Adsorption of Hydrogen and Methane Mixtures on Carbon Cylindrical

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Adsorption of Hydrogen and Methane Mixtures on Carbon Cylindrical Cavities Ana M. Morales-Cas,† Carmen Moya,† Baudilio Coto,† Lourdes F. Vega,‡ and Guillermo Calleja*,† Department of Chemical and EnVironmental Technology, ESCET, Rey Juan Carlos UniVersity, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain), and Institut de Cie` ncia de Materials de Barcelona (ICMAB-CSIC) Consejo Superior de InVestigaciones Cientı´ficas, Campus de la UAB, 08193 Bellaterra Barcelona (Spain) ReceiVed: December 14, 2006; In Final Form: February 20, 2007

The purpose of this work is to provide some insights into the adsorption of hydrogen and methane mixtures on carbon cavities with cylindrical geometry. Hydrogen and methane mixture adsorption has been simulated in pore sizes ranging from micropores to mesopores at room temperature. The grand canonical Monte Carlo method provided the amount adsorbed as a function of pressure and bulk composition. In addition, the microscopic characteristics of the adsorbed phase have been accomplished by calculating density profiles and adsorption energy distribution functions. The results show that the first methane and hydrogen adsorbed layers are co-incident, and there is a second hydrogen layer that is not present in the pure compound adsorption. In addition, the adsorption energy stages for hydrogen in the mixture are more favorable than those for pure hydrogen, revealing that the presence of methane molecules favors energetic hydrogen stabilization (for micropores, hydrogen adsorption energy changes are observed from 6.3 to 75%, depending on the operational conditions). These results can shed light on the knowledge of the underlying adsorption behavior of these mixtures, which are of interest in hydrogen storage and purification by adsorption, and therefore of potential applications in hydrogen technology (clean hydrogen production, fuel cells, etc.).

Introduction Clean hydrogen production is a required technology for extended commercial applications of fuel cells. A considered alternative to obtain hydrogen without producing CO/CO2 as byproducts is methane catalytic decomposition.1 Catalysts used in this reaction are mainly metal-supported materials,2 but recently, the use of carbon-based catalysts have been proposed to avoid catalyst deactivation, frequently produced by metallicbased catalysts.3 Several carbon materials have been proved in this reaction, including activated carbons, carbon-black materials, carbon fibers, and carbon nanotubes.4 Methane decomposition on the surface of carbon catalysts produces solid carbon and hydrogen. The solid carbon is deposited on the internal and the external carbon catalyst surface, incorporating into the carbon material as a part of it, thus producing a change in its textural properties, pore size and pore volume.5 In turn, these changes in textural properties may affect the catalyst behavior as a result of changes in the confinement extension of the reacting mixture (hydrogen and methane). The behavior of hydrogen and methane mixtures confined in carbonaceous cavities has also been studied when considering carbon-based membranes6 for gas separation as a necessary purification stage that follows hydrogen production. In these carbonaceous membranes, hydrogen remains on the feed side, and larger hydrocarbon molecules pass through the membrane.7 The opposite behavior is observed for membranes based on molecular sieving. Dependence on operational pressure and selectivity for methane and hydrogen separation has been shown * To whom correspondence should be [email protected]. † Rey Juan Carlos University. ‡ Consejo Superior Investigaciones Cientı´ficas.

addressed.

