DFT Study of the Hydrogen Spillover Mechanism on Pt-Doped

Jul 23, 2009 - The mechanism of hydrogen storage by atomic hydrogen spillover on a Pt-doped graphite (0001) surface was studied by means of density fu...
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J. Phys. Chem. C 2009, 113, 14908–14915

DFT Study of the Hydrogen Spillover Mechanism on Pt-Doped Graphite George M. Psofogiannakis and George E. Froudakis* Department of Chemistry, UniVersity of Crete, PO Box 2208, Voutes, Heraklion Crete, 710 03 Greece ReceiVed: April 01, 2009; ReVised Manuscript ReceiVed: June 23, 2009

The mechanism of hydrogen storage by atomic hydrogen spillover on a Pt-doped graphite (0001) surface was studied by means of density functional theory. The coronene molecule and a Pt4 cluster were used as primary models for the carbon surface and the metal nanoparticles, respectively. It was found that H2 dissociates spontaneously on a Pt cluster, but the dissociated H atoms have to overcome excessively large energy barriers (>60 kcal/mol) to migrate from Pt to the graphite surface. H atoms on a graphite (0001) surface can be either chemisorbed or physisorbed. The transition from the chemisorbed to the physisorbed state happens at sufficiently high rates. In the physisorbed state, H atom diffusion is essentially free of energy barriers. Physisorbed H atoms readsorb selectively adjacent to other chemisorbed H atoms. Our results indicate that H atom migration from a transition metal to the graphite surface is rate-limiting in the overall spillover process. The implications of the findings are discussed. Introduction Efficient hydrogen storage continues to be the bottleneck for the cost-effective development of fuel cell systems.1,2 Carbon materials have long been identified as potential candidates for adsorptive hydrogen storage. The storage of hydrogen in carbon materials is broadly categorized into two adsorption modes:1 physisorption of H2 molecules, based on weak Van der Waals interactions; and chemisorption of H atoms, caused by the dissociation of H2. The sorption mode of H2 on pure carbon materials is reversible weak physisorption. However, extensive experimental and theoretical work on various materials has shown that high adsorption capacity through H2 physisorption is rather unlikely1 at near-ambient temperatures, required for practical applications. The hydrogen sorption capacity at 298 K and 100 atm of all known sorbents that store H2 in molecular form is2 lower than 1 wt %. Significant enhancement of the hydrogen storage capacity can be brought about by doping the porous materials with small amounts of metals that can act catalytically. This has been shown by very promising experimental results for the adsorption of H2 in a variety of metal-doped sorbents. Initially, Lueking and Yang3 observed that the presence of residual catalyst on carbon nanotubes increased the hydrogen capacity of the material by 40%. Further work4 with the multiwall carbon nanotubes/ NiMgO material resulted in an adsorption capacity of 3.7 wt % at 69 bar and 300 K. In another study,5 a 2- to 3-fold enhancement in the storage capacity of activated carbons was demonstrated by mixing the materials with a palladium catalyst, resulting in absolute capacities of 1.8 wt %. Experimental demonstrations of hydrogen spillover have been reported for a variety of carbon materials, such as graphite nanofibers,6 activated carbons,5,6 single-wall carbon nanotubes,5,6 multi-wall carbon nanotubes,4,6,7 metal-organic frameworks8 and covalentorganic frameworks.8 Spillover hydrogen atoms on carbon supports of metal catalysts were directly identified by inelastic neutron scattering.9 * Corresponding author. Phone: (+302810) 545055. Fax: (+302810) 545001. E-mail: [email protected].

