Molecular simulation of hydrogen adsorption in graphitic nanoÐbres

Roger F. Cracknell

Shell Global Solutions UK, Shell Research L td, Cheshire Innovation Park, PO Box 1, Chester,UK CH1 3SH

Received 3rd January 2001, Accepted 5th April 2001First published as an Advance Article on the web 10th May 2001

Rodriguez, Baker and co-workers (A. Chambers, C. Park, R. T. K. Baker and N. M. Rodriguez, J. Phys. Chem.B, 1998, 102, 4253 ; C. Park, C. D. Tan, R. Hidalgo, R. T. K. Baker and N. M. Rodriguez, Proc. 1998 US DOEHydrogen Program Review, (http : //www.eren.doe.gov/hydrogen/docs/25315toc.html) ; C. Park, P. E. Anderson,A. Chambers, C. D. Tan, R. Hidalgo and N. M. Rodriguez, J. Phys. Chem. B, 1999, 103, 10572) have reporteduptake of hydrogen in graphitic nanoÐbres (GNFs) of 40% by weight. If these results are conÐrmed, then thisclass of material could be a suitable storage medium for hydrogen for use in fuel cell vehicles. In order to testwhether these results are feasible, we report results for grand canonical Monte Carlo simulation of hydrogenadsorption in graphitic pores. A classical technique was employed but the results obtained were shown to beconsistent with previous path integral Monte Carlo calculations of Wang and Johnson (Q. Wang and J. K.Johnson, J. Chem. Phys., 1999, 110, 577 ; Q. Wang and J. K. Johnson, J. Phys. Chem. B, 1999, 103, 277). Theinteraction between hydrogen and the graphitic surface was modelled initially by dispersion forces. Thepredicted uptake (up to 1.5%) was much lower than the BakerÈRodriguez results. The results were found to befairly insensitive as to whether the hydrogen molecule was modelled as a Lennard-Jones sphere or a dumbbellÑuid with two Lennard-Jones sites. Two models for a hypothetical potential for chemisorption were also usedin the simulation. The potential was based on calculation of the interaction between atomic hydrogen and agraphitic surface. Adsorption of up to 17 wt.% was measured with the stronger model potential but there wasnegligible desorption at ambient pressure, making it impractical. A more plausible, though still hypothetical,potential gave loadings of up to 8 wt.% in the model system. These results are still much lower than theBakerÈRodriguez data in spite of the fact that there is no evidence to suggest that chemisorption actuallyoccurs in a real system.

1. Introduction

Carbon based adsorbents are a candidate class of material foradsorptive storage of hydrogen. The US Department ofEnergy hydrogen plan for fuel cell powered vehicles1 requiresa system weight efficiency (weight of stored weight)H2/systemof 6.5% and volumetric density of 62 kg m~3. Clearly thekinetics of adsorption and desorption must be acceptable also.

The results of Rodriguez and co-workers have created con-siderable interest since their original paper2 indicated that upto 2 kg of hydrogen may be adsorbed for every 1 kg of theirgraphitic nanoÐbre (GNF) adsorbent for initial conditions of112 atm and 298 K. Subsequent publications3,4 suggest a 40wt.% uptake which is still very signiÐcant. The GNF adsorb-ents are new materials produced by catalysed decompositionof carbon containing compounds ; they consist of graphiticplatelets, of mean diameter between 30 and 500 which areA� ,arranged either parallel, perpendicular or at an angle to theÐbre axis. The latter type, denoted “herringboneÏ, is found togive optimal adsorption ; the external surface of the Ðbre com-prises the edges of multiple stacked layers of graphene sheets.The presumption is that hydrogen can somehow intercalatewithin the graphite sheets. Turpin5 has reported lower valuesof uptake (D6.5%) in herringbone GNFs. The uptake mea-sured is very sensitive to the method of preparation.

