3056
J. Phys. Chem. C 2009, 113, 3056–3061
Stability of Cubic Ice in Mesopores Kunimitsu Morishige,* Hiroaki Yasunaga, and Hiroaki Uematsu Department of Chemistry, Okayama UniVersity of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan ReceiVed: October 8, 2008; ReVised Manuscript ReceiVed: January 4, 2009
We examined the effect of pore geometry on the stability of cubic ice in mesopores by measuring the change of the X-ray diffraction pattern for ice confined in cylindrical, interconnected cylindrical, interconnected spherical, and interconnected irregular pores of silica during a heating process. The results obtained clearly indicated that the stability of cubic ice in the mesopores depends on the pore geometry. Cubic ice confined to the interconnected spherical cavities of KIT-5 is metastable with respect to hexagonal ice, similar to bulk cubic ice. On the other hand, cubic ice confined to the cylindrical and interconnected cylindrical pores of SBA-15 and KIT-6 is stable up to the melting point of the ice, in accord with previous studies. I. Introduction A second crystalline ambient pressure modification of solid water besides hexagonal ice (ice Ih) is always obtained in the form of very small crystallites.1-15 On crystallographic evidence it was named cubic ice (ice Ic) by Ko¨nig,2 but it has been repeatedly observed that the powder diffraction pattern is not a clean cubic one but contains some extra lines which appear at the positions of Bragg peaks of ice Ih.4-7,9-11,13-15 Whereas ice Ih is readily formed by cooling of liquid water under common environmental conditions, formation of ice Ic requires special techniques such as heating of all known high pressure modifications of ice after release of pressure,6,7,11 heating of the vitrified states of water,10 hyperquenching of liquid water at 170-190 K,9,13 jet expansion of water vapor,12 freezing of pore water,8 and homogeneous freezing of micrometer-sized aqueous droplets.14,15 Ice Ic, except for that formed in mesopores, appears to be always metastable relative to ice Ih; it transforms on heating to ice Ih.2-6,9,10,13-15 On the other hand, ice Ic in the mesopores is stable up to the melting point.16-18 In our previous study we proposed from pore-size dependence of X-ray diffraction (XRD) pattern for pore ice that ice Ic is actually composed of very small crystallites of hexagonal ice that contain a large number of growth faults depending on the crystallite size.17 When the pore size is decreased, the XRD pattern for ice formed in the mesopores gradually changed from that of ice Ih to that of ice Ic. Such a change in the XRD pattern of pore ice with a decrease of the pore size can be accounted for by a rapid increase of growth fault probability in the ice crystallites formed. Very recently, Hansen et al.19-21 have shown that the neutron diffraction pattern of ice Ic obtained from highpressure ice modifications can be well reproduced by the structure model with a complex stacking sequence that is composed of the comparable degrees of cubic and hexagonal packing. They have thought that ice Ic is essentially composed of very small crystallites of cubic packing that contain a considerable number of deformation faults. The proper structure of ice Ic still remains to be settled. The structure of ice Ic formed in the mesopores seems to be not very different from that of ice Ic obtained by other techniques. Molecular dynamics simulations,22 in accord with these experiments, have shown that stacking faults naturally appear in the initial stage of water * Corresponding author.
