Lattice Gas Model for H2 Adsorption in Nanoporous Zinc

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Lattice Gas Model for H2 Adsorption in Nanoporous Zinc Hexacyanometallates ´ vila† Carlos Rodrı´guez,*,†,‡ Edilso Reguera,†,‡ and Manuel A Centro de InVestigacio´n Aplicada y Tecnologı´a AVanzada, Instituto Polite´cnico Nacional, Legaria 694, CP 11500, Me´xico D. F., Me´xico, and Instituto de Ciencia y Tecnologı´a de Materiales and Facultad de Fı´sica, UniVersidad de La Habana, San La´zaro y L, CP 10400, Vedado, La Habana, Cuba ReceiVed: August 11, 2009; ReVised Manuscript ReceiVed: February 4, 2010

Zinc hexacyanometallates Zn3A2[M(CN)6]2 with different exchangeable alkaline cations A+ and framework transition metals M constitute an excellent model system to study H2 adsorption in nanoporous solids. A lattice gas approach, based on experimental data and simple considerations on the position and energies of adsorption sites, is proposed. Coverage and adsorption enthalpies are calculated and compared with experimental results. The interplay of three necessary conditions for H2 storage in porous solidssfree volume to accommodate guest molecules, charge centers to bind them, and fast diffusion during adsorption or desorptionsis discussed. 1. Introduction High-density storage is probably the main challenge for the wide use of molecular hydrogen as a secondary energy bearer, especially for mobile applications.1,2 The limitations of gas and liquid phases are well known. Adsorption in solids with extended internal surfaces and the formation of chemical hydrides appear as the most promising alternatives.3-8 At present, none reported material meets the minimal technological requirements: fast and reversible adsorption and desorption of 6 wt % at moderate temperatures and pressures. Porous zinc hexacyanometallates Zn3A2[M(CN)6]2 have been studied as potential H2 storage materials.9-11 Actually, their reported adsorption capacity is quite far from the established goal. However, systematic variation of framework transition metals M and exchangeable alkaline cations A+ provides an excellent model system to understand H2 storage in porous solids. The structure of these compounds is well known.12-14 They crystallize with a hexagonal unit cell containing 6 formula units, with cell parameters aH ≈ 12.5 Å, cH ≈ 32.6 Å, only slightly dependent on the involved metals M and A. Their network of pores is formed by six ellipsoidal cavities per unit cell, with dimensions close to 15.5 × 11.1 × 7.9 Å. Six elliptical windows of about 6.8 × 8 Å communicate neighbor cavities. Windows are formed by two octahedra [M(CN)6] with tetrahedral coordination to Zn atoms. Approximating12,13 CtN groups by cylinders of radius 1.4 Å, windows resemble small tubes of internal dimensions 4 × 5.2 × 2.8 Å. In Figure 1, elaborated with data taken from a previous work,14 two ellipsoidal cavities are shown (left). The same cavities, now rotated (right), show their common elliptic window. For M ) Co, the cation-free isostructural hydrophobic composition Zn3[Co(CN)6]2 is obtained. In this case windows have zero net charge. The dipolar electric field, resulting from the excess of electron density in the CtN bonds and the deficit on the metal sites, is too weak to bind water dipoles, but it is inhomogeneous enough to create an electric field gradient * To whom correspondence should be addressed. Phone: (537) 8762099. E-mail: [email protected]. † Instituto Polite´cnico Nacional. ‡ Universidad de La Habana.

Figure 1. Porous framework for the materials under study, formed by octahedra [M(CN)6] with tetrahedral coordination to Zn atoms. The exchangeable cations are represented by spheres. Left: two ellipsoidal cavities can be appreciated. Right: The same cavities, now rotated, are shown to be communicated by an elliptic window.