E-mail:

in several works,8 exhibiting a methane selectivity that decreases as the pressure is increased. In addition, the hydrogen-methane mixtures are also used as a fuel in some natural gas engines.8,9 Hydrogen enrichment in natural gas mixtures is desirable to improve power engines8 so that up to 15% of hydrogen is used in natural gas combustible automobile devices. In these applications, one of the most important features is gas storage. Several alternatives have been considered, such as liquefaction, gas compression, solid-state hydride formation, and adsorption on porous media. Adsorption requires lower pressure and room temperature, whereas compression needs high pressures around 100 MPa, and liquefaction requires very low operational temperatures. Hydride formation is not very attractive at the present time due to kinetic limitations, as well as temperature and heat exchange requirements, resulting from the strong interactions that take place. This makes adsorption a very attractive technique as an alternative to the other processes. Natural gas adsorption, and pure methane adsorption, on carbonaceous porous materials has been widely considered in the literature.10 Hydrogen adsorption11-15 has also been considered on carbon-based adsorbants, such as carbon nanotubes16-18 and fibers and various activated carbons.19 It is known that the adsorption capacity of these materials is the result of physisorption and chemisorption, which is not desirable, as it is not reversible in the operational conditions.20 The influence of the textural characteristics of the adsorbent on hydrogen-methane separation using molecular simulation has been studied in several works. Some of them have focused on the dependence of selectivity on pore size7 and on pore network connectivity effects.21 Kowalczyk and Bhatia22 have recently reported some simulation results of adsorption of methane and hydrogen mixtures in carbon slit-shaped micropores to select the optimum pore size for hythane storage.

10.1021/jp068592g CCC: $37.00 © 2007 American Chemical Society Published on Web 04/07/2007

6474 J. Phys. Chem. C, Vol. 111, No. 17, 2007

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When using molecular simulation techniques for studying mixed gas adsorption, focused either on gas storage or gas separation, important information can be also obtained on top of the total amount adsorbed as a function of pressure. This includes component density profiles or mass distributions within the cavity volume and single-pore-size adsorption capacity and selectivity, which allow a microscopic description of the adsorption phenomena. This description can help, to some extent, the material design, focusing on desirable characteristics and performance. The goal of this work is twofold, (1) to obtain, by grand canonical Monte Carlo simulations, the absolute adsorption isotherm of each compound in the mixture, as well as the excess adsorption, as a function of pore size and bulk composition and (2) to provide some microscopic information regarding the structural and energetic characteristics of hydrogen and methane mixtures confined in cylindrical carbon cavities of different sizes, in the micropore and mesopore range. Simulation Model and Method Adsorption equilibrium data were obtained using grand canonical Monte Carlo (GCMC) simulations. Both methane and hydrogen molecules were considered as Lennard-Jones spheres using the following expression for fluid-fluid interaction

Uij ) 4ij

[( ) ( ) ] σij r

12

-

σij r

6

(1)

where r is the distance between molecules and σ and are the size and well-depth parameters of the fluid molecules, respectively. This model approximation is well contrasted for methane, considering the apolar characteristics of this almost spherical molecule.23,24 In principle, it may not hold for hydrogen, as this molecule is not spherical and has a quadrupolar moment. One alternative used in the literature is to model hydrogen as a twosite Lennard-Jones molecule that also takes into account quadrupolar interactions among the molecules. However, previous studies7 have demonstrated that the former considerations make only a slight difference in adsorption equilibrium results as compared to a spherical Lennard-Jones molecule, unless charged walls are considered.25 Also, important quantum effects may appear when studying hydrogen, as already shown by several authors;16,17,22 these quantum effects become important only when the thermal de Broglie wavelength of the particles becomes comparable to the characteristic interparticle distance. In the case that the thermal de Broglie wavelength is small compared to this distance, quantum effects become unimportant, compared to other effects. In order to test if the classical treatment is valid at the conditions investigated here, we calculated the de Broglie thermal wavelength, Λ, at 298K, the temperature simulated in this work

Λ ) h(2πmkBT)-1/2

(2)

where h is the Planck constant, m is the molecular hydrogen mass, and kB is the Boltzmann constant. At 298K, Λ) 0.071 nm. Quantum effects are estimated considering the ratio Λ/a,14,26 where a is the mean nearest-neighbor separation. The mean nearest-neighbor separation can be approximated in a confined system using the averaged density inside the pore, a ) F-1/3. For pure hydrogen adsorption in a cylindrical pore of 1.26 nm at 12 MPa and 298 K, Λ/a ) 0.106; hence, classical treatment

