9220
Langmuir 2006, 22, 9220-9224
Change in Desorption Mechanism from Pore Blocking to Cavitation with Temperature for Nitrogen in Ordered Silica with Cagelike Pores Kunimitsu Morishige,* Masayoshi Tateishi, and Fumi Hirose Department of Chemistry, Okayama UniVersity of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
Kenji Aramaki Graduate School of EnVironment and Information Sciences, Yokohama National UniVersity, Tokiwadai 79-7, Hodogaya-ku, Yokohama 240-8501, Japan ReceiVed May 12, 2006. In Final Form: August 22, 2006 To verify pore blocking controlled desorption in ink-bottle pores, we measured the temperature dependence of the adsorption-desorption isotherms of nitrogen on four kinds of KIT-5 samples with expanded cavities hydrothermally treated for different periods of time at 393 K. In the samples, almost spherical cavities are arranged in a face-centered cubic array and the cavities are connected through small channels. The pore size of the channels increased with an increase in the hydrothermal treatment time. At lower temperatures a steep desorption branch changed to a gradual one as the hydrothermal treatment was prolonged. For the sample hydrothermally treated only for 1 day, the rectangular hysteresis loop shrank gradually with increasing temperature while keeping its shape. The temperature dependence of the evaporation pressure observed was identical with that expected for cavitation-controlled desorption. On the other hand, for the samples hydrothermally treated for long times, the gradual desorption branch became a sharp one with increasing temperature. This strongly suggests that the desorption mechanism is altered from pore blocking to cavitation with temperature. Application of percolation theory to the pore blocking controlled desorption observed here is discussed.
I. Introduction The concept of pore blocking used in understanding hysteresis between adsorption and desorption is always connected with the existence of ink-bottle-type pores, namely, pores consisting of wide bodies fitted with narrow necks. The classical explanation1-4 for the phenomenon of adsorption hysteresis in such pores assumes that capillary condensation during adsorption is governed by the radius of curvature of the wide body of the pores, whereas evaporation, during desorption, of the capillary condensate in the pores is obstructed by liquid remaining condensed in the necks (pore blocking in single ink-bottle pores). On the other hand, the conventional mesoporous materials such as porous glasses and silica gels consist of an interconnected network of pores of varying shape, curvature, and size. Pore blocking controlled desorption from such pores is thought to depend not only on the size of the necks, but also on the connectivity of the network and the state of neighboring pores (pore blocking in a network of ink-bottle pores). Networking effects for capillary evaporation are traditionally accounted for by a percolation theory.5-9 Under several assumptions concerning the pore geometry, topology of the pore network, and adsorptiondesorption mechanism, the theory is able to reproduce satisfactorily the hysteresis loop of type H2 in the IUPAC classification, which is characterized by a steep desorption branch and a smoothly increasing adsorption branch. This, however, does (1) Kraemer, E. O. In Treatise on Physical Chemistry; Taylor, H. S., Ed.; van Nostrand: New York, 1931; p 1661. (2) McBain, J. W. J. Am. Chem. Soc. 1935, 57, 699. (3) Cohan, L. H. J. Am. Chem. Soc. 1944, 66, 98. (4) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 153. (5) Wall, G. C.; Brown, R. J. C. J. Colloid Interface Sci. 1981, 82, 141. (6) Mason, G. Proc. R. Soc. London, Ser. A 1983, 390, 47. (7) Neimark, A. V. Colloid J. 1984, 46, 813. (8) Zhdanov, V. P.; Fenelonov, V. B.; Efremov, D. K. J. Colloid Interface Sci. 1987, 120, 218. (9) Parlar, M.; Yortsos, Y. C. J. Colloid Interface Sci. 1988, 124, 162.
