J. Phys. Chem. C 2008, 112, 11881–11886
11881
Capillary Condensation in the Void Space between Carbon Nanorods Kunimitsu Morishige* and Ryo Nakahara Department of Chemistry, Okayama UniVersity of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan ReceiVed: March 31, 2008; ReVised Manuscript ReceiVed: May 23, 2008
To elucidate the geometrical factor that controls the capillary condensation phenomenon in the void space between the hexagonally arranged cylindrical nanorods of ordered mesoporous carbon material designated as CMK-3 and also to examine the mechanisms of the capillary condensation and evaporation in such pores, we measured the adsorption properties of two kinds of CMK-3 carbons for nitrogen and derived theoretical formulation describing the capillary condensation in the void space between the nanorods by taking into account the influence of adsorption forces on the shape of the liquid-vapor meniscus. Calculations of the equilibrium condensation pressure due to the derived equations gave the relationship between the surfaceto-surface distance between the neighboring nanorods and the condensation pressure of nitrogen at 77 K. Using this relationship, we were able to determine the accurate pore structures of the two carbons only from the X-ray diffraction pattern of CMK-3 carbon and the adsorption isotherm of nitrogen at 77 K. The thermal behavior of the adsorption hysteresis of nitrogen in the void space between the carbon nanorods was similar to that in the more restricted space of the ordered mesoporous silicas, suggesting that the mechanisms of adsorption and desorption in such open pores are identical to those in the ordered mesoporous silicas. Introduction To elucidate the behavior of a fluid in a restricted space and also to establish the fundamentals of pore size analysis by a gas adsorption method, capillary condensation of the fluid in mesoporous materials has been extensively investigated over several decades.1–3 Based on the relation between pore size and the pressure of the condensation or evaporation for the pores of a given geometry and surface chemistry, a pore size distribution (PSD) in the material can be estimated from the adsorption isotherm that represents the amount of adsorbed fluid as a function of vapor pressure. PSDs of conventional mesoporous materials are usually obtained under the assumption that the solid is made up of a collection of independent, noninterconnected pores of cylindrical shape. Since these solids actually consist of pores of varying shape, curvature, and size, however, the meaning of the pore size thus obtained is obscure because the condensation pressure depends not only on the pore size but also on the pore geometry. In this respect, it is very important to elucidate the geometrical factor that controls the capillary condensation phenomenon in pores of various geometries. The effects of pore size and geometry on capillary condensation would be most effectively explored by using ordered mesoporous materials4,5 because of their well-defined porous structures. An ordered mesoporous carbon, CMK-3,6 can be prepared using an ordered mesoporous silica, SBA-15, as the template. The structure of the CMK-3 carbon is exactly an inverse replica of SBA-15 and consists of a two-dimensional (2D) hexagonal array of carbon nanorods. The pores of this material are not voids that were created inside a solid, as is the case for ordinary mesoporous materials. In this case, the pores represent void space between regularly spaced cylindrical rods. The pores are accessible in any direction and constitute a more open system compared to the cylindrical, interconnected cylindrical, or cagelike pores of the ordered mesoporous silicas. Therefore, it * To whom correspondence should be addressed. E-mail: morishi@ chem.ous.ac.jp.
