Monolayer Solids of Kr on Graphitized Carbon Black Surfaces and in

Apr 29, 2013 - ... Radhakrishnan , R.; Sliwinska-Bartkowiak , M. Effects of Confinement on Freezing and Melting J. Phys.: Condens. Matter 2006, 18, R1...
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Monolayer Solids of Kr on Graphitized Carbon Black Surfaces and in Graphitic Hexagonal Pores Kunimitsu Morishige* Department of Chemistry, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan ABSTRACT: To examine the effects of the inherent heterogeneity in graphitic hexagonal pores on Kr adsorption in the monolayer (ML) regime, we measured the powder X-ray diffraction (XRD) patterns of Kr adsorbed on the walls of the graphitic hexagonal pores, as well as the flat surfaces of graphitized carbon black, as a function of surface coverage at several different temperatures. On the flat surfaces of the graphitized carbon black, Kr atoms formed a hexagonally closepacked monolayer incommensurate with the graphite surface in the coverage range of 0.6−1.5 ML and the temperature range of 77−90 K, although the monolayer may coexist with a bilayer at high coverage, and the layers melted between 90 and 120 K. For the flat surfaces of the graphitized carbon black, the diffraction pattern for coverages less than ∼0.6 ML was very broad and very weak in intensity, indicating that two-dimensional (2D) clusters of Kr atoms formed are very small in size or highly defective. On the other hand, for the walls of the graphitic hexagonal pores, Kr atoms formed a hexagonally close-packed monolayer incommensurate with the graphite surface in the coverage range of 0.2−1.5 ML and the temperature range of 60−110 K, although the monolayer may coexist with a bilayer at high coverage, and the layers melted between 110 and 120 K. Formation of 2D crystallites at a low coverage of ∼0.2 ML indicates that a large number of nucleation sites for the 2D clusters exist on the walls of the graphitic hexagonal pores. The inherent heterogeneity due to pore shape in the graphitic hexagonal pores alters the growth mode of an adsorbed layer on the graphite surfaces. At a monolayer coverage, the 2D crystal size of Kr adsorbed on the walls of the graphitic hexagonal pores was smaller than that on the flat surfaces of the graphitized carbon black because the domain size of the carbon layer of the pore walls is smaller than that of the graphitized carbon black.

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INTRODUCTION Thus far the effects of pore wall structure on the freezing and melting behavior of materials confined in mesopores have been seldom examined, especially in experiments, although there is considerable current interest in phase transitions in confinement.1,2 Very recently, we have developed a new type of mesoporous carbon to examine the effect of pore wall structure on the freezing and melting behavior of materials confined in mesopores.3 This mesoporous carbon, which consists of carbon walls with turbostratic stacking structure, possesses regular hexagonal-shaped pores of the order of 9 nm in diameter. For Kr confined in the graphitic hexagonal pores (GHPs), freezing and melting take place almost reversibly in sharp contrast with the general observations that there is always appreciable hysteresis between freezing and melting of materials confined in mesopores of moderate sizes.3 Most of the mesopores experimentally investigated so far for liquid−solid phase transitions in confinement consist of pore walls with an amorphous structure, such as silica and alumina. The structure of the thin layers covering the amorphous walls is not at all compatible with that of the solid crystal formed in the center. Therefore, crystal nucleation 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. When liquid Kr confined in the GHP is cooled, however, a crystalline bilayer film of Kr is © 2013 American Chemical Society