attracting quadrupolar molecules, like H2 and CO2, as shown in adsorption experiments.10,11 In hexacianometallates with M ) Fe, Ru, Os windows have an average negative charge -2e/3. Two exchangeable cations A+ per cavity occupy two of six equivalent sites close to windows, most probably at opposite windows,12,13 as shown in Figure 1. Water molecules are primarily bound to charge centers and then to other water molecules through hydrogen bonding interactions. In hydrated samples, the distance between cations calculated from reported atomic positions12-14 are 3.21 Å for Na, 5.57 Å for K, and 5.49 Å for Rb. A systematic study of H2 adsorption in the hexacyanometallates Zn3A2[M(CN)6]2, with A ) Na, K, Rb, and Cs and M ) Fe, Os, Ru, together with the cation-free isostructural composition Zn3[Co(CN)6]2, taken for comparison, has been presented in refs 10 and 11. As shown by thermogravimetric analysis,10,11 continuous reversible dehydration occurs below 200 °C. Dehydration

10.1021/jp907750v  2010 American Chemical Society Published on Web 04/30/2010

Model for H2 Adsorption in Zinc Hexacyanometallates

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temperature TA increases with cation polarizing power (TCs < TRb < TK < TNa). Only for A ) Na, abrupt dehydration is also observed at 200 °C, indicating the presence of two different binding energies for water molecules. In dehydrated samples, the agglutinating effect of water molecules is no longer present, and cations are expected to move closer to windows. Hydrogen adsorption10,11 shows type I isotherms at 75 and 85 K, except for Zn3Na2[Fe(CN)6]2,, where strong kinetic effects are present even at 258 K. The maximum number of adsorbed molecules per cavity is higher for Zn3[Co(CN)6]2 (N ≈ 6), where the whole volume is free of cations. Adsorption enthalpies ∆H increase with cation polarizing power: ∆HCo < ∆HCs < ∆HRb < ∆HK. In this paper, the regularities of H2 adsorption previously reported10,11 for porous zinc hexacianometallates Zn3A2[M(CN)6]2 with A ) Na, K, Rb, and Cs and M ) Fe, Os, Ru, and Zn3[Co(CN)6]2 are explained with the aid of lattice gas models. From the structural information available, the approximate position and energies of adsorption sites are derived. The adsorption isotherms and enthalpies are calculated and compared to experimental values. The interplay of three necessary conditions for H2 storage in porous solids—free volume to accommodate guest molecules, attracting centers to bind them with optimal strength, and fast diffusion during adsorption or desorption is—discussed. 2. Model Lattice gas models have been extensively used to describe equilibrium localized adsorption in solids.15 Their main assumption is the existence of deep minima Ui for the interaction energy between a foreign molecule and the solid. In a crystal, these minima are periodically ordered, forming a lattice. Molecules adsorbed from gaseous or liquid phases are expected to be localized around these “adsorption sites” and their motion restricted to small center of mass oscillations and to the excitation of their internal degrees of freedom. Intersite overbarrier motion is only considered to describe nonequilibrium phenomena, such as diffusion. These models provide an appropriate description of adsorption when the thermal energy is much lower than the height of the potential energy barriers between neighboring sites. Many variants of this basic idea have been applied in different situations. If the interaction energy Vij between adsorbed molecules is included, an Ising-like model is obtained, where the energy E of a configuration with ni molecules adsorbed at site i is

E(n1, ..., nN) )

N

N

i)1

i,j)1

∑ εini + 21 ∑ Vijninj

(1)

Here εi is the energy of a molecule adsorbed at site i, obtained after averaging over local degrees of freedom (see Supporting Information). It is given by the potential energy minimum Ui plus the free energy of in-site center of mass oscillations and internal molecular motion. This free energy decreases with increasing temperature because its partial derivative with respect to temperature is minus the corresponding contribution to entropy, a positively defined quantity. Then, εi is expected to be a decreasing function of temperature. This dependence becomes important near the activation temperatures of the averaged local degrees of freedom. In the case of porous zinc hexacyanometallates, the saturation of adsorption isotherms observed at relatively low pressures10,11 is an experimental evidence of localized H2 adsorption inside

cavities containing exchangeable cations. The crystal can be regarded as a grand canonical ensemble of unit cells in equilibrium. Inside each cell, adsorbed molecules will be described by a simple lattice gas model like eq 1. 2.1. Adsorption Sites. To build the model, intracell details, such as the geometry and interconnection of cavities, cation positions, and cation sizes, should be taken into account to find the distribution of charge centers and calculate the potential energy for a H2 molecule. The exact determination of the adsorption sites from potential energy minima requires the use of detailed quantum calculations,16 but the approximate positions and energies of these sites can be estimated from elementary classical considerations. In first approximation, the potential energy of a H2 molecule inside a cavity results from the interaction of its induced dipole and permanent quadrupole moments with the electrostatic field of surrounding cations and windows.17 The dipolar energy is always attractive and given by

