, 9, 143.
Figure 5. The relationships dC/d(n/nm) ) f(n/nm) for the examined mesoporous solids. The ordering is similar to Figures 1 and 3. The second derivative d2C/d(n/nm)2 is also shown in dashed lines. The vertical lines define the region of microporosity.
small amount of microporosity around 3-7%. The same was also true for the SBA-15 and the SBA-16 materials. The microporosity arises because there are some regions of the solids with misdeveloped or destroyed mesoporosity. The proposed method seems to be able to detect the percentage of microporosity as low as a few percent, which is impossible by any of the methods used currently. 4.4 Anisotropy of Pores. The estimation of anisotropy in porous media is a subject that has attracted huge interest from people working mainly in the field of crude-oil recovery from soils.28 These studies were mainly concerned with the estimation of macroporosity based on seismic data. As far as the estimation of anisotropy in mesoporous systems is concerned, the only known attempt is that of Wheeler16-18 who discussed the concept of flow through pores in a catalyst pellet. Recently, another approach to the problem of anisotropy was made by Rigby et. al.19 In a recent publication, we proposed a general method based on nitrogen adsorption isotherms for estimating the pore anisotropy b in mesoporous solids containing cylindrical pores.15 The anisotropy bi for each group i of pores may be defined as
bi ) Li/Di
(9)
in which Li and Di are the length and diameter of the group i of pores filled at a relative pressure Pi () Pi/P0), respectively. There is a distribution of the anisotropy of the pores of each solid. If the pore geometry deviates substantially from the Euclidean cylindrical model, then the model is incorrect. Briefly, the proposed method15 involves the use of the differential specific surface area Si as well as of the differential specific pore volume Vi estimated via a standard algorithm. For example, the BJH methodology29 at each pressure Pi () Pi/P0) (28) (a) Thomsen, L. Geophysics 1986, 51, 1954. (b) Thomsen, L. Geophysics 2001, 66, 40. (29) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. J. Am. Chem. Soc. 1951, 73, 373.
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Figure 6. The distribution of the pore anisotropy b as a function of the pore radius r for all the examined solids.
may be used. Then the following relationship applies:
Li ) Dibi ) 2ribi ) riai
(10)
in which ai is a scaling parameter to be determined. The dimensionless parameter Si3/Vi2 may be calculated, which, for cylindrical pores, takes the form
Si3
[Ni(2πri)Li]3
Vi
[Ni(πri2)Li]2
) 2
)
[Ni(2πri)(2ribi)]3 [Ni(πri2)(2ribi)]2 [Ni(2πri)(ri)ai]3 [Ni(πri2)(ri)ai]2
) 16πbiNi ) ) 16πNi
( )
riai-1 (11) 2
in which Ni is the number of pores filled with N2 at each pressure Pi () Pi/P0) having radius ri and diameter Di. The term
λi ) (Si3/16πVi2) ) Nibi
(12)
corresponds to the total anisotropy λi of the group Ni of the pores with anisotropy bi. Equation 12 in combination with eq 11, after taking logarithms, obtains the form
log(λi) ) log
()
Ni + (ai - 1) log ri 2
(13)
The slopes (Ri - 1) in eq 13 are calculated from the lines log λi versus log ri, where λi ) (Si3/16πVi2), and Si, and Vi are the differential surface area and differential pore volume, respectively, as mentioned above. Then, the values of anisotropy bi for each group i of pores are given by the simple relationship
bi ) 0.5ri(ai-1)
(14)
The estimated values of bi are plotted in Figure 6 as a function