freezing. The structure of small crystallites of ice is characterized by a large number of stacking faults generated in the initial stage of a growth process. When ice crystals become large, the structure of the ice is dominated by a thermodynamically stable phase (ice Ih). Therefore, suppression of the crystal growth of ice in the mesopores was thought to be a vital factor for the formation and the stability of cubic ice. The purpose of the present study is to examine the effect of pore geometry on the stability of cubic ice in the mesopores by measuring the change of the XRD pattern for ice confined in cylindrical, interconnected cylindrical, interconnected spherical, and interconnected irregular pores of silica during a heating process. The stability of cubic ice in mesopores is relevant to the structure of the ice. The large surface area-to-volume ratio of materials confined in porous media provides an opportunity for fundamental studies of the effects of finite size and surface interactions on the phase transitions, structures, and thermodynamic parameters of the confined materials.23 One of the benefits of our experimental configuration is that crystal growth during a heating process is restricted since the ice crystals are confined in the mesopores. The results obtained clearly indicate that the suppression of the crystal growth of ice in the mesopores is not responsible for the stability of cubic ice, contrary to the abovementioned expectation. II. Experimental Section II.1. Materials. SBA-15 with cylindrical pores was prepared by using Pluronic 123 triblock copolymer at an aging temperature of 373 K according to the procedure of Kruk et al.24 KIT-6 with interconnected cylindrical pores was prepared by using P123 triblock copolymer at an aging temperature of 373 K according to the procedure of Kleitz et al.25 KIT-5 with expanded spherical cavities was prepared by using Pluronic F127 triblock copolymer as a structure directing agent and benzene or mesitylene as a solubilizing agent.26 The obtained KIT-5 silicas are denoted KIT-5-xy, where x corresponds to the hydrothermal treatment time (day) at 393 K, and y is either “b” or “m” for materials prepared with benzene or mesitylene as the solubilizing agent, respectively. The spherical cavities of KIT-5 are arranged in a face-centered-cubic array and connected with each other through narrow necks (interconnected spherical pores). The assynthesized materials were calcined for 5 h at 823 K (heating rate 1 deg/min) in a flow of air. Controlled pore glasses, which
10.1021/jp8088935 CCC: $40.75 2009 American Chemical Society Published on Web 02/02/2009
Stability of Cubic Ice in Mesopores
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3057
TABLE 1: Specific Surface Areas, Total Pore Volumes, Pore Diameters, and Pore Shape/Connectivity of the Mesoporous Materials, as well as Freezing and Melting Temperatures of Pore Water sample
surface area SBET (m2/g)
total pore vol Vp (cm3/g)
pore diameter D (nm)
pore shape/ connectivity
freezing temp Tf (K)
melting temp Tm (K)
SBA-15 KIT-6 CPG75A CPG120A KIT-5-1m KIT-5-3m KIT-5-1b KIT-5-3b
552 556 144 108 618 664 542 583
0.858 0.916 0.543 0.581 0.484 0.906 0.600 0.807
8a 8a 16a 24a 10b 14b 17b 17b
cylindrical unconnected cylindrical interconnected irregular interconnected irregular interconnected spherical interconnected spherical interconnected spherical interconnected spherical interconnected
247 255 261 264 232 240 232 238
257 259 264 266 256 260 261 261
a
Cylindrical pore diameter. b Spherical pore diameter.
possess interconnected pores of irregular shape, were supplied by CPG Inc., USA. II.2. Measurements. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II (Bell Japan Inc.). An experimental apparatus of X-ray diffraction for freezing/melting measurements has been described in detail elsewhere.27 The intensities were measured every 0.1° 2θ, using Cu KR radiation in a Bragg-Brentano geometry and recorded as counts/30 s. Sample powder (∼0.1 g) was packed in the shallow pit of a sample holder of Cu and covered with a 7.5µm-thick film of Kapton and then a 0.1-mm-thick sheet of Be. The sample holder was then attached to a cold head of a He closed cycle refrigerator and sealed in a sample cell constructed of a cylindrical Be window and a Cu flange, with an In O-ring. After prolonged evacuation at room temperature, the sample was cooled and then the background spectrum was measured. The adsorption isotherm of water on porous silicas inside the X-ray cryostat was measured at 275 K. Prior to X-ray diffraction measurements, the adsorbed amount was reduced slightly below the saturation, in order to avoid contamination in diffraction pattern from the bulk ice formed outside the mesopores. Both cooling and heating rates of the sample are ∼1 deg/min and the sample was left at measurement temperatures for 10 min before XRD measurements. The XRD measurements were usually carried out at 5-deg intervals and sometimes at 1-deg intervals in the temperature range where a large change in diffraction pattern was expected. One run took ∼200 min. After correction for attenuation due to adsorbed water, the diffraction pattern of confined ice was obtained by subtraction of data for charged and empty substrate. III. Results and Discussion III.1. Porous Structure. SBA-15 with cylindrical pores showed a well-defined XRD pattern that can be indexed on a two-dimensional