1 b2 UD ) - R|E | 2

(2)

where b E is the electric field intensity at the center of a molecule and R is the polarizability17 of H2

R ) 8.79 × 10-41 C2 m2 J-1 The quadrupolar energy UQ depends of the orientation of the molecule. When the molecular axis (the line joining nuclei) is along OZ, the expression for UQ is

UQ ) -

Q ∂EZ 2 ∂Z

(3)

where the quadrupole moment Q of H2 is17

Q ) 2.21 × 10-40C m2 To evaluate the electrostatic field b E, cations will be approximated by spheres of charge e and radius RA and windows by rings of charge -2e/3 and radius R0 ≈ 3.7 Å (isoperimetric with the elliptical windows). For an idealized ellipsoidal cavity centered at origin, with dimensions 15.5 × 11.1 × 7.9 Å and six windows in octahedral positions ((a, 0, 0), (0, (a, 0), and (0, 0, (a), simple geometry leads to a distance 2a ≈ 10.4 Å between the centers of opposite windows (see Supporting Information). The equilibrium positions of cations in the absence of adsorbed molecules can be estimated from their potential energy minima in the field of windows and other cations. Two configurations are possible. Configuration I, with cations near opposite windows at positions ((xc, 0, 0), where xc ≈ 0.82a ≈ 4.25 Å, is more stable and will be assumed in the following. Configuration II, corresponding to cations at (xc, 0, 0) and (0, xc, 0), with xc ≈ 0.89a ≈ 4.6 Å is about 34 kJ mol-1 less stable (see Supporting Information). As expected, in the absence of water molecules, the equilibrium distance between cation centers is larger than in hydrated samples. Taking into account finite cation sizes, there is a free distance 2(xc - RA) between cations. The presence of a cation at (xc, 0, 0) partially occludes the closest window, which is

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Rodrı´guez et al. TABLE 1: Calculated Potential Energy (kJ mol-1) for a H2 Molecule Oriented along OZ at Adsorption Sites A, B, and C and the Origin UA UB UC U0

Figure 2. Schematic representation of cavities (large ellipsoids) with axis joining opposite windows, cations (spheres) and type A, B, and C adsorption sites for H2 molecules (small ellipsoids) in Zn3A2[M(CN)6]2.

located at (a, 0, 0), preventing H2 molecules from entering or leaving the cavity through that window. Figure 2 shows an idealized ellipsoidal cavity centered at the origin of a coordinate system with axis passing across windows. Cations are represented by spheres. Two (of six) neighboring cavities are also represented. By assuming cation equilibrium positions at ((xc, 0, 0), and approximating windows by charged rings, it is easy to calculate the electrostatic field, its gradient, and the potential energy U ) UQ + UD inside a cavity (see Supporting Information). The potential energy for a molecule whose axis is oriented along OZ has minima at positions between and just close to cations: ((c, 0, 0), with c ) xc - RA - RH (see Figure 2). There are also minima near the centers of windows located at b ra (0, (a, 0) and a saddle point at origin. Analogously, a molecule oriented along OY has potential energy minima at b rc ((c, 0, 0) and near the centers of windows located at (0, 0, (a). For a molecule oriented along OX the quadrupolar interaction with cations is repulsive and its potential energy is much higher. Hydrogen molecules bind to adsorption sites with their axis perpendicular to the line joining the center of the molecule with the site (T configuration). Since every window belongs to two cavities, the potential energy near windows is influenced by the interaction of the molecule with cations and windows from two neighboring cavities. There are two possible situations giving rise to sites with different energies. In type A sites (see Figure 2), both sides of the window are free of cations, and two H2 molecules (one from each side) can bind to the window, which has a depth about 2.8 Å.12,13 At that distance two H2 molecules are expected to repel each other.18 Intercavity diffusion takes place through these sites, since other windows are occluded from one side by cations. In type B sites, located in Figure 2 at b rb (0, b, 0), where b ) 2a - xc - RA - RH, a molecule can be adsorbed close to a cation located at the other side of the window. There are six adsorption sites per cavity, 36 per unit cell. Two sites per cavity are type C. Since one of three windows

