Heterogeneity Characterization of Ordered Mesoporous Carbon

13024

J. Phys. Chem. C 2008, 112, 13024–13036

Heterogeneity Characterization of Ordered Mesoporous Carbon Adsorbent CMK-1 for Methane and Hydrogen Storage: GCMC Simulation and Comparison with Experiment Xuan Peng,*,† Dapeng Cao,*,‡ and Wenchuan Wang‡ College of Information Science and Technology and DiVision of Molecular and Materials Simulation, Key Laboratory of Nanomaterials, Ministry of Education, Beijing UniVersity of Chemical Technology, Beijing 100029, P.R. China ReceiVed: January 24, 2008

Grand-canonical Monte Carlo (GCMC) simulations were performed to investigate the adsorption behavior of methane and hydrogen on a highly ordered carbon molecular sieve CMK-1 material. The rod-aligned slitlike pore (RSP) model was used to emphasize the grooved structure of the material, and the pore size distribution (PSD) was introduced to characterize the geometrical heterogeneity of the materials quantitatively. The PSD determined from adsorption isotherms of N2 at 77 K indicates that the CMK-1 adsorbent is a mesoporous material. By combining the GCMC and PSD techniques, adsorption isotherms of CH4 at 303 K and H2 at 303 and 77 K in the CMK-1 materials were obtained. The simulated isotherms are in an excellent agreement with experimental data, suggesting that it is necessary and efficient to use the PSD to characterize the materials. The GCMC predictions demonstrate that gravimetric uptakes of CH4 and H2 in the CMK-1 material at 30 MPa and 303 K are 31.23 and 1.19 wt %, respectively. Although a greater loading of 4.58 wt % for H2 is favored at 77 K and the same pressure, it does not reach the U.S. Department of Energy target of 6.5 wt %. By analyzing isosteric heats, we found that the adsorptions of CH4 at 303 K and H2 at 77 K exhibit an evidently energetic heterogeneous behavior in CMK-1 materials, with a broad range of isosteric heats of 10-27 kJ/mol for CH4 and 2.73-9.9 kJ/mol for H2. However, the adsorption behavior tends to be energetically homogeneous for H2 at 303 K, because the isosteric heat mainly centers on the range 4.82-6.65 kJ/mol. In addition, by exploring the relationship between the pore width and the surface excess, we found that, for CH4 at 303 K, the optimal operating conditions corresponding to the maximum surface excess are w ) 1.2422 nm and P ) 6 MPa, whereas for H2 at 77 K, they are w ) 1.0647 nm and P ) 3 MPa. 1. Introduction With the exhausted exploitation of the natural resources by human society, the effective utilization of energy becomes one of the most urgent and significant topics worldwide. Moreover, associated environmental problems such as air pollution have attracted a great deal of attention in considering energy usage. Currently, methane, the key component of natural gas, and hydrogen are still regarded as clean alternatives for automobile fuel. Although their use is completely feasible for automotive power systems, a technical bottleneck suppressing development in this area is how to store these gases in an effective way. For methane, three techniques are currently proposed to achieve storage, i.e., liquefied natural gas (LNG), compressed natural gas (CNG), and adsorbed natural gas (ANG).1 For hydrogen, apart from the approaches mentioned above, the formation of metal hydrides is a complementary option to attempt.2 In terms of implementation, LNG and CNG cannot be liquefied at ambient temperature because of their relatively low critical temperatures (119 K for CH4 and 33K for H2). As a result, application of these techniques requires extremely difficult conditions of low temperature and high pressure. This is usually impractical in terms of economics and safety, thus hindering their further application. Metal hydrides, in turn, are disadvantageous because of the gravimetric density of H2, as well as * Corresponding authors. E-mail: [email protected] (X.P.), [email protected] (D.C.). † College of Information Science and Technology. ‡ Division of Molecular and Materials Simulation.

problems with dendrite crystal and grain refinement during recycle usage.2 For practical applications of gas storage, two basic properties need to be achieved simultaneously, namely, high energy density and low cost. If a suitable adsorbent is available, physisorption is a very promising technology for its inherent low cost and high efficiency. Numerous porous materials, for instance, active carbons,3–5 single-walled carbon nanotubes (SWCNTs),6–8 graphite nanofibers (GNFs),9 pillared clays,10,11 and metal-organic frameworks (MOFs)12–14 have been synthesized and accordingly tested for use in ANG technology. Compared to experimental research, molecular simulation is a very useful tool for understanding interfacial phenomena at a microscopic level. Furthermore, one advantage of molecular simulation is that it can predict properties of materials under extreme conditions with less cost. Using different theoretical tools such as equation of state (EOS) theory,15 grand-canonical Monte Carlo (GCMC)16,17 or constant-pressure Gibbs10,18 MC methods, and nonlocal density functional theory (NDFT),19,20 researchers have completed a great number of work on the adsorption storage of methane and hydrogen. In 1990, Tan and Gubbins investigated the adsorption behavior of methane and ethylene in model carbon micropores using NDFT and GCMC simulations.21 In the next year, Matranga et al. performed GCMC simulations of the adsorption of natural gas on activated carbon.22 Subsequent simulations by Wang and Johnson23,24 suggested that nanotube arrays are not suitable adsorbents for H2 storage at ambient temperature and 77 K. However, Yin et

10.1021/jp8034133 CCC: $40.75  2008 American Chemical Society Published on Web 07/29/2008

