Kinetics and Mechanistic Model for Hydrogen Spillover on Bridged

Yingwei Li, Frances H. Yang, and Ralph T. Yang*. Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109. J. Phys. Chem...
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J. Phys. Chem. C 2007, 111, 3405-3411

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Kinetics and Mechanistic Model for Hydrogen Spillover on Bridged Metal-Organic Frameworks Yingwei Li, Frances H. Yang, and Ralph T. Yang* Department of Chemical Engineering, UniVersity of Michigan, Ann Arbor, Michigan 48109 ReceiVed: August 18, 2006; In Final Form: January 10, 2007

The kinetics of hydrogen adsorption on IRMOF-8 by hydrogen spillover from a Pt/AC catalyst (activated carbon support) was studied at various pressures (0-100 atm) and temperatures (273-348 K). The sorbent studied was a mixture of IRMOF-8 and Pt/AC with added carbon bridges. The overall isosteric heats of adsorption (-25 to -20 kJ/mol) and the apparent activation energy for surface diffusion (9.3 kJ/mol) were determined from the temperature dependence of respectively equilibrium isotherm and diffusion time constant. Ab initio molecular orbital calculations were performed for the bonding energies between the spiltover hydrogen atom and various sites on the IRMOF structure. The overall heats of adsorption fell reasonably within the range of bond energies. Surface diffusion of the spiltover hydrogen at near ambient temperature was a slow process, which resulted in slow hydrogen uptake rates especially at higher pressures (higher surface concentrations). Desorption rates were relatively faster, and also decreased with increasing pressure or surface concentration. Desorption appeared to follow a reverse spillover process. Finally, a simple mechanistic model was formulated for the equilibrium isotherm for spiltover hydrogen. The model is capable of interpreting various shapes of isotherms, i.e., concave, convex, of nearly linear isotherms. The declining diffusion time constant (D/a2) with surface concentration provided strong evidence that the adsorbed hydrogen served as bridges between the catalyst and the IRMOF receptor thereby causing further spillover.

1. Introduction Hydrogen is one of the best alternative fuels for vehicles powered with fuel cells.1 Efficient storage of hydrogen will play a key role in the utilization of hydrogen. There are several candidate storage systems including liquid or high-pressure H2 gas, reversible metal hydrides, chemical hydrides, and porous adsorbents. However, at the present time none is capable of satisfying the DOE criteria of size, recharge, kinetics, cost, and safety requirements for personal transportation vehicles.2,3 Recently we have demonstrated that hydrogen storage by hydrogen spillover is promising for enhancing the hydrogen storage capacities in nanostructured carbon materials and isoreticular metal-organic frameworks (IRMOF-1 and IRMOF8).4-9 By using a simple technique for bridge-building for spillover, the storage capacity of IRMOF-8 has been enhanced by a factor of 8 at 298 K and 10 MPa.9 Furthermore, the storage was shown to be totally reversible at 298 K. The phenomenon of “hydrogen spillover” has long been known.10 The first direct evidence for hydrogen spillover originated from Khoobiar, who found the formation of the hydrogen bronze HxWO3 from WO3 at room temperature after exposure to hydrogen in the presence of a platinum-containing catalyst.11,12 The experimental result could only be interpreted by the diffusion of atomic hydrogen from the platinum catalyst to WO3. During the last four decades, hydrogen spillover has been extensively studied particularly in the field of catalysis. A number of comprehensive reviews on hydrogen spillover are available.13,14 Hydrogen spillover has been defined as the dissociative chemisorption of hydrogen on one site, such as a * Corresponding author. Fax: (734) 764-7453. E-mail address: yang@ umich.edu.