TABLE 1: Lennard-Jones Interaction Parameters28 molecule

σ/nm

(kB-1)/K

CH4 H2 CCH4 CH2

0.381 0.296 0.361 0.318

148.0 34.2 64.3 30.9

is justified in this case. However, quantum effects should be considered for lower temperatures, such as, at 77 K for hydrogen adsorption in a slit pore, Λ ) 0.14 nm and Λ/a ) 0.4.27 The hydrogen and methane interaction parameters used along this work are provided in Table 1. The carbon cylindrical cavity was considered as a homogeneous surface. Thus, an integrated expression of Lennard-Jones potential in an infinite tube was applied for solid-fluid interactions29

{

Usf(a, R) ) π2sfFsσ2sf a 63 R - a 1+ 32 σsf R a R-a -3 1+ σsf R

[ ( )] ( [ ( )] ( -10

-4

(Ra) ) a F - 3/2, - 3/2,1; ( ) ) R F - 9/2, - 9/2,1;

2

2

}

(3)

where R is the cylinder radius, a is the distance between the molecule and the wall, F(R,β,1;γ) denotes the hypergeometric function, Fs ) 38.2 atom nm-2 is the area density of carbon atoms, and σsf and sf are the Lennard-Jones parameters for the solid-fluid interaction (see Table 1). This may represent a crude model of a carbon nanotube, carbon membranes with cylindrical cavities, or ordered mesoporous carbons (OMC). Lennard-Jones parameters for interactions between unlike adsorbates and for the solid-fluid interactions were calculated using the standard Lorentz-Berthelot combining rules. In the grand canonical ensemble, the chemical potential, volume, and temperature are taken as independent thermodynamic variables.30 In this work, chemical potentials were related to pressures by means of the Soave-Redlich-Kwong equation of state (SRK)31 for a specified pressure and temperature. The ideal gas was taken as the reference state for chemical potentials, and it was calculated from its partition function.32 Three kinds of moves were attempted to construct the Markov chain of system configurations following the Norman and Filinov scheme,33 particle creation, particle displacement, and particle deletion. In order to keep the microscopic detailed balance and avoid systematic errors, attempting probabilities were 0.2, 0.4, and 0.4 for displacement, creation, and deletion, respectively, regardless of the number of particles.34 The probabilities (for acceptance) related to each type of move can be found elsewhere.35 In every simulation, 2 × 107 configurations were generated; the cutoff distance used was 6σ, and no long-range corrections were added in the calculation due to the difficulty of computing them in a nonhomogeneous system. However, this cutoff value has proved to be enough to simulate the full-range potential.36 The density of each component confined in the cavity was obtained by averaging the number of molecules during the simulation according to

Fi ) /Vpore

(4)

where is the average number of molecules of component i, and Vpore is the cavity volume. Both absolute and excess adsorption data were obtained. The excess adsorption was computed discounting the proportional amount that corresponds to the compressed gas37 according to

H and CH4 Mixtures on Carbon Cylindrical Cavities

nei ) nai - FbVpore yi

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(5)

where nei is the excess amount adsorbed of compound i, nai is the total number of molecules of compound i contained in the cavity, which represents the absolute adsorbed amount, Fb is the gas density, Vpore is the cavity volume, and yi is the mole fraction of compound i in the fluid phase. The gas density for the specified pressure and temperature was calculated using the SRK equation of state. In addition, GCMC simulations provide a microscopic description of confined fluids. This description consists of the density profiles across the cavity diameter and the solid-fluid interaction energy distribution functions, both obtained for each adsorbate in the mixture separately. The density profile F(r) was achieved by computing the number of molecules in a differential 2 volume L‚(ri+1 - r2i ), where L is the cylinder length, according to 2 - r2i ) F(z) ) N(ri) L (ri+1