is very interesting to determine the geometrical factor that controls the condensation pressure of nitrogen for such pores and also to examine the mechanisms of the capillary condensation and evaporation. To this end, we measured the adsorption properties of two kinds of CMK-3 carbons for nitrogen and derived theoretical formulation describing the capillary condensation in the void space between the hexagonally arranged cylindrical nanorods of the CMK-3 carbon. The adsorption isotherms of nitrogen at 77 K were analyzed on the basis of the derived formulation to give accurate pore structures of the CMK-3 carbons. The mechanisms of the capillary condensation and evaporation were further examined by measuring the temperature dependence of the adsorption-desorption isotherm of nitrogen. Experimental Section Materials. Two kinds of SBA-15 samples, SBA-15 (P123) and SBA-15 (P85), were prepared using Pluronic P123 and P85 triblock copolymers, respectively, as structure-directing agents.7 The calcined silica samples were impregnated with an ethanol solution of AlCl3. After the solvent was completely evaporated at 373 K, the samples were calcined in air at 823 K. The Alincorporated samples are denoted as Al-SBA-15. The CMK-3 carbon was prepared according to the procedure of Kim et al.,8 except that the silica sample was infiltrated with furfuryl alcohol only once. One gram of Al-SBA-15 (P123) was uniformly infiltrated with 1.9 mL of furfuryl alcohol (1.5 mL of furfuryl alcohol for Al-SBA-15 (P85)) at room temperature. The AlSBA-15 sample containing furfuryl alcohol was placed in an oven at 308 K for 1 h and then at 368 K for 1 h. The resultant polymer/silica composite sample was further heated for 2 h at 623 K and then at 1173 K for 4 h for carbonization of the polymer. All heating treatments were performed under selfgenerated gas atmosphere using a quartz reactor closed with a ceramics wool plug. The Al-SBA-15 templates were removed with HF solution. The carbons prepared by using Al-SBA-15
10.1021/jp8027403 CCC: $40.75 2008 American Chemical Society Published on Web 07/16/2008
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Figure 1. Powder XRD patterns of CMK-3 carbon and SBA-15 silica used as template for the CMK-3 synthesis: (a) CMK-3 carbon; (b) SBA15 silica.
(P123) and Al-SBA-15 (P85) as templates are denoted as CMK-3 (P123) and CMK-3 (P85), respectively. Measurements. Adsorption isotherms of nitrogen at liquid nitrogen temperature were measured volumetrically on a Belsorp-mini II (Bell Japan Inc.). Temperature dependence of the adsorption isotherm was measured volumetrically on a homemade semiautomated instrument equipped with a Baratron capacitance manometer (model 690A) with a full scale of 25 000 Torr. The experimental apparatus and procedure have been described elsewhere.9 Calculations of adsorption at higher pressures took the nonideality of gas into consideration on the basis of a modified BWR equation.10 Powder X-ray diffraction (XRD) patterns were obtained on a Rigaku RAD-2B diffractometer in the Bragg-Brentano geometry arrangement using Cu KR radiation with a graphite monochromator and a scintillation detector. Transmission electron microscopy (TEM) images were recorded on a JEOL JEM-2000EX electron microscope, operating at 200 kV.
Figure 2. Adsorption isotherms of nitrogen at 77 K on SBA-15 (P123) (circles) and SBA-15 (P85) (triangles). Empty and closed symbols denote adsorption and desorption points, respectively. Inset: pore size distributions.
Results and Discussion Structure and Adsorption Properties of CMK-3. Figure 1 shows the XRD patterns for CMK-3 (P123) and CMK-3 (P85), compared to their silica templates, SBA-15 (P123) and SBA15 (P85). The XRD patterns for the CMK-3 carbons resembled the patterns for the corresponding SBA-15 silica templates, indicating that the structure of the CMK-3 carbon is an inverse replica of SBA-15. The pattern for CMK-3 (P123) exhibited three peaks assigned to the (100), (110), and (200) reflections of the 2D hexagonal space group (P6mm), while the pattern for CMK-3 (P85) showed only one peak ascribed to the (100) reflection of the same space group. The 2D arrangement of carbon nanorods in CMK-3 (P85) is less ordered compared to that in CMK-3 (P123). The lattice parameters (a) of the 2D hexagonal unit cell for CMK-3 (P123) and CMK-3 (P85) were 10.3 and 7.6 nm, respectively, while those for the silica templates, SBA-15 (P123) and SBA-15 (P85), were 10.6 and 8.5 nm, respectively. Structural shrinkage occurred during the carbonization process and subsequent dissolution of silica framework. The shrinkage for the Al-SBA-15 (P85) template was larger than the Al-SBA-15 (P123) template. As Figure 2 shows, the adsorption isotherms of nitrogen at 77 K for both templates showed sharp steps due to capillary condensation, indicating that the templates possess uniform pores suitable to
Figure 3. Typical TEM images of CMK-3 carbon: (a) CMK-3 (P123); (b) CMK-3 (P85).
