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Improved Comparison Plot Method for Pore Structure Characterization of MCM-41 H. Y. Zhu, X. S. Zhao, G. Q. Lu,* and D. D. Do Department of Chemical Engineering, The University of Queensland, St. Lucia, Queensland 4072, Australia Received June 3, 1996X MCM-41 samples of various pore dimensions are synthesized. Plotting of nitrogen adsorption data at 77 K versus the statistical film thickness (comparison plot) reveals three distinct stages, with a characteristic of two points of inflection. The steep intermediate stage caused by capillary condensation occurred in the highly uniform mesopores. From the slopes of the sections before and after the condensation, the surface area of the mesopores is calculated. The linear portion of the last section is extrapolated to the adsorption axis of the comparison plot, and this intercept is used to obtain the volume of the mesopores. From the surface area and pore volume, average mesopore diameter is calculated, and the value thus obtained is in good agreement with the pore dimension obtained from powder X-ray diffraction measurements. The principle of the calculation as well as problems associated are discussed in detail.
Introduction Many mesoporous materials possess irregular pore structures and a broad pore size distribution. Recently, there is a great deal of interest in a novel family of mesoporous materials that exhibit highly uniform mesopore structure.1,2 One of these solids, known as MCM41, can be synthesized to consist mostly of a long-rangeordered hexagonal arrays of uniform mesopores.3,4 Therefore, the peak at [100] in X-ray diffraction spectra provides an independent estimate of the pore size in MCM41. The conventional method of determining pore size is the nitrogen adsorption method.5 Although a number of theories have been developed for deriving parameters of pore structure from such a method, the applicability and accuracy for estimating the pore structure of solids that consist of supermicropores and small mesopores are often in question. According to several researchers,6 MCM-41 is regarded as the most suitable model adsorbent currently available for verification of methods for pore parameter calculations. In general, calculations of mesoporosity are based on the Kelvin equation with the assumption of a 0° contact angle of liquid nitrogen with pore walls and correction for the statistical thickness of adsorbed N2.5 As pointed out by Branton et al.,7 application of the Kelvin equation may give a false assessment of the true pore size distribution since the data used for the calculation are from a region where the meniscus of liquid nitrogen is unstable. On the other hand, t-plot8 and Rs-plot9 methods, based on comparing adsorption on the porous solid with that of * Corresponding author: phone, 61 7 33653735; fax, 61 7 33654199; e-mail,
[email protected]. X Abstract published in Advance ACS Abstracts, December 1, 1996. (1) Beck, J. S.; Vartuli, 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, 10834-10843. (2) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710-712. (3) Chen, C. Y., Li, H. X.; Davis, M. E. Microporous Materials 1993, 2, 17-26. (4) Zhao, X. S.; Lu, G. Q.; Millar, G. J.; Li, X. S. Catal. Lett. 1996, in press. (5) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: New York, 1982. (6) Ravikovitch, P. I.; Domhnaill, S. C.; Neimark, A. V.; Schu¨th, F.; Unger, K. K. Langmuir 1995, 11, 4765-4772. (7) Branton, P. J.; Hall; Sing, K. S. W. J. Chem. Soc., Chem. Commun. 1993, 1257-1258. (8) Lippens, B. C.; De Boer, J. H. J. Catal. 1965, 4, 319-323.