Metal doping results in the following phenomena,10 collectively termed as the spillover mechanism: (1) H2 molecules dissociate on the metal catalyst particles, (2) H atoms migrate from the metal catalyst particles to the carbon substrate material, and (3) H atoms diffuse on the substrate by a site-hopping mechanism. Despite the fact that these elementary steps are generally considered to be operative during the process, neither the mechanism nor the factors that affect the storage capacity by spillover, are well understood. Recent experimental studies have reported that increased hydrogen storage capacity can be induced through altering the chemical composition of the spillover system. Studies by Yang et al.5,8,11 have shown that carbon bridges, formed via carbonization of sugar molecules in a spillover material that contains Pt or Pd, lead to enhanced hydrogen uptake. Furthermore, a significant enhancement in the storage capacity of Pt-doped activated carbons was induced by chemically modifying the material to add oxygen functional groups.12 Another observation that creates further confusion about the mechanism of hydrogen spillover is the experimental work of Jain et al.,13 in which no increase in hydrogen storage capacity was observed when a graphite nanofiber material was doped with Pt nanoparticles. Previous computational studies of the interaction of atomic H with the graphite (0001) surface, being one of the primary subjects in this work, will be discussed in further detail. Atomic H can be either physisorbed or chemisorbed on graphite. The physisorption of H atoms on graphite, using the H on coronene (C24H12) model system, has been previously studied14 at the MP2 level. The physisorption interaction energy was computed to be 0.92 kcal/mol with H being at the hollow site of the center of the benzene ring. The authors predicted an energy barrier of only 0.09 kcal/mol for the migration of physisorbed H to an adjacent hollow site. On the basis of the computed energies, it was predicted that H atoms are mobile on the surface, even at temperatures close to 0 K. The interaction of H atoms on the graphite (0001) surface was studied15 by DFT-GGA (PW91) computations (see the Appendix for definitions of acronyms), using coronene as a model for the graphite surface. The presence of both shallow and a deep chemisorption wells was confirmed. The estimated

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Hydrogen Spillover Mechanism on Pt-Doped Graphite interaction energies were 1.38 kcal/mol for the physisorbed state and 13.1 kcal/mol for the chemisorbed state, both at on-top sites. The results suggested that the chemisorption process is accompanied by extensive surface relaxation as the bonding C atom is displaced outward, manifesting sp2 to sp3 rehybridization at the binding site. The interaction of H atoms with the graphite (0001) surface has also been studied16 with periodic DFT calculations and plane-wave basis sets. The results suggested that the potential energy surface is characterized by physisorption (1.85 kcal/mol) and (15.5 kcal/mol) wells. They also determined an approximate energy barrier to chemisorption (4.6 kcal/mol) from the physisorbed state. The authors indicated that the well depth of the weak physisorbed state could not be accurately calculated due to the well-known failure of DFT methods to describe Vander-Waals interactions properly. There remains a pressing need to understand the mechanism of hydrogen spillover and quantify the rates of the relevant processes at the atomic level. In the present work, we used DFT calculations to quantify the energetics of all the atomic-scale processes in the mechanism of spillover. We chose a typical spillover system composed of Pt metal nanoparticles and graphite. The coronene molecule (C24H12) was used as a model for the graphite (0001) surface, while small Pt clusters of maximum four metal atoms were used to simulate the metal phase. The coronene molecule has been previously14,15 found to be a good model for the graphite (0001) surface. Subsurface C layers have no significant effect on adsorbed species because of the large interlayer distance between weakly bound graphene layers in graphite.14,15 Furthermore, the C-H bond involves only a single C atom, whereas the surrounding C atoms are not distorted during bond formation.14,15 Thus, an excessively large surface model is not required to accurately describe the interaction of atomic H with the graphite (0001) surface. The small size of the system allowed us to perform calculations with all system components (Pt cluster, coronene molecule and H atoms), vibration analysis for the coronene-H system, and reaction energy scans to compute energy barriers. These calculations are computationally demanding and would have been practically impossible for a much bigger model system. Vibration analysis was found to be essential for the description of the kinetics of H diffusion on graphite and has not been included in any previous model of this process. The effects of using a small Pt cluster will be further discussed in the Results section, and it will be shown that the conclusions of the present work should not be affected by the small size of the system.