hexagonal lattice. KIT-6 with interconnected cylindrical pores showed also a well-resolved cubic Ia3d XRD pattern. All the adsorption isotherms of nitrogen at 77 K on SBA-15, KIT-6, and two kinds of CPG exhibited hysteresis loops of type H1 in the IUPAC classification,28 indicating that all these materials have very sharp distributions of pore size. In a previous study,29 we examined capillary condensation of nitrogen in KIT-6 in comparison to SBA-15 in order to know the accurate relationship between pore size and the pressure of capillary condensation or evaporation and also to elucidate the pore-connectivity effects on adsorption hysteresis. The results clearly indicated that interconnections among pores of almost the same size do not have a significant effect on the adsorption hysteresis and the mean pore size of KIT-6 can be approximated by the pore size obtained by using the gas adsorption method under the assumption of the cylindrical pores with no networking
effects. The mean diameters of these cylindrical and nearly cylindrical pores were obtained from the adsorption branch of the isotherm with use of the Barrett-Joyner-Halenda method.30 The adsorption isotherm of nitrogen at 77 K on KIT-5 varied in shape depending on the hydrothermal treatment time at 393 K.31 The shape of a desorption branch changed drastically as the hydrothermal treatment was prolonged. On the other hand, the shape of an 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 KIT-5 samples indicates the presence of uniform cavities. The mean diameters of the spherical pores were estimated by using the relationship between capillary condensation pressure and pore diameter reported by Broekhoff and de Boer.32 These pore sizes are in reasonable agreement with those obtained by X-ray structural modeling.31 In cage-like pores, desorption is controlled by the narrow necks.31,33 For the samples hydrothermally treated for only 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 ∼4 nm. However, in the case of a sample hydrothermally treated for 3 days, desorption started at a slightly higher relative pressure, indicating that the narrow necks were enlarged with the prolonged hydrothermal treatment. Table 1 summarizes the specific surface areas, total pore volumes, pore diameters, and pore shape/connectivity of the samples used in the present study, as well as the freezing and melting temperatures of pore water as described in the next section. III.2. X-ray Diffraction of Pore Ice. Ice Ih and Ic are isomorphous to wurtzite and sphalerite, respectively; the oxygen atoms in ice Ih and Ic occupy the positions of Zn and S atoms in the wurtzite and the sphalerite structure of ZnS, respectively. Both modifications of ZnS (ice) differ in the stacking sequence of Zn-S (O-O) double layers. The structure of wurtzite corresponds to the hexagonal close packing (2H) with AB stacking along [001] and that of sphalerite to the cubic close packing (3C) with ABC sequence along 〈111〉 directions. Therefore, stacking faults are a prominent defect in these structures and the effect of stacking faults on the 2H and the 3C diffraction pattern has been extensively explored.34 Incorporation of stacking faults in the 3C structure cannot reproduce the strong hexagonal 100 peak in the 3C pattern. The oxygen atoms in ice Ic are arranged in puckered-hexagonal rings identical with those found in ice Ih; however, each layer of oxygens is displaced one-half the diameter of the ring relative to adjacent layers. This arrangement gives rise to a repetitive structure of the type · · · ABCA · · · characteristic of the diamondcubic system. Figure. 1 shows the schematic powder XRD
3058 J. Phys. Chem. C, Vol. 113, No. 8, 2009
Figure 1. Schematic powder XRD patterns of bulk cubic and hexagonal ices with idealized structures.
patterns of bulk Ih and Ic ices with idealized structures. There are no lines in the cubic pattern that are not also found at essentially identical positions for ice Ih. It is well-known that the powder diffraction pattern of bulk Ic ice depends on the preparation method and the sample history.2-15 That is to say, samples of cubic ice give a range of powder diffraction patterns. We never obtain a sample of cubic ice that gives a powder diffraction pattern expected from idealized cubic structure. In most cases, one noncubic peak is clearly observable on the lowangle side of the cubic 111 reflection, almost exactly at the position where the 100 peak of hexagonal ice is expected. This peak shows tail at the high-angle side (asymmetry of the peak). Furthermore, skewness at the high-angle side of the cubic 111 and at the low-angle side of the 311 reflection, as well as sometimes a bump between the 220 and 311 reflections, are observed. These extra lines cannot be attributed to the presence of ice Ih impurities because a linear combination of two separate patterns of ice Ih and Ic does not reproduce the observed pattern. Pore water freezes at low temperatures upon cooling depending on the pore size and geometry. Figure 2 shows some of the XRD patterns from the pore ice confined in SBA-15, KIT-6, CPG75A, and CPG120A when the temperature was then successively increased. Pore water confined in SBA-15 with a cylindrical pore diameter of 8 nm froze around 247 K when the temperature was successively lowered, giving rise to a XRD pattern typical of ice Ic. When the temperature was then