Characterization of CMK-1 for CH4 and H2 Storage al.25 found that optimized triangular SWNT arrays can reach the U.S. Department of Energy (DOE) target for hydrogen-fuel vehicles at 77 K. To confirm the above results, Cracknell designed a hypothetical chemisorption potential for H2 and found that, even if chemical adsorption occurs, the simulated results were still much lower than the earlier results.26 By using computer simulations, Cao et al. not only optimized the structural parameters of pillared clay materials27 and SWNT arrays,28 but also recommended the proper operating conditions for supercritical methane storage.27 In particular, Cao et al.28 found a separation of twice the diameter of a fluid molecule to be suitable for the adsorption of fluids in SWNT arrays. A further report by Cao et al. indicated that graphitic carbon inverse opal (GCIO) is a promising candidate, because GCIO materials show a H2 uptake of 5.9 wt % at 298 K and 30.25 MPa.29 In addition, Shao et al. found that the amount of CH4 adsorbed in mesocarbon microbeads can reach 36 wt % at 298 K and 4 MPa and the amount of H2 can reach 3.2 wt % at 298 K and 10 MPa, which is superior to the results for other carbon materials.30 In 2005, Tanaka et al. investigated the quantum effects on hydrogen isotopes adsorbed in single-walled carbon nanohorns (SWNHs) by experiment and simulation.31 A similar work considering quantum effects by Kowalczyk et al. demonstrated that the maximum storage of H2 at 303 K in graphite pores is about 1.4 wt % and the enthalpy of adsorption is almost constant with loading in the narrow range of 7.28-7.85 kJ/ mol.32 Recently, Do et al. also investigated the adsorption of CH4 on graphite and slit pores.33 In 2006, Bhatia and Myers performed thermodynamic analysis and GCMC simulations to find the optimum conditions for adsorptive storage.34 Kowalczyk et al. conducted GCMC simulations of CH4 storage at 293 K in (10,10) SWNTs and wormlike carbon pores.35 In view of the above information, it seems that these studies on the adsorption storage of energy gases have never been terminated. The enthusiasm promotes continuing research into many diverse adsorbents. In recent years, there has been growing demand for the development of mesoporous carbon materials with uniform and controlled pore structures. To meet these requirements, great attention has been paid to the template carbonization method using various precursors and optimizing synthesis conditions. A series of ordered mesoporous carbon materials designated as CMK type have been synthesized with ordered silicate mesoporous templates.36–41 Using sucrose inside mesoporous silica molecular sieve MCM-48 as the carbon source in the presence of sulfuric acid, Ryoo et al. first prepared ordered carbon molecular sieves, CMK-1, which exhibits a uniform pore distribution from micropore to mesopore, with a high BET (Brunauer-Emmett-Teller) surface area of 1380 m2/ g.37 Because of the advantages of high specific surface areas, large pore volumes, chemical inertness, ordered pore structures, and tunable pore diameters, the CMK-type material attracts extensive interest for potential applications, including shapeselective catalysts, gas separation materials, battery electrodes, adsorbents for energy storage,42 and immobilization supports for biomolecules such as vitamins43 and proteins.44 To the best of our knowledge, only a few works have emphasized experimental and theoretical studies of the adsorption storage of CH4 and H2 in CMK-1. Ohkubo et al. pioneered the investigation for N2 and CH4 at the adsorbent.45 They used the rod-aligned slitlike pore (RSP) model to characterize the groove structure of the material and also performed GCMC simulations for comparison with experiment. Unfortunately, because their work omitted the heterogeneity of the materials, the RSP model was not sufficiently realistic to describe

J. Phys. Chem. C, Vol. 112, No. 33, 2008 13025 TABLE 1: Molecular Potential Parameters of Adsorbates and Adsorbent species

σ (nm)

/kBa (K)

F2-C (nm-2)

ref

C

0.340

Adsorbent 28.0

38.2

45

N2 CH4 H2

0.3549 0.3810 0.296

Adsorbates 94.95 148.2 34.2

a

45 45 48

kB is the Boltzmann constant.

quantitatively the adsorption behavior in CMK-1 adsorbent. More recently, H2 adsorption in two mesoporous ordered carbons MOC-MCM-48 (namely, CMK-1) and MOC-SBA-15 (namely, CMK-3 or CMK-5) was reported based on thermodynamic and neutron scattering studies.46 For both materials, the information is still insufficient to depict the gas adsorption at high pressure. More importantly, the influence on the isosteric heat of heterogeneity arising from pore size was not considered thoroughly. Herein, we address these neglected issues. This article is organized as follows: First, an illustration of the potential model used here and the GCMC simulation details is provided, followed by a discussion of the characterization of the adsorbent. Then, the pore size distribution (PSD) is determined from experiment and simulation of the N2 adsorption isotherm at 77 K and subsequently used to predict the adsorptions of CH4 and H2. The energetic heterogeneity of the adsorbent is also analyzed. Finally, the effects of the pore width on the surface excess and isosteric heat are explored. 2. Potential Model For a fluid molecule confined in CMK-1 adsorbent, the total potential energy is the sum of the potential energy between fluid molecules, φff, and the potential energy between a fluid molecule and a solid wall, φsf. In our simulation, all of the fluid molecules were modeled as a single Lennard-Jones (LJ) sphere for simplicity and accuracy. The Buch potential parameters48 were directly adopted here for hydrogen, because the study by Wang et al.47 suggested that they provide excellent agreement with experimental data, as well as with the results from the Silvera and Goldman (SG) potential49 that involves the quantum correction. The fluid-fluid interaction, φff, was computed from the classical 12-6 LJ potential,45 and the LJ parameters of nitrogen,45 methane,45 and hydrogen48 are listed in Table 1. As proposed by Ohkubo et al.,45 the RSP model45 was used here to reflect the textural and grooved characteristics of the CMK-1 adsorbent. The simulation unit cell consisted of three carbon rods aligned similarly to a slit pore, as shown in Figure 1a-c. Therefore, the solid-fluid interaction, φsf, is the sum of the interactions between fluid molecules and the carbon rods 3

φsf )

∑ [Vsf(|li|) + Vsf(|li - H|)]

(1)

i)1

where Vsf(li) is the interaction between a fluid molecule and the carbon rod surface and H is the physical pore width vector of the pore measured from the plane of the centers of the top carbon rods to the plane of the centers of the opposite rods (see Figure 1b). The effective pore width w, defined as the minimum effective pore width between aligned sheets, is generally specified in GCMC simulations. H in eq 1 was calculated as |H| ) w + 2a5 + (2z0 - σff), where the radius of the outermost rod layer is a5 ) 1.582 nm and z0 is the position where the

13026 J. Phys. Chem. C, Vol. 112, No. 33, 2008

Peng et al.