of the radius ri, while the maximum values of bi found for each porous solid are shown in Table 3. The plots in Figure 6 are the PAD values, and the bmax values correspond to the same maxima of the PSD. The maxima in the PSD show the most probable pore diameters, whereas the maxima in the PAD show the most probable pore anisotropies. From Table 3, the maximum values of pore anisotropy bi for the MCM-48, SBA-15, and SBA-16 materials are to be found in the range 10 < bi < 1800. The corresponding pore lengths L ) Dxb are then found in the range of 85-13360 nm. The values of pore lengths in the range of hundreds to a few thousand nanometers are acceptable. We are not aware of many TEM microphotographs in the literature that provide first-hand evidence of the length of pores in MCM-48 or similarly ordered mesoporous solids. The only data known to us is by Zheng et al.30 who prepared and studied TiOxNy-oxynitrided mesoporous silica MCM-14, the pole length of which appears in the range of 100200 nm in TEM, which is in good agreement with the findings of the present work. Nevertheless, if the maximum value of the pore length for sample SBA-15(100) is around 10 µm, this is almost equal to the diameter of the particles of such samples. In other words, those particles that possess large pores, as seen in Figure 1f, should be open systems from one end to the opposite end. This point is in agreement with the observation by Zhang et al.31 that SBA-15 materials, somehow similar to the present SBA-15(100), show pore channels that run across the cuboidlike particles and parallel to their small axis. In Figure 6 we observe that, for certain radii ri, there are clear peaks in the pore anisotropy for all the samples studied, whereas, for radii near this central value in the range ri ( dri, the values of bi drop to near unity or even below. Also, the samples Cu/ TiO2-SESA and PyPzH-Cu/TiO2-SESA showed very low values of maximum pore anisotropy (0.5-0.02), while the pore lengths were in the range of 1-0.1 nm. The values of bi near unity mean that the pores filled in this pressure range are characterized by almost equal length Li and diameter Di (bi ) 1), which is in perfect agreement with the work of Dullien who, on the basis of various microphotographs of materials with random porosity, showed that the length and diameter of the pores are almost similar.32 But in the cases of very low anisotropies, as well as in the case of very high anisotropy discussed above, it is possible that the model theory, which is based on cylindrical geometry (see eq 11), does not apply, and some correction factor F is needed, as discussed in ref 15. Nevertheless, the determination of such correction factors F, although predictable in model systems,18 might not be trivial for real ones since a certified value of bi is needed from another totally independent method, for example, electron tomography.33-35 This powerful technique could be used to complement anisotropy data obtained via the present methodology. 4.5 Interrelationship between the b and mic% Values. Figure 7 shows the values of the logarithm of the anisotropies (log b) as well as the mic% for all the studied materials. The purpose is to facilitate an internal comparison between the log b and mic% values for all the solids as well as within each group of solids. The first important observation is that high values of log b tend to correspond to low values of mic% and vice versa. This (30) Zheng, S.; Li, Z.; Gao, L. Mater. Chem. Phys. 2004, 85, 195. (31) Zhang, H.; Sun, J.; Ma, D.; Klein-Hoffmann, A.; Weinberg, G.; Su, D.; Schlogl, R. J. Am. Chem. Soc. Commun. 2004, 126, 7441. (32) Dullien, F. A. L. Porous Media: Fluid Transport and Pore Structure, 2nd ed.; Academic Press: San Diego, CA, 1992. (33) Ziesse, U.; de Jong, K. P.; Koster, A. J. Appl. Catal., A 2004, 260, 71. (34) Datye, A. K. J. Catal. 2003, 216, 144. (35) de Jong, K. P.; Koster, A. J. Chem. Phys. Chem. 2002, 3, 776.
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Figure 8. Interdependence between log b and mic%. The lower three points correspond to the TiO2-SESA materials with random mixed micro- and mesoporosity (see adsorption isotherms in Figure 2). The upper group corresponds to the rest of the solids with more or less ordered porosity.
Figure 7. Bar chart of the values of the log of anisotropy b (upper part) and the percent microporosity (lower part).