the preparation of the CMK-3 carbon. The PSDs were obtained using the Barrett-Joyner-Halenda method11 from the adsorption branch and the distributions for SBA-15 (P123) and SBA15 (P85) were centered at 4.05 and 2.35 nm in radius, respectively. Since the carbon nanorods are formed inside the cylindrical pores of SBA-15, the rod diameter for CMK-3 (P85) is expected to be significantly smaller than CMK-3 (P123). The formation of the thinner carbon nanorods would be responsible for the poor ordering in 2D arrangement of the carbon nanorods for the former. Figure 3 shows the TEM images for CMK-3 (P123) and CMK-3 (P85) viewed along the direction of the carbon nanorods. As the TEM images show, the structure of the CMK-3 carbon is exactly an inverse replica of SBA-15. The center-tocenter distances of the carbon nanorods for CMK-3 (P123) and
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Figure 5. Liquid meniscus formed in void space between cylindrical rods of CMK-3 (P123). Z is the axial coordinate, a is the center-tocenter distance between rods, and R is the radius of a rod.
Figure 4. Adsorption isotherms of nitrogen at 77 K on CMK-3 (P123) (circles) and CMK-3 (P85) (triangles). Empty and closed symbols denote adsorption and desorption points, respectively.
CMK-3 (P85) were ∼11 and 8 nm, respectively. These values are in reasonable agreement with the lattice parameters of the unit cell determined by XRD. Figure 4 shows the adsorption isotherms of nitrogen at 77 K for both carbon materials. The two isotherms exhibited relatively steep hysteresis loops due to capillary condensation of nitrogen in the void space between the hexagonally arranged cylindrical rods at nearly identical relative pressures, indicating that the pore sizes of these two materials are similar. Many researchers have estimated the pore size for their CMK-3 samples by means of a conventional method of pore size analysis by gas adsorption in the past (see the structural parameters of the silica templates and carbon replicas shown in Supporting Information Table 1S).6,12–20 This is obviously incorrect because the conventional method assumes the pores of cylindrical shape, different from the void space between the carbon nanorods. Capillary Condensation in the Space between Cylindrical Rods. Very recently, we constructed an accurate relation between pore size and the capillary condensation and evaporation pressure of nitrogen at 77 K for the cylindrical pores of the ordered mesoporous MCM-41 and SBA-15 silicas, in order to examine the theoretical relations between the pore size and the pressure of capillary condensation or evaporation proposed so far.21 Here, the pore size was determined from a comparison between the experimental and calculated XRD patterns due to X-ray structural modeling. Among the many theoretical relations that differ from each other in the degree of theoretical improvements, a macroscopic thermodynamic approach based on the Broekhoff-de Boer equations22,23 was found to be in fair agreement with the experimental relation obtained. Their approach was based on Derjaguin’s idea24 that significant improvement of the classical Kelvin equation for capillary condensation can be achieved by taking into account the influence of adsorption forces on the shape of the liquid-vapor meniscus. Along the same concept, Philip has independently developed a unitary approach to capillary condensation and adsorption in pores of various geometries such as a slit pore and a wedge-shaped pore.25 In this approach, the capillary component of the potential ψ, the partial specific Gibbs free
Figure 6. Relationship between the equilibrium condensation pressure of nitrogen at 77 K and the surface-to-surface distance between adjacent cylindrical rods.