Figure 1. Schematic diagrams of the RSP model used in GCMC simulation for the characterization of CMK-1 adsorbent. (a-c) RSP model and (d) electron density distribution Fourier map of the (211) section excerpted from the literature.42

adsorbate potential for a plane wall passes through zero, i.e., z0 ) 0.850σsf. The graphite intersheet distance of coaxial cylinders was set at 0.3354 nm. More details about this model can be found in the original article of Kaneko et al.50 By summing the interactions of a fluid molecule with a carbon cylinder, the term of Vsf(li) in eq 1 can then be calculated as45 5

Vsf(li) ) 4F2-Cεsf

∑ (σsf12I12 - σsf6I6)

(2)

n)1

where li is the distance from the center line of a carbon rod to a fluid molecule; F2-C is the two-dimensional density of a carbon cylinder; and εsf and σsf are the cross solid-fluid interaction parameters from potential parameter of solid rod which are also listed in Table 1. The cross energy and size parameters were calculated by Lorentz-Berthelot (LB) mixing rules. The terms of I12 and I6 were obtained as45

I12 ) I6 )

63π2(an/li)11

[1 - (an/li) ]

128a10 n

2 10

3π2(an/li)5

[1 - (an/li) ]

4a4n

2 4

9 9 F - , - , 1, (an/li)2 2 2

[

]

3 3 F - , - , 1, (an/li)2 2 2

[

]

(3)

where an is the radius of the carbon cylinder consisting of the nth layer and F is a hypergeometric function.

Figure 2. GCMC simulation results for N2 adsorption at T ) 77 K and single-pore individuals. (a) Absolute pore density versus relative pressure and (b) isosteric heat versus absolute pore density. The three different pore widths plotted are w ) (9) 0.7098, (b) 1.5971, and (2) 2.4843 nm. Lines are a guide for the eye only.

3. GCMC Simulations To simulate the adsorption of fluids confined in the CMK-1 adsorbent, we used the standard GCMC algorithm, where the chemical potential, pore volume, and temperature are independent variables. In the unit cell, the box length along the x direction, Lx, equaled 4.0a5, and the box length along the y direction, Ly, was set to 2Lx. The cutoff radius was 5 times the size parameter of the fluid molecule. In our simulations, periodic boundary conditions were applied only in the x and y directions, as shown in Figure 1a. The initial configuration was generated randomly. For each state point, we generated 2 × 107 configurations, discarded the first 1 × 107 configurations to guarantee equilibrium, and collected the remaining 1 × 107 configurations

for the ensemble average. In the simulations, the absolute pore density, 〈F〉, was defined as the ensemble average of the number of particles, 〈N〉, per unit accessible volume V, where V ) LxLyH - 2πa52Ly. The average surface excess is given by51

Γsurf )

〈N 〉 -VFb Ssurf

(4)

where Ssurf is the surface area in the RSP model, which equals 4πa5Ly, and Fb is the number density in the bulk phase. To investigate the microstructure of the fluid molecules confined in the RSP model, we defined the local density profile, F*(z*), of the center of mass as

Characterization of CMK-1 for CH4 and H2 Storage

F*(z*) )

〈N(z*)〉 A*∆z*

J. Phys. Chem. C, Vol. 112, No. 33, 2008 13027

(5)

where 〈N(z*)〉 is the ensemble average of the number of adsorbed molecules in a differential layer (including accessible and solid volumes) located in the range from z* to z* + ∆z*. Here, the unit cell was divided into 500 layers along the z direction. All variables were reduced with respect to the fluid molecules. The modified Bennedict-Webb-Rubin (MBWR) equation of state52,53 was used to convert chemical potential into pressure. 4. Characterization of Heterogeneous Adsorbent CMK-1 4.1. Structural Heterogeneity. The pore size analysis shows that the CMK-1 is structurally microporous and mesoporous.37 A structurally heterogeneous material such as this is generally characterized by a combination of the GCMC and PSD method with adsorption isotherms of N2 at 77 K, as most previous works

have done for activated carbon.30,54,61 The total adsorption amount, Ntot(Pi), from a PSD is described as a weighted aggregation of isotherms in individual pores54

Ntot(Pi) )

∫0∞ F(H,Pi) f(H) dH

(6)

where F(H,Pi) is the absolute pore density obtained from GCMC simulation for a single-pore width H and pressure Pi and f(H) dH is the volume of pores occupying a width between H and H + dH. In practice, we selected 27 pore widths from 0.3549 to 4.9686 nm to replace the integral of eq 6 by a summation over the discrete interval of ∆H ) 0.17745 nm using the PSD. Similarly to Nguyen and Do,54 we used the optimization toolbox of the Matlab platform55 to determine the f(H) dH term. The objective function, Fobj, was defined as the sum of the squares of the residual of the adsorption amount between the experimental data and the simulated values.30 4.2. Energetic Heterogeneity. In adsorption studies, a thermodynamic quantity of interest is the isosteric heat, which is the heat released for each molecule added to the adsorbed phase. Using fluctuation theory, the isosteric heat was calculated from56

qst )

〈Uff 〉 〈N 〉 -〈UffN〉 〈N 〉 -〈N 〉 〈N〉 2

+ kT +

〈Usf 〉 〈N 〉 -〈UsfN〉 〈N2 〉 -〈N 〉 〈N〉

(7)

where the broken brackets denote the ensemble average obtained from simulation, N is the number of adsorbed fluid molecules, and U is the configuration energy of the system. The first term on the right of eq 7 is the contribution from the fluid-fluid interactions, and the second term is the contribution due to fluid-solid interactions. Similarly to the structural heterogeneity, the isosteric heat on a heterogeneous adsorbent should be calculated from that of individual pores to reflect the energetic heterogeneity of CMK-1. Birkett and Do pointed out that the common procedure of weighting the total isosteric heat, qst,tot, with the total adsorption amount is incorrect, as it would lead to a serious error in the calculation of the isosteric heat on activated carbon.57 They suggested that the isosteric heat should be weighted with an incremental amount and proposed two techniques for this calculation. Here, we adopt the discrete form of these techniques, which calculates qst,tot by an incremental change in the pressure, as given by the equation57

qst,tot(Pi) ≈

{ [( 0.5

{∫ (

∞

0

[(

qst(H,Pi)0.5

)

F(H,Pi) - F(H,Pi-1) + Pi - Pi-1

)]

}

F(H,Pi+1) - F(H,Pi) f(H) dH ⁄ Pi+1 - Pi

)(

Ntot(Pi) - Ntot(Pi-1) Ntot(Pi+1) - Ntot(Pi) + Pi - Pi-1 Pi+1 - Pi

)]}

(8)

where qst(H,Pi) is the simulated isosteric heat for a single-pore width H and pressure Pi. A good accuracy was validated for activated carbon as long as a sufficient number of isotherm points are available.

Figure 3. GCMC simulation results of isosteric heat versus absolute pore density for N2 adsorption at T ) 77 K and single-pore individuals for w ) (a) 0.7098, (b) 1.5971, and (c) 2.4843 nm. Symbols denote the isosteric heats contributed by the (9) total, (2) fluid-fluid, and (1) solid-fluid interactions. Lines are a guide for the eye only.