not necessarily prove that pore blocking controlled desorption actually takes place in these mesoporous materials. Recently, Kierlik et al.,10 Woo et al.,11 Pellenq et al.,12 and Gelb and Gubbins13 have obtained a hysteresis loop of type H2 for fluid adsorption on disordered mesoporous silicas without invoking pore blocking or percolation effects in their theoretical and simulation works. In the past several years pore blocking effects in single inkbottle pores have attracted renewed attention.14-19 These theoretical and simulational studies show that two kinds of desorption mechanisms (cavitation and pore blocking) take place depending on the size of the necks, the nature of the fluid-solid interaction, and the temperature. In cavitation, liquid condensed in a large cavity can desorb via spontaneous evaporation while liquid in the necks remains condensed, as opposed to that in pore blocking. Experimental examination of capillary evaporation from single ink-bottle pores seems to be an extremely difficult task, although Wallacher et al.20 have measured the adsorption hysteresis in the linear mesopores that were produced by controlled etching of Si wafers. Ink-bottle-type pores in real materials are always interconnected to form a three-dimensional network of pores. Networking of pores does not seem to affect the desorption (10) Kierlik, E.; Monson, P. A.; Rosinberg, M. L.; Sarkisov, L.; Tarjus, G. Phys. ReV. Lett. 2001, 87, 055701. (11) Woo, H.-J.; Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, 7472. (12) Pellenq, R. J.-M.; Rousseau, B.; Levitz, P. E. Phys. Chem. Chem. Phys. 2001, 3, 1207. (13) Gelb, L. D.; Gubbins, K. E. In Fundamentals of Adsorption 7; Kaneko, K., Kanoh, H., Hanzawa, Y., Eds.; IK International: Chiba, Japan, 2002; p 333. (14) Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, 7600. (15) Ravikowitch, P. I.; Neimark, A. V. Langmuir 2002, 18, 1550. (16) Ravikowitch, P. I.; Neimark, A. V. Langmuir 2002, 18, 9830. (17) Vishnyakov, A.; Neimark, A. V. Langmuir 2003, 19, 3240. (18) Libby, B.; Monson, P. A. Langmuir 2004, 20, 4289. (19) Coasne, B.; Pellenq, R. J.-M. J. Chem. Phys. 2004, 121, 3767. (20) Wallacher, D.; Ku¨nzner, N.; Kovalev, D.; Knorr, N.; Knorr, K. Phys. ReV. Lett. 2004, 92, 195704.
10.1021/la061360o CCC: $33.50 © 2006 American Chemical Society Published on Web 09/23/2006
Desorption Mechanism Change for Nitrogen in Silica
behavior due to cavitation in single ink-bottle pores because spontaneous evaporation of liquid in cavities takes place independent of the size of the necks and the connectivity of the network when the neck size is smaller than a certain critical value. On the other hand, the desorption behavior due to pore blocking in single ink-bottle pores would be changed drastically by the networking of the pores. The percolation theory is still a good candidate to describe pore blocking controlled desorption in real materials, if it actually takes place.21 Ordered silicas with cagelike pores, such as SBA-1622 and FDU-1,23 are regarded as the most suitable model adsorbents currently available for examination of cavitation or pore blocking controlled desorption that is expected for an ink-bottle pore. In these materials, almost spherical cavities are arranged in a threedimensional lattice and connected through narrow necks. The porous structure is just the same as that assumed for the application of percolation theory to desorption: the pore space is treated as a lattice of voids interconnected by necks in a three-dimensional network. In previous studies,24,25 we have shown that, for various liquids confined to the spherical cavities of SBA-16, the temperature dependencies of the capillary evaporation pressure are consistent with those expected for cavitation. Ravikovitch and Neimark16 have examined the temperature dependencies of the spinodal of bulk liquid nitrogen and the equilibrium pressure of the liquid confined to the cylindrical pores using a nonlocal density functional theory (NLDFT). They concluded that the mechanism of capillary evaporation from ink-bottle-type pores may be changed from pore blocking to cavitation with increasing temperature. The crossover temperature depends on the neck size. Their prediction is reasonable because the temperature dependence of the cavitation pressure for the liquids confined to the cavities of SBA-1624,25 is apparently larger than that of the desorption pressure for the liquids confined to the cylindrical pores of MCM-41.26,27 Although, to verify the prediction, they have measured the adsorption isotherms on FDU-1 and SBA-16 at only two different temperatures, experimental verification is insufficient. The neck size of SBA-16 is ∼2.3 nm.28 Therefore, the crossover temperature of the liquids confined in the SBA-16 is expected to be well below the lowest temperature examined in our previous studies.24,25 If we obtained ordered mesoporous silicas with a larger neck size, we could actually observe the crossover temperature of desorption and thus examine the pore blocking controlled desorption in a network of ink-bottle pores. The neck size of ordered mesoporous silicas with cagelike structure is controllable by simply adjusting the temperature and time of hydrothermal treatment of the materials.29-32 KIT-5 is a highly ordered large-cage mesoporous silica with a cubic Fm3m close(21) Hoinkis, E.; Ro¨hl-Kuhn, B. Langmuir 2005, 21, 7366. (22) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024. (23) Yu, C.; Yu, Y.; Zhao, D. Chem. Commun. 2000, 575. (24) Morishige, K.; Tateishi, N.; Fukuma, S. J. Phys. Chem. B 2003, 107, 5177. (25) Morishige, K.; Tateishi, N. J. Chem. Phys. 2003, 119, 2301. (26) Morishige, K.; Ito, M. J. Chem. Phys. 2002, 117, 8036. (27) Morishige, K.; Nakamura, Y. Langmuir 2004, 20, 4503. (28) Sakamoto, Y.; Kaneda, M.; Terasaki, O.; Zhao, D. Y.; Kim, J. M.; Stucky, G.; Shin, H. J.; Ryoo, R. Nature 2000, 408, 449. (29) Fan, J.; Yu, C.; Gao, F.; Lei, J. Tian, B.; Wang, L.; Luo, Q.; Tu, B.; Zhou, W.; Zhao, D. Angew. Chem., Int. Ed. 2003, 42, 3146. (30) Kim, T.-W.; Ryoo, R.; Kruk, M.; Gierszal, K. P.; Jaroniec, M.; Kamiya, S.; Terasaki, O. J. Phys. Chem. B 2004, 108, 11480. (31) Kruk, M.; Celer, E. B.; Matos, J. R.; Pikus, S.; Jaroniec, M. J. Phys. Chem. B 2005, 109, 3838. (32) El-Safty, S. A.; Mizukami, F.; Hanaoka, T. J. Phys. Chem. B 2005, 109, 9255.
Langmuir, Vol. 22, No. 22, 2006 9221
Figure 1. Experimental (plus signs) and simulated (solid line) X-ray diffraction patterns of KIT-5 samples with expanded cavities hydrothermally treated for different periods of time at 393 K.
packed structure.33 In the present study we aim at observing the change of the desorption mechanism from pore blocking to cavitation with increasing temperature and examining the mechanism of pore blocking controlled desorption in a network of ink-bottle pores of ordered silica. To this end we measure the temperature dependence of the adsorption-desorption isotherms of nitrogen on four kinds of KIT-5 samples with different neck sizes. II. Experimental Section II.1. Sample Preparation and Characterization. KIT-5 with expanded spherical cavities was prepared using Pluronic F127 triblock copolymer as a structure-directing agent and benzene as a solubilizing agent. The preparation procedure was similar to that of Kleitz et al.,33 except for use of benzene as an expander. A 2.5 g sample of F127 was dissolved in 95 g of distilled water and 30 g of 2 M HCl, and then 12 g of TEOS was added to the solution with stirring at 318 K. After the resulting mixture was allowed to stir for 1 h, 4 g of benzene was added, and the resulting mixture was allowed to stir for another 23 h. Subsequently, the reaction mixture was heated for 1, 3, 5, or 7 days at 393 K under static conditions for hydrothermal treatment. The solid product was filtered off and then washed with distilled water repeatedly. After being dried at 373 K, the product was calcined at 823 K (heating rate 1 K/min) for 5 h in flowing air. Adsorption isotherms of N2 at liquid nitrogen temperature were measured volumetrically on a homemade semiautomated instrument equipped with a Baratron capacitance manometer (model 127 AA) with a full scale of 1000 Torr. X-ray diffraction (XRD) powder patterns were measured on a Rigaku Nanoviewer equipped with a CCD detector, using Cu KR radiation. The experimental apparatus and procedure have been described in detail elsewhere.34 TEM images were recorded on a JEOL JEM-2000EX electron microscope, operating at 200 kV. II.2. Measurement of Adsorption Isotherms at High Pressures. Adsorption isotherms at high pressures were measured volumetrically on a homemade semiautomated instrument equipped with a Baratron capacitance manometer (model 690A) with a full scale of 25000 Torr. The calculation of adsorption at higher pressures took the nonideality of gas into consideration on the basis of a modified BWR equation. The experimental apparatus and procedure have also been described in detail elsewhere.26
III. Results and Discussion III.1. Porous Structure. Figure 1 shows the XRD powder patterns of four kinds of KIT-5 samples prepared with use of (33) Kleitz, F.; Liu, D.; Anilkumar, G. M.; Park, I.-S.; Solovyov, L. A.; Shmakov, A. N.; Ryoo, R. J. Phys. Chem. B 2003, 107, 14296. (34) Rodriguez, C.; Izawa, T.; Aramaki, K.; Lopez, A.; Sakamoto, K.; Kunieda, H. J. Phys. Chem. B 2004, 108, 20083.