J. Phys. Chem. C, Vol. 113, No. 33, 2009 14909 TABLE 1: Experimental28-31 and Calculated (riDFT/TPSS/ def2-TZVP) Bond Lengths and Atomization Energies for Pt2, PtH, PtC, and C6H6 bond Pt2 PtH PtC C 6 H6

Pt2 PtH PtC C6 H 6

exptl

Bond Length (Å) Pt-Pt 2.37 Pt-H 1.53 Pt-C 1.67 C-C 1.39 C-H 1.09 Eatomization (kcal/mol) 72.4 79.3 144.8 1304.8

calcd 2.34 1.53 1.68 1.40 1.09 74.3 80.7 150.9 1311.5

To benchmark our theoretical model (riDFT/TPSS/def2TZVP) for systems involving C, H, and Pt, atomization energies for Pt2, Pt-H, Pt-C, and a benzene molecule were calculated through the defining expression

Eatomization ) ΣEatoms - (Emolecule + ZPE)

(1)

and compared with experiment (Table 1). The results indicate that the model is very successful in describing Pt-Pt, Pt-H, Pt-C, and C-H bonds in terms of both geometries and energies. Results and Discussion Interaction of H with Coronene. The interaction of a single H atom with coronene (C24H12) was studied first. By performing full optimizations with DFT-d, it was found that there exist two minima. There is a deep chemisorption well (Figure 1, inset, left structure), where H is adsorbed on top of a C atom that is displaced outward from the molecular surface. There is also a physisorption well, where the H atom lies at the center of the middle ring around 3 Å from the closest C atoms (inset, right structure), in good agreement with the MP2 results of Bonfanti et al.14 This result is physically meaningful because the hollow site can be expected to maximize dispersive interactions with all C atoms of the ring. We found that DFT calculations without

Computational Methods DFT calculations were performed using Turbomole.17 The resolution-of-the-identity (RI) approximation18 was used in all calculations for computing the electronic Coulomb interaction. DFT methods do not account for dispersion interactions.19 Thus, empirical dispersion corrections of the type proposed by Grimme20,21 were added to the calculations that involved physisorbed H atoms on a graphite (0001) model surface. The DFT-d (DFT-dispersion) calculations were performed using the B-P86 functional.22,23 The nonempirical meta-GGA exchangecorrelation functional of Tao, Perdew, Staroverov, and Scuseria (abbreviated TPSS24,25) was used in all calculations that involved metals (Pt). In all cases, the basis set that was employed was the def2-TZVP26 for all atoms, with the corresponding effective core potential for Pt and the corresponding auxiliary basis sets27 for the RI method.

Figure 1. Electronic energy versus C-H bond distance for the interaction of a single H atom with coronene. The inset arrows show electronic and Gibbs energy changes between the chemisorbed state, the physisorbed state, and the TS. All energies are referenced to the physisorption minimum. Inset optimized structures (left to right): chemisorption minimum, transition state, and physisorption minimum. The line connecting the points is a guide to the eyes.

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Figure 2. The diagram shows the electronic energy (E), enthalpy (H) at 298 K, and Gibbs energy (G) at 298 K of the chemisorbed state, all with respect to the physisorbed state, as well as the breakdown of energy components. The quantities UVIB and T∆S were calculated for T ) 298 K.

