Freezing and Melting of Kr in Hexagonally Shaped Pores of

Jan 24, 2011 - Maddox , M. W.; Gubbins , K. E. J. Chem. Phys. 1997, 107, 9659. [Crossref], [CAS]. 40. A molecular simulation study of freezing/melting...
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Freezing and Melting of Kr in Hexagonally Shaped Pores of Turbostratic Carbon: Lack of Hysteresis between Freezing and Melting Kunimitsu Morishige* Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan ABSTRACT: To examine the effect of pore-wall structure on freezing and melting behavior of a confined material in mesopores, we measured X-ray diffraction patterns from Kr confined in two kinds of ordered mesoporous carbons with hexagonally shaped pores, compared with ordered mesoporous silica with cylindrical pores, during freezing and melting processes. The ordered mesoporous carbon possesses crystalline carbon walls with turbostratic stacking structure, whereas the pore walls of the mesoporous silica are amorphous. Large depressions in melting point of the confined Kr were observed for both the ordered mesoporous carbon and silica. For the Kr confined in the amorphous pores of the mesoporous silica, thermal cycling showed pronounced hysteresis between freezing and melting, in agreement with previous results. On the other hand, for the Kr confined in the crystalline pores of the mesoporous carbon, freezing and melting took place almost reversibly.

I. INTRODUCTION There is considerable current interest in the freezing and melting behavior of materials confined in mesoporous solids because of its fundamental and technological importance.1,2 Most of the mesopores experimentally investigated so far consist of pore walls with amorphous structure such as silica and alumina. In such cases, one of the most interesting, well-known phenomena is the depression in freezing and melting temperatures of the confined materials. In addition, thermal cycling shows pronounced hysteresis, with melting occurring at a higher temperature than freezing, except for in the very small mesopores.3-6 On the basis of a balance of bulk and surface free energy terms between solid and liquid in a pore, it has been suggested that the depression in the equilibrium melting point of the confined solid is proportional to the ratio S/V of the pore with volume V and surface area S, irrespective of pore geometries.1 ΔTm ¼ T 0 - Tm ¼

Vm T 0 ðγsw - γlw Þ S ΔHf V

ð1Þ

Here, Vm is the molar volume of the material; ΔHf is the latent heat of melting; γsw is the solid-wall interfacial energy; γlw is the liquid-wall interfacial energy; and Tm and T0 are the melting temperatures of a pore solid and a bulk solid, respectively. Very recently, we have shown that for ordered mesoporous materials with several different pore geometries the melting-point depression of a pore ice is almost proportional to the S/V ratio of the pores confining it.7 The sign of ΔTm depends on whether the walls prefer the solid or the liquid, i.e., whether γsw is greater or less than γlw. The depression in melting point, which is always r 2011 American Chemical Society

observed for the materials confined in mesopores, strongly suggests that the solid almost never wets the pore walls (γsw > γlw). Indeed, the presence of nonfreezing liquid layers between the confined solid and the pore walls has been often reported.4-6,8-13 For the materials confined in the cylindrical pores with pore walls that can be wetted by the liquid in the presence of the solid crystal, eq 1 is reduced to the well-known Gibbs-Thomson equation ΔTm ¼

2Vm γsl T 0 rΔHf

ð2Þ

where r is the pore radius and γsl is the solid-liquid interfacial energy. For water confined in the cylindrical pores of silica, it has been revealed that eq 2 is valid to describe the relationship between the melting-point depression and the effective pore radius.4-6,11 When the liquid wets the pore walls in the presence of the solid crystal, a free energy barrier between a surface melted state and the liquid droplet in the pore emerges. Therefore, in principle, the thermal hysteresis between freezing and melting of the confined material in the cylindrical pores of silica can be accounted for by the appearance of a metastable liquid and/or a metastable solid in the pore.10,14,15 In very small mesopores, the energy barrier is so small that the melting and freezing temperatures would be the same.16,17 Porous silicas that have been extensively used in the study of freezing/melting behavior of a confined Received: August 25, 2010 Revised: November 11, 2010 Published: January 24, 2011 2720