5. Results and Discussion 5.1. Nitrogen Adsorption at 77 K. Adsorbents are generally characterized by N2 adsorption at 77 K. To represent the geometrical heterogeneity of the CMK-1 adsorbent, the PSD was used. First, we simulated the adsorption of N2 at 27 various pore widths. The experimental data for N2 adsorption on CMK-1 was taken from the literature.45 The simulated pressures were


Peng et al.

Figure 4. Side views of snapshots of N2 in the RSP model at T ) 77 K as functions of pressure and effective pore width.

selected according to the measured experiments. As a representative, the three pore widths w ) 0.7098, 1.5971, and 2.4843 nm were chosen to illustrate the adsorption amount and isosteric heat of nitrogen, as shown in Figure 2. It can be observed from Figure 2a that there exist two types of adsorption isotherms in these pores. At w ) 0.7098 nm, the absolute pore density quickly reaches a saturated value at a low relative pressure, corresponding to micropore filling of a type-I isotherm.58 At the larger pore widths, w ) 1.5971 and 2.4843 nm, the isotherms show a slightly layering at a relative pressure of about P/P0 ) 0.6, followed by filling, and gives a clear S-shaped isotherm, which is characteristic of an adsorption isotherm of type IV for mesoporous materials.58 However, the vertical jump in the adsorption isotherm is not observed distinctly, compared to that in slit pores. The phenomenon is consistent with the results from Ohkubo et al.45 This is due to the fact that the RSP model used here has a grooved structure, which leads to the surface heterogeneity, compared to slit pores. Figure 2b shows the dependence of the isosteric heat on the absolute pore density at three pore widths. We observe that the isosteric heat decreases with increasing pore width. At the smallest pore width, w ) 0.7098 nm, the isosteric heat first exhibits a local maximum at the pore density of 0.41, followed by a decline and then a sharp rise, and finally fluctuation at the saturated density of 0.65. For w ) 1.5971 and 2.4843 nm, the isosteric heat presents a wavy drop until a discontinuous upward

jump at the pore densities of 0.52 and 0.4, respectively. For the two pore widths, the reason for the discontinuous fluctuation of isosteric heat at high density is that condensation occurs in the pore phase. In this situation, particle insertion is very difficult at high density. Therefore, it is unreliable to calculate the isosteric heat using eq 7 after condensation, as interpreted by Birkett and Do.57 In fact, all of these phenomena can be explained in term of the interactions between the fluid molecules and the solid rods. Figure 3 demonstrates the two independent contributions to the isosteric heat from the fluid-fluid and solid-fluid interactions. For all of the pores, the isosteric heat contributed by the solid-fluid interactions decreases with the loading, except for w ) 0.7098 nm at the condensed density of 0.6. On the contrary, the isosteric heat contributed by the fluid-fluid interactions shows an increasing trend with the uptake. As expected, the contribution of the solid-fluid interactions dominates at low loadings because of the overlapping of the solid-fluid potential from both neighboring and opposite rods.59 However, the contribution from the fluid-fluid interactions is of more importance at high adsorption densities because of the greater number of neighboring adsorbed molecules involved in interactions.60 As a result, there is a crossover of the isosteric heat curves between solid-fluid and fluid-fluid interactions. Moreover, this crossover shifts from high loadings to low loadings with increasing pore width. This is because a competitive



Figure 5. Local density profiles of the center of mass of N2 in the RSP model at T ) 77 K as functions of pressure and effective pore width.

balance exists between the solid-fluid and fluid-fluid interactions. For the same reason, a local maximum in the total isosteric heat was found for these three pore widths (see Figures 2 and 3), as previously described. To analyze the microstructure in the RSP model using the N2 adsorption isotherm at T ) 77 K, we display in Figure 4 the side views of snapshots of fluid molecules at different relative pressures P/P0 and three pore widths. For all pore widths at P/P0 ) 7.12 × 10-5, the first adsorbed layer arises on the solid surface, but is not yet fully filled. Furthermore, most molecules prefer to assemble in the corner of the unit cell, suggesting a stronger solid-fluid potential field in these places. When P/P0 increases to 1.01 × 10-3, the first adsorbed layer is completely formed on the surface. In particular, monolayer formation for the narrow pore width, w ) 0.7098 nm, corresponds to a large change of the absolute pore density from 0.27 (P/P0 ) 7.12 × 10-5) to 0.41 (P/P0 ) 1.01 × 10-3), as shown in Figures 2b and 3a. However, the total isosteric heat is almost unaltered during the process, compared to that at w ) 1.5971 and 2.4843 nm. At P/P0 ) 1.01 × 10-1, the amount of N2 adsorbed in the pores with w ) 0.7098 nm has already reached saturation, whereas it presents only two adsorbed layers of fluid molecules for the other pore widths. Similarly, at P/P0 ) 4.12 × 10-1, condensation occurs for w ) 1.5971 nm but not for w ) 2.4843 nm. With a further increase in the relative pressure to 1.0, capillary condensation also appeared for w ) 2.4843 nm.

To provide further insight into the microstructures, we plot in Figure 5 the local density profiles of fluids at the corresponding simulation conditions. It should be pointed out that the solid volume of the grooves is also included in the calculation of the local density profile of the fluid (see eq 5), for convenience. Because the density of the solid walls is constant, this treatment alters only the strength of the peaks in the local density profile rather than the position. Examination of the local density profiles in Figure 5 shows that there are always five pairs of symmetrical peaks for each pore width and pressure. This is caused by the adsorption of the groove structure. The snapshots in Figure 4, where the grooves can accommodate five layers of fluid molecules along the z direction, also confirm this observation. Additionally, other redundant molecules are subsequently adsorbed within the pore space defined by the effective pore width w. For example, for w ) 0.7098 nm, the local density of P/P0 ) 1.01 × 10-3 presents a very slight peak near the center of the pore (see Figure 5d), demonstrating that adsorption mainly occurs on the groove surface. In addition, the local density of P/P0 ) 1.01 × 10-1 presents a major peak in the same position (see Figure 5h), indicating the adsorption ability of the effective pore. Similar behavior was also found for the other two pore widths. By comparing the strengths of the peaks, we emphasize that the uptake arising from the groove structure of CMK-1 makes a particularly significant contribution to the adsorption.


Peng et al.