metal particle, and the subsequent transportation of atomic hydrogen onto another substrate, which by itself has no or little activity for dissociative hydrogen adsorption.13-16 The spiltover hydrogen atoms can continue to migrate on the second substrate via surface diffusion. Sometimes, spillover can be considered as a total process including both the transportation of adsorbates from one phase to the different phase and the subsequent surface diffusion.15 The nature of the spiltover hydrogen and the kinetics of hydrogen spillover have also been investigated.17-26 It was found that hydrogen molecules were dissociated rapidly on metal sites and then diffused slowly away from them to the receptor. Therefore, surface diffusion of hydrogen atoms has been proposed to be the rate-determining step in hydrogen spillover. Hattori et al. investigated the kinetics of hydrogen adsorption on SO42--ZrO2, and WO3-ZrO2 supported platinum catalysts in the temperature range 323-573 K.27,28 They observed very slow uptake rates of hydrogen on these two supported platinum samples (over 10 h to adsorption equilibriums). The activation energy for the diffusion was measured to be 35.5 kJ/mol for Pt/WO3-ZrO2 and 84 kJ/mol for Pt/SO4-ZrO2, respectively. Despite continued investigations and research on the kinetics of hydrogen spillover, to the best of our knowledge, there is no report on the kinetics study of surface diffusion of hydrogen atoms at room temperature. Furthermore, the mechanistic details of hydrogen spillover are still poorly understood. In the present paper, we report the kinetic and mechanistic model of hydrogen adsorption on the bridged IRMOF-8 sample. The adsorption amounts and rates of adsorption/desorption were measured quantitatively at different temperatures and pressures. The heats of adsorption and activation energy for surface diffusion were calculated. A mechanistic model was proposed

10.1021/jp065367q CCC: $37.00 © 2007 American Chemical Society Published on Web 02/06/2007

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Li et al. TABLE 1: Energy of Adsorption (kJ/mol of H) for a Hydrogen Atom on Possible Sites on the IRMOF Model (Figure 1) Eads (kJ/mol of H)

O1 O2 C1 C2 C3 C4 Zn

-3.60 -40.33 -7.66 -15.15 -49.62 -41.82 -3.26

where Eads is the hydrogen adsorption energy, EIRMOF-H is the total energy of the system, EIRMOF is the energy of the bare IRMOF, and EH is the energy of the hydrogen atom. A higher value of Eads corresponds to a stronger adsorption.

Figure 1. A computational model for IRMOF.

to elucidate the obtained results. On the basis of the experimental results, an isotherm was derived for spiltover hydrogen. 2. Experimental Methods The preparation of IRMOF-8 and bridged IRMOF-8 has been described in detail in our previously published papers.8,9 Briefly, 2,6-naphtalenedicarboxylic acid and Zn(NO3)2‚6H2O were dissolved in N,N-dimethylformamide (DMF) with the addition of three drops of H2O2 aqueous solution. Triethylamine was slowly added dropwise to the above solution under vigorous stirring. The white product (IRMOF-8) was collected by repeated filtering, and thorough washing with DMF three times. To prepare the bridged IRMOF-8 sample, specific ratios of dried IRMOF-8 (solvent free), 5%Pt/AC catalyst, and sucrose were ground together for 1 h. The mixture was heated in flowing helium to 473 K and held for 3 h, then at 523 K for 12 h at a heating rate of 1 deg/min. After slow cooling to room temperature, the sample was stored in vacuum before hydrogen storage measurement. Low-pressure H2 adsorption isotherms (0-1 atm) were measured with a standard static volumetric technique (using Micromeritics ASAP 2010). Hydrogen adsorption at 298 K and pressures greater than 0.1 MPa and up to 10 MPa was measured, using a static volumetric technique with a specially designed Sievert’s apparatus. The apparatus was previously tested to prove to be leak free and proven for accuracy through calibration by using LaNi5, AX-21, zeolites, and IRMOFs at 298 K. All isotherms matched the known values. Prior to measurements, the samples were degassed in vacuum at 473 K for at least 12 h. 3. Ab Initio Molecular Orbital Computational Details Molecular orbital (MO) studies on adsorption of spillover hydrogen atoms on single-wall carbon nanotubes were investigated and reported elsewhere.29 In this study, similar MO studies were extended to the isoreticular metal-organic framework A model of IRMOF-8 shown in Figure 1. The Gaussian 03 package30 and Cerius2 molecular modeling software31 were used for all MO calculations. Geometry optimizations were performed at the Hartree-Fock (HF) level first, then binding energies were performed at the density functional theory (DFT) level, using effective core potentials (ECPs).32-35 The optimized structures were used for bond energy calculations according to the following expression