S0743-7463(96)00541-0 CCC: $12.00
a nonporous reference, have been widely used to determine the micropore volume of porous solids. These plots can be used to derive more detailed information on porosity of a solid as demonstrated by Brunauer and his coworkers.10 They proposed a micropore analysis method, termed as the MP method, to calculate the micropore size distribution using t-plot. The MP method is an extension of the t method of Lippens and de Boer.8 The t-curve provides a relation between the statistical thickness of the adsorbed film and the relative pressure P/P0 for a nonporous reference solid. The isotherm data of the porous solid is then plotted against t, and such a plot is known as the t-plot. If the multilayer adsorption mechanism is applicable over the entire range of pressure, the t-plot is a straight line passing through the origin and its slope is proportional to the surface area of the solid. The adsorption behavior of the solid is the same as that of a nonporous solid. However, in a porous solid with pore size distribution, smaller pores are completely filled with adsorbate molecules as the relative pressure increases. Hence those pores are no longer available for further accommodating of adsorbate molecules. As a result, the slope of the t-plot decreases as the adsorption progresses further. de Boer et al. found that the surface areas that are still available can be related to the slope of the t-plot at the considered P/P0 point.11 In the MP method,10 surface area of a group of pores with similar pore size is obtained from the difference in slopes of the tangents drawn at two adjacent points on the t-plot. In addition, the average of the t values at those two points is used to represent the size of the pores in that group. The pore volume of the pore group is then calculated from the information of surface area and pore size assuming a pore shape. For instance, if the pore shape is slit, the pore width is 2 times the mean t value. It is known that the statistical thickness t can not indicate the size of mesopores in which capillary condensation occurs at a certain pressure. The material takes up more adsorbate than the volume of the multilayer adsorbate. Therefore, the MP method can not be applied to estimate the dimension of mesopores. (9) Sing, K. S. W. In Surface Area Determination, Proc. Int. Symp., 1969; Everett, D. H., Ottewill, R. H., Eds.; Butterworths: London, 1970; p 25. (10) Mikhail, R. S. H.; Brunauer, S.; Bodor, E. E. J. Colloid Interface Sci. 1968, 26, 45-53. (11) De Boer, J. H., Lippens, B. C.; van der Plas, Th.; Zondervan, G. J. J. Catal. 1965, 4, 649-653.
© 1996 American Chemical Society
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Figure 2. N2 adsorption isotherm of a commercial silica gel.
Figure 1. N2 adsorption isotherms of MCM-41.
In the present study, the comparison plots, t-(or Rs-)plots are used to evaluate the volume and surface area of mesopores in several MCM-41 samples. The pore size is then obtained from the volume and surface area. With the proposed improvement, we can extend the application of the MP method to mesoporous solids. The obtained pore sizes are compared well with the results of X-ray diffraction. Discussions on the influence of pore shape and the limitations of the improved method are also presented. Experimental Section Pure silica MCM-41 samples with various pore sizes were synthesized in a hydrothermal system of 14.4 NH4OH:30 SiO2: 5.2 CnH2n+1(CH3)3NCl:700 H2O. The pore sizes can be tailored by choosing the surfactants with n ) 12, 16, 18 by adding the auxiliary organic compound, mesitylene, using cetyltrimethylammonium chloride surfactant (mesitylene/surfactant ) 1). The samples are referred to as MCM-41(d), where d represents the pore size (nm) derived from the proposed method. Details of the synthesis procedure are reported elsewhere.4 The morphology of MCM-41 was examined by scanning electron microscopy (SEM; Phillips 505). X-ray powder diffraction (XRD) patterns were obtained on a PW 1840 diffractometer (Phillips), with Co KR radiation, 40 kV, 25 mA. Nitrogen adsorption was performed at 77.3 K using an automated surface area and pore structure analyzer, (NOVA 1200), Quantochrome, and the samples were degassed at 573 K for 3 h prior to adsorption analysis.
Results Isotherms and t-Plots. The isotherms of nitrogen adsorption at liquid nitrogen temperature (77.3 K) on the MCM-41(3.2), MCM-41(3.8), and MCM-41(4.5) samples are shown in Figure 1. The stepwise shape is the typical characteristic of the N2 isotherm of MCM-41. The relative pressure (P/P0) at which the adsorption reaches the last plateau shifts to the right for samples with larger pore diameter. This characteristic relative pressure (P/P0) has
Figure 3. t-Plots (b) and the corresponding slope curves (O) of MCM-41 samples.