9222 Langmuir, Vol. 22, No. 22, 2006
Morishige et al.
Figure 2. Transmission electron microscopy image of KIT-5 with expanded cavities hydrothermally treated for 7 days at 393 K viewed from the [110] direction. Table 1. Structural Properties of the Samples Hydrothermally Treated for Different Periods of Time at 393 K sample
a (nm)
RXRD (nm)
hw (nm)
Rgas (nm)
1 day 3 days 5 days 7 days
26.8 ( 0.1 27.0 ( 0.1 27.6 ( 0.1 28.3 ( 0.1
7.3 ( 0.5 7.7 ( 0.5 8.7 ( 0.5 8.7 ( 0.5
4.4 ( 1.0 3.7 ( 1.0 2.1 ( 1.0 2.6 ( 1.0
8.4 8.7 9.2 9.6
benzene as the expander. In contrast with the KIT-5 sample prepared without use of the expander,33 the patterns did not resolve the (111) and (200) reflections expected for face-centered closepacked structures. This indicates that the porous structures of the present samples are less ordered compared to that of the original KIT-5 sample. All the XRD patterns can be nevertheless indexed to the face-centered-cubic Fm3m symmetry lattice. The lattice parameter increased with an increase in the hydrothermal treatment time at 393 K. In addition, the relative intensities of the diffraction peaks changed with the hydrothermal treatment time. Further structural information was obtained by X-ray structural modeling using the continuous density function approach according to Kleitz et al.33 The centers of the cavities were located in 4a Wyckoff positions of the cubic Fm3m lattice, and the interconnections between the cavities were not included in the structure model. The cavity radius (RXRD) and the cubic lattice parameter (a) were varied to obtain the best agreement between the experimental and calculated XRD profiles. As Figure 1 shows, the structure model provided reasonable fits between the experimental and calculated XRD peak positions and intensities for all the samples. The final structure parameters obtained are listed in Table 1. The wall thickness (hw) along a line from one pore center to the next was obtained by subtraction (a/x2 - 2R). The cavity radii of the samples were almost 2 times that of the original KIT-5 prepared without use of the expander. There was a tendency for the cavity radius to increase more rapidly than the lattice parameter with an increase in the hydrothermal treatment time. This seems to result in the decrease of the wall thickness with an increase in the hydrothermal treatment time. The unit-cell parameters of KIT-5 prepared in the present study were 27-28 nm. This indicates considerable expansion of the unit cell with retention of the Fm3m structure.33 The expansion of the unit cell was further confirmed by transmission electron microscopy. Figure 2 shows the TEM image of KIT-5 prepared by hydrothermal treatment for 7 days at 393 K. It reveals that the material possesses excellent 3-D cubic mesoscopic order. The lattice parameters estimated from the
Figure 3. Adsorption-desorption isotherms of nitrogen at 77 K on KIT-5 samples with expanded cavities hydrothermally treated for different periods of time at 393 K. (Volumes adsorbed for the samples prepared from the hydrothermal treatment for 3, 5, and 7 days were incremented by 400, 800, and 1200 mL (STP)/g, respectively.)
TEM images were in reasonable agreement with those determined from the XRD patterns. From NLDFT calculations, Ravikovitch and Neimark15,16 have shown that, for nitrogen at 77 K in ink-bottle pores, a classical pore blocking effect takes place when the neck size is greater than ∼5 nm, assuming that the neck can be considered as a cylindrical pore. If the neck diameter is smaller than this critical value, desorption from the pore body occurs via cavitation. Figure 3 shows the adsorption-desorption isotherms of nitrogen at 77 K on four kinds of KIT-5 samples with expanded cavities. Contrary to modeling of single ink-bottle systems, real mesoporous materials always possess pore size distribution. For the present materials, the pore size distribution is significantly wider for necks than for spherical cavities and the pore volume of the necks is much smaller than that of the cavities. Therefore, we cannot observe a desorption step due to capillary evaporation in the necks. The shape of the desorption branch changed drastically as the hydrothermal treatment was prolonged. On the other hand, the shape of the adsorption branch remained almost unchanged. Since capillary condensation during adsorption is controlled by the size of the cavities, the sharp adsorption branch observed for all the samples indicates the presence of uniform cavities. The average radius (Rgas) of the spherical cavities was estimated using the relationship between capillary condensation pressure and pore diameter reported by Broekhoff and de Boer.4 The pore radii of the spherical cavities thus obtained are also included in Table 1. It should be noted that the cavity radii obtained by the XRD modeling and physisorption data differ only by ∼1 nm. For the sample hydrothermally treated only for 1 day, the hysteresis loop closed sharply at a relative pressure of 0.47 corresponding to the lower limit of the adsorption-desorption hysteresis. This indicates that desorption takes place via cavitation and the diameter of the narrow necks is smaller than ∼5 nm. However, in the cases of samples hydrothermally treated for long times (3, 5, and 7 days), the hysteresis loops gradually closed above the lower limit of hysteresis, which indicates the neck diameters are above ∼5 nm. With an increase of the
Desorption Mechanism Change for Nitrogen in Silica
Figure 4. Temperature dependence of the adsorption-desorption isotherm of nitrogen on a KIT-5 sample with expanded cavities prepared by hydrothermal treatment for 1 day at 393 K.