energy associated with the solid-liquid interactions, is taken to depend on the liquid-vapor interface mean curvature, while the adsorptive component is taken to depend on the normal distance from the solid surface. The equilibrium condition that it is a surface of constant ψ then yields the differential equation of the interface. Two types of menisci formed in the planes parallel and perpendicular to the carbon nanorod may be considered for a liquid in the void space between the hexagonally arranged cylindrical nanorods of the CMK-3 carbon. The liquid meniscus formed in the plane parallel to the carbon nanorod is directly related to the occurrence of capillary condensation of vapor giving rise to a steep step in the adsorption isotherm. We derived the theoretical formulation describing the capillary condensation in the void space between the hexagonally arranged cylindrical nanorods of the CMK-3 carbon, according to the approach of Philip. Taking cylindrical coordinates (r, z) and letting r ) R, be the external surface of a cylindrical rod, we find that the differential equation describing the geometry of the liquid-vapor interface, along a line from one rod center to the next (see Figure 5), in the space between hexagonally arranged cylindrical rods becomes approximately
(
d2r 1 dz2 F(r - R) + γVm dr 2 1⁄2 dr r 1+ 1+ dz dz
2 3⁄2
( ( )) ( ( ))
)
) Ψ* (1)
The first and second terms of the left side of the equation denote an adsorption component and a capillary component of ψ, respectively. γ is the surface tension at the interface, Vm is
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the molar volume of the liquid, and ψ* is the value of ψ at equilibrium. For N2 at 77.4 K, γ ) 8.72 mN/m and Vm ) 34.68 × 10-6 m3/mol. The function F(t) at 77.4 K of nitrogen is given by23
(
F(t) ) 2.303RgT
16.11 - 0.1682 exp(-0.1137t) t2
)
(2)
Here t is the distance in angstroms from the solid surface to the interface, taken normal to the solid surface, Rg is the gas constant, and T is the absolute temperature. The t curve of multimolecular nitrogen adsorption is known to be universal for the surfaces of many solids including carbon blacks. From eq 1, we obtain the following equations giving the capillary condensation pressure of nitrogen at 77.4 K as a function of R for a given lattice parameter (a).
r∞ ) R + F-1 Ψ * -r
γVm
(
∞
)
(3)
∫
r∞ γVmr∞ + a rF(r - R)dr 2 Ψ*) 2 r∞ a2
2
-
(4)
8
Here r∞ is the value for r in the limit as z becomes infinite, and we write F-1 for the inverse of F, i.e., F-1(F(t)) t t. The capillary condensation pressure (P/P0) is given by
(P ⁄ P0)cond ) exp(Ψ * ⁄ RgT)
(5)
Equations 3 and 4 can be solved by a simple iterative procedure with the aid of eq 2. With Ψ* found thus for a given a and R, the whole solution follows by numerical quadrature. The required equations of the liquid-vapor interface are
z(r) ) w(r) )
∫r 1 r
a 2
(( ) ) γVm 2 -1 w(r1)
Figure 7. Temperature dependence of the adsorption-desorption isotherm of nitrogen on CMK-3 (P123).