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The Journal of Physical Chemistry C phase have amorphous pore walls. The first several layers adjacent to the pore walls do not participate in freezing and melting transitions of the interior phase4-6,8-13,18 and take amorphous structure even below the freezing temperature of the interior.18,19 The structure of the thin layers covering the pore walls is not at all compatible with that of the solid crystal formed in the center. Therefore, the nucleation of the confined solid is not easy on the thin layers adjacent to the pore walls, and hence the thermal hysteresis can be attributed to the appearance of kinetic supercooling of a confined liquid, at least in the absence of the bulk solid outside the pores. Such a view has been supported by specific heat measurements12 of freezing and melting of Ar in the cylindrical pores of silica, as well as a very recent study7 concerning the effect of pore shape on freezing and melting temperatures of water. If the pores have large fluctuations in size along the pore axis, pore-blocking-controlled freezing occurs, and thus large thermal hysteresis is observed.20,21 In any event, except for very small mesopores, hysteresis between freezing and melting of a confined phase is always observed for porous silicas with amorphous walls. On the other hand, it is known that the monolayer films of rare gases on the flat surfaces of graphite take a two-dimensional hexagonal structure and show a considerably elevated melting temperature by the compression due to substrate attraction and interactions with higher layers.22 The structure of the monolayers is compatible with that of the bulk crystals of rare gases.23 Therefore, it is expected that no new interface needs to be created to grow additional layers in a solid crystal of a facecentered cubic structure with ABC stacking sequence, and thus no barrier to growth will exist. Turbostratic carbon consists of random stacking of graphite sheets.24 The surfaces are atomically rather smooth, and thus the crystalline monolayers of the materials are expected to be formed on its surfaces as well. The purpose of the present study is to examine the freezing and melting behavior of Kr confined in the hexagonally shaped pores of turbostratic carbon, compared with the cylindrical pores of amorphous silica of comparable size. Since the crystalline monolayer of Kr formed on the crystalline pore walls may be nucleation sites on freezing of the inner phase, kinetic supercooling is expected to be considerably suppressed.

II. EXPERIMENTAL SECTION II.1. Materials and Characterization. Ordered mesoporous carbon (C-ORNL-1) with hexagonally shaped pores was prepared by self-assembly of resorcinol-formaldehyde and Pluronic F127 triblock copolymer according to the procedure of Wang, Liang, and Dai.25 Carbonization was carried out under an N2 atmosphere at 673 K for 2 h and then at 1123 K (850 °C) for 3 h. Further heat treatment of C-ORNL-1 was carried out in a hightemperature furnace under argon atmosphere at 2473 K (2200 °C) for 1 h. Ordered mesoporous silica (SBA-15) with cylindrical pores was prepared using Pluronic P123 triblock copolymer as a structure-directing agent at an aging temperature of 373 K according to the procedure of Kruk et al.26 The copolymer-silica complex was calcined at 823 K for 5 h in air to remove the copolymer template. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II. X-ray diffraction (XRD) powder patterns were measured on a Rigaku RAD-2B diffractometer in the Bragg-Brentano geometry arrangement using Cu KR radiation with a graphite monochromator. Transmission

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Figure 1. X-ray diffraction patterns of the as-prepared mesoporous carbon and the heat-treated mesoporous carbon. Solid curves denote the simulated XRD pattern of turbostratic carbon as described in the text.

electron microscopy (TEM) images were recorded on a JEOL JEM-2000EX electron microscope, operating at 200 kV. II.2. Measurements. An experimental apparatus of XRD for freezing/melting measurements has been described elsewhere.27 The measurements were carried out with Cu KR radiation in a Bragg-Brentano geometry. Sample powder (∼0.1 g) was packed in a shallow pit of a sample holder of Cu and covered with a 7.5 μm thick film of Kapton and then a 0.1 mm thick sheet of Be. The sample holder was then attached to a sample cell constructed of a cylindrical Be window and a Cu flange, with In O-ring. After prolonged evacuation at room temperature, the sample was cooled, and then the background was measured. The adsorption isotherm of Kr on the sample inside the X-ray cryostat was measured at 108 K. The substrate was then cooled to a desired temperature between 80 and 108 K, and the spectrum was measured. The diffraction pattern of the confined phase was obtained by subtraction of data for charged and empty substrate after correction for gas attenuation. The correction for gas attenuation was done by scaling the observed scattering to the intensity of the (002) graphite peak, the latter assumed to be essentially unaffected by diffraction from the confined phase.28