Eads ) EIRMOF-H - EIRMOF - EH

MOF model site

(1)

4. Results and Discussion 4.1. Molecular Orbital Calculation Results. The computational model used for IRMOF shown in Figure 1 is the smallest repeating unit found in IRMOF-1, with the -CO2 unit terminated with two hydrogen atoms. The molecular orbital computation results are given in Table 1. It is seen that the H atom can form bonding with all the sites on the IRMOF structure (since all Eads values are negative), although the bond energies fell in a wide range from -3.26 to -49.6 kJ/mol. Thus, the sites on IRMOF are energetically heterogeneous. It is expected that the measured heats of adsorption would be over all values and would be in this range of energies. The lowest hydrogen binding energies are found in the central Zn4O cluster of the IRMOF structure, i.e., 3.26 kJ/mol on Zn and 3.60 kJ/ mol on O. The next set of hydrogen binding energies, which are in the medium range, are found on C1 and C2, i.e., 7.66 kJ/mol on C1 and 15.15 kJ/mol on C2; and the highest set of values are found on O2, C3, and C4, i.e., 40.33 kJ/mol on O2, 41.82 kJ/mol on C4, and 49 kJ/mol on C3. The binding energies between the H atom and MOF have not been studied previously either experimentally or computationally. However, results of a number of studies have been published for the binding energies between the H atom and various carbon materials, including graphite and single-wall carbon nanotubes. A comparison between our results and those obtained on these carbons is of interest. Mitchell et al.36 studied the spillover of H atoms on metal-supported carbon samples (e.g., Pt/C) by both inelastic neutron scattering and computation. By using coronene (C24H12) as a graphite model in their computation, the following binding energies were obtained: 9.65 kJ/mol for H on the “top site” (of the basal plane), 13.9 kJ/mol for H on the “hollow site”, and 21.7 kJ/mol for H on the “bridge” site. These results were in agreement with their experimental results on the vibrational levels in the neutron scattering data. Their results are close to the low end of our results for H binding on carbon sites on MOF. The binding energies for H on single-walled carbon nanotubes depend on H occupancy, tube diameter, helicity (or chirality), and location (endohedral vs exohedral).29 A wide range of H binding energies have been reported in the literature.29 The range of the high binding energies on the MOF sites falls completely within the reported values on carbon nanotubes. The comparison above indicates that our results are reasonable. 4.2. Apparent Heats of Adsorption. The isosteric heat of adsorption can be calculated from the adsorption isotherms for

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Figure 2. Low-pressure H2 equilibrium adsorption isotherms on the bridged IRMOF-8 sample at 298 (]), 323 (9), and 348 K (4).