(6)

where N(ri) is the number of molecules contained in the differential volume. The energy distribution was calculated by dividing the solidfluid energy range and counting the number of molecules whose solid-fluid interaction energy corresponded to each interval. Both calculations, density profiles and energy distribution functions, were performed during the GCMC simulation technique and averaged at the end of the simulations. Besides these results, equilibrium methane selectivity with respect to hydrogen was calculated according to

SCH4,H2 )

(xCH4/xH2)pore (yCH4/yH2)bulk

(7)

where x denotes the mole fraction in the confined phase and where y is the mole fraction in the bulk phase. Two series of simulations were performed, differing in fluid phase composition and size of the carbon cylindrical cavity. In the first of these series, a molar ratio of 0.8/0.2 CH4/H2 was imposed for the fluid phase, and for the second one, the molar ratio was fixed to 0.2/0.8 CH4/H2. The cylinder diameter was varied to consider adsorption in microporous materials (D ) 0.46 nm) up to a pore size ranging in the mesoporous region (D ) 4.16 nm). The diameter considered in this work has been measured as the distance between two opposite carbon atom centers minus 0.34 nm (σc). Results and Discussion Simulation results for adsorption of methane and hydrogen mixtures are presented below, considering absolute adsorption isotherms for each compound in the mixture, for six pore sizes: D ) 0.46, 0.86, 1.26, 1.66, 2.66, and 4.16 nm. We also report excess adsorption isotherms and compare both results. Selectivities are presented as a function of pressure for each cavity and mixture. Finally, the microscopic description of adsorbed mixtures is discussed in terms of density profiles and energy distribution functions. Methane adsorption isotherms for the 0.8/0.2 CH4/H2 mixture, as obtained by GCMC, are shown in Figure 1. Adsorption data for this and subsequent figures are displayed as the averaged adsorbed molar density. In Figure 1a, methane absolute adsorption isotherms for six cylindrical cavities are shown. It is remarkable to observe that the amount of adsorbed methane

confined in the smallest cylinder is the highest. For the remainder of the pores, as pore width increases, methane adsorption decreases. The excess adsorption isotherms are depicted in Figure 1b, where the same tendency is observed. It is noticeable that, for the pore sizes of 0.46, 0.86, and 1.26 nm, a maximum in the excess adsorption isotherm is achieved. These maxima are the result of the increasing ratio between the bulk and adsorbed density, especially for pressures beyond isothermal saturation. This saturation is clearly observed in Figure 1a for the 0.46 and 0.86 nm pores; however, for the pore size of 1.26 nm, a crescent value in the absolute adsorption density is achieved. For this pore size, the maxima that is observed in the excess adsorption isotherm is the result of the increasing ratio of bulk-to-adsorbed density. The pressure that corresponds to the maximum in the excess adsorption increases with pore width according to a small saturation degree. Figure 2 depicts the absolute and excess adsorption isotherm for hydrogen in the 0.8/0.2 CH4/H2 mixture for the two pore sizes which present a nonzero absolute adsorption for hydrogen, 2.66 and 4.16 nm. Both absolute and excess adsorption densities are plotted together with the hydrogen bulk density. For the remaining pores, methane displaces hydrogen in the adsorbed phase, turning out the infinite methane selectivity. It is noticeable that, for almost the whole pressure range, the excess adsorption is below zero. This is the result of the lower density of the absolute adsorbed hydrogen with respect to the gas bulk density. Negative excess data are obtained for adsorption of pure compounds and pressures greater than pc, defined as the pressure for which bulk and absolute adsorbed densities are equal.38 For the adsorption of binary mixtures, negative excess adsorption data are obtained for the component in the adsorbed phase, as it is shown for hydrogen in Figure 2. In addition, contrary to the dependence between methane absolute density and pore size, absolute hydrogen density increases with pore size. This is a direct result of the decrease of selectivity for wider pores, as it is shown later. Adsorption data for the 0.2/0.8 CH4/H2 mixture are shown in Figures 3 and 4. Isotherms for methane absolute adsorption are shown in Figure 3a. Similar to the former mixture results (Figure 1a), the methane-averaged absolute density decreases as the pore width increases, although the decrease is more noticeable for pores wider than 1.26 nm. The excess isotherms in Figure 3b do not present the maxima achieved in the previous results (Figure 1b) as a consequence of the lower bulk density of this mixture, enriched in the light component, hydrogen. In addition, as it is observed in Figure 3, the density of methane confined in the pore of 0.86 nm is 5 mmol cm-3 superior to the density achieved in the pore of 1.26 nm, whereas this difference in Figure 1 (0.8/0.2 CH4/H2 mixture) is just 1 mmol cm-3. These results suggest that increasing the hydrogen proportion in the bulk phase produces a decrease in the methane density for pores wider than 1.26 nm. Hydrogen adsorption isotherms for the 0.2/0.8 CH4/H2 mixture are shown in Figure 4. Pores having a diameter between 0.46 and 0.86 nm do not adsorb any hydrogen. As shown in Figure 2, the bulk gas density has been plotted to re-mark the relationship between absolute and excess adsorption density. A different tendency is observed for data above and below 1 MPa. For pressures less than 1 MPa, the hydrogen density decreases as the pore diameter is increased; on the contrary, for pressures higher than 1 MPa, the opposite tendency is observed. The maximum achieved in the excess adsorption isotherm for the pore size of 1.66 nm is a pronounced one; thus,