CMK-3 (P123) and CMK-3 (P85) are ∼7.2 and 4.6 nm in diameter, respectively. This is in reasonable agreement with the estimation by the high-resolution TEM images of the CMK-3 carbon prepared using a similar template.6 The surface-to-surface distance (∼3.1 nm) determined for the CMK-3 (P123) sample was slightly larger than the thickness (∼2.7 nm)21 of the pore walls of the silica template (SBA-15 (P123)), as expected for the inverse replica structure of the template. The liquid-vapor interface calculated for nitrogen at 77 K in the void space between the carbon nanorods of CMK-3 (P123) is also shown in Figure 5. Next, we considered the liquid meniscus formed in the plane perpendicular to the carbon nanorod. Taking the origin of polar coordinates (r, θ) at the center of one cylinder, the differential equation describing the geometry of the meniscus for two neighboring cylindrical rods becomes25
d r1
∫ar r1(Ψ * -F(r1 - R)) dr1
(6) (7)
2
The origin is fixed by z(a/2) ) 0. We calculated the condensation pressure of nitrogen at 77.4 K in the void space between hexagonally arranged cylindrical rods as a function of rod diameter for two sets of the unit cell parameter (10.3 and 7.6 nm). The calculated data were transformed into the plots of the condensation pressure of nitrogen as a function of the surface-to-surface distance between adjacent rods. As Figure 6 shows, the two relations for different lattice parameters nearly agreed in the small separation between the surfaces of two neighboring rods of less than ∼4 nm, and thus, the relation between the condensation pressure and the surface-to-surface distance obtained herein can be taken to be almost universal in the corresponding region of the relative pressure less than ∼0.6, irrespective of the dimension of the unit cell of the CMK-3 carbons. One can estimate the accurate pore size in surface-to-surface distance between adjacent nanorods for their CMK-3 carbons from the position of the step in the adsorption isotherm of nitrogen. The difference between the two relations became visible as the rods were widely separated. Using this relation, the mean surface-tosurface distances between the carbon nanorods for CMK-3 (P123) and CMK-3 (P85) were determined to be ∼3.1 and 3.0 nm, respectively, from the relative pressures at the midpoint of the adsorption branch (CMK-3 (P123), 0.49; CMK-3 (P85), 0.47). These distances indicate that the carbon nanorods in
(
)
dr 2 d2r -r 2 dθ dθ ) Ψ* dr 2 3⁄2 2 r + dθ
( ) ( ( ))
γVm r2 + 2
-1⁄2
F(r - R) +
(8)
The equations giving the relationship between the equilibrium pressure and the shape of the meniscus are given by
r∞ ) R + F-1(Ψ * -γVm ⁄ r∞)
(
γVm r∞ Ψ* )
)
a tanθ0 + 2
∫asecθ r∞
0
2
r∞2 a2 2 8 cos2θ
(9)
rF(r - R) dr (10)
0
Here r∞ is the value for r where the thickness of the adsorbed film is no longer varied, and θ0 is the value for θ where the vapor-liquid interface intersects normally the plane of symmetry between neighboring cylinders. Calculations based on these equations clearly indicated that the vapor pressure required for formation of a liquid meniscus spanning the space between neighboring cylindrical rods is the same as that for the liquid meniscus formed in the plane parallel to the carbon nanorod considered above. Mechanisms of Condensation and Evaporation. Figure 7 shows the temperature dependence of the adsorption-desorption isotherm of nitrogen on CMK-3 (P123) in the temperature range 76-110 K. At lower temperatures, all isotherms clearly revealed capillary condensation accompanied by a hysteresis loop. When the temperature was increased, the hysteresis loop shrank gradually and eventually disappeared at the hysteresis critical
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Figure 8. Temperature dependence of the capillary condensation and evaporation pressures of nitrogen on CMK-3 (P123) (circles) in comparison with that on SBA-15 (triangles).27 Open and closed symbols denote condensation and evaporation pressures, respectively. Solid lines are guides for the eye.