Figure 3. Plots of ln(P) vs T-1 at different H2 adsorption amounts at low pressures (573 K).20 They found that the hydrogen uptake increased with temperature. A positive heat of adsorption (∼33 kJ/mol) was obtained from the hydrogen isotherms. This result could be attributed to the much higher temperatures used in their experiments than ours (298-348 K). As the temperature is further increased (>573 K), more and stronger bonds between hydrogen atoms and more energetic sites on carbon could be formed, leading to increased amounts adsorbed. Such strong C-H bonds cannot be formed at around 298 K, and can only be broken by heating to 873 K.37 The process in the formation of these stronger bonds is endothermal (requiring energy input). Hence the apparent heats of adsorption were positive in their cases. We measured the heats of adsorption of hydrogen on the bridged IRMOF-8 sample at around 298 K. The adsorption of hydrogen atoms on the surface sites of IRMOF-8 was spontaneous, and the interaction between hydrogen atoms with IRMOF-8 was relatively weak at 298 K because our hydrogen isotherms were shown to be totally reversible at 298 K.7-9 Like physical adsorption, the interaction would be further weakened with increasing temperature. So the adsorption amounts decreased with increasing temperature. The adsorption process is exothermal, hence the apparent heats of adsorption were negative in this study. 4.3. Adsorption Rates and Apparent Activation Energy for Surface Diffusion. Hydrogen dissociation on Pt is a very fast process, which occurs readily at room temperature. Surface diffusion of atomic hydrogen has been widely suggested to be the rate-determining step for the hydrogen spillover process.17-26 Our results would support this suggestion. In this study, we found that the adsorption rates over the Pt/AC catalyst were faster than that over the bridged IRMOF-8 sample. Furthermore, IRMOF-8 was the predominant component in the bridged IRMOF-8, while Pt/AC catalyst was very small (only 10 wt %). Therefore, it is clear that surface diffusion on IRMOF-8 should be the rate-determining step in our model. Thus, the kinetics of spillover may be characterized by a surface diffusivity (D) or diffusion time constant (D/a2, where a is the characteristic radius of the sphere for spillover). From the diffusion time constants at different temperatures, the activation energy for surface diffusion may be obtained. To calculate the activation for surface diffusion (Ea, kJ/mol), the adsorption rates of hydrogen on the bridged IROMF-8 sample were measured. Since the adsorption sites on IRMOF are energetically heterogeneous, only an apparent activation energy for the system could be obtained. Figure 4 shows the uptake rates of hydrogen at various temperatures and at ∼80 Torr. As shown in Figure 4, the sample adsorbed hydrogen very rapidly at all temperatures at this low pressure (which was not true for uptakes at high pressures, as will be shown shortly). It took less than 20 s to reach equilibrium adsorption capacity at all temperatures studied. The adsorption rates increased with temperature. The temperature effect can be explained by the increase of diffusivity of atomic hydrogen on the surface of activation carbon and IRMOF-8. A model is needed for evaluating the diffusion time constants from the uptake rates. A two-dimension sectional plot of the spherical model for the bridged sample is shown in Figure 5. In this model, H2 is dissociated on the surface of the Pt particle, where equilibrium is maintained. The atomic hydrogen undergoes surface diffusion onto the surface of the activated carbon

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Li et al. where r, C, and D denote the radial distance from the center of the Pt source, the surface concentration of the spiltover hydrogen atoms, and the diffusion coefficient of the spiltover hydrogen, respectively.38 The initial and boundary conditions are such that the surface is initially clean and after time zero, hydrogen is equilibrated with the point source of Pt and undergoes diffusion to the sphere that is bounded by R2. Due to the lack of a simple solution for this problem, and the fact that we are interested in comparing the diffusivities at various temperatures and surface concentrations, we will use the available simplified solution for the case where the source is on the outer boundary rather than at the center. The diffusion time constant thus obtained (from the experimental uptake rates) will be consistently lower than the actual values; however, the information on the temperature and concentration dependences is correct. The initial and boundary conditions for the simplified case are

Figure 4. Hydrogen adsorption kinetics at different temperatures on the bridged IRMOF-8 sample (P ) ∼80 Torr). Q∞ is the equilibrium adsorption capacity at each temperature. Relative adsorption ) percent completion.

u ) 0, r ) 0, t > 0

(5a)

u ) aC0, r ) a, t > 0

(5b)

u ) r f(r), 0 < r < a, t ) 0

(5c)

where C0 is the constant concentration at the surface of the Pt sphere, a is the characteristic radius of receptor for spiltover hydrogen atoms, and f(r) is the initial distribution or zero in this case. The approximate solution for small times, or when Mt/M∞ < 0.3, is

()

Mt 4 Dt ) M∞ xπ a2

Figure 5. Two-dimension sectional plot of the spherical model for hydrogen spillover on bridged IRMOF-8 sample, including Pt/AC catalyst (AC: activated carbon support) bridged with a receptor sorbent.

( )

∂u ∂2u )D 2 ∂t ∂r

(3)

u ) Cr

(4)

(6)

where Mt and M∞ denote the total amounts of the spiltover hydrogen at time t and at equilibrium with Pt, respectively.38 From the kinetic data presented in Figure 4, D/a2 values at various temperatures can be calculated from eq 6. Surface diffusion is an activated process and the temperature dependence of surface diffusivity can be correlated by the Eyring equation:

( )