Morales-Cas et al.

Figure 1. Methane adsorption isotherms in the 0.8/0.2 CH4/H2 mixture at room temperature (T ) 298 K) for several carbon cylindrical pores, (a) absolute amount and (b) excess amount. Symbols represent the simulation results, while the lines are a guide to the eyes.

Figure 2. Hydrogen adsorption isotherms in the 0.8/0.2 CH4/H2 mixture at room temperature (T ) 298 K) for carbon cylindrical pores, (a) D ) 2.66 nm and (b) D ) 4.16 nm. Excess adsorption (n) and absolute adsorption (B).

Figure 3. Methane adsorption isotherms in the 0.2/0.8 CH4/H2 mixture at room temperature (T ) 298 K) for several carbon cylindrical pores, (a) absolute amount and (b) excess amount.

such a pore size is proposed as the optimal for achieving the highest hydrogen density.

Adsorption data for these binary mixtures is used to establish equilibrium selectivity for the set of pores studied. The variation



Figure 4. Hydrogen adsorption isotherms in the 0.2/0.8 CH4/H2 mixture at room temperature (T ) 298 K) for carbon cylindrical pores, (a) D ) 1.26 nm, (b) D ) 1.66 nm, (c) D ) 2.66 nm, and (d) D ) 4.16 nm. Excess adsorption (n) and absolute adsorption (B).

Figure 5. Evolution of the methane adsorption selectivity with pressure for several pore sizes; empty symbols correspond to the 0.8/0.2 CH4/ H2 mixtures, while filled symbols represent the 0.2/0.8 CH4/H2 mixtures.

of equilibrium selectivity with pressure is shown in Figure 5 for both mixtures. The pores and mixtures that result in zero hydrogen adsorption have not been plotted in Figure 5, as methane selectivity is infinite in those cases. As a rule, the selectivity decreases as the pressure increases. The same behavior has been observed experimentally in hydrogen separation from hydrocarbons using membranes.39 This dependence