been used to qualitatively compare the pore dimension of different samples.1,2 A higher value of the characteristic (P/P0) indicates a larger pore size. Figure 2 shows an isotherm of a commercial mesoporous silica, KG-40 of Merck KG, Damstart, Germany, which has a mean pore size of about 4.0 nm. Nitrogen adsorption data on a nonporous hydroxylated silica, from Gregg and Sing,5 are used to construct the comparison plots, t-plot. Adsorption amount, Va, is plotted as a function of t, which is the statistical thickness of nitrogen film adsorbed on the nonporous silica at the same relative pressure (Figures 3 and 4). Three distinct linear stages are observed in the t-plots, as defined by Branton et al.:7 A, multilayer adsorption on the pore wall; B, reversible condensation; and C, adsorption on the external surface. In contrast, for the commercial silica, the stages A and B are not so distinctive. Calculation of Specific Surface Areas. BET surface areas of the samples were calculated from the N2 adsorp-
Pore Structure Characterization of MCM-41
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Figure 4. t-Plots (b) and the corresponding slope curves (O) of silica gel. Table 1. Pore Parameters Derived from N2 Adsorption Data MCM-41 SBET (m2/g) CBET St (m2/g) Sext (m2/g) Spore (m2/g) Vpore (cm3/g) dh (nm) dth (nm) dXRD (nm) dmBJH (nm) 4 × tb
(3.22) (3.08)
(3.23)
(3.80) (3.71) (4.51)
809.9 117.0 821.1 104.9 716.2 0.572 3.22 3.19 3.21 2.80 2.48
1002.5 87.9 992.0 62.3 929.7 0.758 3.23 3.26 3.39 2.85 2.34
858.2 95.9 856.5 165.3 691.2 0.658 3.80 3.81 3.95 3.30 2.70
768.4 60.2 734.0 136.5 597.5 0.486 3.08 3.25 3.34 2.91 2.28
787.7 81.7 765.0 162.5 602.4 0.580 3.71 3.85 3.87 3.20 2.24
837.5 99.7 837.9 116.6 721.2 0.813 4.51 4.51 4.48 3.85 2.84
silica40 524.8 42.3 474.9 12.7 462.2 0.472 3.68 4.08 3.88 3.12
tion data in a P/P0 range of 0.05-0.2, and the results, SBET, are summarized in Table 1 together with corresponding C values. It was proposed8,10 that as long as the adsorbate multilayer is formed unhindered, the t-plot is a straight line that goes through the origin; the slope of this straight line, ksample, is a measure of the specific surface area of the sample:
St )
ksample ksample ‚Sref ) 38.7 (m2/g) kref 2.51
(1)
where St is the surface area calculated from the t-plot. kref and Sref are the slope of the t-curve and the specific surface area of the nonporous silica, respectively, being 2.51 and 38.7 m2/g.12 In all cases, the first part of the curves (stage A) is a straight line passing through the origin, and St values calculated from it are listed in Table 1. This surface area is slightly different from the corresponding BET surface area, SBET, for all MCM-41 samples. Calculation of Surface Area, Volume and Size of the Mesopores. The linear portion of the stage C is of particular importance in the calculation of porosity. First, the external surface area, Sext, can be obtained from the slope of the t-plot at stage C, using the same formula for the calculation of St. Moreover, when the straight line is extrapolated to the adsorption axis (as illustrated in Figures 3 and 4), the intercept on the axis indicates the volume of the pores which have been filled by nitrogen molecules at the onset of stage C. This method has been widely used to evaluate the micropore volume of a solid.5 (12) Payne, D. A.; Sing, K. S. W.; Turk, D. H. J. Colloid Interface Sci. 1973, 43, 287-293.
Figure 5. Powder X-ray diffraction patterns of MCM-41 samples.
As discussed later, this volume is the pore volume of the uniform mesopores in the MCM-41 sample, Vmeso. Accordingly, the difference between St and Sext is the surface area of the uniform mesopores, Spore. The mean dimensions of the mesopores are then derived13 from the data of Spore and Vmeso rather than from the t value as in the original MP method. In general, the mesopores of MCM41 are visualized to be cylindrical, according to the information obtained by XRD, and thus the hydraulic diameter of a pore is apppliable (eq 2).14 Values of dh calculated for all samples are also given in Table 1.
( )
dh ) 2r ) 4
Vpore 4Vpore πr2L ) 4‚ ) 2πrL Spore St - Sext
(2)
Results of X-ray Diffraction and Scanning Electron Microscopy. The X-ray diffraction patterns of the MCM-41 samples are shown in Figure 5. The sharp d100 peaks as well as the secondary reflections observed at larger angles indicate the presence of hexagonally arranged pore structures, being characteristic of MCM-41. The pore dimension can be derived from the position of the [100] peak: dxrd ) a0 - wall thickness (a0 ) 2d100/x3), assuming that the wall thickness for silicate is 10 Å.3 These results are shown in Table 1. It is seen that the obtained dh of MCM-41 by the improved MP method is in good agreement with the pore dimension derived from XRD. SEM micrograph in Figure 6 shows the morphology of the grains of MCM-41(3.8). The particles are seen to consist of small grains with a size of about 0.1 µm. If a spherical shape is assumed for these grains, one can estimate the external surface area of the sample. The density of the sample was measured to be about 0.2 g/cm3, and thus the calculated external surface area is 150 m2/g. It is comparable with the external surface area obtained from the comparison plot, Sext of 162 m2/g, as listed in Table 1. Discussion All three cases with respect to the shape of Va - t curves, as summarized by Lippens and de Boer,8 are observed for (13) Zhu, H. Y.; Vansant, E. F. J. Porous Mater. 1995, 2, 107-113. (14) Brunauer, S.; Mikhail, R. S. H.; Bodor, E. E. J. Colloid Interface Sci. 1967, 24, 451-463.