D ) D0 exp particle, with radius R1, followed by diffusion onto the surface of the IRMOF receptor. The average sphere of diffusion for the IRMOF receptor is taken as R2, which depends on the connectivity through bridging as well as the ratio of Pt/AC catalyst over receptor. Further discussion on the model will be given below. To estimate the surface diffusion time constants under different conditions, an approximate solution for the model is needed. Our main interest is in the dependence of the diffusion time constant on both temperature and surface concentration. Since the receptor is in excess (over the amount of catalyst), and the resistance for uptake rates is apparently due to a lack of connectivity to the receptor particles, we will characterize the system by a single diffusion time constant (D/a2), i.e., that on the receptor. Thus, the governing equation for surface diffusion is

1/2

Ea RT

(7)

where D0 is the surface diffusivity at zero loading, Ea is the activation energy for surface diffusion, R is the gas constant, and T is absolute temperature. D0, Ea, and R are all constants for a given system. Therefore, D is only a function of temperature T. The activation energy Ea can be obtained by an Arrhenius plot of ln(D/a2) against 1/T. The Arrhenius plot is shown in Figure 6. Good linearity of the plot is observed. The value of Ea for hydrogen adsorption on the bridged IRMOF-8 sample was calculated to be 9.3 kJ/mol from the slope of the plot. The relationship between the heat of adsorption and the activation energy for surface diffusion is important because, if it is known, surface diffusivity may be predicted.25 Sladek et al. have made a correlation of the literature data for such a relationship.26 Their correlation was made for both physical adsorption and chemisorption. They found that the activation energy for surface diffusion could be expressed as 1/n of the value of the hest of adsorption, where n ) 1, 2, or 3. For diffusion of H atoms on metals, n ≈ 3.25,26 In our case, the value of Ea was 9.3 kJ/mol, compared with the values of

H2 Spillover on Bridged Metal-Organic Frameworks

Figure 6. Determination of activation energy: plot of ln(D/a2) vs T-1 at a pressure of ∼80 Torr.

20-25 kJ/mol for heats of adsorption. Thus, the comparison with literature is a reasonable one. Hattori et al. obtained much higher activation energies for hydrogen diffusion over WO3-ZrO2 and SO4-ZrO2, which were 35.5 kJ/mol for Pt/WO3-ZrO2, and 84 kJ/mol for Pt/SO4-ZrO2, respectively.27,28 The high activation energies indicated rather strong interactions of atomic hydrogen with the surface sites. WO3-ZrO2 and SO4-ZrO2 are very strong solid acids (possessing strong Lewis acid sites) that act as efficient catalysts for isomerization, cracking, and alkylation of hydrocarbons.39,40 For the Pt-doped WO3-ZrO2 and SO4-ZrO2 samples, hydrogen atoms from the dissociation of H2 at the Pt site reach those Lewis acid sites and donate electrons to H+ ions. The H+ was further stabilized on an O atom near the Lewis acid site. Therefore, the interactions between the spiltover hydrogen with the surface Lewis acid sites of WO3-ZrO2 or SO4-ZrO2 were considerably stronger than our case. As a result, diffusion of hydrogen on the WO3-ZrO2 and SO4-ZrO2 surfaces would be difficult. This was evident from their kinetics data because the adsorption to equilibrium on the two samples took over 10 h. In addition, it can be expected that desorption of hydrogen from the strong acid surface sites would be very difficult, although the authors did not study the desorption behavior of hydrogen over Pt/WO3-ZrO2 and Pt/SO4-ZrO2. Our isotherms on the bridged IRMOF-8 sample were measured at much lower temperatures (298-348 K), and the adsorption was shown to be fully reversible at 298 K.8,9 The adsorption equilibrium time was less than 20 s at 298 K and at a similar pressure as that used by Hattori et al. (Figure 4). Therefore, the activation energy for hydrogen adsorption on the bridged IRMOF-8 sample should be much lower than that obtained by Hattori et al. Figure 7 shows the adsorption and desorption kinetics of hydrogen on the bridged IRMOF-8 at higher and various pressures (5-100 atm) and 298 K. The D/a2 values for both adsorption and desorption on the surface of the bridged IRMOF-8 at different pressures estimated from eq 6 are plotted as a function of hydrogen adsorption capacity or surface concentration. The plots are shown in Figure 8. In comparison with the adsorption kinetics at low pressures (Figure 4), the adsorption was much slower at high pressures (5-100 atm). As shown in Figure 7a, the adsorption rates decreased steadily with increasing pressure. The desorption rates were relatively faster than the adsorption rates, for the same pressure (Figure 7b). As can be seen from Figure 8, the D/a2 values dropped sharply at low loadings of hydrogen (at low pressures),