already in place at the boundary between the liquid and the carbon pore walls at the equilibrium freezing point.4 The crystalline bilayer is formed due to the geometrical smoothness of the carbon pore walls and is commensurate with the bulk structure of the confined solid Kr. This plays a role as a critical nucleus in freezing of the interior phase, leading to lack of the thermal hysteresis. In conformity with this idea, methanol and ethanol confined in the GHP showed profound hysteresis between freezing and melting5 because thin films of methanol and ethanol on the carbon walls of the GHP did not crystallize even at 100 K, well below the freezing points of the liquids confined in the hexagonal pores. Methanol and ethanol, however, are known to form crystalline monolayers with zigzag chains of hydrogen bonds on flat graphite surfaces at around 140 and 210 K, respectively.6,7 This strongly suggests that the nature of the carbon walls of the GHP is different from that of the flat graphite surfaces. This mesoporous carbon is also regarded as an ideal adsorbent for study of the effects of nanoconfinement on the behavior of the confined adsorbate because adsorption in the material occurs solely inside the GHP, unlike carbon nanotubes. Adsorption in the carbon nanotubes occurs simultaReceived: December 5, 2012 Revised: April 26, 2013 Published: April 29, 2013 10360

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Brentano geometry, with a step width of 0.1° in 2θ and a counting time of 30 s. 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 an In O-ring. After prolonged evacuation at room temperature, the sample was cooled to a required temperature, and then the background was measured. The XRD measurements of adsorbed phases were carried out as a function of coverage at constant temperatures in the temperature range above 77 K. Below 77 K, the diffraction patterns of adsorbed phases were measured as a function of temperature for several coverages after adsorption at 77 K because at low temperatures Kr vapor condenses inside the stainless steel tube connecting the sample cell and an external gas-handling system. The diffraction pattern of the adsorbed Kr was obtained by subtraction of data for the 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.14

neously in various regions of the tube bundle, and therefore it is difficult to distinguish the contributions from each region of the overall uptake. A detailed comparison of the isotherms and isosteric heats of Ar adsorption in the GHP with the grand canonical Monte Carlo (GCMC) simulation has given a model that is the most suitable to describe the experimental data for Ar adsorption.8 In this model, the carbons at the junctions between two adjacent surfaces are assumed to be more energetic than the carbon atoms on the basal plane because an adsorbate in the neighborhood of the corner has more adsorbent atoms at closer separation distances, resulting in a greater solid−fluid potential compared to that of the flat graphite surface. A subsequent computer simulation and experimental study of the difference between Kr adsorption on a graphite surface and in a graphitic hexagonal pore has indicated that two-dimensional (2D) condensation of Kr, which occurs on the flat graphite surfaces below 86 K, is not observed in the GHP.9 Two-dimensional condensation is a dilute−dense phase transition in two dimensions.10 Lack of 2D condensation of Kr in the hexagonal pores indicates the importance of the inherent heterogeneity due to the strong adsorption sites near the corners and to the confinement (potential overlap) effects9 in the hexagonal pores because the onset of adsorption is the spreading of adsorbate from the corner toward the basal planes until the first layer is completed. Apart from the above-mentioned dilute−dense phase transition in two dimensions, the krypton/graphite system shows structural phase transitions in the monolayer regime. The monolayer has been extensively investigated with vaporpressure measurements,11 low-energy electron diffraction (LEED),12 specific heat,13 neutron,14 and X-ray scattering.15 In the submonolayer regime, krypton is commensurate, with the (√3 × √3)R30° structure. Above one monolayer krypton undergoes a hexagonal commensurate to hexagonal incommensurate transition. These monolayers melt at high temperatures depending on the surface density. These structural transitions are thought to be strongly affected by surface heterogeneities as well. To examine the effects of the inherent heterogeneity in the GHP on Kr adsorption in the monolayer regime, we measure the powder X-ray diffraction (XRD) patterns of Kr adsorbed on the walls of the GHP, as well as the flat surfaces of graphitized carbon black, as a function of surface coverage at several different temperatures.

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RESULTS AND DISCUSSION Graphitized Carbon Black. Figure 1 compares the XRD powder pattern of the graphitized carbon black (GCB) with

Figure 1. X-ray diffraction patterns of the graphitized carbon black and ordered mesoporous carbon. Solid curves denote the simulated XRD pattern of turbostratic carbon as described in the text. Intensities for the XRD pattern of the graphitized carbon black and its simulated pattern were incremented by 500 cps, respectively.