Chen and co-workers6 have produced lithium and pot-assium doped carbon nanoÐbres (where the graphene sheetsare parallel to the Ðbre axis so as to give a tubular geometry)

that can adsorb around 14 and 20 mass% respectively atambient pressure and temperatures between 473 and 673 K,although one recent study7 has suggested that the measureduptake may in fact be due to adsorption of water. Heben andco-workers8 have looked at single walled carbon nanotubes(SWNTs) and have demonstrated that it is possible to store3.5È4.5 wt.% under ambient conditions in a SWNT where theadsorbed hydrogen is “cappedÏ by carbon dioxide at theentrance to the pore.

Modern molecular simulation techniques9 have been shownto provide invaluable insights into the properties of Ñuids con-Ðned in micropores. A considerable complication in the mod-elling of hydrogen adsorption arises from quantum e†ects.Wang and Johnson10,11 have applied path integral MonteCarlo (PIMC) techniques to investigate adsorption of hydro-gen on nanotubes and graphitic Ðbres. They conclude that noreasonable model for the physisorption of hydrogen in GNFscan explain the results of Rodriguez and co-workers.

Molecular hydrogen can exist in two forms depending onnuclear spin : the even-J and odd-J species, which are knownrespectively as para and ortho-hydrogen. In low temperaturecondensed phases, hydrogen molecules act as free rotors intheir ground rotational states, with para-hydrogen acting as aspherical atom-like entity whilst ortho-hydrogen could beviewed as having a far more elongated body. Liquid hydrogenis 100% para but hydrogen at room temperature is 75% orthoand 25% para. The PIMC calculations of Wang and Johnsonwere for adsorption of para-hydrogen and used a sphericalmodel for hydrogen. Given the amount of ortho-hydrogen at

DOI: 10.1039/b100144m Phys. Chem. Chem. Phys., 2001, 3, 2091È2097 2091

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room temperature, it is likely therefore that a two-centre(dumbbell-type) model for hydrogen might be more realisticfor ambient temperature adsorption.

One objective of this work has been to test the conclusionsof Wang and Johnson by modelling hydrogen as an elongatedmolecule as well as a sphere adsorbed within a slit-like poreof a GNF. Previous work on the adsorption of mixtures ofethane and methane has demonstrated that the structure ofparticles in narrow pores can have a signiÐcant inÑuence onÑuid behaviour.12 A classical simulation methodology hasbeen employed throughout and we have attempted to ascer-tain a posteriori the extent to which choice of simulation tech-nique a†ects the conclusions that may be drawn fromsimulations of this system.

A further major objective of this work has been to look atthe possible consequences of chemisorption of hydrogen ontographitic sheets. If indeed no reasonable physisorption modelcan explain the level of reported uptake by Rodriguez andBaker, then it is reasonable to look at the kind of forcesbetween adsorbent and adsorbate that would be required togive rise to high loadings. The analysis presented hereinshould not be construed as supporting the existence of suchforces.

2. Physisorption model

2.1. Methodology

In the grand canonical Monte Carlo method, the chemicalpotential (or gas fugacity), volume and temperature of thesystem are Ðxed and the simulation calculates the number ofparticles in the system and the conÐgurational energy corre-sponding to a particular choice of k, V and T . The method isdiscussed in detail in a number of books.13,14 As a Ðrstapproximation, the system was a classical one. This is likely tobe a tolerable approximation at ambient temperatures if theÑuid is not particularly dense. It is something we can test aposteriori by comparison with the conclusions of Wang andJohnson.10,11

HydrogenÈhydrogen interactions were modelled usingLennard-Jones potential.

uHH \ [4eHHCApHH

rB6

[ApHH

rB12D

(1)

where is the energy of the (pairwise) interaction betweenuHHLennard-Jones sites and and are the well depth energyeHH pHHand hard sphere diameter parameters for the interaction,respectively. Two sets of simulations were run, one set used asingle Lennard-Jones site to model the molecule (i.e. a spher-ical model) whilst the other set used a two-site model, with theinteractions summed over all siteÈsite interactions. Theparameters for the two-site model were devised according tothe following criteria :(i) The hydrogenÈhydrogen distance in the model was takento be the actual bond length.(ii) The hard sphere diameter for the 2 site model was approx-imated as

(pHH)2CLJ\ (pHH)Spherical[ 0.5 HÈH bond length

(iii) The well depth parameter, for the two-centre modeleHH ,was determined so as to give the same isosteric heat ofadsorption on a graphite surface at 298 K as the sphericalmodel. [Note that this is approximately a quarter of thespherical valueÈthere are now 4 siteÈsite interactions deter-mining the potential of interaction between the two hydrogenmolecules. The lack of spherical symmetry means that itwould not be expected to be exactly one quarter.]