could be explained in view of the comparative sizes of the two adsorbates. The condensation degree for methane increases as the pressure is increased, allowing smaller hydrogen molecules to locate in the interstices that are not suitable for methane. Thus, hydrogen density increases and methane selectivity decreases. It is noticeable that, for pores having a finite selectivity for methane in both mixtures, D ) 2.66 and 4.16 nm, at pressures greater than 1 MPa, methane selectivity is higher in the 0.2/0.8 CH4/H2 mixture, whereas the contrary is observed for the lower pressure range. These results, together with the infinite selectivity, which is achieved for the 0.8/0.2 mixture and smaller pore sizes, lead to a change in selectivity dependence with pore size for both mixtures. As it is shown later, this change in selectivity is related to the accessible pore volume for hydrogen adsorption in its mixture with methane. In Figure 6, some density profiles for both adsorbates and the two mixtures are shown. Density is referred to bulk density for each mixture. A reduced unit system is used for both density and distance. The distance is measured from the cylinder axis (r ) 0) to the pore wall (r ) R). All profiles in Figure 6 represent the adsorbed layers in the pore volume. In Figure 6a, the hydrogen profile is composed of two peaks, each having almost the same density value, whereas the methane profile shows two layers, one directly adsorbed onto the pore wall and a second one exhibiting a lower density value. In Figure 6b (D


Morales-Cas et al.

Figure 6. Methane and hydrogen density profiles for several pore sizes and both mixtures; (a)-(d) 0.2/0.8 CH4/H2 and (e)-(f) 0.8/0.2 CH4/H2.

) 1.66 nm and 0.2/0.8 CH4/H2), the second adsorbed layer for methane is hardly observed (r ) 0.5-0.9 σsf) since it presents a very low density; nonetheless, the second adsorbed layer for hydrogen appears in this region, r ) 0.5-0.9 σsf. The pure hydrogen density profile for this pore size (1.66 nm), not shown here, does not present the second layer but a constant density region. These results suggest that the methane presence promotes hydrogen adsorption forming two layers. It is remarkable that the first layers for both adsorbates show a coincidence of their distance from the pore wall. Figure 6c, e, and d, f differ in the mixture composition. For the mixture enriched in hydrogen, the hydrogen profiles in Figure 6c and d show two regions, one corresponding to the first layer and another one where the density is almost constant. As methane does not present a twolayer profile, there is no second layer for hydrogen either. For the mixture enriched in methane, Figure 6e and f, methane profiles are composed of two layers, although the second one corresponds to a very low-density value. Hydrogen density profiles exhibit a plateau for the middle region of the pore volume. At the location of the methane layers, such a plateau becomes a peak in the density profile. These local increments in hydrogen density could be explained as the consequence of the favorable interaction between hydrogen molecules and

TABLE 2: Methane and Hydrogen Adsorption in the 0.8/0.2 CH4/H2 Mixture at Room Temperature for Cylindrical Pores na/mmol cm-3 D/nm

0.46

P/MPa 0.1 0.3 0.5 0.7 1.0 3.0 5.0 7.5 10.0 12.0

0.86

1.26

CH4 20.090 21.470 22.020 22.240 22.520 23.170 23.500 23.610 23.720 23.810

4.389 8.728 10.800 12.000 13.210 16.110 17.170 17.850 18.170 18.420

1.267 3.545 5.384 6.836 8.491 13.140 14.980 16.210 17.010 17.440

1.66

2.66 CH4

4.16 H2

0.673 0.312 0.010 1.939 0.918 0.030 3.084 1.483 0.049 4.082 2.017 0.067 5.377 2.748 0.092 9.938 6.028 0.227 12.050 7.902 0.339 13.570 9.520 0.459 14.500 10.700 0.574 15.070 11.470 0.657

CH4

H2

0.182 0.535 0.877 1.200 1.657 3.942 5.437 6.797 7.887 8.650

0.009 0.026 0.043 0.059 0.083 0.223 0.347 0.494 0.639 0.742

methane adsorbed layers, as compared to that for hydrogenhydrogen interactions. It is interesting to compare the microscopic arrangement of hydrogen molecules in the pure state and in the mixture with methane, trying to further explore the behavior of this compound in the mixture in a confined environment. Figure 7 depicts a comparison between density profiles for pure hydrogen adsorption and hydrogen adsorbed in a mixture with methane (0.2/0.8