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EXPERIMENTAL SECTION Materials and Characterization. Ordered mesoporous carbon with GHPs was prepared by self-assembly of resorcinolformaldehyde and Pluronic F127 triblock copolymer according to the procedure of Wang, Liang, and Dai.16 Carbonization was carried out in a high-temperature furnace under an argon atmosphere at 2473 K for 1 h. Characterization of the ordered mesoporous carbon has been given in detail elsewhere.3,8 Cabon black graphitized at 3273 K under an argon atmosphere (Mitsubishi MA-600) was donated. Adsorption isotherms of nitrogen at 77 K were measured volumetrically on a BELSORP-mini II. X-ray diffraction powder patterns were measured on a Rigaku RAD-2B diffractometer in the Bragg−Brentano geometry arrangement using Cu Kα radiation at 30 kV and 20 mA with a graphite monochromator. Measurement. An experimental apparatus for measurements of XRD patterns of Kr monolayers on the substrates has been described elsewhere.17 The measurements were carried out with Cu Kα radiation at 50 kV and 180 mA in a Bragg−

that of the ordered mesoporous carbon as reported previously.3 The ordered mesoporous carbon exhibited four broad diffraction peaks that can be indexed as the 002, 10, 004, and 11 reflections in the turbostratic stacking structure of carbon.18 In the turbostratic stacking of graphite sheets, parallel graphite layers have random orientation about the layer normal.18 GCB exhibited the 002 reflections composed of three components, one of which is broad, indicating that the material consists of a large fraction of the turbostratic stacking structure of carbon. To know the structure of the GCB, we calculated the XRD pattern of turbostratic carbon using the Warren−Bodenstein equation.18,19 The parameters are the in-plane graphite lattice constant (a0), the spacing between the layers (d002), the domain size of the carbon layer along the a-axis (La), and the crystallite size along the c-axis (Lc). For the GCB, a good fit between the calculated and observed diffraction patterns was obtained with 10361

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the fixed values of a0 = 0.24612 nm, d002 = 0.345 nm, La = 10.09 nm, and Lc = 2.415 nm (eight sheets of carbon layer). These values can be compared with the refined parameters for the ordered mesoporous carbon reported previously: a0 = 0.24612 nm, d002 = 0.345 nm, La = 4.67628 nm, and Lc = 1.035 nm.3 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. The La for the GCB is larger than that for the ordered mesoporous carbon, suggesting that the crystal size of a monolayer solid formed on the external surfaces of the GCB would be larger than that on the walls of the GHP in the ordered mesoporous carbon. Figure 2 compares the adsorption−desorption isotherm of nitrogen at 77 K on the GCB with that on the ordered

certain values of coverage and temperature. In this phase the krypton atoms rest in the center of every third graphite hexagon. When at 90 K the coverage is increased beyond ∼0.8 of a complete monolayer, the Kr forms the commensurate phase on the flat graphite surfaces.13 Above one commensurate monolayer the Kr undergoes a commensurate−incommensurate transition. Both the commensurate and incommensurate phases persist up to ∼130 K at coverages larger than a complete monolayer.13 Figure 3 shows the powder XRD pattern from Kr adsorbed on the surfaces of the GCB at 90 K as a function of coverage in

Figure 3. Evolution of the X-ray diffraction pattern of Kr adsorbed on the graphitized carbon black as a function of the amount adsorbed at 90 K. Several sharp features arise from the incomplete subtraction of diffraction peaks of the graphite and the Be sheet. Intensities for the XRD patterns of Kr at the amount adsorbed of 0.73, 0.89, 1.05, 1.15, 1.23, 1.30, 1.39, and 1.49 mmol g−1 were incremented by 4000, 8000, 12 000, 16 000, 20 000, 24 000, 28 000, and 32 000 counts, respectively.