Na

K

Rb

Cs

–2.6 –14.6 –19.9 –3.4

–2.6 –8.7 –11.6 –3.4

–2.6 –7.7 –10.0 –3.4

–2.6 –6.1 –7.6 –3.4

has a cation bound, there are 16 type A sites and 8 type B sites per unit cell. The maximum occupation of type C sites depends of the free space 2(xc - RA) available between cations. Only one H2 molecule (RH ≈ 1.45 Å) can be accommodated between large cations like K, Rb, and Cs (RK ≈ 1.38 Å, RRb ≈ 1.49 Å, RCs ≈ 1.70 Å) and two between smaller Na+ cations (RNa ≈ 1.02 Å). In Table 1 the calculated potential energy values (in kJ mol-1) r a, b r b, for a H2 molecule oriented along OZ at adsorption sites b b rc, and the origin, for A ) Na, K, Rb, and Cs, are presented. These energy values are crude estimates, but they are consistent with experimental adsorption enthalpies both in order of magnitude and dependence with cation radius.10 The smaller the cation, the closer to it is a molecule at type B or C sites and the stronger is their interaction. According to the above discussion, the unit cell has 8 pairs of type A sites with energy εA and nA ) 0, 1, or 2 adsorbed molecules, 8 type B sites with energy εB and nB ) 0 or 1 molecules, and 6 pairs of type C sites with energy εC and nC ) 0, ..., NC molecules, where NC depends on cation size. The energy of a given configuration can be expressed as

8

E)

∑ i)1

[

εAnAi +

]

VA i i n (n - 1) + 2 A A 6

∑ i)1

[

8

∑ εBnBi + i)1

εCnCi +

]

VC i i n (n - 1) 2 C C

(4)

The maximum number of adsorbed molecules per cell is N ) 24 + 6NC. For Zn3A2[Fe(CN)6]2, with A ) Cs, Rb, and K, only one H2 molecule can be accommodated in the space available between two large cations, and calculations will be made supposing that NC ) 1. For the smaller Na+ cation in Zn3Na2[Fe(CN)6]2, one expects NC ) 2. However, in a cavity with two molecules adsorbed at type C sites, intracavity diffusion becomes impossible, and thermodynamic equilibrium is not attained at low pressures, as observed in experimental adsorption isotherms.10 For Zn3[Co(CN)6]2, 36 type A sites per unit cell will be assumed. 2.2. Partition Function, Coverage, and Adsorption Heat. Taking into account eq 4, the grand partition function for H2 molecules adsorbed in the unit cell is

Ξ ) ΞAΞBΞC

(5)

Model for H2 Adsorption in Zinc Hexacyanometallates

{∑( ) 2

ΞA )

2 -β[(εA-µ)n+ UA n(n-1)] e 2 n

n)0

) [1 + 2e

-β(εA-µ)

{∑ 1

ΞB )

e-β(εB-µ)n

n)0

{∑( ) 1

ΞC )

n)0

}

8

-2β

+e

(

εA+

}

VA

pA ) p0eβεA

8

-µ

2

]

}

2 -β[(εC-µ)n+ n(n-1)] e 2 n

p p0

p0 )

8

Taking into account eqs 9-14, the adsorption enthalpy ∆H is obtained from

(7) ∆H ) kBT2

) [1 + 2e-β(εC-µ)]6

(8)

( )

1 mp β πβp2

3/

2

ZR

(9)