Figure 6. Pore size distribution (PSD) of CMK-1 adsorbent from the GCMC simulation for the single-pore adsorption of N2 at T ) 77 K. In the optimization of the PSD, we selected 27 pore widths of pore size in the range w ) 0.3549-4.9686 nm, with equal intervals of ∆H ) 0.17745 nm.

The optimized PSD and fitted adsorption isotherms are shown in Figures 6 and 7a, respectively. Figure 7a shows that the isotherms from the simulations and experiment are in excellent agreement, suggesting that the obtained PSD is reliable for further applications. We also observe in Figure 6 that the peaks mainly focus on the range of effective pore widths w ) 1.5-2.7 nm. To compare the simulated PSD with experiment, the key point is how to define the pore width for CMK-1 materials. In the RSP model, it is defined as the effective pore width w. In fact, the groove structure in the RSP model plays the role of an additional pore width. It is known that the experimental pore size for mesopores in CMK-1 is about 3.0 nm. This is close to neither Ohkubo et al.’s value of w ) 1.264 nm45 nor our average effective pore width of w ) 1.83 nm. We consider that the two groove parts (top and bottom) have an effective pore width of about 1.2-1.7 nm, so as to be consistent with the mesoporous characteristic of the CMK-1 adsorbent. By using eq 8, we determined the isosteric heat with the PSD, as presented in Figure 7b. It can be seen that the isosteric heat drops sharply for adsorbed amounts in the range of 9-20 mmol/g and then fluctuates, which reveals that the adsorption behavior of N2 at 77 K is extraordinary because of the heterogeneity in this type of material. 5.2. AdsorptionStorageofMethaneandHydrogen. 5.2.1. Methane Adsorption at 303 K. To investigate the adsorption storage of CH4 in CMK-1 absorbent, we simulated the adsorption isotherms of CH4 at an ambient temperature of 303 K. To compare with experimental data in the literature,45 we plot in Figure 8a the calculated adsorption isotherm of CH4 in CMK-1 with the PSD in Figure 6. It is obvious that the experimental and simulated results exhibit a satisfactory consistency in the range of pressure studied. It should be noted that Ohkubo et al.45 also compared their simulated results with experiment. They found good agreement for εsf ) 1.2εsf-0 and εsf ) 1.3εsf-0 in the high- and low- pressure regions, respectively, where εsf-0 is the initial value of the crossing interaction parameter. Because

Figure 7. Adsorption of N2 at T ) 77 K on the CMK-1 adsorbent with the PSD in Figure 6. (a) Adsorption amount versus pressure, where the symbols and solid line denote the experimental results from the literature45 and the simulation results, respectively. (b) Isosteric heat versus adsorption amount, where the lines are a guide for the eye only.

their method involves a multiplier for the pore potential, instead of emphasizing the heterogeneity of the materials through the PSD, their simulated results are suitable only for a qualitative description of the adsorption behavior of fluids in CMK-1, in contrast to the quantitative approach in our work. We further predicted the amount of methane adsorbed at high pressure. As shown in Figure 8a, the uptake of CH4 can reach 31.23 wt % at 30 MPa, which is comparable to the value of 36 wt % for activated mesocarbon microbeads (a-MCMBs) reported in our



Figure 8. Adsorption of CH4 at T ) 303 K on the CMK-1 adsorbent with the PSD in Figure 6. (a) Adsorption amount versus pressure, where the symbols and solid line denote the experimental results from the literature45 and the simulation results. (b) Isosteric heat versus adsorption amount, where the lines are a guide for the eye only.

previous work.30 However, the latter adsorbent is still recommended in view of its low operating cost at 4 MPa.30 Figure 8b displays the corresponding isosteric heat versus adsorption amount, showing that the isosteric heat rapidly decreases with increasing loading and reaches a local minimum of 10.23 kJ/ mol (close to the isosteric heat of 11 kJ/mol for CH4 adsorption on a Cu-based metal-organic framework, which is more than 3 kJ/mol higher than the liquefaction heat of CH4 at its boiling point62) at the amount of 14.83 mmol/g, corresponding to 12 MPa. The zero covered isosteric heat is about 27.22 kJ/mol, which is considerably higher than that of any other well-known adsorbent, such as activated carbon (11.8 kJ/mol21 at 298.15 K and 13.3 kJ/mol22 at 296 K), carbon nanotubes (17-20 kJ/mol),63 isoreticular metal-organic frameworks (IRMOFs, 12-15.5 kJ/mol),63 and silicalite (19.7 kJ/mol).63 However, the average isosteric heat of 15.46 kJ/mol still lies in the range of 12-19 kJ/mol34 of physisorption. In other words, the isosteric heat of CH4 at 303 K falls in an extensive range of 10.23-27.22 kJ/mol, suggesting that the adsorption behavior of CH4 in CMK-1 adsorbent is rather heterogeneous at ambient temperature.

Figure 9. Adsorption of H2 at T ) 303 K on the CMK-1 adsorbent with the PSD in Figure 6. (a) Adsorption amount versus pressure and (b) iososteric heat versus adsorption amount. Lines are a guide for the eye only.

5.2.2. Hydrogen Adsorption at 303 and 77 K. First, we simulated the adsorption of hydrogen in CMK-1 at 303 K. The adsorption of H2 in CMK-1 adsorbent with the PSD in Figure 6 is presented in Figure 9a. It can be observed that the adsorption capacity is much lower at 3 MPa, with a value of 0.12 wt %. Even at 30 MPa, the uptake reaches only 1.19 wt % (5.90 mmol/ g), far from the U.S. DOE storage target of 6.5 wt % for gravimetric density. Figure 9b shows that the isosteric heat decreases slightly with loading in the range of 4.82-6.65 kJ/ mol, indicating that the adsorption behavior of H2 in CMK-1 adsorbent tends to be energetically homogeneous at T ) 303 K. The average isosteric heat is about 5.85 kJ/mol, which


Figure 10. Adsorption of H2 at T ) 77 K on the CMK-1 adsorbent with the PSD in Figure 6. (a) Adsorption amount versus pressure, where the symbols and solid line denote the experimental results from the literature46 and the simulation results, respectively. (b) Isosteric heat versus adsorption amount, where the symbols denote (2) our results from the GCMC+PSD method and (9) the isosteric heat of D2 in MOCSBA15 for comparison,46 and the lines are a guide for the eye only.