Figure 2. Adsorption−desorption isotherms of nitrogen at 77 K on the graphitized carbon black (triangles) and ordered mesoporous carbon (circles). Open and closed symbols denote adsorption and desorption branches, respectively.

mesoporous carbon as reported previously.3 Here, p0 is the saturation vapor pressure of nitrogen. The isotherm of the ordered mesoporous carbon showed a hysteresis loop due to capillary condensation and evaporation of nitrogen in the GHP. On the other hand, the isotherm of the GCB showed a narrow hysteresis loop at relative pressures higher than ∼0.8. This indicates that the material is essentially nonporous, and gaps between the carbon particles result in capillary condensation of the vapor only at high relative pressures. The specific surface area of the GCB, which was calculated by using the BET method20 from the nitrogen adsorption data, was 137 m2/g, while that of the ordered mesoporous carbon was 204 m2/g. Monolayer krypton on graphite has already been the subject of extensive experimental and theoretical investigations. The Lennard-Jones separation of a pair of krypton atoms is 0.404 nm compared with the (√3 × √3)R30° graphite superlattice separation of 0.426 nm.21 Thus, to form a commensurate phase, the krypton mean separation need only be expanded by 5.4%. The commensurate (√3 × √3)R30° phase is stabilized for

the monolayer range. Several sharp features arise from the incomplete subtraction of diffraction peaks of the Be sheet covering the substrate, as well as the sharp peak of the graphite 002 reflection. As described below, Kr atoms did not form the commensurate phase on the surfaces of this material in the coverage range of 0.6−1.5 ML and the temperature range of 77−90 K. Therefore, a monolayer capacity was estimated to be ∼1.3 mmol g−1 by applying the B-point method to the isotherm.22 Here, a monolayer corresponds to a single layer of hexagonally close-packed Kr atoms. The Kr adsorbed on the GCB did not exhibit well-defined diffraction at coverages less than ∼0.5 ML (0.65 mmol g−1). This indicates that in this coverage range 2D clusters of Kr atoms formed on the surfaces of the GCB are very small in size or highly defective. When the surface coverage was increased beyond ∼0.6 ML (0.78 mmol g−1), the diffraction peaks grew rapidly in intensity. At coverages larger than ∼0.8 ML (1.05 mmol g−1), the monolayer 10362