For a mixture of 75% o-hydrogen and 25% p-hydrogen, at the experimental temperatures to be considered (75 and 85 K), ZR is the rotational partition function per molecule and is determined by the contribution of the J ) 1 states of o-hydrogen

(

ZR ≈ 3e-

2TR 3/4 T

)

, with TR ≈ 81.4 K

(14)

(6)

Here β ) (kT)-1 and µ is the chemical potential of the gaseous phase at pressure p and temperature T

µ ) kT ln

pC ) p0eβεC pAA ) p0eβ(εA+ 2 )

)]8

[

6

pB ) p0eβεB

VA

) 1 + e-β(εB-µ)

VC

J. Phys. Chem. C, Vol. 114, No. 20, 2010 9325

[

d p ln dT p0

]

(15)

θ

3. Results and Discussion Figure 3 shows a comparison of isotherms calculated from eqs 12 and 13 with experimental values reported10 for Zn3[Co(CN)6]2, Zn3K2[Fe(CN)6]2, and Zn3Rb2[Fe(CN)6]2 at 75 and 85 K. The fitting was carried out by the multiparameters least-squares minimization algorithm programmed in the Microcal Origin software package 8.0. In Table 2 the values of the parameters used to fit experimental data are listed. The explicit analytic expressions for ∆H are available from Supporting Information. Figure 4 shows a comparison between measured and calculated adsorption enthalpies at low coverage. Experimental values were obtained from isotherms recorded at 75 and 85 K using the Clausius -Clapeyron equation. Theoretical points are the average of values calculated at those temperatures with the parameters given in Table 2.

(10)

As discussed before, site energies εs (s ) A, B, C) must decrease with increasing temperature because they include the free energy of center of mass oscillations and internal motion of adsorbed molecules. In the present case, the temperature dependence is dominated by hindered rotations of adsorbed H2 molecules. The interaction energies between neighboring molecules at type A or type C sites have been designed by VA and VC. Coverage θ as a function of p and T is obtained from eqs 5-8

θ)

1 ∂ ln Ξ N ∂βµ

(11)

The isotherm for Zn3[Co(CN)6]2 is

( ) ( )

p p 2 + pA pAA θ) p p 1+2 + pA pAA

2

(12)

While for Zn3A2[Fe(CN)6]2 (A ) K, Rb, Cs) the result is

( ) ( )

p p 2 + pA pAA 8 θ) 15 p p 1+2 + pA pAA

2

4 + 15

p pB

p 2 pC + 5 p p 1+ 1+2 pB pC (13)

Figure 3. Adsorption isotherms. Experimental (spheres) and calculated (full lines) values of coverage for Zn3[Co(CN)6]2, Zn3K2[Fe(CN)6]2, and Zn3Rb2[Fe(CN)6]2 at 75 and 85 K.

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TABLE 2: Site Energies (in kJ mol-1) Used to Fit Experimental Isotherms at T ) 75 and T ) 85 K energy

T (K)

A)K

A ) Rb

Zn3[Co(CN)6]2

εA

75 85 75 85 75 85 75 85

–5.9 –6.4 –8.1 –8.6 –8.1 –8.4 1.3 1.3

–5.6 –5.9 –6.7 –7.2 –7.0 –7.4 1.2 1.1

–6.0 –6.3

εB εC VA

presence of adsorption sites with very different energies. At low coverage, the adsorption enthalpy ∆H0 is dominated by adsorption at sites with the lowest energies εB and εC