TABLE 3: Methane and Hydrogen Adsorption in the 0.2/0.8 CH4/H2 Mixture at Room Temperature for Cylindrical Pores na/mmol cm-3 D/nm

0.46

P/ MPa 0.1 0.3 0.5 0.7 1.0 3.0 5.0 7.5 10.0 12.0

0.86 CH4

17.220 19.610 20.450 20.890 21.330 22.340 22.680 22.870 23.120 23.220

1.300 3.490 5.180 6.510 7.970 11.700 13.840 14.140 15.670 16.100

1.26

1.66

2.66

4.66

CH4

H2

CH4

H2

CH4

H2

CH4

H2

0.322 0.947 1.550 2.120 2.910 6.630 8.650 10.140 11.120 11.630

0.063 0.189 0.306 0.415 0.562 1.260 1.680 2.080 2.420 2.630

0.170 0.504 0.997 1.650 2.590 4.020 5.660 7.080 8.030 8.630

0.053 0.159 0.312 0.515 0.807 1.240 1.810 2.360 2.840 3.160

0.079 0.234 0.387 0.536 0.751 2.020 3.010 3.950 4.680 5.160

0.042 0.125 0.207 0.288 0.404 1.100 1.710 2.360 2.940 3.360

0.045 0.136 0.225 0.313 0.439 1.210 1.850 2.500 3.010 3.390

0.036 0.107 0.178 0.247 0.350 0.989 1.570 2.240 2.840 3.300

CH4/H2). It is observed that pure hydrogen results, for the four pores (Figure 7a-d), show only one molecular layer for hydrogen inside the pore, next to the pore wall, and a plateau for the middle region of the pore volume; on the contrary, density profiles for hydrogen in the mixture show two layers, even in large pores (Figure 7 c-d). These results from the mixture reveal that methane presence makes hydrogen able to gain additional structure near the walls. However, the density of the first hydrogen layer in the mixture is always less than the one obtained for pure hydrogen, probably due to methane presence occupying some of the available volume. For the pore of 1.26 nm (Figure 7a), the second hydrogen layer for the mixture has a higher density than the plateau for the pure hydrogen adsorption, and for the pore of 1.66 nm (Figure 7b), these density values are almost co-incident. Results shown in Figure 7 reveal that methane presence does not improve the overall density of adsorbed hydrogen, but it causes local higher hydrogen densities inside the pore, close to the walls, where methane is also adsorbed. Figure 8 shows the hydrogen adsorption energy distribution functions for both mixtures and pore diameters from 1.26 to 4.16 nm. The pure hydrogen adsorption energy distributions confined in the same pores are also plotted for comparison. As a rule, hydrogen presents two energy stages, the lower one, which corresponds to those molecules adsorbed onto the pore wall, and the energy stage for molecules in the second layer or

in the middle of the pore volume. It is worth mentioning that, for the smaller pores (Figure 8a and b), the intensity of the lower energy stage (-5 kJ mol-1 approximately) is higher than that corresponding to the higher one (-1.3, -0.3 kJ mol-1), but as pore size increases, the reverse tendency is observed. Thus, the proportion of molecules adsorbed in the minimum energy stage diminishes as pore size increases, revealing that carbon cylindrical micropores are preferred for hydrogen storage. Furthermore, when hydrogen adsorption takes place with methane in the micropores (0.2/0.8 CH4/H2 mixture), energy stages for hydrogen decrease, that is, in a pore of 1.26 nm (Figure 8a) from -4.96 to -5.27 kJ mol-1 for the lower energy stage and from -0.8 to -1.25 kJ mol-1 for the second energy stage. A hydrogen energy decrease is also present in a pore diameter of 1.66 nm, but it is barely observed for pores in the mesopore range (Figure 8c and d.). These results bring out the possibility of hydrogen stabilization within the pore cavity, as shown in Figure 7a and b. Finally, Figure 9 shows the energy distribution functions for methane and hydrogen from the 0.2/0.8 CH4/H2 mixture for a pore size of 1.26 nm. Methane also presents two energy stages, a lower one (-14 kJ mol-1) and a second energy stage for few molecules at -3.3 kJ mol-1. No methane energy stages match with hydrogen ones; consequently, selective desorption could be possible. Summary and Conclusions Adsorption of hydrogen and methane mixtures in carbon cylindrical pores at room temperature has been studied using grand canonical Monte Carlo molecular simulations, considering