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submonolayers were impossible to be obtained. When at 90 K the coverage was further increased beyond ∼0.7 of a monolayer capacity, L started to increase rapidly and attained a maximum at a monolayer coverage (1.3 mmol g−1). The maximum 2D crystal size of ∼6 nm is reasonable because it is smaller than the domain size of the carbon layer (10 nm) obtained from an analysis of the 10 reflection of the GCB. A decrease of L with further increase in coverage originates partly from bilayer formation because the diffraction peak profile changes during transformation of monolayer to bilayer.4,23,25 Nguyen, Do, and Nicholson have carried out extensive simulation studies for the isosteric heat of adsorption versus loading of simple fluids adsorbed on a graphitic surface over a range of temperatures.26 Adsorption on the flat graphite surfaces has no preferred sites for the onset of adsorption, and the adsorbate distributes randomly across the surfaces. Twodimensional (2D) condensation of Kr in the first layer takes place on the flat graphite surfaces below 86 K, the 2D critical temperature for the first layer.11 In the 2D transition the isosteric heat of adsorption remains constant because the size of the cluster remains constant while the number of clusters increases with an increase in surface coverage. 2D clusters grow in size only at high surface coverages. This trend is still observed even at 90 K. Interestingly, we found that the coverage at which we observed 2D crystal formation in the XRD pattern in Figure 3 coincides with the coverage at which Nguyen et al. predicted that the isosteric heat of adsorption starts to increase linearly with coverage. At 120 K, L did not at all increase with an increase in coverage, indicating that the adsorbed phase does not crystallize even at coverages larger than a complete monolayer. Therefore, the melting points of the Kr monolayers on the GCB are lower than 120 K. This clearly indicates that the monolayer of Kr adsorbed on the graphene surfaces of a small coherence length melts at a lower temperature than that on the basal plane of graphite with a large coherence length. As Figure 4b shows, the commensurate monolayer phase was not at all formed on the surfaces of the GCB in the coverage range of 0.6−1.5 ML and the temperature range of 77−90 K. Instead, a weakly incommensurate monolayer phase appeared at coverages below a monolayer capacity at 77 and 90 K. This surface layer may be composed of locally commensurate regions separated by a periodic array of misfit dislocations.15 When the surface coverage was increased, a started to decrease rapidly in the vicinity of a monolayer capacity at all three temperatures of 77, 90, and 120 K because the atoms are more densely adsorbed on the surfaces. A nearest-neighbor distance in the bulk solid at 77, 90, and 116 K (a triple point) is 0.406, 0.408, and 0.412 nm, respectively.21 When the coverage was further increased beyond a monolayer capacity, a decreased well below the nearest-neighbor distance in the bulk solid. However, this does not necessarily indicate that the monolayer is in a more compressed state than the bulk solid. The monolayer model used in the present study underestimates a nearest-neighbor distance in the bilayer film. In the submonolayer range, a decreased with an increase in temperature because the effect of the substrate corrugation on the adsorbed phase is less important at high temperatures. Graphitic Hexagonal Pores. A detailed comparison of the isotherms and isosteric heats of Ar adsorption in the GHP with the grand canonical Monte Carlo (GCMC) simulation has given the model that is the most suitable to describe the experimental data for Ar adsorption.8 This model consists of a

exhibited a diffraction peak of a sawtooth shape typical of a 2D crystal,15,23−25 near 2θ = 25.0°. This peak can be assigned to the 10 reflection expected from a simple triangular lattice of Kr incommensurate with the surface structure of the GCB because the commensurate monolayer gives a Kr−Kr separation of 0.426 nm, and thus the 10 reflection for the commensurate monolayer is expected to appear at 2θ = 24.1° for Cu Kα radiation. The peak position shifted into higher scattering angle with a further increase in coverage. Similar measurements were performed at 77 and 120 K. The reciprocal lattice of a 2D crystal consists of an ordered array of rods, aligned normal to the crystal plane. In a sample of 2D crystallites randomly oriented in 3D space, this produces a diffraction line with a characteristic “sawtooth” shape, i.e., a line with a sharply rising leading edge on the low-angle side, followed by a trailing edge extending to larger scattering angles.15,23−25 A Bragg rod of the single 2D crystallite is assumed to have a Gaussian cross section. A powder-averaged Gaussian line shape was convoluted numerically with the resolution function and corrected for a polarization factor. To obtain accurate peak parameters, a powder-averaged Gaussian line shape with a linearly changing background was fitted to the observed peak profile of the 10 reflection in a 2θ range of 20− 40°. The fitting parameters are the lattice constant (a), 2D crystal size (L), and amplitude. Fitted values of a and L from Gaussian fits to the profiles are shown in Figure 4. Below coverage of ∼0.6 ML (0.78 mmol g−1), the diffraction pattern of the adsorbed phase was very broad and very weak in intensity, and thus the reliable peak parameters for these

Figure 4. Crystallite size (a) and lattice constant (b) of the 2D triangular solid as a function of coverage for Kr on the graphitized carbon black at 77, 90, and 120 K. Horizontal solid and dotted lines in (b) denote the lattice constant expected from the commensurate monolayer with the (√3 × √3)R30°structure and the Lennard-Jones separation of a pair of Kr atoms, respectively. 10363