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Figure 6. SEM micrograph of MCM-41(3.8) with visible primary gains having a dimension of about 0.1 µm.
MCM-41 as illustrated in Figure 3. Since stage A is a straight line through the origin and extends up to a relative pressure of 0.09 at which the monolayer adsorption has completed,10 it represents the unhindered multilayer adsorption mechanism on the entire surface. The difference between St and the corresponding SBET is found to be less than 5%. The surface of siliconeous MCM-41 samples is chemically similar to that of the silica reference. This difference is interpreted in terms of the BET C, following the convincing argument of Mikhail et al.10 The BET C of the three MCM-41 samples varies from 60 to 117, with the low values being much smaller than that of the nonporous silica reference (about 100).12 The constant C is related to the adsorption heat5 by
q1 - qL ) RT ln C
(3)
where (q1 - qL) is the net heat of adsorption. When C of a sample is below 100, the heats of adsorption on the sample are smaller than that on the nonporous silica, and correspondingly, at a given relative pressure, in particular where the coverage θ is low, the t value on the surface of a MCM-41 sample is smaller than that of the reference. This results in a small slope of the stage A in the Va - t curves and thus too low a value for St, and vice versa. This argument is confirmed by a correlation of the relative difference between SBET and St, (SBET - St)/SBET, with relative differences in C values between sample and the reference, (Creference - Csample)/Creference, as illustrated in Figure 7. Nevertheless, the discrepancy between St and SBET is not significant in the present study, and the pore sizes derived using both St and SBET are almost the same, as shown in Table 1. When the BET C of a tested sample is significantly different from that of the nonporous reference, the pore size discrepancy could be noticeable. For instance, the discrepancy for MCM-41(3.08) is 0.17 nm. When compared with another nonporous silica, TK800,12 having a higher CBET of about 130, the discrepancy becomes 0.22 nm. No relation between the CBET and pore dimension is established. For physical adsorption, the enhancement adsorption energy in a pore approaches zero when the pore size is more than 3 times the diameter of the adsorbate molecule.15 The CBET value is mainly influenced by the surface nature of pore walls in MCM-41 samples, such as the polarity of the surface. Because nitrogen molecules have a quadrupole, the interaction between the adsorbed nitrogen molecules and the surface increases with the polarity thus resulting in an enhancement of the adsorption heat. It is expected that the sample with a low CBET (15) Everett, D. H.; Powl, J. C. J. Chem. Soc., Faraday Trans. I 1976, 72, 619-636.
Figure 7. Correlation of the difference in CBET between the sample and reference with the deviation of St from SBET.