effect is systematic not only for the whole set of solids but also within each group. For example, the incorporation of PyPzH and Cu-PyPzH into the MCM-48 parent material increases the microporosity, presumably because some mesopores are restricted, and at the same time decreases its anisotropy because some pores are restricted almost to the point of complete blocking. The same effect in relation to anisotropy occurs with the incorporation of PyPzH into the Cu/MCM-48, but, in this case, the mic% drops for reasons that might be related to the complete blockage of a large fraction of micropores when Cu(II) has been preadsorbed into them. Also, the two SBA-15 materials show similar trends since the one with larger mic% has lower b values. For the four SBA-16 solids, this observation does not apply for the SBA-16 /TMB(5.6) and SBA-16 /TMB(10) samples. This must be related to some differentiation in their porosities, which are misrepresented by the models used for the calculations. Finally, the same inverse tendency between mic% and b is also apparent for the three samples based on TiO2-SESA. There again, the incorporation of Cu as well as PyPzH plus Cu into the parent materials results in an increase in mic% but a drop in anisotropy b for reasons related to the restriction and blocking effects of additives into the pores. A comparison between the mic% and log b values for all the samples is shown in Figure 8. There is a tendency for small anisotropies to correspond to large percentages of microporosity. This tendency does not seem to be the same for all the solids. In Figure 8, the three samples based on TiO2-SESA, which possess random micro- and mesoporosity (see adsorption isotherms in Figure 2), follow a different trend. The rest of the samples with more or less ordered porosity obey a different trend. The two samples Cu/MCM-48 and SBA-16/TMB(0), with a higher mic% (13%), seem to be out of this last subtrend in Figure 8. However, the general trend is unmistakable. A porous network with perfectly ordered mesopores is expected to have large anisotropy and zero microporosity. Any introduction of micropores, presumably connected to
mesopores, will decrease the anisotropy of the porous network because then the directions in the mesochannels are not unique but may be interrupted by fine micro-bypasses. What’s more, this effect is exponential. A small addition (1-2%) of microporosity results in a drop of anisotropy by around 1 order of magnitude. A full quantitative description of this effect will require more data from similar materials and also dissimilar ones. A direct indication that the one-dimensional channels in mesoporous MCM-41 materials, like the present ones, are permeable to other adsorbents like water and/or disordered and bent has been provided by pulse field gradient nuclear magnetic resonance self-diffusion measurements of adsorbed water.36 In those studies, the molecular propagation of the guest molecules was found to be highly anisotropic. The possible permeability of the mesochannels might originate from microcracks, or structural micropores, which are connected to mesopores and thus decrease the uninterrupted movement along them. Again, a quantitative description of this effect, especially in relation to the data shown in Figure 8, necessitates further study.
Conclusions A methodology has been proposed for estimating the pore anisotropies b, the percentage microporosities mic%, as well as the specific surface areas of porous materials. The underlying ideas for these calculations have been published previously elsewhere,9,13-15 but this the first time they have been applied to nanostructured ordered mesoporous solids. All the calculations are based on N2 adsorption-desorption isotherms. An inverse relationship was observed between the log b on one hand and the mic% on the other, which may be differentiated for different kinds of solids. Acknowledgment. We acknowledge financial support from EU (program GROWTH/INORGPORE, project G5RD-CT200000317) and the programs PYTHAGORAS and HERAKLEITOS financed by EU and the Greek Ministry of Education in the context of project EPEAEK. (36) Stallmach, F.; Karger, J.; Krause, C.; Jeschke, M.; Oberhagemann, U. J. Am. Chem. Soc. 2000, 122, 9237.
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SI(m2/g) ) 4.356Vm
Appendix The I-point method for the estimation of specific surface areas13,14 and micropore percent volume8 can be applied using the follow steps: Step I. The original and well-known BET equation
V/Vm ) C(P/P0)/[1 - (C - 1) (P/P0)][1 - (P/P0)]
(I)
is written not in the usual linear way but instead in the nonlinear form
[V[1 - (P/P0)]/(P/P0) ) CVm - (C - 1)(V[1 - (P/P0)] (II) Then plots of the right-hand part [V[1 - (P/P0)]/(P/P0) versus V[1 - (P/P0)] provide lines that have the shape of an inclined V, that is, >, with the inversion point termed the I-point for short. Such I-plots are in Figure 2 (upper and right-hand axes) for all the studied samples. Step II. Experimental evidence shows that the projection of the I-point on the horizontal axis V[1 - (P/P0)] corresponds exactly to the volume Vm of the adsorbed monolayer; in other words, Vm ) VI[1 - (PI/P0)]. Therefore, the values of the specific surface area S, for N2 as adsorbent, can be found via the simple relation
(III)
which equals Vm[(cc/g)/22400(cc/mol)]6.0231023 (molecules/ mole) (16.210-20(m2/N2 molecule)) Step III. The slopes (slp’s) of the lines V[1 - (P/P0)]/(P/P0) versus V[1 - (P/P0)] (see eq II above and the plots in Figure 2) correspond to 1 - C, and therefore C ) 1 - slp, from which the values of C can be found in the whole range 0 < P