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at low coverages less than ∼0.5 ML. Eventually, the submonolayer showed a diffraction peak of a sawtooth shape typical of a 2D crystal at a coverage of ∼0.8 ML (1.43 mmol g−1). Similarly, this peak can be assigned to the 10 reflection expected from a simple triangular lattice of Kr incommensurate with the wall structure of the GHP. Formation of 2D crystallites at a low coverage of ∼0.2 ML indicates that a large number of nucleation sites for the 2D clusters exist on the pore walls of the GHP. This is in good agreement with the suggestion of the previous simulation study9 that inside the GHP strong nucleation sites are arranged in 1D at the corners of the hexagonal pores, and thus 2D clusters of moderate sizes grew even at relatively small coverages. The peak position shifted into higher scattering angle with a further increase in coverage. Similar measurements were performed at 60, 65, 70, 77, and 120 K. Fitted values of a and L from Gaussian fits to the profiles are also shown in Figure 6. L took relatively large values even at

hexagonal pore with six graphene surfaces composed of 5 nm patches. The gap between patches is 1 nm, and the carbons at the junctions between two adjacent surfaces are assumed to be more energetic than the carbon atoms on the basal plane. A subsequent computer simulation and experimental study of Kr adsorption isotherms suggest the following scenario for Kr adsorption inside the GHP.9 At low coverage Kr atoms adsorb predominantly along the six junctions and at the gaps between patches of graphene because they are the strongest sites. As coverage is increased, the junctions are completely filled with Kr atoms in a 1D configuration, and adsorption starts to spread in two-dimensions across the basal planes of the hexagonal pore. This continues until the basal plane is covered with Kr atoms. To examine such a scenario for Kr adsorption on the pore walls of the GHP, we measured X-ray diffraction from Kr adsorbed inside the hexagonal pores. Figure 5 shows the

Figure 5. Evolution of the X-ray diffraction pattern of Kr adsorbed on the walls of the graphitic hexagonal pores as a function of the amount adsorbed at 90 K. Several sharp features arise from the incomplete subtraction of diffraction peaks of the graphite and the Be sheet. Intensities for the XRD patterns of Kr at the amount adsorbed of 0.61, 0.90, 1.19, 1.43, 1.62, 1.79, and 1.99 mmol g−1 were incremented by 5000, 10 000, 15 000, 25 000, 35 000, 45 000, and 55 000 counts, respectively.

Figure 6. Crystallite size (a) and lattice constant (b) of the 2D triangular solid as a function of coverage for Kr in the graphitic hexagonal pores at 60, 65, 70, 77, 90, and 120 K. Horizontal solid and dotted lines in (b) denote the lattice constant expected from the commensurate monolayer with the (√3 × √3)R30° structure and the Lennard-Jones separation of a pair of Kr atoms, respectively.

powder XRD pattern from the Kr adsorbed inside the GHP at 90 K as a function of coverage in the monolayer range. Similarly, Kr atoms did not form the commensurate phase on the pore walls of the GHP in the coverage range of 0.5−1.5 ML and the temperature range of 60−90 K. Therefore, a monolayer capacity was estimated to be ∼1.8 mmol g−1 by applying the Bpoint method to the isotherm. A diffraction peak from the Kr adsorbed on the pore walls of the GHP appeared even at a low coverage of 0.17 ML (0.31 mmol g−1), in sharp contrast with the case in the GCB. When the coverage was increased, the diffraction profile of the submonolayer became gradually sharp

small coverages because 2D clusters of moderate sizes can be easily formed in the vicinity of the corners of the GHP. When the coverage was increased, L increased steadily and attained a constant value near a monolayer capacity at all temperatures examined here, except for at 120 K. At a monolayer coverage, however, the 2D crystal size of Kr adsorbed on the walls of the GHP was smaller than that on the flat surfaces of the GCB because the domain size of the carbon layer of the pore walls is smaller than that of the GCB. The maximum 2D crystal size of ∼3 nm was reasonable because it is smaller than the domain size of the carbon layer (4.7 nm) of the GHP. At 120 K, L did 10364