Figure 5. Temperature dependence of the adsorption-desorption isotherm of nitrogen on a KIT-5 sample with expanded cavities prepared by hydrothermal treatment for 3 days at 393 K.
Figure 6. Temperature dependence of the adsorption-desorption isotherm of nitrogen on a KIT-5 sample with expanded cavities prepared by hydrothermal treatment for 5 days at 393 K.
hydrothermal treatment time, the onset of the evaporation shifted into higher relative pressures and the evaporation took place more gradually. This indicates a gradual enlargement of the narrow necks with prolonged hydrothermal treatment, being consistent with the previous studies.29-32 The gradual enlargement of the narrow necks seems to be concerned with the decrease of the wall thickness with an increase in the hydrothermal treatment time at 393 K. III.2. Change of the Desorption Mechanism with Temperature. Figures 4-7 show the temperature dependencies of the adsorption-desorption isotherm of nitrogen on four kinds of KIT-5 samples in the temperature range 72-118 K. At lower temperatures all isotherms clearly revealed capillary condensation accompanied by a very wide hysteresis loop. For the sample hydrothermally treated only for 1 day, both branches of adsorption and desorption were steep. The hysteresis loop shrank gradually with increasing temperature while keeping its shape. The temperature dependence of the evaporation pressure observed was identical with that expected for cavitation-controlled desorption.25 On the other hand, for the samples hydrothermally
Langmuir, Vol. 22, No. 22, 2006 9223
Figure 7. Temperature dependence of the adsorption-desorption isotherm of nitrogen on a KIT-5 sample with expanded cavities prepared by hydrothermal treatment for 7 days at 393 K.
Figure 8. Temperature dependence of the capillary condensation and evaporation pressures of nitrogen on KIT-5 samples with expanded cavities hydrothermally treated for different periods of time at 393 K. Open and closed symbols denote condensation and evaporation pressures, respectively.
treated for long times, the shape of the desorption branch changed gradually with increasing temperature: a gradual desorption branch became a sharp one with increasing temperature. To the best of our knowledge, this is the first systematic observation of a change of a desorption branch in shape with temperature. Our observation is compatible with the change in shape of the hysteresis loop observed at the two temperatures of 77 and 87 K by Ravikovitch and Neimark.16 This clearly indicates that the desorption mechanism changes with temperature. The crossover temperature of desorption from a gradual to a sharp branch was increased with an increase of the hydrothermal treatment time at 393 K. Figure 8 shows the plots of the capillary condensation and evaporation pressures against temperature for nitrogen on four kinds of KIT-5 samples. Here the transition pressures were determined at the midpoint of the adsorption or desorption branch. The plots for capillary condensation in these samples almost overlapped because the sizes of the large cavities in the samples are not so different. The plots for capillary evaporation, for the KIT-5 sample prepared by hydrothermal treatment for 1 day, show the temperature dependence of the cavitation pressure expected for liquid nitrogen confined to the large cavities of silica.25 At lower temperatures, the plots for other samples revealed considerable deviations from this temperature dependence, although all the plots begin to merge into the cavitation curve with increasing temperature. This strongly suggests that the desorption mechanism is altered from pore blocking to cavitation with increasing temperature. The crossover temperature is increased with an increase of the hydrothermal treatment time of the sample, reflecting that the narrow necks are enlarged by the prolonged hydrothermal treatment. Knowing the exact
9224 Langmuir, Vol. 22, No. 22, 2006
Figure 9. Comparison of the cavitation pressure of nitrogen within the expanded cavities of a KIT-5 sample hydrothermally treated for 1 day at 393 K with the evaporation pressure of nitrogen within the cylindrical pores of ordered mesoporous silicas with different pore diameters (D) as a function of temperature.