successively increased, melting took place around 257 K without change in shape of the XRD pattern from the pore ice. This proves that ice Ic in the cylindrical pores is stable up to the melting point, in accord with previous studies.16-18 The structure of the ordered mesoporous KIT-6 silica with a cubic space group symmetry of Ia3d consists of an amorphous wall following the periodic minimal surface of gyroid.29,35 The wall separates two interpenetrating and noninterconnecting channel systems with different chiralities and each forms a three-dimensional (3D) network of pores of almost cylindrical shape. The distance between pore intersections is comparable to the pore diameter. The present KIT-6 sample possesses highly interconnected cylindrical pores of almost the same size as that of the cylindrical pores of SBA-15.29 Pore water confined in KIT-6 froze around 255 K when the temperature was successively lowered. As Figure 2 shows, the resulting XRD pattern was indistinguishable from that for the pore ice confined to the cylindrical pores of SBA-15. When the temperature was then successively increased, melting took place around 259 K without change in shape of the XRD pattern from the pore ice similarly to that of the pore ice confined to the cylindrical pores of SBA-15. This indicates
Morishige et al. that interconnections among pores of almost the same size do not affect appreciably the structure and melting behavior of the pore ice. It is known that controlled pore glass possesses pores of uniform size, although the pores are irregular in shape and highly interconnected.36 Pore water confined in CPG75A and CPG120A froze around 261 and 264 K, respectively, when the temperature was successively lowered. The XRD patterns for the pore ice in these materials contain some extra lines which appear at the positions of Bragg peaks of ice Ih similarly to bulk Ic ice prepared by other techniques.4-7,9-11,13-15 When the temperature was then successively increased, melting of the pore ice in CPG75A and CPG120A took place around 264 and 266 K, respectively, without change in shape of the XRD pattern from the pore ice. Therefore, it is apparent that ice Ic in the cylindrical, interconnected cylindrical, and interconnected irregular pores of silica is stable up to the melting point. This confirms the previous studies.16-18 The ordered mesoporous KIT-5 silica has spherical cavities arranged in a face-centered-cubic array and connected through narrow necks.26 KIT-5 samples showed large thermal hysteresis between freezing and melting for the pore ice. Freezing of the pore water confined to the spherical cavities of KIT-5 is controlled by the size of the necks that connect the spherical cavities.37 When the neck size is smaller than ∼4 nm in diameter, the pore water in the spherical cavities freezes via homogeneous nucleation around 232 K on cooling. When the diameter of the necks was increased beyond this critical size, the freezing temperature was increased and the freezing became broad because of a gradual percolation of the ice front that grows by traveling through the connected pore network. Since the necks in KIT-5-3m and KIT-5-3b were slightly enlarged beyond the critical size by the prolonged hydrothermal treatment, pore water confined in these materials froze around 240 and 238 K, respectively, on cooling. Figure 3 shows changes in the XRD pattern from the pore ice confined in KIT-5-1m, KIT-5-3m, KIT5-1b, and KIT-5-3b, respectively, when the temperature was then successively increased. As opposed to the cylindrical pores of SBA-15 and the interconnected pores of KIT-6, CPG75A, and CPG120A, the pore ice confined to the interconnected spherical cavities of KIT-5 showed unusual melting behaviors on heating. The XRD patterns from the pore ice in KIT-5 at low temperatures were almost the same as those in SBA-15 with cylindrical pores and KIT-6 with interconnected cylindrical pores. The three peaks can be indexed to the (111), (220), and (311) reflections of ice Ic, respectively. Melting temperature of the pore ice confined to the spherical cavities of KIT-5 is controlled by the size of the spherical cavities. Surprisingly, however, in the course of the melting process the XRD pattern of Ic microcrystals changed into that of Ih microcrystals. Such a melting behavior of the pore ice confined to the spherical cavities seems to be compatible with that of Ic microcrystals prepared outside the mesopores by other methods.2-6,9,10,13-15 The seven peaks in the XRD pattern for the pore ice in KIT-5 that appear in the course of the melting can be indexed to the (100), (002), (101), (102), (110), (103), and (112) reflections of Ih, respectively. Peak broadening due to the small size of the crystallites was significant for the XRD pattern of the pore ice confined in KIT-5-1m so that only one additional peak assigned to the (103) reflection of Ih was observed in the course of the melting. All these results clearly indicate that the melting process of the pore ice is affected by the shape of the pores. For the interconnected spherical cavities, the XRD pattern of Ic microcrystals changed into that of Ih microcrystals in the
Stability of Cubic Ice in Mesopores
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3059
Figure 2. Change of the X-ray diffraction pattern of ice confined in SBA-15, KIT-6, CPG75A, and CPG120A slightly below complete filling upon heating.