III. RESULTS III.1. Porous Structure. Figure 1 shows the XRD powder patterns of two kinds of C-ORNL-1 samples. The as-prepared sample exhibited two broad diffraction peaks that can be indexed as the 002 and 100 reflections in the turbostratic stacking structure of carbon. In the turbostratic stacking of graphite sheets, neighboring graphite sheets are parallel to each other, but translational and rotational correlations within a sheet plane are random. Heat treatment at 2473 K resulted in sharpening of these two peaks, as well as an appearance of additional two diffraction peaks that can be indexed as the 004 and 110 reflections of turbostratic carbon, which suggests an increase in crystallinity of pore walls with the heat treatment at high temperature. To know the structure of the pore walls, we calculated the XRD pattern of turbostratic carbon using the 2721

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Figure 2. Crystallite sizes of turbostratic carbon along the a- and c-axes.

Figure 3. TEM images of the heat-treated mesoporous carbon taken along the [001] (a) and [110] (b) directions.

Warren-Bodenstein equation.24,29 The parameters are the inplane graphite lattice constant (a0), spacing between the layers (d002), carbon layer plane size along the a-axis (La), and carbon layer stacking size along the c-axis (Lc) (see Figure 2). For the sample heat treated at 2473 K, a good fit between the calculated and observed diffraction patterns was obtained with the fixed values of a0 = 0.24612 nm, d002 = 0.345 nm, La = 4.67628 nm, and Lc = 1.035 nm (four sheets of carbon layer). The layer spacing obtained is wider by a few percent than that of the ideal graphite crystal (0.3354 nm), which is typical for the turbostratic stacking of graphite sheets. Figure 3 shows the TEM images of the heattreated sample taken along the [001] and [110] directions, respectively. Long-range hexagonal arrangement of hexagonally shaped pores is clearly visible. Therefore, it is evident that the ordered mesoporous carbon thus obtained possesses hexagonally shaped pores consisting of carbon walls with a turbostratic stacking structure. The porous structure of the ordered mesoporous carbon resembles the inner pores of a multiwalled carbon nanotube.30 Figure 4 shows the adsorption-desorption isotherms of nitrogen at 77 K on two kinds of mesoporous carbon and one kind of SBA-15 silica with cylindrical pores. The as-prepared carbon exhibited a large amount of adsorption in the initial stage, perhaps due to micropores. The isotherm showed a hysteresis loop of type H1 typical of cylindrical pores.31 The amount of adsorption in the initial stage was considerably reduced by the heat treatment at 2473 K, although the shape of the hysteresis loop remained almost unchanged. The adsorption and desorption branches for the mesoporous carbon were more gradual than those for the mesoporous silica, although the positions of adsorption and desorption steps on these mesoporous materials were almost identical. This indicates that the pore sizes of these materials are comparable and that the pore size distribution of the mesoporous carbon is wider. The specific surface area was calculated by using the BET method from the nitrogen adsorption data.32 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.33 The micropore volume and total pore volume were estimated by

Figure 4. Adsorption-desorption isotherms of nitrogen at 77 K on the heat-treated mesoporous carbon (circles), the as-prepared mesoporous carbon (triangles), and the mesoporous silica (squares). Open and closed symbols denote adsorption and desorption branches, respectively.