dispersion corrections erroneously predicted the physisorption minimum at the on-top site, which could not be avoided in some previous DFT works.15,16 The middle inset structure in Figure 1 corresponds to the transition state (TS) between the physisorbed and chemisorbed states. At the TS (C-H distance ∼ 1.8 Å), and up to a distance of 2.5 Å away from the C atom, the H atom still lies on top of the C atom. The curve in Figure 1 shows the binding energy of a single H atom on coronene as a function of the distance from the bonding C atom, referenced to the energy of the physisorbed state. The reaction energy scan was performed by fixing the C-H distance and optimizing the structure with respect to all other degrees of freedom. The binding energy of the chemisorbed state was calculated to be 16.6 kcal/mol. The binding energy of the physisorbed state was 0.70 kcal/mol and compares well with an existing experimental value32 for physisorbed H on a graphite layer (0.90 kcal/mol). Chemisorption of the physisorbed H atom requires overpassing a 3.0 kcal/mol energy barrier, whereas the transition from the chemisorbed to the physisorbed state requires an 18.7 kcal/mol energy barrier. The calculated chemisorption energy (16.6 kcal/mol) is in relatively good agreement with the slab calculation of Sha and Jackson16 (15.5 kcal/mol). The expectation value of the spin-squared operator , for the selected DFT method for H chemisorbed on coronene was 0.767, very close to the ideal value of 0.75. This indicates no significant admixture of higher spin states. This is important because spin contamination problems have been cited33 in ab initio calculations of H interaction with aromatic hydrocarbons. Frequency Calculations and Gibbs Energy Analysis. Frequency calculations were subsequently performed to study the thermodynamic equilibrium between physisorbed and chemisorbed H atoms on a graphite (0001) surface. The riDFT-d/ BP86/def2-TZVP level was used. The calculated vibrational frequencies are available from the authors upon request. Only real frequencies were observed for the chemisorbed and physisorbed converged minima. Two low frequencies, corresponding to translations parallel to the surface, were observed for the physisorption minimum. Visualization of the DFT-calculated frequencies showed that the chemisorption minimum had two frequency modes corresponding to the vibration of the C-H bond (2655 cm-1 for normal vibration and 1176 cm-1 for vibration parallel to the molecular plane). Experimentally, these frequencies have been determined34 for H-covered HOPG via

high-resolution electron energy loss (HREEL) spectroscopy to be 2650 and 1210 cm-1, in good agreement with the present results. The diagram of Figure 2 shows the ZPE, thermal vibrational, and entropy contributions to the energy difference between the physisorbed and chemisorbed states. In both Figures 1 and 2, all quantities (electronic energy, A; enthalpy, H; and free energy, G) are reported with respect to the physisorbed state. ZPE was calculated using the following expression,35,36 where the summation runs over all frequencies, νi (Hz), and h is Planck’s constant:

ZPE )

∑ i

hνi 2

(2)

The vibrational thermal energy was also calculated through the expression35,36

Uvib )

hν

∑ (ehν /k T i- 1) i

(3)

i B

where kB is Boltzmann’s constant. The standard state entropies are given by35,36

Svib ) kB

hν

∑ k T(ehν /k iT - 1) - ln(1 - e-hν /k T) i

i B

i B

B

(4) The Gibbs free energy difference between the physisorbed and chemisorbed states can be calculated as35,36

∆G ) ∆H - T∆S

(5)

As expected, the ZPE of the physisorbed state was significantly lower as compared to the chemisorbed state because the latter has a strong bond to the surface. Using the computed vibrational frequencies, the ZPE correction to the energy difference between the physisorbed and chemisorbed states was calculated to be 4.4 kcal/mol. The vibrational thermal energy correction at 298 K contributed -0.9 kcal/ mol to the enthalpy difference. Therefore, the enthalpy change, ∆H, between the

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Figure 3. Semilogarithmic plot of equilibrium distribution between physisorbed and chemisorbed H atoms on graphite. The line connecting the points is a guide to the eyes.

Figure 4. Calculated residence time of a chemisorbed H atom on a graphite (0001) site as a function of temperature. The line connecting the points is a guide to the eyes.

chemisorption and physisorption minima amounts to 12.4 kcal/ mol at T ) 298 K. The entropy of the physisorbed state was calculated to be greater by about 7.2 cal/(mol K). This result is expected on the basis of the increased mobility of the weakly adsorbed H atom parallel to the surface. Thus, the Gibbs free energy difference, ∆G, for the transition from the chemisorbed to the physisorbed state at 298 K amounts to 10.3 kcal/mol (Figures 1, 2). It is significantly smaller than the enthalpy change, owing to the entropy contribution. The equilibrium concentration of physisorbed and chemisorbed H atoms can be given by the relationship35,36