approximates the value of 5.8 kJ/mol found for activated carbon34 and is also comparable to the value of 4.39 kJ/mol at 298 K obtained from IRMOF-8 simulations.64 On the basis of this observation, it seems that H2 adsorption storage is not favorable in CMK-1 materials at ambient temperature. To explore the latent storage capacity, we also predicted the adsorption of H2 in the CMK-1 absorbent at 77 K. Figure 10a presents the simulated adsorption isotherms of H2 in CMK-1

Peng et al. with the PSD in Figure 6. The experimental data at low pressure are also provided for comparison. For clear illustration, the adsorption isotherms of H2 in the low-pressure range of 0-0.015 MPa are enlarged in the inset. It can be seen that the adsorption isotherms of H2 from experiment and simulation coincide well, although the simulated isotherm is slightly higher than the experimental points in the low-pressure range of 0.003-0.006 MPa. There are two possible reasons for this deviation. On one hand, the CMK-1 sample used for simulation was different from that used for the H2 adsorption experiments, which would lead to different PSDs determined by N2 adsorption in the simulations. Given an appropriate PSD for the correct CMK-1 sample, a better agreement should be anticipated. On the other hand, the isotherm at low pressure reflects the adsorption in micropores, where quantum effects are more visible in the relatively narrow space. Inclusion of quantum effects generally results in a decrease in the estimation of the uptake of H2, compared to calculations with the common LJ potential.32 Therefore, if we incorporated quantum corrections, the simulated results at 0.003-0.006 MPa might decrease to be more consistent with experiment. The current consistency is fairly satisfactory in a reasonable range, suggesting that quantum effects are not significant at 77 K for the system studied in this work and that the adsorption can be described well by the Buch potential. It also confirms that the method of GCMC simulation with PSD is a very efficient way to characterize the heterogeneity of the CMK-1 adsorbent. Further analysis of Figure 10a indicates that the adsorption amount of 2.76 wt % (13.75 mmol/ g) was obtained at a moderate pressure of 5 MPa. Given a higher pressure of 30 MPa, a loading of 4.58 wt % (22.81 mmol/g) was obtained, approaching but not reaching the 6.5 wt % U.S. DOE target for 2010 and far from the 9 wt % target for 2015.34 As one can see in Figure 10b, the curve of the isosteric heat of H2 at 77 K differs from that at 303 K. For instance, it falls dramatically with loading, exhibiting typical heterogeneous adsorption behavior in the range of 2.73-9.9 kJ/mol. This transition from homogeneity to heterogeneity with temperature is very similar to that observed in simulations of IRMOF-8 at 303 and 77 K.63 In addition, the average isosteric heat was found to be about 4.55 kJ/mol, equivalent to that of IRMOF-8 at 77 K (3.5-4.25 kJ/mol).63 For comparison, we also plot in Figure 10b the isosteric heat of D2 at 77 K in MOC-SBA-15 adsorbent. It should be pointed out that it is uncertain whether the MOCSBA-15 sample is a CMK-3 or CMK-5 adsorbent, because the authors46 did not show indicate whether it contained nanorods or nanotubes. However, the data are worth comparing because they are in the same family of CMK-type materials. As described in the literature, these data were determined by the well-known Clausius-Clapeyron equation. The ranges and trends of the isosteric heats of both types of materials are similar to those of CMK-1 adsorbent in this work. By extrapolating, the isosteric heat at zero coverage was found to be around 8 kJ/mol for MOC-SBA-15.46 This is slightly lower than our result of 9.9 kJ/mol for CMK-1 and also lower than the 9 kJ/mol reported for single-walled carbon nanotube bundles.46 Based on the above information, we concluded that CMK-1 adsorbent might not provide a promising capacity for H2 storage at 303 and 77 K. This can be explained by the local density distributions of H2 in the RSP model at 30 MPa for both temperatures (see Figure 11). As determined from the adsorption of N2, a groove can accommodate at most five layers along the z direction. However, a groove induces only one pair of peaks at the bottom for H2 adsorption at 303 K, because of the weak solid-fluid interactions. Furthermore, at the narrowest pore



Figure 11. Local density profile of center of mass of H2 in the RSP model at 30 MPa and T ) 303 and 77 K as function of effective pore width for w ) (a) 0.3549, (b) 0.7098, (c) 2.1294, and (d) 4.0814 nm.

width of w ) 0.3549 nm, one sharp peak is observed at the center of pore due to confinement in the pore. For the larger pore width of w ) 0.7098 nm, the sharp peak disappears and splits into two symmetrical peaks in the opposite and parallel planes that are tangent to the vertex of the rods. As the pore width is continuously increased, the number of peaks is unaltered. In this situation, the adsorbed density in the center of the pore is close to the bulk-phase density, and the adsorption is more appropriately replaced by “densification” due to the weak fluid-fluid interactions. Compared to 303 K, the adsorption amount is improved at 77 K. For example, five double peaks emerge at the groove structure, due to the fact that the solid-fluid interactions play a more prominent role at low temperature, even though the phenomenon of densification is still dominant for supercritical adsorption. 5.2.3. Surface Excess Adsorption. The surface excess amount is also presented here to determine the optimal pore width for gas storage, as shown in Figure 12. Because of a larger bulk density in eq 4, s negative surface excess occurs at high pressure

for all species and pore widths. As expected, each surface excess isotherm exhibits a maximum.21,56 In addition, a more pronounced cusp21 is observed for the maximum of H2 adsorption at 77 K. The reason might be that the temperature is closer to the critical temperature of 33 K. We further plot in Figure 13 the maximum surface excess and the isosteric heat at the corresponding pressure. It can be seen that, for CH4 at 303 K and H2 at 77 K, there is a maximum in the curves of the maximum surface excess.56 However, the surface excess declines monotonously for H2 at 303 K, probably owing to the higher supercritical temperature. The maximum for CH4 is about 5.04 µmol/m2 with an optimal pore width of w ) 1.2422 nm (approaching the optimal value 1.14 nm for methane adsorption in activated carbon22) at 6 MPa, whereas it is 11.60 µmol/m2 for H2 at 77 K, corresponding to w ) 1.0647 nm at 3 MPa. Interestingly, all of the surface excess values become constant when the pore width exceeds 2.0 nm, which is consistent with the observation for methane in slit pores.56


Peng et al.

Figure 12. Surface excess adsorption isotherms of CH4 and H2 in RSP model for different pore widths. (a) CH4 at 303 K, (b) H2 at 303 K, (c) H2 at 77 K. For simplicity, only parts of 27 pore widths are plotted in the figure. Lines are a guide for the eye only.