Separate calculations suggest that simulated bulk propertiesremain essentially the same in moving from a single centre toa multi-centre model, however it is the equivalence in the

adsorbed phase which is more critical (Table 1). The potentialwas cut-o† at 2 nm and no long range correction was applied.

The model pore is assumed to be bounded by inÐnitestacked planes of graphitic sheets (Fig. 1), the separation ofwhich is D\ 0.335 nm. We have deÐned the pore width, H, asthe carbon to carbon distance on opposing pore walls. Thismay have a number of values depending on the method ofpreparation of the GNF. The smallest value that H can haveis equal to D. Because the simulation employs periodic bound-ary conditions, the pore is modelled as being inÐnite in twodimensions. The simulation does not therefore model any edgee†ects.

The interaction between the hydrogen and each wall of themicropore was given by the “10-4-3 Ï potential of Steele.16

uCH\ 2pos eCH pCH2 D

]C25

ApCHzB10

[ApCH

zB4

[pCH4

3D(0.61D] z)3D

(2)

This just models dispersion forces between adsorbate andadsorbent. The Lennard-Jones parameters for the hydrogenÈwall interaction were given from the parameters above whichwere then combined with graphite Lennard-Jones parameters

nm, K) using the standard LorentzÈ(pCC\ 0.340 eCC/k \ 28.0Berthelot rules, viz. IneCH\ JeCC eHH , pCH \ 1/2 [pCC] pHH].addition to the above, z is the distance between the Lennard-Jones site on the adsorbent and the plane of carbon atoms inthe pore wall and is the number of carbon atoms per unitosvolume in graphite (114 nm~3). The potential Ðeld in the poreis calculated by the sum of the interactions between thehydrogen and both pore walls.

The simulations were typically run for 5 million conÐgu-rations and used up to 500 particles. The rate of acceptancefor particle creations and deletions was typically in the rangeof 5 to 15%.

Table 1 Lennard-Jones potentials for HÈH interactions. The energyis reduced by BoltzmannÏs constant and expressed in K

Potential No. of sites HÈH distance/nm pHH/nm eHH/k

Buch15 1 È 0.296 34.2 KThis work 2 0.074 0.259 12.5 K

Fig. 1 Pore space with a graphitic nanoÐbre modelled as a slit ofwidth H.

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Fig. 2 Simulated hydrogen adsorption (spherical model) in graphiticmicropores of width 0.9 and 1.2 nm. T \ 298 K.

2.2. Spherical model

Fig. 2 shows the simulation results for the spherical model forhydrogen. Simulations were run for two pore widths, H \ 0.9and 1.2 nm where H represents the separation between carbonatoms in graphitic layers on opposing surfaces of the pore.Note that based on a physical model for adsorption, a pore ofwidth H \ D\ 0.335 nm would not be able to adsorb hydro-gen because the potential would be strongly repulsive. Theactual width available for hydrogen atoms, H@ after allowingfor the physical size of the carbon atoms, is approximated as0.655 and 0.955 nm in the pores of width H \ 0.9 and 1.2 nmrespectively according to the method of deÐning e†ective porewidths of Kaneko et al.17

H \ H@] 2z0 [ pHH (3)

where This means for this system thatz0\ 0.8506 pCH .

H \ H@] 0.245 nm (4)

Wider pores than these can be modelled (indeed Wang andJohnson10,11 have done so) but previous work9 has shownthat pores capable of allowing only two or three layers ofadsorbate, give the best performance from the perspective ofadsorptive storage.