temperature (Tch). During this, the shape of the desorption branch changed from a gradual to a sharp one. Such thermal behavior of the hysteresis loop was similar to that for SBA-12 with cagelike pores,26 where the adsorption mechanism was altered from pore blocking to cavitation with increasing temperature. Figure 8 shows the plots of capillary condensation and evaporation pressures against temperature for nitrogen on CMK-3 (P123), in comparison with those on SBA-15 prepared by hydrothermal treatment at 323 K using P123 surfactant.27 Here, the transition pressures were determined at the midpoint of the hysteresis loop. The plots of T ln(P/P0) versus temperature for capillary condensation formed an almost linear relationship over a wide temperature range spanning Tch, whereas the same plots for capillary evaporation broke at Tch, in good agreement with our previous results26,27 for the more restricted pore space of the ordered mesoporous silicas. In addition, the hysteresis critical point of nitrogen in CMK-3 (P123), which is defined as a threshold of temperature (Tch) and pressure above which reversible capillary condensation takes place in a given size and shape of pores, was found to fall on the common line26 of the hysteresis critical points that were observed in the ordered mesoporous silicas with different pore sizes and geometries. All these facts strongly suggest that the mechanisms of capillary condensation and evaporation in the space between the carbon nanorods of CMK-3 are the same as those in the more restricted pore space of the ordered mesoporous silicas and the evaporation follows a cavitation process in the vicinity of Tch. Capillary condensation is growth of multilayer films on the carbon nanorods with increasing pressure and eventual filling of the void space between neighboring nanorods with a liquid. The carbon nanorods of CMK-3 are located on a 2D triangular lattice, as illustrated in Figure 9. We consider capillary condensation of a vapor in the space surrounded by three rods (A, B, C) with different diameters placed at the vertices of a regular triangle. When the vapor pressure is increased, a liquid bridge is first formed between the two rods of the largest (A) and moderate (B) diameters and then between the two rods of the largest (A) and smallest (C) diameters. The filling of the space surrounded by the three rods with the liquid takes place when the liquid bridge is finally formed between the two rods of the moderate (B) and smallest (C) diameters. The largest surface-to-surface distance between the three neighboring rods plays a role as pore size in capillary condensation. Although the 2D array of the carbon nanorods of CMK-3 constitutes an open pore system, each space surrounded by neighboring three rods on the 2D triangular lattice behaves as a unit of pore,
Figure 9. Schematic illustration of desorption in CMK-3 carbon.
namely, a domain, in capillary condensation. The filling takes place first in the space around the widest rods and then successively in the space around smaller rods. The shape of the adsorption branch observed indicates that there is a distribution of the surface-to-surface distances between adjacent nanorods in the CMK-3 samples to some extent. In other words, the rod diameter varies from one rod to the next, as well as along a rod axis. At a saturation pressure, the void space between the carbon nanorods is completely filled with the liquid. During the desorption process, evaporation can occur only from the spaces that have access to the vapor phase and not from the spaces that are surrounded by other liquid-filled spaces. There is thus a pore blocking effect in which a metastable liquid phase is preserved below the condensation pressure until evaporation occurs in a neighboring space. The relative pressure at which evaporation occurs therefore depends on the surfaceto-surface distance between two neighboring rods, the connectivity of the pore space network, and the state of neighboring spaces. The situation is just the same as capillary evaporation in a porous network consisting of voids and necks that is frequently considered for the ordinary mesoporous solids.28,29 The space between adjacent rods plays a role as a connecting window between adjacent pore spaces. For a particular pore space to empty, one of the adjacent pore spaces must be empty and then the liquid-vapor meniscus must pass through the connecting window. The desorption mechanism is a vapor invasion that starts from the outer surface (see Figure 9). When the temperature is increased, the desorption mechanism is altered from pore blocking to cavitation because homogeneous nucleation for evaporation becomes increasingly easy to occur at higher temperatures.30 Conclusions The adsorption isotherm of nitrogen at 77 K on the ordered mesoporous CMK-3 carbon exhibits a relatively steep hysteresis loop due to capillary condensation of nitrogen in the void space between the hexagonally arranged cylindrical rods. To examine the geometrical factor that controls the capillary condensation phenomenon in the void space between the carbon nanorods of CMK-3, we derived the theoretical formulation describing the capillary condensation in the void space between the nanorods by taking into account the influence of adsorption forces on
11886 J. Phys. Chem. C, Vol. 112, No. 31, 2008 the shape of the liquid-vapor meniscus. Calculations of the equilibrium condensation pressure due to the derived equations give the almost universal relationship between the surface-tosurface distance between the neighboring nanorods and the condensation pressure of nitrogen at 77 K in the region of the relative pressure less than ∼0.6, irrespective of the dimension of the unit cell of the CMK-3 carbons. Using this relationship, we are able to determine the accurate pore structure of the CMK-3 carbon only from the XRD pattern and the adsorption isotherm of nitrogen at 77 K. The thermal behavior of the adsorption hysteresis of nitrogen in the void space between the carbon nanorods is similar to that in the ordered mesoporous silicas. This strongly suggests that the mechanisms of capillary condensation and evaporation in the space between the carbon nanorods of CMK-3 are the same as those in the more restricted pore space of the ordered mesoporous silicas. Acknowledgment. This research was supported by “HighTech Research Center” Project for Private Universities: matching fund subsidy from MEXT (Ministry of Education, Culture, Sports, Science and Technology), 2006-2008. Supporting Information Available: Table 1S with structural parameters of the silica templates and carbon replicas. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: New York, 1982. (2) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; SliwinskaBartkoviak, M. Rep. Prog. Phys. 1999, 62, 1573. (3) Neimark, A. V.; Ravikovitch, P. I.; Vishnyakov, A. J. Phys.: Condens. Matter 2003, 15, 347. (4) Yanagisawa, T.; Shimizu, T.; Kuroda, K.; Kato, C. Bull. Chem. Soc. Jpn. 1990, 63, 988.