using the t-plot method.34 Table 1 summarizes the main physicochemical parameters of the samples used in the present study. III.2. Hysteresis between Freezing and Melting. The bulk solid of Kr consists of a face-centered cubic (fcc) lattice and melts at 115.8 K.35 Figure 5 shows some of the powder XRD patterns from the Kr confined in the heat-treated mesoporous carbon when the temperature was successively lowered and then when the temperature was successively increased. Several sharp features denoted by vertical lines arise from the incomplete subtraction of diffraction peaks of the Be sheet because correction for absorption of the X-rays on the substrate is larger than that on the Be sheet covering the substrate in the reflection mode. When the temperature was lowered through ∼103 K, there was a gradual change in the diffraction pattern of the Kr from a liquid to a solid form. The latter is characterized by sharpening of the diffraction peak at 2θ = 26.7°, as well as an appearance of four peaks at 2θ = 30.6, 44.3, 52.6, and 55.0°. The five peaks can be indexed to the 111, 200, 220, 311, and 222 reflections of a solid Kr with a fcc structure, respectively. When the resulting solid was heated, the melting took place at almost the same temperature as the freezing. This is in sharp contrast with the observations1,2 that there is always appreciable thermal hysteresis between freezing and melting of materials confined in mesopores of moderate sizes. Figure 6 shows some of the XRD patterns from the Kr confined in the as-prepared mesoporous carbon. When the substrate was cooled through ∼100 K, there was a gradual change in the diffraction pattern from a liquid to a solid form. The 200 reflection was less prominent in the diffraction pattern of the resulting solid compared to that for the mesoporous carbon heat-treated at 2473 K. In addition, the melting took place at a temperature (∼102 K) slightly higher than freezing. Figure 7 shows some of the XRD patterns from the Kr confined in the SBA-15 on cooling and then on heating. When the temperature was lowered through 96 K, there was a rather abrupt change in the diffraction pattern from a liquid to a solid form. The 200 reflection was less prominent compared to the diffraction pattern for the heat-treated mesoporous carbon. When the resulting 2722

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Table 1. Physicochemical Parameters sample

surface area (m2/g)

pore size (nm)

micropore volume (cm3/g)

total pore volume (cm3/g)

C-ORNL-1 (2473 K)

263

7.0

0

C-ORNL-1 (1123 K)

621

7.0

0.14

0.59

SBA-15

594

8.0

0

0.85

0.41

Figure 5. Change of the X-ray diffraction pattern of Kr confined in the heat-treated mesoporous carbon at nearly complete filling upon cooling and subsequent heating.

solid was heated, the melting took place at a temperature (∼101 K) distinctly higher than freezing, being consistent with the previous results on mesoporous materials.3-7,10-12,18,20,21 To obtain accurate peak parameters, the observed peak profile in the 2θ region of 20-35° was fitted to two Lorentzian line shapes with a linearly changing background. Figure 8 shows the peak width [full width at half-maximum (fwhm)] of the main diffraction peak at 2θ = 26.7° as a function of temperature. For the Kr confined to the hexagonally shaped pores of the heattreated mesoporous carbon, the peak width changed almost reversibly around ∼104 K on cooling and subsequent heating. This clearly indicates that there is no appreciable thermal hysteresis between freezing and melting in this system. On the other hand, for the Kr confined in the as-prepared mesoporous carbon, the temperature at which the peak width rapidly decreases on cooling was slightly lower than that at which the peak width rapidly increases on heating, indicating an appearance of thermal hysteresis between freezing and melting. The thermal hysteresis became more prominent for the Kr confined to the cylindrical pores of the ordered silica. The peak width rapidly decreased at ∼96 K on cooling, while the peak width suddenly increased at ∼101 K on heating. A thermal hysteresis of ∼5 K was observed for this system. Figure 9 compares the main peak profiles from the Kr confined to the mesopores of the heat-treated mesoporous carbon, the asprepared mesoporous carbon, and the mesoporous silica at 80 K. The structure of solid Kr in pores has previously been studied by X-ray diffraction.36-38 All these studies indicate that the solid Kr confined to the amorphous mesopores of silica contains a considerable amount of random stacking faults and an amorphous component depending on the pore size. Therefore, the

peak profile was deconvoluted into three components, that is, the 111 reflection at 2θ = 26.7°, the 200 reflection at 2θ = 30.6°, and the broad peak due to the amorphous solid centered at 2θ = 27.8°. The proportion of the amorphous component in the solid Kr confined to the hexagonally shaped pores of the ordered carbon treated at high temperature is obviously smaller than those in the as-prepared carbon and the mesoporous silica. It is almost certain that the presence of micropores in the as-prepared mesoporous carbon as well as the amorphous pore walls of the ordered mesoporous silica are responsible for an appearance of a greater amount of the amorphous solid in the pores.