J. Phys. Chem. C, Vol. 111, No. 8, 2007 3409 and became nearly constant at >2 wt % hydrogen capacity. A similar trend was also observed for the desorption, i.e., D/a2 declined with hydrogen amount adsorbed. These results indicate that the main mechanism for desorption would be through the spiltover hydrogen atoms that diffused from the activated carbon or IRMOF-8 receptor to the Pt sites where the hydrogen atoms recombined to hydrogen molecules and desorbed from the metal at 298 K (i.e., reverse spillover). The reverse spillover phenomenon has been widely observed and it has been used to interpret its important roles in surface characterization and also some catalytic reactions, although the mechanism of reverse spillover still remains unknown.41-43 4.4. Hydrogen Spillover Model and Derived Equilibrium Isotherm for Spillover. Our previous papers showed that the hydrogen adsorption isotherms on bridged AX-21 and IRMOFs appeared to be nearly linear (up to the highest pressures measured, 100 atm) at 298 K.7-9 The linear isotherms are very different from that of physical adsorption, which is characterized by an isotherm concave to the pressure axis, e.g., Langmuirian type. Therefore, our results cannot be explained by the traditional adsorption models such as that of Langmuir. The mechanistic model for hydrogen spillover remains poorly understood. On the basis of the hydrogen adsorption isotherms and the kinetic results, a model will now be formulated based on the experimental data. Figure 5 shows a two-dimensional model for the bridged IRMOF-8 material. A Pt particle is located at the center of a circle of the carbon particle (i.e., activated carbon support) with radius R1, which is sitting on a larger circle of MOF with radius R2. R1 is constant, while R2 is an average distance for spillover on the receptor. So R2 should be the radius of the area that is equal to the total reachable surface area of the receptor divided by the number of Pt particles. As such, R2 should depend on the ratio of the amount of the receptor to the amount of Pt/AC catalyst. Importantly, it also depends on the connectivity, or the bridges that are introduced by our bridgebuilding technique. We have previously shown that constructing carbon bridges between the carbon and MOF particles can enhance the connectivity and hence substantially increase the hydrogen storage capacities.7-9 The Pt particle is covered with hydrogen atoms in equilibrium with gaseous molecular hydrogen. The surface concentration of H atoms on Pt (CPt) depends only on H2 pressure at a constant temperature (298 K). Let us assume that there is an equilibrium constant K1 that relates the surface concentration of H on Pt to that on the activated carbon support (CAC):

K1 )

CAC CPt

(8)

Likewise, K2 is the equilibrium constant between carbon and the neighboring MOF:

K2 )

CMOF CPt

(9)

Here, K1 and K2 may also be regarded as partition coefficients. These constants depend on the chemistry of the two surfaces involved, and should be temperature dependent. They can, in principle, be measured independently. At equilibrium, the total hydrogen adsorption amount can be expressed as follows:

q ) K1qPt +

()

R2 3 Kq R1 2 Pt

(10)

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Li et al.

Figure 7. Rates of adsorption (a) and desorption (b) at different pressures on the bridged IRMOF-8 sample (T ) 298 K). Q∞ is the equilibrium adsorption (a) or desorption (b) amount at each pressure. Relative adsorption ) percent completion.

Figure 8. D/a2 as a function of H2 uptakes at 298 K for the bridged IRMOF-8 sample: (2) adsorption and (9) desorption.