sorbed state and the TS, the differences are not particularly pronounced. The ZPE, vibrational thermal energy, and entropy of the transition state were calculated for the TS using eqs 2-4, where the negative frequency is excluded from the calculations.35,36 The electronic energy change, from the chemisorbed state to the TS, as shown in Figure 1, is 18.7 kcal/mol. On the basis of the frequencies of the initial and transition states, the ZPE correction to the electronic energy change is 4.2 kcal/mol. This corresponds to the extra ZPE of the initial state due to the C-H bond stretching. The vibrational thermal energy correction was also calculated, but its value (0.14 kcal/mol at 298K) was insignificant. The entropy of the TS was then calculated. The entropy difference from the chemisorbed state is very small (increased by 0.4 cal/(mol K)). This result is expected on the basis of the fact that the vibrational frequency that disappears from the chemisorbed state is quite large (2655 cm-1) and does not contribute much to the total entropy, while all other frequencies are not significantly affected. At 298 K, the Gibbs free energy of activation (∆G‡ ) ∆H‡ - T∆S‡), is 14.6 kcal/ mol (illustrated in Figure 1). Zecho et al.34 have found experimentally through leading-edge analysis of thermal desorption spectra that the activation energy for H desorption from HOPG is ∼14 kcal/mol. This value is close to the DFTcalculated free energy barrier. The rate constant for the transition from the chemisorbed to the physisorbed state can be calculated using the equation35,36

θphys -∆G ) exp θchem RT

(

)

(6)

At 298 K, using ∆G ) 10.3 kcal/mol in eq 6, the equilibrium distribution can be calculated to be θphys ∼ 3 × 10-8 θchem. Thus, at room temperature, the thermodynamic driving force for desorption and diffusion of chemisorbed H atoms is very small. At higher temperatures, however, the equilibrium is shifted toward higher concentrations of physisorbed H atoms. By calculating ∆G for a variety of temperatures, we obtained the plot of the distribution versus temperature, as shown in Figure 3 (semilogarithmic plot). It is evident in the figure that as the temperature is increased, the thermodynamic driving force for the transition from chemisorbed to physisorbed H is increased. TS and Rate Constant for H Transition from Chemisorbed to Physisorbed State. An important quantity of interest is the rate of chemisorbed H atoms passing to the physisorbed state or, equivalently, the mean residence time of a chemisorbed H atom on the surface. To calculate this quantity, the transition state for the desorption (chemisorbed to physisorbed transition) of an isolated chemisorbed H atom was found, and a frequency calculation was performed for the TS at the riDFT-d/BP86/def2TZVP level of theory. The TS corresponds to the maximum of the plot shown in Figure 1 and was found by performing closely spaced restricted optimizations with respect to the C-H distance. Numerical frequencies were then calculated for the optimized structure of the top of the curve. At the TS, the H atom still resides on top of the C atom, but at a distance of ∼1.8 Å (Figure 1). It was verified that this structure possesses a single negative imaginary frequency and is, thus, a TS on the PES. Furthermore, at the TS, the frequency that corresponds to C-H bond stretching has been transformed into the negative frequency, which signifies the nature of the TS, corresponding to desorption of the chemisorbed H atom. Although some other frequencies are also affected by the structure change between the chemi-

k)

(

k BT ∆G* exp h RT

)

(7)