IV. DISCUSSION Large depressions in melting point of the confined Kr were observed for both the ordered mesoporous carbon and silica. In the crystalline pores of the heat-treated mesoporous carbon, however, freezing and melting of the confined Kr took place almost reversibly, whereas in the amorphous pores of the mesoporous silica a large hysteresis between freezing and melting was observed. In the less crystalline pores of the as-prepared carbon, the freezing and melting showed a small hysteresis. All of these results indicate that the pore-wall structure affects significantly the mechanisms of freezing and melting of the confined Kr. The solid-liquid transition of the confined Kr in the crystalline pores of the mesoporous carbon was more gradual compared to that in the amorphous pores of the mesoporous silica because the size distribution of the pores in the former was exceedingly wider than that in the latter. IV.1. Amorphous Pore. The large depression in melting point of the confined Kr strongly suggests that for the mesoporous silica liquid Kr wets the amorphous pore walls in the presence of 2723

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Figure 6. Change of the X-ray diffraction pattern of Kr confined in the as-prepared mesoporous carbon at nearly complete filling upon cooling and subsequent heating.

Figure 7. Change of the X-ray diffraction pattern of Kr confined in the mesoporous silica at nearly complete filling upon cooling and subsequent heating.

solid Kr. In other words, a contact angle of a solid Kr on the pore walls is almost 180°, and thus γsw - γlw = γsl according to Young’s equation. Therefore, we calculated the melting-point depression of a solid Kr confined to the cylindrical pores of the mesoporous silica using the Gibbs-Thomson equation and the parameters Vm = 34.3 cm3/g, γsl = 0.9  10-6 J/cm2, T° = 115.8 K, ΔHf = 1639 J/mol,39 and r = 4.0 nm. For a confined Ar in porous silica, it has been reported that at least the first two layers adjacent to the pore walls do not participate in freezing and melting transitions of the interior phase owing to the amorphous structure of the pore walls.10 The melting temperature of the confined Kr in the mesoporous silica was calculated to be 103 K, taking into account the dead layers. The calculated melting temperature of

the solid Kr in the mesoporous silica is in reasonable agreement with the observed one. When the liquid wets the pore walls in the presence of the solid crystal, a free energy barrier between a surface melted state and the liquid droplet in the pores emerges,10,14,15 and thus a kinetic effect of nucleation plays an important role in controlling the phase transition temperatures. Indeed, Schaefer et al. have observed several freezing peaks due to heterogeneous and homogeneous nucleation for Ar confined in the cylindrical pores of SBA-15 in their heat capacity spectra.12 Large depressions in melting point of the confined Kr were also observed for two kinds of the mesoporous carbons. For the Kr confined in the crystalline pores of the mesoporous carbon, however, freezing and melting took place almost reversibly. Therefore, the 2724

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Figure 8. Width (fwhm) of the main diffraction peak as a function of temperature for Kr confined at nearly complete filling in the heat-treated mesoporous carbon (a), the as-prepared mesoporous carbon (b), and the mesoporous silica (c). Open and closed symbols denote cooling and heating processes, respectively.