temperature dependence of the evaporation pressure for the liquid confined to the narrow necks as a function of neck size, we could determine the pore size of the largest necks in the sample. We have previously reported the temperature dependence of the capillary evaporation pressure of nitrogen confined to the cylindrical pores of ordered mesoporous silicas with several different pore sizes.26,27 Figure 9 shows the plots of the evaporation pressure against temperature for nitrogen on four kinds of mesoporous materials with different sizes of cylindrical pores compared to the cavitation curve observed for the KIT-5 sample prepared by hydrothermal treatment for 1 day at 393 K. Although the desorption pressure of a liquid in narrow necks may differ from that in cylindrical pores with the same diameter, we can estimate the pore size of the largest necks in the KIT-5 samples by comparing Figure 8 with Figure 9. In ink-bottle pores, the crossover temperature in the desorption mechanism from pore blocking to cavitation with increasing temperature is given by the point of intersection of the evaporation curve for the liquid confined to the narrow necks with the cavitation curve observed for the KIT-5 sample prepared by hydrothermal treatment for 1 day. We can obtain the relation between the size of the necks and the crossover temperature from Figure 9. The crossover temperature observed in Figure 8 may be converted to the size of the largest necks using this relation. The pore diameters of the largest necks in the KIT-5 samples hydrothermally treated at 393 K for 3, 5, and 7 days are ∼7.6, 8.0, and 8.4 nm, respectively. III.3. Application of Percolation Theory. The desorption mechanism of nitrogen confined to the cavities of KIT-5 hydrothermally treated for long times is altered from pore blocking to cavitation with increasing temperature. The gradual desorption, which is observed at lower temperatures, is controlled by pore blocking of the liquid condensed in the narrow necks between (35) Liu, H.; Zhang, L.; Seaton, N. A. J. Colloid Interface Sci. 1993, 156, 285. (36) Parlar, M.; Yortsos, Y. C. J. Colloid Interface Sci. 1989, 132, 425.
Morishige et al.
the cavities. As Figure 9 suggests, the critical size of the narrow necks, below which cavitation takes place, is increased with increasing temperature. When the size of the largest of the necks fitted to each cavity is smaller than the critical size, the liquid confined to the cavity desorbs via cavitation. The number of cavities in which the confined liquid desorbs via cavitation increases with increasing temperature. Therefore, the desorption branch changes from a gradual to a sharp one with increasing temperature. Percolation theory deals with the transmission of a fluid to sites within a medium against randomly distributed barriers (bonds) which determine whether the fluid can move from one site to an adjacent one. To apply the theory to gas desorption, one regards the voids in the porous medium as the sites and the necks between the voids as the bonds of percolation theory. The conditions applied in such a medium are analogous to those of bond-controlled percolation in a three-dimensional lattice. The theory tells us that the main part of the desorption takes place over a narrow range of pressures where the necks in a narrow range of pore size distribution are allowed to desorb when the pressure is decreased from saturation. This range of fractions of necks open is about 0.1-0.2 for a face-centered-cubic lattice appropriate to KIT-5.5,35 Accordingly, despite the wide distribution of neck size, we can obtain a steep desorption branch for disordered mesoporous materials, namely, a hysteresis loop of type H2. On the other hand, the desorption branch observed at lower temperatures, for the KIT-5 samples hydrothermally treated for long times, is very gradual. It is evident that the percolation effect, expected for a large lattice with a noncorrelated distribution of cavity and neck sizes, is unable to account for the desorption behavior of the liquid confined to the cavities of the KIT-5 samples. It is well-known that reduction of the size of the pore network5,35 and/or easy occurrence of heterogeneous nucleation36 lead to a gradual desorption. However, these effects are not applicable for the present case. When the hydrothermal treatment was prolonged, the cavity radius increased and the neck size also increased. This indicates the presence of correlation between cavity and neck sizes in the present samples. It is probable that the pores in the outer shell of each particle would expand more rapidly than those in the inner shell as the hydrothermal treatment is prolonged. In this case, the correlated distribution of cavity and neck sizes may lead to the very gradual desorption of a liquid confined in the three-dimensional network of ink-bottle pores. Acknowledgment. We express our sincere thanks to Mr. T. Hirasawa for measurement of the small-angle X-ray diffraction patterns for the ordered mesoporous silicas. This work was supported by the High-Tech Research Center Project for Private Universities through a matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), 2006-2008. LA061360O