Figure 7. Hydrogen density profiles for several pore sizes. Pure adsorbate and mixture, 0.2/0.8 CH4/H2, adsorption are represented by full and dashed lines, respectively.

Figure 8. Hydrogen adsorption energy distribution functions for several pore sizes for pure hydrogen and its mixtures with methane, (a) D ) 1.26 nm, (b) D ) 1.66 nm, (c) D ) 2.66 nm, and (d) D ) 4.16 nm.


Morales-Cas et al. anonymous referees, whose comments improved the manuscript. Partial financial support for this work has been provided by the Spanish government under Projects PPQ2003-07964 and CTQ2005-00296/PPQ and by the Generalitat de Catalunya SGR2005-00288. This research has been carried out partially using computational resources from CESCA (Catalunya, Spain). References and Notes

Figure 9. Hydrogen and methane adsorption energy distribution functions for a pore size of 1.26 nm for the 0.2/0.8 CH4/H2 mixture.

pore sizes in the micropore and mesopore regions. Adsorption isotherms for both adsorbates reveal that methane is the preferred adsorbed compound, mainly in micropores. The amount of adsorbed hydrogen diminishes as the pore size is increased for pressures below 1 MPa. Methane equilibrium selectivity is higher for micropores, and it remains almost constant for pressures below 1 MPa; it decreases in the higher pressure interval (up to 12 MPa). In this pressure range, hydrogen adsorption occurs in void space around adsorbed methane molecules, as is observed in the molecules’ density profiles for both adsorbates. Methane and hydrogen’s first adsorbed layer on the pore wall are co-incident, and a second adsorbed hydrogen layer is present, in contrast to pure adsorbed hydrogen profiles. In addition, adsorption energy distribution functions were obtained, providing further insights into the microscopic behavior of these systems. Hydrogen presents two energy stages, which are minor for molecules adsorbed in micropores. Hydrogen stabilization to lower energy stages is observed when comparing pure hydrogen energy stages with those corresponding to the adsorbed binary mixtures. Thus, the methane presence brings out hydrogen stabilization, mainly in the micropores. This can be a consequence of the stronger hydrogen-methane interaction compared to the hydrogen-hydrogen interaction (a direct consequence of the application of the Lorentz-Berthelot combining rules). It is observed that a stronger hydrogen-methane interaction makes hydrogen able to locate nearer the pore wall than pure adsorbed hydrogen. The result of this phenomenon is a lower adsorption energy, which is calculated from solid-fluid interactions. Despite this, the amount of hydrogen adsorbed, even in the most optimal conditions, is still very small. A main conclusion of this work is that, although the hydrogen adsorption is enhanced in the mixture versus pure hydrogen adsorption in the same material, in local density terms and energetic terms, the total amount adsorbed is still insufficient to solve the problem of hydrogen storage by physisorption near ambient temperature. A possible solution would be to investigate materials in which the hydrogen-solid interactions are also enhanced, in addition to fluid-fluid interactions. Acknowledgment. The authors thank Dr. Carmelo Herdes for his useful help and fruitful discussions and one of the

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Adsorption of Hydrogen and Methane Mixtures on Carbon Cylindrical

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