Figure 9. Main peak profiles of the X-ray diffraction pattern of Kr confined at nearly complete filling in the heat-treated mesoporous carbon (a), the as-prepared mesoporous carbon (b), and the mesoporous silica (c) at 80 K. Solid curves represent three components due to the 111 and 200 reflections of the crystalline solid, as well as the amorphous solid.

results for the mesoporous carbons cannot be simply explained within the framework of such a surface-melted-layer model. IV.2. Crystalline Pore. It is well-known that multilayer solid films of rare gases are formed on the flat surfaces of graphite, and unlike the amorphous pore walls nonfreezing liquid layers do not exist between the solid crystal and the graphite surfaces. This suggests that the graphite walls prefer a solid Kr, and thus γsw is less than γlw in the crystalline pores of the mesoporous carbon. As a result, melting-point elevation of the confined Kr is expected. Large depressions in melting point of the confined Kr, however, were observed in the crystalline pores of the mesoporous carbon as well. This strongly suggests that large strains are induced in the crystalline solid confined in the pores with crystalline carbon walls because the geometrical constraints in pore shape hinders freezing.40,41 γsw is actually greater than γlw in the crystalline pores of the mesoporous carbon because γsw in eq 1 contains contributions from a change in thermodynamic properties of a solid in confinement.

Nevertheless, the first monolayer adjacent to the pore walls may form a close-packed triangular lattice commensurate with the bulk crystal well above the freezing temperature of the confined liquid because the monolayer solid in contact with liquid is free from such strains. When the equilibrium freezing point is approached, the freezing of inner layers may take place layer-by-layer, starting from the first layer. Since the freezing of the interior phase does not require formation of a new interface, kinetic supercooling will not appear. Growth of a fcc solid on each side of the crystalline walls of the hexagonally shaped pores competes against each other in the pore center, which will result in large strains in the solid formed. VI.3. Metastable Melting Model. We have here suggested that melting of a confined solid always occurs at the equilibrium melting point regardless of pore-wall structures, and in amorphous pores the freezing may take place from a metastable liquid state, leading to the appearance of hysteresis between freezing and melting of the confined phase in the amorphous pores. On 2725

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The Journal of Physical Chemistry C the other hand, it has sometimes been assumed that hysteresis arises from the persistence of a metastable solid up to a temperature higher than the equilibrium melting temperature, while freezing occurs at the equilibrium freezing temperature.14,15 For the confined Kr in the crystalline pores of the mesoporous carbon, lack of hysteresis between freezing and melting clearly indicates that neither the metastable solid nor the metastable liquid appears in the pores. We consider the reason why melting occurs at the equilibrium melting temperature in the following way. At pore end, the solid confined in the nearly cylindrical pores has inevitably a free surface in contact with a vapor under the present experimental conditions. Surface melting appears to be a relatively general phenomenon.42 It occurs whenever the sum of the specific solid-liquid plus liquid-vapor interfacial energies is lower than the solid-vapor interfacial energy. A surface may hence act as a nucleation center for the melt. When melting takes place by the movement of the hemispherical solid-liquid interface in the direction of the pore axis, the phase transition is expected to occur at the equilibrium melting temperature, as is the case for bulk melting transition. Furthermore, the metastable melting model predicts a depression in melting point exceedingly smaller than actually observed because in this model the depression in melting point is only half that in freezing point.15 However, the depression in melting point of the Kr confined to the amorphous pores of the ordered mesoporous silica was almost equal to that expected from the equilibrium freezing (melting) point.

’ ACKNOWLEDGMENT We thank Y. Matsutani for his technical assistance in the preparation of the materials and the measurements of TEM images and XRD patterns of the materials. This work was supported by matching fund subsidy for private universities from MEXT (Ministry of Education, Culture, Sports, Science and Technology). ’ REFERENCES (1) Christenson, H. G. J. Phys.: Condens. Matter 2001, 13, R95. (2) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys.: Condens. Matter 2006, 18, R15. (3) Akporiaye, D.; Hansen, E. W.; Schmidt, R.; St€ocker, M. J. Phys. Chem. 1994, 98, 1926. (4) Morishige, K.; Kawano, K. J. Chem. Phys. 1999, 110, 4867. (5) Schreiber, A.; Ketelsen, I.; Findenegg, G. H. Phys. Chem. Chem. Phys. 2001, 3, 1185. (6) J€ahnert, S.; Chavet, F. V.; Schaumann, G. E.; Schreiber, A.; Sch€onhoff, M.; Findenegg, G. H. Phys. Chem. Chem. Phys. 2008, 10, 6039. (7) Morishige, K.; Yasunaga, H.; Matsutani, Y. J. Phys. Chem. C 2010, 114, 4028. (8) Overloop, K.; Van Gerven, L. J. Magn. Reson. A 1993, 101, 179. (9) Stapf, S.; Kimmich, R. J. Chem. Phys. 1995, 103, 2247. (10) Wallacher, D.; Knorr, K. Phys. Rev. B 2001, 63, 104202–1. (11) Endo, A.; Yamamoto, T.; Inagi, Y.; Iwakabe, K.; Ohmori, T. J. Phys. Chem. C 2008, 112, 9034. (12) Schaefer, C.; Hofmann, T.; Wallacher, D.; Huber, P.; Knorr, K. Phys. Rev. Lett. 2008, 100, 175701–1. (13) Amanuel, S.; Bauer, H.; Bonventre, P.; Lasher, D. J. Phys. Chem. C 2009, 113, 18983. (14) Denoyel, R.; Pellenq, R. J. M. Langmuir 2002, 18, 2710.