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(4) Morishige, K. Layer-by-Layer Freezing of Kr Confined in Hexagonal Pores with Crystalline Carbon Walls. J. Phys. Chem. C 2011, 115, 12158−12162. (5) Morishige, K.; Mikawa, K. Tensile Effect on Crystal Nucleation of Methanol and Ethanol Confined in Pores. J. Phys. Chem. C 2012, 116, 3618−3622. (6) Morishige, K.; Kawamura, K.; Kose, A. X-ray Diffraction Study of the Structure of a Monolayer Methanol Film Adsorbed on Graphite. J. Chem. Phys. 1990, 93, 5267−5270. (7) Morishige, K. Structure and melting of a monolayer ethanol film on graphite. J. Chem. Phys. 1992, 97, 2084−2089. (8) Wang, Y.; Nguyen, P. T. M.; Sakao, N.; Horikawa, T.; Do, D. D.; Morishige, K.; Nicholson, D. Characterization of a New Solid Having Graphitic Hexagonal Pores with a GCMC Technique. J. Phys. Chem. C 2011, 115, 13361−13372. (9) Wang, Y.; Razak, M. A.; Do, D. D.; Horikawa, T.; Morishige, K.; Nicholson, D. A Computer Simulation and Experimental Study of the Difference between Krypton Adsorption on a Graphite Surface and in a Graphitic Hexagonal Pore. Carbon 2012, 50, 2908−2917. (10) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterwords: Guildford, 1962; Chapter 4. (11) Thomy, A.; Duval, X.; Regnier, J. Two-Dimensional Phase Transition As Displayed by Adsorption Isotherms on Graphite and Other Lamellar Solids. Surf. Sci. Rep. 1981, 1, 1−38. (12) Chinn, M. D.; Fain, S. C., Jr. Structural Phase Transition in Epitaxial Solid Krypton Monolayers on Graphite. Phys. Rev. Lett. 1977, 39, 146−149. (13) Butler, D. M.; Litzinger, J. A.; Stewart, G. A. Completion of the Phase Diagram for the Monolayer Regime of the Krypton-Graphite Adsorption System. Phys. Rev. Lett. 1980, 44, 466−468. (14) Marti, C.; Croset, B.; Thorel, P.; Coulomb, J. P. a Neutron Investigation of Krypton Adsorbed on a Graphite. Surf. Sci. 1977, 65, 532−538. (15) Stephens, P.; Heiney, P. A.; Birgeneau, R. J.; Horn, P. M.; Moncton, D. E.; Brown, G. S. High-Resolution X-ray-Scattering Study of the Commensurate−Incommensurate Transition of Monolayer Kr on Graphite. Phys. Rev. B 1984, 29, 3512−3532. (16) Wang, X.; Liang, C.; Dai, S. Facile Synthesis of Ordered Mesoporous Carbons with High Thermal Stability by Self-Assembly of Resorcinol-Formaldehyde and Block Copolymers under Highly Acidic Conditions. Langmuir 2008, 24, 7500−7505. (17) Morishige, K.; Inoue, K.; Imai, K. X-ray Study of Kr, Xe, and N2 Monolayers on Boron Nitride. Langmuir 1996, 12, 4889−4891. (18) Warren, B. E.; Bodenstein, P. The Diffraction Pattern of Fine Particle Carbon Blacks. Acta Crystallogr. 1965, 18, 282−286. (19) Fujimoto, H. Theoretical X-ray Scattering Intensity of Carbons with Turbostratic Stacking and AB Stacking Structures. Carbon 2003, 41, 1585−1592. (20) Brunauer, S.; Emmett, P. H.; Teller, E. Adsorption of Gases in Multimolecular Layers. J. Am. Chem. Soc. 1938, 60, 309−319. (21) Pollack, G. L. The Solid State of Rare Gases. Rev. Mod. Phys. 1964, 36, 748−791. (22) Emmett, P. H.; Brunauer, S. The Use of Low Temperature van der Waals Adsorption Isotherms in Determining the Surface Area of Iron Synthetic Ammonia Catalysts. J. Am. Chem. Soc. 1937, 59, 1553. (23) Kjems, J. K.; Passell, L.; Taub, H.; Dash, J. G.; Novaco, A. D. Neutron Scattering Study of Nitrogen Adsorbed on Basal-PlaneOriented Graphite. Phys. Rev. B 1976, 13, 1446−1462. (24) Schildberg, H, P.; Lauter, H. J. Lineshape Calculations for TwoDimensional Powder Samples. Surf. Sci. 1989, 208, 507−532. (25) Larese, J. Z.; Harada, M.; Passell, L.; Krim, J.; Satija, S. NeutronScattering Study of Methane Bilayer and Trilayer Films on Graphite. Phys. Rev. B 1988, 37, 4735−4742. (26) Nguyen, V. T.; Do, D. D.; Nicholson, D. On the Heat of Adsorption of Layering Transitions in Adsorption of Noble Gases and Nitrogen on Graphite. J. Phys. Chem. C 2010, 114, 22171−22180.