∆H0 ) -

4εAθ-βεA + 2εBθ-βεB + 3εCθ-βεC -βεA

4θ

-βεC

+ 2θ-βεB + 3θ

≈ -εC

(16) 0.6 0.5

As can be appreciated from Figures 3 and 4, experimental isotherms and adsorption enthalpies at low coverage are well described by a lattice gas model of six adsorption sites and a maximum number of five molecules adsorbed per cavity. Moreover, the site energies resulting from the fitting procedure and listed in table 2 show the behavior predicted in section II. In first place, εA, εB, εC have the same order of magnitude and cation dependence and follow the same order as the calculated binding energies UA> UB > UC listed in Table 1. The reason is that in sites type B and C adsorbed molecules are very close to cations, whereas at sites type A they are near less polarizing charge centers distributed along the windows perimeter. The smaller the cation the closer to it the molecules at sites type B or C and the stronger their induced dipolar and quadrupolar interactions. On the other hand, site energies A, B, and C decrease approximately the same amount (0.3-0.5 kJ/mol), almost independently of the cation and the type of site, as the temperature increases from 75 to 85 K. This is consistent with the expected contribution to the free energy of hindered rotations of adsorbed molecules, as well as any change, due to adsorption, in the vibrational zero-point energy and the entropy of mixture per molecule. Finally, VA > 0, showing that molecules adsorbed in type A sites at both sides of a window repel each other, as expected from the windows depth (2,8 Å). The repulsive interaction energy VA is much smaller for Zn3[Co(CN)6]2, indicating a larger distance between molecules adsorbed near windows. For Zn3K2[Fe(CN)6]2 the calculated adsorption enthalpy decreases with increasing pressure as a consequence of the

As pressure increases, type A sites, with higher energy εA, are progressively occupied with an smaller change of the system’s enthalpy. The experimental data shown in Figure 4 reproduces this behavior. Zinc hexacyanometallates Zn3A2[M(CN)6]2, when compared to the isostructural cation-free compound Zn3[Co(CN)6]2, illustrate very well the interplay of three necessary conditions for high density H2 storage in porous materials: free volume to accommodate guest molecules, charge centers to bind them, and fast diffusion during adsorption or desorption. Although a complete discussion of diffusion is not possible with the present lattice gas model, proposed to describe equilibrium adsorption, the positions occupied by cations and adsorbed molecules, together with their sizes, have clear implications for the adsorption and desorption kinetics. In Zn3[Co(CN)6]2 the entire volume of the cavities is available to accommodate H2 molecules which easily diffuse across large free windows, but the absence of charge centers to bind the molecules leads to adsorption enthalpies which are very low compared to the values (20-30 kJ mol-1) required for high density storage. The presence of large cations like K+, Rb+, and Cs+ slightly increases adsorption enthalpies but reduces the space for H2 adsorption and partially occludes windows. For Zn3Na2[Fe(CN)6]2 the smaller Na+ cations bind H2 at a shorter distance so that the combined effect of the induced dipolar and quadrupolar interactions promises higher adsorption enthalpies (about 20 kJ mol-1) and a larger number of adsorbed molecules per cavity. However, once two molecules are adsorbed at the lower energy type C sites, located near the center of a cavity, diffusion across that cavity at moderate pressures is inhibited, preventing the system from reaching thermodynamic equilibrium and leading to the kinetic effects observed10 in adsorption isotherms even at 258 K. This effect could be overcome at higher pressures, hopefully without appreciable distortion of the framework, opening the possibility, interesting for certain applications, of high density H2 storage at a high pressures and desorption at a low pressures. Unfortunately, experimental results at high pressures are still not available. Conclusions

Figure 4. Adsorption enthalpies. Experimental values (spheres) were obtained in ref 12 from isotherms recorded at 75 and 85 K using the Clausius-Clapeyron equation. Theoretical points (squares) are the average of values calculated from 12-15 at 75 and 85 K using the parameters given in Table 2.

Adsorption isotherms and enthalpies previously reported10,11 for H2 in porous zinc hexacyanometallates Zn3A2[M(CN)6]2 can be adequately described by a lattice gas model with six adsorption sites per cavity, thirty six per unit cell, where H2 molecules can be adsorbed in a T configuration. The positions and energies of these sites are essentially determined by quadrupolar and (induced) dipolar interactions of H2 molecules with charged cations and windows. They show a strong dependence on the size of the involved A cation but depend weakly on the framework metal M. Eight pairs of type A sites, located near cation-free windows, can accommodate up to two molecules, one from each side of the window, with a weak repulsion between them. Eight type B sites at windows occluded from one side by a cation can bind a molecule at the opposite side. Six pairs of type C sites located between cations and near