course of the melting process. Ice Ic confined to the interconnected spherical cavities is metastable with respect to ice Ih similarly to ice Ic obtained outside the mesopores by other methods. On the other hand, ice Ic confined to the cylindrical pores and the interconnected pores is stable up to the melting point. III.3. Stability of Cubic Ice in Mesopores. The stability of cubic ice confined to the mesopores of silica depended on the geometry of a restricted space. Ice Ic confined to the cylindrical, interconnected cylindrical, and interconnected irregular pores of silica is stable up to the melting point, whereas that confined to the interconnected spherical cavities transforms to ice Ih in the course of the melting process. This strongly suggests that cubic ice is not necessarily a pure phase with a cubic structure as envisaged by Ko¨nig2 because the relative stability of a phase does not seem to depend on the outer shape of the phase although it may depend on the size of the phase. Previously, we proposed that ice Ic is actually composed of very small crystallites of hexagonal ice that contain a large number of growth faults depending on the crystallite size and thus the transformation of ice Ic to ice Ih observed outside the mesopores accompanies elimination of the stacking faults induced by the
growth of the Ic crystallites.17 Therefore, the suppression of crystal growth of ice in the mesopores was thought to be a vital factor for the formation and the stability of cubic ice. The present experimental results, however, clearly indicate that the restriction of the growth of the Ic crystallites within the mesopores is not responsible for the stability of ice Ic in the restricted space. The Ic crystallites confined to the spherical cavities of KIT-5 are not able to grow on heating because of the restricted space. Hansen et al. have considered that ice Ic is essentially composed of very small crystallites of cubic ice with a considerable number of deformation faults.19-21 In this case, the transformation of ice Ic to Ih during a heating process is a phase change. Again, it seems to be very difficult to imagine that a phase change depends on the outer shape of the sample. Recently, according to an extension of the Gibbs-Thomson effect to solid-solid phase transformations, it has been suggested that the stability of ice Ic with respect to ice Ih would depend on the size of the ice.38,39 Our observations, however, are not phase inversion on decreasing the size of the sample. Dislocations and stacking faults are normally metastable defects which would disappear if sufficient activation energy was provided to make them mobile.34 They persist in solids since
3060 J. Phys. Chem. C, Vol. 113, No. 8, 2009
Morishige et al.
Figure 3. Change of the X-ray diffraction pattern of ice confined in KIT-5-1m, KIT-5-3m, KIT-5-1b, and KIT-5-3b slightly below complete filling upon heating.
the energy required for their movement is high and not readily available at low temperatures. X-ray topography of ice single crystals has shown that two types of stacking faults with fault vectors of 1/6 〈203〉 and 1/3 〈100〉 are formed in the crystals.40 The former is accompanied by one layer of cubic structure and thus corresponds to a growth fault, whereas the latter is accompanied by two cubic layers and thus corresponds to a deformation fault. These stacking faults are eliminated when they are swept by partial dislocations. Therefore, it would be reasonable to consider that the easiness of movement of the partial dislocations in the ice microcrystals is relevant to the stability of ice Ic. When the temperature is increased, the ice in the narrow necks of KIT-5 is first melted to leave the microcrystals of ice Ic in the spherical cavities. The coherence length of the ice microcrystals in the spherical cavities was estimated from the peak widths of the (111) and (220) reflections of ice Ic by using the Scherrer equation. The estimated sizes of the ice microcrystals in KIT-5 were comparable to the pore diameters of the spherical cavities, suggesting that the ice microcrystals are single crystals rather than polycrystals consisting of grain boundaries. On the other hand, the pore ice confined to the cylindrical, interconnected cylindrical, and interconnected irregular pores of silica inevitably takes the form of polycrystals. Grain boundary is known to be an obstacle to the movement of
the dislocations.41 Therefore, the cubic ice confined to the cylindrical and interconnected cylindrical pores may be stable up to the melting point. In any event, further studies of freezing and melting behavior of water in the mesopores with welldefined geometries would provide invaluable insight into the structure, formation, and stability of cubic ice. Acknowledgment. This research was supported by the “HighTech Research Center” Project for Private Universities: matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), 2006-2008. References and Notes (1) Burton, E. F.; Oliver, W. F. Proc. R. Soc. London A 1935, 153, 166. (2) Ko¨nig, H. Z. Kristallogr. 1944, 105, 279. (3) Lisgarten, N. D.; Blackman, M. Nature 1953, 178, 39. (4) Shallcross, F. V.; Carpenter, G. B. J. Chem. Phys. 1957, 26, 782. (5) Dowell, L. G.; Rinfret, A. P. Nature 1960, 188, 1144. (6) Arnold, G. P.; Finch, E. D.; Rabideau, S. W.; Wenzel, R. G. J. Chem. Phys. 1968, 49, 4365. (7) Bertie, J. E.; Jacobs, S. M. J. Chem. Phys. 1977, 67, 2445. (8) Steytler, D. C.; Dore, J. C.; Wright, C. J. J. Phys. Chem. 1983, 87, 2458. (9) Mayer, E.; Hallbrucker, A. Nature 1987, 325, 601. (10) Elarby-Aouizerat, A.; Jal, J.-F.; Dupuy, J.; Schildberg, H.; Chieux, P. J. Phys., Colloq., C1 1987, 48, 465.