not increase at all with an increase in coverage. This indicates that at this temperature the adsorbed phase does not freeze on the walls of the GHP even after completion of a monolayer. Our previous X-ray study has shown that the Kr monolayer adsorbed on the walls of the GHP keeps its crystallinity even at 110 K.4 Therefore, the melting point of the Kr monolayer adjacent to the pore walls is placed between 110 and 120 K. Lattice constant a decreased monotonically with an increase in coverage. A weakly incommensurate submonolayer gradually changed into an incommensurate monolayer that is mainly controlled by adsorbate−adsorbate interactions.

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CONCLUSIONS On both the flat surfaces of the GCB and the carbon walls of the GHP, Kr atoms formed a hexagonally close-packed monolayer incommensurate with the graphite surface but did not at all form a commensurate monolayer, in contrast to those on the basal plane of graphite with a large coherence length. The Kr adsorbed on the GCB did not exhibit well-defined diffraction at coverages less than ∼0.5 ML, indicating that in this coverage range 2D clusters of Kr atoms formed on the flat surfaces of the GCB are very small in size or highly defective. On the other hand, the Kr adsorbed on the walls of the GHP exhibited well-defined diffraction even at a low coverage of ∼0.2 ML. This indicates that a large number of nucleation sites for the 2D clusters exist on the walls of the GHP, being in good agreement with the suggestion of the previous simulation study9 that inside the hexagonal pores strong nucleation sites are arranged in 1D at the corners of the hexagonal pores, and thus 2D clusters of moderate sizes grow even at relatively small coverages. The inherent heterogeneity due to pore shape in the graphitic hexagonal pores alters the growth mode of an adsorbed layer on the graphite surfaces. At a monolayer coverage, the 2D crystal size of Kr adsorbed on the walls of the GHP was smaller than that on the flat surfaces of the GCB because the domain size of the carbon layer of the pore walls is smaller than that of the GCB.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +81 86 256 9494. Fax: +81 86 256 9757. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank K. Mikawa for his technical assistance in the analysis of some of the diffraction profiles. This work was supported by MEXT (Ministry of Education, Culture, Sports, Science and Technology)-Supported Program for the Strategic Research Foundation at Private Universities, 2009−2013.

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REFERENCES

(1) Christenson, H. G. Confinement Effects on Freezing and Melting. J. Phys.: Condens. Matter 2001, 13, R95−R133. (2) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Effects of Confinement on Freezing and Melting. J. Phys.: Condens. Matter 2006, 18, R15−R68. (3) Morishige, K. Freezing and Melting of Kr in Hexagonally Shaped Pores of Turbostratic Carbon: Lack of Hysteresis between Freezing and Melting. J. Phys. Chem. C 2011, 115, 2720−2726. 10365

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