The mean residence time of a chemisorbed atom is the reverse of the above quantity and is plotted in Figure 4 as a function of temperature. H Diffusion on Graphite. The above results indicate that at intermediate temperatures, the process of H diffusion on graphite is facile. The free energy barrier to desorption (14.6 kcal/mol) is such that the process happens thermally with sufficiently high rates. For example, at 298 K, the mean residence time of a chemisorbed hydrogen atom is 8.6 × 10-3 s, whereas at 398 K, it is 1.2 × 10-5 s. Once a chemisorbed atom crosses the barrier and enters the physisorbed state, the barrier to diffusion parallel to the surface (48 kcal/mol) is much greater than any other elementary step in the spillover process. Thus, the conclusions of our work cannot be affected by small cluster-size effects. Discussion. The present work suggests that the rate-limiting step in the mechanism of hydrogen spillover for a Pt-doped graphite material that contains no other components (such as carbon bridges or functional groups) is the migration of H atoms from the metal nanoparticles to the substrate carbon surface. The results can aid in revisiting previous conclusions and observations regarding the mechanism of hydrogen spillover. In the computational work of Chen et al.,10 the spillover mechanism was studied. On the basis of the high diffusion barriers of chemisorbed H atoms on graphite and nanotubes, it was suggested that H atoms can diffuse on the carbon surface in the physisorbed state. The authors postulated that possibly “cold” H atoms can be trapped in the physisorption well upon migration from the metal nanoparticle. This postulate would further raise the energy requirements of the migration step because the barrier to migration would be excessively high. Our results indicate that such a postulate is not necessary because chemisorbed H atoms can thermally enter the physisorption state with sufficiently high rates. The experimental results of Jain et al.,13 which showed no enhancement in hydrogen uptake of graphite by Pt doping, can also be justified. It is inferred from the calculations that the spillover mechanism cannot operate in a system that is composed entirely of metal nanoparticles and the carbon support because H atoms will not migrate to the carbon surface, except possibly at very high temperatures. On the other hand, in some experiments, other components were introduced into the spillover material, such as carbon bridges5,8,11 and oxygen functional groups.12 These components are expected to modify the metal-carbon interfaces. The observation of enhanced storage by spillover in these cases is very possibly the result of reduction of the energetic requirements for the migration of atomic H from the metal to the carbon phase. Conclusions Our first-principles study of the spillover mechanism of hydrogen on a Pt-doped graphite surface can be summarized in the following conclusions: 1. A single H atom on a graphite (0001) surface has a chemisorption minimum with a binding energy 16.6 kcal/mol where it is bound on top of a C atom. There is also a physisorption minimum at a ring-center site with a binding energy of 0.70 kcal/mol. 2. DFT energy, ZPE, and entropy calculations show that the Gibbs free energy of the physisorbed state is 10.3 kcal/mol greater than the chemisorbed state at 298 K. This value is reduced as the temperature is increased, thus increasing the thermodynamic driving force for the transition from the chemisorbed to the physisorbed state. 3. The reaction coordinate for desorption of a chemisorbed H atom to the physisorbed state follows the reduction of the C-H stretching frequency, which becomes negative at the transition state. The Gibbs energy of activation for desorption is 14.6 kcal/mol at 298 K. The mean residence time of a chemisorbed H atom before it becomes physisorbed is around 0.01 s at 298 K and decreases with increasing temperature. 4. The diffusion of a H atom on the graphite surface takes place at the physisorption regime. Physisorbed H atoms travel

Hydrogen Spillover Mechanism on Pt-Doped Graphite large distances on the surface due to the very low diffusion barrier (50 kcal/mol) have to be overcome. The migration of H atoms from the Pt cluster to the graphite surface is the rate-limiting step in the overall spillover process for systems composed exclusively of graphite and metal particles. In this regard, experiments that show increased hydrogen storage by spillover and contain other components in the system (such as “carbon bridges” or oxygen functional groups) possibly function by increasing the migration rate of H atoms from the Pt nanoparticles to the carbon surfaces. Acknowledgment. Financial support from the European Union ToK grant GRID-COMPCHEM (MTKD-CT-2005029583) is kindly acknowledged. Funding in part by the European Commission on DG RTD (FP6 Integrated Project NESSHY, Contract SES6-518271) is gratefully acknowledged by the authors. Glossary Acronyms DFT TZVP TPSS riDFT MP2 TS HOPG

density functional theory triple-zeta valence basis set augmented with polarization functions meta-GGA exchange-correlation functional of Tao, Perdew, Staroverov, and Scuseria resolution-of-the-identity approximation to DFT second-order Moller-Plesset perturbation theory transition state highly-ordered pyrolytic graphite

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