is more hydrophobic, and this information could be useful for some particular adsorption studies where water adsorption is important. In stage B, the Va - t plot of MCM-41 is very steep, with a large gradient and a negative intercept when the linear portion is extrapolated to the adsorption axis. This upward deviation from the straight line of stage A indicates that capillary condensation occurs. The uptake of nitrogen in this stage is much greater than the amount required by multilayer adsorption. In this region, therefore, the t-plot can not be used for the calculation of surface area. If pores in a sample are uniform, then capillary condensation should occur at a certain P/P0 or within its near vicinity. Differential plots, dVa/dt, versus the corresponding t are shown in Figures 3 and 4 (open circles) to illustrate variations of Va with t. For MCM-41, sharp peaks as observed between t ) 5.2 and 6.3 Å. The sharp peak means that filling of all the mesopores in the sample occurs at almost the same relative pressure, indicating a uniform pore structure. In contrast, for the commercial mesoporous silica, for which a disordered pore structure is known, a broad peak on the differential curve is expectably observed, reflecting a wide pore size distribution. In summary, a sharp peak on the differential curve reflects uniform pore structure, and vice versa. Therefore, in analogy to XRD patterns, one may readily obtain qualitative information on the pore size distribution from the shape of the differential curve of dV/dt or dV/d(Rs). When some mesopores have been completely filled, the surface areas in such pores are no longer accessible to the adsorbate. Adsorption will proceed on the external surface of the sample crystals, and a significantly low slope of the linear portion in stage C is observed. This explanation is supported by the fact that the external surface area of the grains, estimated from the SEM micrograph, is in agreement with the Sext obtained from slope of stage C on the Va - t curve, as mentioned earlier. The t value where the point of inflection between stage B and C varies from sample to sample, and the greater this t value, the larger is the pore diameter. However, diameters of the mesopores in MCM-41 samples derived by the MP method (by d ) 4tb, where tb represents the t value at the second inflection point as indicated in Figure 2) fail to match with those obtained from XRD measurement (Table 1). For comparisons, the pore
Pore Structure Characterization of MCM-41
diameter at the maximum of the pore size distribution curve derived by the BJH method, which is based on the Kelvin equation and includes the correction on the thickness of adsorbed layer,5 dmBJH, is also included in Table 1. For various porous solids, micropore volumes calculated by the comparison plot methods, t-plot or Rs-plot method, have been widely accepted since they provide rational explanation on the porosity and/or are consistent with data obtained by other experimental means. The pore volume is derived by extrapolating the linear portion of the Va - t curve, in a high relative pressure region where micropores have been filled and adsorption proceeds on the external surface or the surface of larger pores, to the adsorption axis. The intercept indicates the volume of micropores which have been filled by nitrogen molecules. In the present study, the volume of the uniform mesopores was derived in the same way, by back-extrapolating the linear portion of stage C. The ratio of pore volume to pore surface area, Vpore/ Spore, gives reasonable results of hydraulic diameter which are in good agreement with those from XRD measurement. Even for the commercial silica, the mean pore size calculated by this method is 4.08 nm, closely matching with the known pore dimension of 4 nm. Using the t value directly from a t-plot to calculate pore size is not appropriate for several reasons. Firstly, as pointed out by Gregg and Sing,5 the t is a statistical thickness rather than a real one in any specific pore. As discussed previously, the t value depends, to a large extent, on the adsorption heat reflected by the BET C. Finally, it is only applicable in a multilayer adsorption regime. In fine micropores, ultramicropores, the adsorption heat is much higher than that on an open surface.13 They may be filled at a very low P/P0, where the corresponding t value is so small that the pore diameter calculated by the MP method is below 0.36 nm, the kinetic diameter of a N2 molecule. Our study on other porous materials such as pillared clays (published elsewhere16 ) shows that in some cases the original MP method has unacceptable errors even for the calculation of micropores.
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For mesoporous solids, as shown above, the MP method fails to provide a correct pore dimension of mesopores because of capillary condensation. Therefore, we come to the conclusion that the MP method is not applicable for certain micropores and the entire mesopore range. This disadvantage or limitation of the method is mainly brought about by using the t value to represent the pore size. The improvement on the MP method as demonstrated in this paper is a possible solution to this problem, that is, to use the linear portion of the t-plot in the high-P/P0 region to derive the pore volume which has been filled and the remaining surface area and to calculate the diameter of the pores from the volume/surface area ratio. To avoid the ambiguity brought about by t, the Rs-plot, as proposed by Sing,9 may be a good substitution for the t-plot. Conclusion For MCM-41 samples of highly ordered pore structures, the process of nitrogen adsorption can be clarified by the comparison plots of three distinct stages, with two points of inflection. The pore structure properties, such as surface area, volume, and dimension of the pores, can be readily evaluated using an improved MP method. The pore diameters obtained by the proposed method are in good agreement with those calculated by XRD measurements. Based on the comparison of nitrogen adsorption on the tested sample with that on a nonporous reference, the method provides reliable results but involves no complicated theoretical treatment or assumptions. The improvement proposed in the present study removes the limitations of the MP method and makes it promising for pore structure characterization over a wide pore size range, including micropores and mesopores. Acknowledgment. Financial support from the Australian Research Council (ARC) to this project is gratefully acknowledged. LA960541V (16) Zhu, H. Y.; Lu, G. Q.; Zhao, X. S. Improved MP-Method for the Determination of Pore Size Distributions of Porous Materials. Proceedings of COPS IV, Bath, U.K., Sept. 15-18, 1996.