Figure 9. Diffusion distance R (or a) as a function of H2 uptake. Filled triangles indicate the data derived from Figure 8 assuming constant D.

where qPt is the equilibrium adsorption amount of H atoms on the Pt particle, which is proportional to xPH2:15,44

of adsorption amount q, as shown in Figure 9. The dependence of R2 on q may be represented by the following empirical relationship:

qPt )

k1xPH2 1 + k2xPH2

R2 ) k′q1/3

(11)

In eq 10, we have neglected a term, qPt, i.e., the amount adsorbed on the Pt metal. This is valid since the amount of Pt is very small and its contribution to the total amount adsorbed is also small, particularly at high pressures. In cases when this is not valid, the term can be included, and the final isotherm will remain in the same form. A most interesting phenomenon for surface diffusion is its concentration dependence.25 Surface diffusion is the result of a hopping process, for both physical adsorption and chemisorption of small molecules or atoms. Within the monolayer coverage, the surface diffusivity usually increases with surface concentration. The concentration dependence has been explained satisfactorily by models by Higashi et al.45 and Yang et al.46 The concentration dependence has been discussed in detail elsewhere.25 The results in Figure 8 showed that the diffusion time constant, D/a2, decreases sharply with surface concentration. This result clearly indicates that the diffusion distance, a (or R2 in Figure 5), was increasing with surface concentration. If we assume that the diffusion coefficient (D) of H atoms is constant, from the data in Figure 8, we could plot R as a function

(12)

Introducing eqs 11 and 12 to eq 10 yields the following isotherm for spillover:

q)

K1k1xPH2 1 + k2xPH2 - K′k1xPH2

(13)

where K′ ) (k′/R1)3K2. In most cases, k2xPH2is very small. Therefore, eq 11 may be simplified as follows:

q=

K1k1xPH2 1 - K′k1xPH2

(14)

Equation 13 is the final isotherm for adsorption resulting from spillover. All of the constants involved could, in principle, be measured independently. The shape of the isotherm is determined by the relative magnitudes of the two terms in the denominator, k2xPH2 vs K′k1xPH2. The isotherm will be concave in shape (i.e., concave toward the pressure axis) if k2

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xPH

> K′k1xPH2 or k2 > K′k1. The isotherm can become convex (i.e., against the pressure axis) if k2xPH2< K′k1xPH2 or k2 < K′k1. The seemingly linear isotherms that we reported earlier7,9 can be explained by this isotherm. In addition, as the pressure PH2 is further increased, the term k2xPH2 - K′k1xPH2 will be greater than 1. At very high pressures, the adsorption amount q will be a constant (corresponding to saturation adsorption capacity): 2

q=

K1k1 k2 - K′k1

(15)

In addition, the average diffusion distance (R2) should have a limit, which depends on the connectivity through bridging as well as the ratio of Pt/AC catalyst over receptor. Thus, a linear isotherm should eventually level off at very high pressures based on our model. An experimental system with the capability of very high pressures would be needed to verify the predicated shape of the isotherm at very high pressures. An important result obtained form the experimental data and the analysis above is the concentration (qH2) dependence of R2 (Figure 9). This result indicates that the connectivity for spillover increases as more hydrogen is spilt over, and it levels off at higher surface concentrations. This result indicates, in turn, that the adsorbed hydrogen actually serves as bridges for further spillover. Indeed, adsorbed water molecules47 as well as adsorbed hydrocarbon molecules such as perylene48 have also been observed to serve as bridges for spillover. 5. Conclusions H2 molecules were dissociated rapidly on the Pt species, and the dissociated hydrogen diffused slowly to the various surface sites of the receptors. The overall heat of adsorption of H2 on the bridged IRMOF-8 material decreased with surface coverage, falling in the range -24.8 to -20 kJ/mol at low pressures (0-1 atm). The overall heats of adsorption were in reasonable agreement with the ab intio molecular orbital results for bonding of H atom on various possible sites on the surface of IRMOF-8. The apparent activation energy of surface diffusion was measured to be 9.3 kJ/mol. The diffusion time constant (D/a2) decreased sharply with increasing pressure (or surface concentration). This result provided strong evidence that the average diffusion distance (a) increased with surface concentration. This result, in turn, indicates that the adsorbed hydrogen served as new bridges for further spillover. Desorption was relatively faster than adsorption under the same conditions. A mechanistic model was formulated that could be used to interpret all experimental results. Acknowledgment. The authors acknowledge the funding provided by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy within the Center of Excellence on Carbon-based Hydrogen Storage. References and Notes (1) Schlapbach, L.; Zu¨ttel, A. Nature 2001, 414, 353-358. (2) Dillon, A. C.; Heben, M. J. Appl. Phys. A 2001, 72, 133-142.

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