Model for H2 Adsorption in Zinc Hexacyanometallates cavity centers can be occupied by one or two molecules, depending on cation sizes and intercationic distances. Molecules bind stronger to sites type B and C, which are closer to cations. The smaller the cation, the closer to it is adsorbed the H2 molecule and the stronger is their interaction. Such a site and cation size dependence is confirmed in the values εA, εB, and εC obtained by fitting experimental isotherms10,11 and explains why adsorption enthalpy decreases with increasing coverage for Zn3K2[Fe(CN)6]2. These site energies lie in the range from -5 to -10 kJ mol-1 and slightly decrease with increasing temperature, because they include the free energy of in site molecular motion. In the case of Zn3Na2[Fe(CN)6]2, the smaller Na+ cation should allow the adsorption at low pressures of two H2 molecules strongly bound at type C sites, but this probably inhibits the diffusion across that cavity of new molecules, leading to the kinetic effects reported in experimental isotherms. Adsorption experiments at higher pressures are necessary to verify this conclusion. Acknowledgment. This study was partially supported by the Projects SEP-Conacyt 61-541 and ICyTDF PIFUT P08-158. C.R. and M. A. thank Conacyt for sabbatical and doctoral scholarships, respectively. Supporting Information Available: Supporting Information contains the detailed calculations of windows and cation positions, adsorption sites, isotherms and enthalpies. This material is available free of charge via the Internet at http:// pubs.acs.org.

J. Phys. Chem. C, Vol. 114, No. 20, 2010 9327 References and Notes (1) Crabtree, G. W.; Dresselhaus, M. S. MRS Bull. 2008, 421. (2) Dunn, S. Int. J. Hydrogen Energy 2002, 27, 235. (3) Principi, G.; Agresti, F.; Maddalena, A.; Lo Russo, S. Energy 2008, 1. (4) Bathia, S. K.; Myers, A. L. Langmuir 2006, 22, 1688. (5) Nijkamp, M. G.; Raaymakers, J. E. M.; van Dillen, A. J.; de Jong, K. P. Appl. Phys. A: Mater. Sci. Process. 2001, 72, 619. (6) Conte, M.; Prosini, P. P.; Passerini, S. Mater. Sci. Eng. 2004, B108, 2. (7) Thomas, K. M. Catal. Today 2007, 120, 389. (8) Chen, Ping; Zhu, Min. Mater. Today 2008, 11, 12. (9) Kaye, S. S.; Long. Long, J. R. Chem. Commun. 2007, 4486. (10) Reguera, L.; Balmaseda, J.; Krapp, C. P.; Avila, M.; Reguera, E. J. Phys. Chem. C 2008, 112, 5589. (11) Reguera, L.; Balmaseda, J.; del Castillo, L. F.; Reguera, E. J. Phys. Chem. C 2008, 112, 17443. (12) Garvereau, P.; Garnier et, E. Acta Crystallogr. 1979, B35, 2843. (13) Garnier, E.; Garvereau, P.; Hardy, A. Acta Crystallogr. 1982, B38, 1401. (14) Rodrı´guez-Herna´ndez, J.; Reguera, E.; Lima, E.; Balmaseda, J.; Martı´nez-Garcı´a, R.; Yee, H. J. Phys. Chem. Solids 2007, 68, 1630. (15) Bell, G. M.; Lavis, D. A. Statistical Mechanics of Lattice Models; Ellis Howood Limited: Chichester, UK, 1989. (16) Solans-X.; Branchadel, V.; Sodupe, M.; Zicovih-Wilson, C. M.; Gribov, E.; Spoto, G.; Busco, C.; Ugliengo, P. J. Phys. Chem. B 2004, 108, 8278. (17) Lochan, Rohit C.; Head-Gordon, Martin Phys. Chem. Chem. Phys. 2006, 8, 1357. (18) Patkowsky, K.; Cencek, W.; Jankowsky, P.; Szalewicz, K.; Mehl, J. B.; Garberoglio, G.; Harvey, A. The J. of Chem. Phys. 2008, 129, 094304.

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