Morishige and Nakahara (5) 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. (6) Jun, S.; Joo, S. H.; Ryoo, R.; Kruk, M.; Jaroniec, M.; Liu, Z.; Ohsuna, T.; Terasaki, O. J. Am. Chem. Soc. 2000, 122, 10712. (7) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024. (8) Kim, T.-W.; Ryoo, R.; Gierszal, K. P.; Jaroniec, M.; Solovyov, L. A.; Sakamoto, Y.; Terasaki, O. J. Mater. Chem. 2005, 15, 1560. (9) Morishige, K.; Ito, M. J. Chem. Phys. 2002, 117, 8036. (10) Younglove, B. A. J. Phys. Chem. Ref. Data 1982, 11 (Suppl. 1). (11) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. J. Am. Chem. Soc. 1951, 73, 373. (12) Shin, H. J.; Ryoo, R.; Kruk, M.; Jaroniec, M. Chem. Commun. 2001, 349. (13) Lee, J.-S.; Joo, S. H.; Ryoo, R. J. Am. Chem. Soc. 2002, 124, 1156. (14) Kruk, M.; Dufour, B.; Celer, E. B.; Kowalewski, T.; Jaroniec, M.; Matyjaszewski, K. J. Phys. Chem. B 2005, 109, 9216. (15) Gierszal, K. P.; Kim, T.-W.; Ryoo, R.; Jaroniec, M. J. Phys. Chem. B 2005, 109, 23263. (16) Liu, X.; Zhou, L.; Li, J.; Sun, Y.; Su, W.; Zhou, Y. Carbon 2006, 44, 1386. (17) Smith, M. A.; Lobo, R. F. Microporous Mesoporous Mater. 2006, 92, 81. (18) Wang, D.-W.; Li, F.; Fang, H.-T.; Liu, M.; Lu, G.-Q.; Cheng, H.M. J. Phys. Chem. B 2006, 110, 8570. (19) Wang, H.; Lam, F. L. Y.; Hu, X.; Ng, K. M. Langmuir 2006, 22, 4583. (20) Lin, M.-L.; Huang, C.-C.; Lo, M.-Y.; Mou, C.-Y. J. Phys. Chem. C 2008, 112, 867. (21) Morishige, K.; Tateishi, M. Langmuir 2006, 22, 4165. (22) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 368. (23) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 377. (24) Derjaguin, B. V. Proc. Intern. Conf. on Surface ActiVity, 2nd ed.; Butterworth: London, 1957; pp 153-159. (25) Philip, J. R. J. Chem. Phys. 1977, 66, 5069. (26) Morishige, K.; Ishino, M. Langmuir 2007, 23, 11021. (27) Morishige, K.; Nakamura, Y. Langmuir 2004, 20, 4503. (28) Wall, G. C.; Brown, R. J. C. J. Colloid Interface Sci. 1981, 82, 141. (29) Mason, G. Proc. R. Soc. London, A 1988, 415, 453. (30) Ravikovitch, P. I.; Neimark, A. V. Langmuir 2002, 18, 9830.
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