From the energetic point of view, one can see in Figure 13 that the isosteric heat contributed by fluid-fluid interactions exhibits a very slight decrease with increasing pore width and remains basically unchanged for H2 at 303 K. This is because the fluid-fluid interactions are relatively weak at T ) 303 K. On the contrary, the isosteric heat from solid-fluid interactions decreases more evidently, because of the stronger dependence of the solid-fluid potential on the pore width. Consequently, the total isosteric heat decreases with increasing pore width. It is generally acknowledged that the dependencies of the maximum surface excess and isosteric heat on the pore width exhibit an oscillatory behavior due to the packing effect in small pores for activated carbon.56,65 However, such an oscillation is not observed for CMK-1 adsorbent under the conditions studied. This reason might be that structural differences between activated carbon and CMK-1 lead to extra grooves in CMK-1, invisibly enlarging the pore width, and that the extra grooves act as a buffered vessel to weaken the oscillatory behavior, even though the two adsorbents are identical in terms of having slitlike shapes.

6. Conclusions We have systematically investigated the adsorption storage of CH4 and H2 on highly ordered carbon molecular sieve CMK-1 using GCMC simulations. In our simulations, the fluid molecules were modeled as the Lennard-Jones (LJ) potential, and the rodaligned slitlike pore (RSP) model was used to characterize the CMK-1 material in order to emphasize its grooved textural structure. Considering the geometrical heterogeneity of the adsorbent, the pore size distribution (PSD) was determined from the experimental and simulated data of N2 adsorption at 77 K. The majority of the PSD was in the range of 1.5-2.7 nm, suggesting that CMK-1 is typically a class of mesoporous materials. Using the PSD, the adsorption of CH4 at 303 K in CMK-1 adsorbent was predicted. Good consistency of the isotherm between experiment and simulation was obtained, confirming that the PSD was reliable for predictions. The greatest uptake of 31.23 wt % of CH4 was attained only at 30 MPa. The isosteric heat at zero coverage was found to be 27.22 kJ/mol, which is



Figure 13. Effect of the pore width in RSP model on the maximum surface excess (1) and the corresponding isosteric heats contributed by the (9) total, (b) fluid-fluid, and (2) solid-fluid interactions. (a) CH4 at 303 K, (b) H2 at 303 K, (c) H2 at 77 K. Lines are a guide for the eye only.

superior to that of any other kind of adsorbent. The average isosteric heat was 15.46 kJ/mol, belonging to the range of physisorption (12-19 kJ/mol). However, the broad range of isosteric heat (10-27 kJ/mol) indicates that the adsorption behavior of CH4 at 303 K is energetically heterogeneous in CMK-1 materials. The adsorption of H2 at 303 and 77 K in CMK-1 was also predicted. The isosteric heat with the simulated PSD was about

6.65 kJ/mol at zero coverage for T ) 303 K and 9.9 kJ/mol for T ) 77 K. More importantly, compared to 303 K, the energetic heterogeneity of adsorption was more favored at 77 K. In terms of the adsorption capacity, the gravimetric uptake of H2 at 303 K was only 0.12 wt % at 3 MPa and rose to 1.19 wt % at 30 MPa. At the low temperature of 77 K, better uptakes of 2.76 and 4.58 wt % were obtained at 5 and 30 MPa, respectively. However, these values do not reach the U.S. DOE target of 6.5 wt % for 2010.

13036 J. Phys. Chem. C, Vol. 112, No. 33, 2008 Finally, we surveyed the dependence of surface excess on pore width and found a maximum of surface excess of 5.04 µmol/m2 for CH4 at 303 K and 11.60 µmol/m2 for H2 at 77 K. The corresponding optimal pore width is w ) 1.2422 nm at 6 MPa for CH4 and w ) 1.0647 nm at 3 MPa for H2. However, no optimal pore width corresponding to the maximum was observed for H2 at 303 K. More surprisingly, in contrast to activated carbon, the maximum surface excess and isosteric heat did not show oscillatory behavior with the pore width. This result can be attributed to the structural differences between the materials. Even though the two adsorbents have identical slit shapes, the extra groove in CMK-1 plays a buffering role to weaken the oscillations. Acknowledgment. This work was supported by the National Natural Science Foundation of China (No. 20776005, 20736002), NCET Program from Ministry of Education of China (NCET06-0095), and “Chemical Grid Project” and Excellent Talent Foundation of BUCT and the Young Scholars Fund of Beijing University of Chemical Technology. We are also grateful to Professor Mingsheng Yang at Dalian University of Technology for his instructive suggestions about nonlinear optimization problems. References and Notes (1) Cheng, H. M. Carbon Nanotubes Synthesis, Microstructure, Properties and Applications; Chemical Industry Press: Beijing, 2002. (2) Reilly, J. J.; Wiswall, R. H. Inorg. Chem. 1968, 7, 2254. (3) Zhou, L.; Zhou, Y. P.; Li, M.; Chen, P.; Wang, Y. Langmuir 2000, 16, 5955. (4) Muller, E. A.; Hung, F. R.; Gubbins, K. E. Langmuir 2000, 16, 5418. (5) Jin, W. Z.; Wang, W. C. J. Chem. Phys. 2001, 114, 10163. (6) Iijima, S. Nature 1991, 354, 56. (7) Jiang, J. W.; Sandler, S. I. J. Am. Chem. Soc. 2005, 127, 11989. (8) Zhang, X. R.; Wang, W. C.; Chen, J. F.; Shen, Z. G. Langmuir 2003, 19, 6088. (9) Chambers, A.; Park, C.; Baker, R. T. K. J. Phys. Chem. B 1998, 102, 3862. (10) Peng, X.; Wang, W. C.; Huang, S. P. Fluid Phase Equilib. 2005, 231, 138. (11) Peng, X.; Zhao, J. S.; Cao, D. P. J. Colloid Interface Sci. 2007, 310, 391. (12) Li, Y. W.; Yang, R. T. J. Am. Chem. Soc. 2006, 128, 726. (13) Babarao, R.; Hu, Z. Q.; Jiang, J. W.; Chempath, S.; Sandler, S. I. Langmuir 2007, 23, 659. (14) Snurr, R. Q.; Hupp, J. T.; Nguyen, S. T. AIChE J. 2004, 50, 1090. (15) Peng, X.; Wang, W. C.; Xue, R. S.; Shen, Z. M. AIChE J. 2006, 52, 994. (16) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1987. (17) Frenkel, D.; Smit, B. Understanding Molecular Simulations; Academic Press: New York, 2002. (18) McGrother, S. C.; Gubbins, K. E. Mol. Phys. 1999, 97, 955. (19) Tarazona, P. Mol. Phys. 1987, 60, 573. (20) Zhang, X. R.; Cao, D. P.; Chen, J. F. J. Phys. Chem. B 2003, 107, 4942. (21) Tan, Z.; Gubbins, K. E. J. Phys. Chem. 1990, 94, 6061. (22) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1992, 47, 1569. (23) Wang, Q. Y.; Johnson, J. K. J. Chem. Phys. 1999, 110, 577. (24) Wang, Q. Y.; Johnson, J. K. J. Phys. Chem. B 1999, 103, 4809.