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(15) Petrov, O.; Furo, I. Phys. Rev. E 2006, 73, 011608-1. (16) Vanfleet, R. R.; Mochel, J. M. Surf. Sci. 1995, 341, 40. (17) Cooper, S. J.; Nicholson, C. E.; Liu, J. J. Chem. Phys. 2008, 129, 124715. (18) Huber, P.; Knorr, K. Phys. Rev. B 1999, 60, 12657. (19) Morishige, K.; Kawano, K.; Hayashigi, T. J. Phys. Chem. B 2000, 104, 10298. (20) Morishige, K.; Yasunaga, H.; Denoyel, R.; Wernert, V. J. Phys. Chem. C 2007, 111, 9488. (21) Khokhlov, A.; Valiullin, R.; K€arger, J.; Steinbach, F.; Feldhoff, A. New J. Phys. 2007, 9, 272. (22) Zhu, D.-M.; Dash, J. G. Phys. Rev. B 1988, 38, 11673. (23) Larese, J. Z.; Zhang, Q. M.; Passell, L.; Hastings, J. M.; Dennison, J. R.; Taub, H. Phys. Rev. B 1989, 40, 4271. (24) Fujimoto, H. Carbon 2003, 41, 1585. (25) Wang, X.; Liang, C.; Dai, S. Langmuir 2008, 24, 7500. (26) Kruk, M.; Jaroniec, M.; Ko, C. H.; Ryoo, R. Chem. Mater. 2000, 12, 1961. (27) Morishige, K.; Inoue, K.; Imai, K. Langmuir 1996, 12, 4889. (28) Marti, C.; Croset, B.; Thorel, P.; Coulomb, J. P. Surf. Sci. 1977, 65, 532. (29) Warren, B. E.; Bodenstein, P. Acta Crystallogr. 1965, 18, 282. (30) Kiang, C. -H.; Endo, M.; Ajayan, P. M.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rev. Lett. 1998, 81, 1869. (31) 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. (32) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (33) Barrett, E. P.; Joyner, L. G.; Halenda, P. H. J. Am. Chem. Soc. 1951, 73, 373. (34) Lippens, B. C.; de Boer, J. H. J. Catal. 1965, 4, 319. (35) Pollack, G. L. Rev. Mod. Phys. 1964, 36, 748. (36) Sch€afer, B.; Balszunat, D.; Langel, W.; Asmussen, B. Mol. Phys. 1996, 89, 1057. (37) Brown, D. W.; Sokol, P. E.; Ehrich, S. N. Phys. Rev. Lett. 1998, 81, 1019. (38) Morishige, K.; Kawano, K. J. Phys. Chem. B 2000, 104, 2894. (39) Bilgram, J. H.; Firmann, M.; H€urlimann, E. J. Cryst. Growth 1989, 96, 175. (40) Maddox, M. W.; Gubbins, K. E. J. Chem. Phys. 1997, 107, 9659. (41) Kanda, H.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 8529. (42) van der Veen, J. F. Surf. Sci. 1999, 433-435, 1.

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