Stability of Cubic Ice in Mesopores (11) Kuhs, W. F.; Bliss, D. V.; Finney, J. L. J. Phys., Colloq., C1 1987, 48, 631. (12) Huang, J.; Bartell, L. S. J. Phys. Chem. 1995, 99, 3924. (13) Kohl, I.; Mayer, E.; Hallbrucker, A. Phys. Chem. Chem. Phys. 2000, 2, 1579. (14) Murray, B. J.; Knopf, D. A.; Bertram, A. K. Nature 2005, 434, 202. (15) Murray, B. J.; Bertram, A. K. Phys. Chem. Chem. Phys. 2006, 8, 186. (16) Morishige, K.; Kawano, K. J. Chem. Phys. 1999, 110, 4867. (17) Morishige, K.; Uematsu, H. J. Chem. Phys. 2005, 122, 044711. (18) Liu, E.; Dore, J. C.; Webber, J. B. W.; Khushalani, D.; Ja¨hnert, S.; Findenegg, G. H.; Hansen, T. J. Phys.: Condens. Matter 2006, 18, 10009. (19) Hansen, T. C.; Falenty, A.; Kuhs, W. F. In Physics and Chemistry of Ice; Special Publication Vol. 311; Kuhs, W. F., Ed.; Royal Society of Chemistry: Cambridge, England, 2007; p 201. (20) Hansen, T. C.; Koza, M. M.; Kuhs, W. F. J. Phys.: Condens. Matter 2008, 20, 285104. (21) Hansen, T. C.; Koza, M. M.; Lindner, P.; Kuhs, W. F. J. Phys.: Condens. Matter 2008, 20, 285105. (22) Carignano, M. A. J. Phys. Chem. C 2007, 111, 501. (23) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys.: Condens. Matter 2006, 18, R15. (24) Kruk, M.; Jaroniec, M.; Ko, C. H.; Ryoo, R. Chem. Mater. 2000, 12, 1961. (25) Kleitz, F.; Choi, S. H.; Ryoo, R. Chem. Commun. 2003, 2136.
J. Phys. Chem. C, Vol. 113, No. 8, 2009 3061 (26) 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. (27) Morishige, K.; Inoue, K.; Imai, K. Langmuir 1996, 12, 4889. (28) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (29) Morishige, K.; Tarui, N. J. Phys. Chem. C 2007, 111, 280. (30) Barrett, E. P.; Joyner, L. G.; Halenda, P. H. J. Am. Chem. Soc. 1951, 73, 373. (31) Morishige, K.; Tateishi, M.; Hirose, F.; Aramaki, K. Langmuir 2006, 22, 9220. (32) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 153. (33) Ravikowitch, P. I.; Neimark, A. V. Langmuir 2002, 1, 8–1550. (34) Sebastian, M. T.; Krishnan, P. Non-Random and Periodic Faulting in Crystals; Gordon and Breach Science: Langhorne, 1994. (35) Sakamoto, Y.; Kim, T.-W.; Ryoo, R.; Terasaki, O. Angew. Chem., Int. Ed. 2004, 43, 5231. (36) Morishige, K.; Uematsu, H.; Tateishi, N. J. Phys. Chem. B 2004, 108, 7241. (37) Morishige, K.; Yasunaga, H.; Denoyel, R.; Wernert, V. J. Phys. Chem. C 2007, 111, 9488. (38) Johari, G. P. J. Chem. Phys. 2005, 122, 194504. (39) Johari, G. P. Philos. Mag. B 1998, 78, 375. (40) Hondoh, T.; Itoh, T.; Amakai, S.; Goto, K.; Higashi, A. J. Phys. Chem. 1983, 87, 4040. (41) Hansen, N. Scr. Mater. 2004, 51, 801.
JP8088935