Peng et al. (25) Yin, Y. F.; Mays, T.; McEnaney, B. Langmuir 2000, 16, 10521. (26) Cracknell, R. F. Phys. Chem. Chem. Phys. 2001, 3, 2091. (27) Cao, D. P.; Wang, W. C.; Duan, X. J. Colloid Interface Sci. 2002, 254, 1. (28) Cao, D. P.; Zhang, X. R.; Chen, J. F.; Wang, W. C.; Yun, J. J. Phys. Chem. B 2003, 107, 13286. (29) Cao, D. P.; Feng, P. Y.; Wu, J. Z. Nano Lett. 2004, 4, 1489. (30) Shao, X. H.; Wang, W. C.; Xue, R. S.; Shen, Z. M. J. Phys. Chem. B 2004, 108, 2970. (31) Tanaka, H.; Kanoh, H.; Yudasaka, M.; Iijima, S.; Kaneko, K. J. Am. Chem. Soc. 2005, 127, 7511. (32) Kowalczyk, P.; Tanaka, H.; Holyst, R.; Kaneko, K.; Ohmori, T.; Miyamoto, J. J. Phys. Chem. B 2005, 109, 17174. (33) Do, D. D; Do, H. D. J. Phys. Chem. B 2005, 109, 19288. (34) Bhatia, S.; Myers, A. L. Langmuir 2006, 22, 1688. (35) Kowalczyk, P.; Solarz, L.; Do, D. D.; Samborski, A.; MacElroy, J. M. D. Langmuir 2006, 22, 9035. (36) Sakintuna, B.; Yurum, Y. Ind. Eng. Chem. Res. 2005, 44, 2893. (37) Ryoo, R.; Joo, S. H.; Jun, S. J. Phys. Chem. B 1999, 103, 7743. (38) Kruk, M.; Jaroniec, M.; Ryoo, R.; Joo, S. H. J. Phys. Chem. B 2000, 104, 7960. (39) Kaneda, M.; Tsubakiyama, T.; Carlsson, A.; Sakamoto, Y.; Ohsuna, T.; Terasaki, O.; Joo, S. H.; Ryoo, R. J. Phys. Chem. B 2002, 106, 1256. (40) Jun, S.; Joo, S. H.; Ryoo, R.; Kruk, M.; Jaroniec, M.; Liu, Z.; Ohsuna, T.; Terasaki, O. J. Am. Chem. Soc. 2000, 122, 10712. (41) Joo, S. H.; Choi, S. J.; Oh, I.; Kwak, J.; Liu, Z.; Terasaki, O.; Ryoo, R. Nature 2001, 412, 169. (42) Solovyov, L. A.; Zaikovskii, V. I.; Shmakov, A. N.; Belousov, O. V.; Ryoo, R. J. Phys. Chem. B 2002, 106, 12198. (43) Hartmann, M.; Vinu, A.; Chandrasekar, G. Chem. Mater. 2005, 17, 829. (44) Vinu, A.; Miyahara, M.; Ariga, K. J. Phys. Chem. B 2005, 109, 6436. (45) Ohkubo, T.; Miyawaki, J.; Kaneko, K.; Ryoo, R.; Seaton, N. A. J. Phys. Chem. B 2002, 106, 6523. (46) Roussel, T.; Pellenq, R. J.-M.; Bienfait, M; Vix-Guterl, C.; Gadiou, R.; Beguin, F.; Johnson, M. Langmuir 2006, 22, 4614. (47) Wang, Q. Y.; Johnson, J. K.; Broughton, J. Q. Mol. Phys. 1996, 89, 1105. (48) Buch, V. J. Chem. Phys. 1994, 100, 7610. (49) Silvera, I. F.; Goldman, V. V. J. Chem. Phys. 1978, 69, 4209. (50) Kaneko, K.; Cracknell, R. F.; Nicholson, D. Langmuir 1994, 10, 4606. (51) Do, D. D.; Do, H. D. J. Phys. Chem. B 2006, 110, 17531. (52) Nicolas, J. J.; Gubbins, K. E.; Streett, W. B.; Tildesley, G. J. Mol. Phys. 1979, 37, 1429. (53) Johnson, J. K.; Zollweg, J. A.; Gubbins, K. E. Mol. Phys. 1993, 78, 591. (54) Nguyen, C.; Do, D. D. Langmuir 2000, 16, 1319. (55) Matlab 6.51; The Math Works Inc.: Natick, MA; available at www. mathworks.com. (56) Kowalczyk, P.; Tanaka, H.; Kaneko, K.; Terzyk, A. P.; Do, D. D. Langmuir 2005, 21, 5639. (57) Birkett, G. R; Do, D. D. Langmuir 2006, 22, 9976. (58) Brunauer, S.; Demings, L. S.; Deming, W. E.; Teller, E. J. Am. Chem. Soc. 1940, 62, 1723. (59) Do, D. D.; Do, H. D. Langmuir 2004, 20, 7103. (60) Do, D. D.; Do, H. D. Langmuir 2004, 20, 10889. (61) Seaton, N. A.; Walton, J. P. R. B.; Quike, N. Carbon 1989, 27, 853. (62) Noguchi, H.; Kondo, A.; Hattori, Y.; Kajiro, H.; Kanoh, H.; Kaneko, K J. Phys. Chem. C 2007, 111, 248. (63) Duren, T.; Sarkisov, L.; Yaghi, O.; Snurr, R. AIChE J. 2004, 20, 2683. (64) Garberoglio, G.; Skoulidas, A. I.; Johnson, J. K. J. Phys. Chem. B 2005, 109, 13094. (65) Ustinov, E. A.; Do, D. D. Langmuir 2003, 19, 8349.

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