The mass of the adsorbent was taken by assuming themaximum possible surface area for adsorption on a graphiticmaterial, namely 2680 m2 g~1, and therefore represents the

most optimistic case with the slit-like pores bounded by singlelayers of graphitic material. The volumetric calculation isbased on this assumption also. The adsorption excess wasdetermined by subtracting the bulk density in the e†ectivepore width, H@ for a given pressure (assuming an ideal gas)from the actual density of particles in the simulation.

It can be argued that there is a slight inconsistency in mod-elling the interaction between a hydrogen and a graphiticsheet using the 10-4-3 potential, since the 10-4-3 potentialassumes that all graphite sheets outside the pore are stackedat a distance D apart, whereas the calculation method for themass of adsorbent for the mass adsorbed assumes that all thesheets are distance H apart. In practice, this means thatthe results presented in Fig. 2 are an upper bound on whatcould be adsorbed in a practical system.

The results in Fig. 2 are presented in three ways, as massper mass of adsorbed, as excess mass per mass of adsorbentand as mass of hydrogen per volume of adsorbent. The resultsare in very good agreement with those reported by Wang andJohnson,10 in spite of the fact that they used path integralMonte Carlo, whereas a classical simulation was performedhere. Both Wang and Johnson and the calculations reportedhere using a spherical model, suggest an (absolute) adsorptionof around 1.5 mass% at 100 bar for pores of these dimensions.

2.3. Two-centre Lennard-Jones model

For consistency of comparison, the e†ective width of the poreH@ was related to H according to eqn. (3) rather than using theslightly smaller value of for the two-centre Lennard-JonespHHmodel. This makes a negligible di†erence to the results.

Modelling hydrogen as a two-centre Lennard-Jones adsorb-ate can be seen from Fig. 3 to have made only a very smalldi†erence to the results. Considerations of molecular packing

Fig. 3 Simulated hydrogen adsorption (two-centre) in graphiticmicropores of width 0.9 and 1.2 nm. T \ 298 K.

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mean that slightly less molecules are adsorbed in the 12 A�pore for the two-centre Lennard-Jones model than the spher-ical model. The converse is true in the 9 pore. These e†ectsA�are second order and no molecular packing argument couldreasonably be invoked to explain the discrepancy between theuptake from simulation and the data of Rodriguez and co-workers.

2.4. Discussion

Using a classical simulation technique, we have obtainedresults that are in good agreement with the work of Wang andJohnson10,11 for prediction of hydrogen adsorption in gra-phitic micropores. The modelling of hydrogen as a non-spherical rather then spherical adsorbent was found to makelittle di†erence to the total uptake. At 100 bar and 298 K, an(absolute) weight for weight hydrogen uptake of around 1.5%is predicted with a volumetric density of 10 g of hydrogen perlitre of system. Because of the way that the results are present-ed, this is an upper bound on what would be achievable in apractical system. This is based on some optimistic assump-tions about the structure of the adsorbent but it is still lessthan the required uptakes in the US Department of Energyplan.1

The uptake predicted by these simulations is more than anorder of magnitude less than that reported by Rodriguez andco-workers.2h4 In agreement with Wang and Johnson, weconclude that no reasonable model based on physisorptioncan account for the discrepancy between simulation predic-tions and the reported results.

3. Chemisorption model

3.1. Methodology

Johnson and Wang10 performed additional simulations inwhich they increased the strength of the solid/wall potentialby a factor of up to 50 from that which would be expectedfrom dispersion forces. They found that only by making sucha drastic hypothetical increase could they get close to theamount reported by Rodriguez and Baker. Both the results ofJohnson and the results presented in section 2 suggest that thelevel of adsorption claimed by Rodriguez and Baker can notbe attributed to physisorption alone.

This has prompted the question of what would a realisticchemisorption potential be like. A suitable place to begin theanalysis would be with density functional theory (DFT) calcu-lations of the interaction between atomic hydrogen and alarge polycyclic aromatic hydrocarbon to represent part of agraphitic surface.

Jeloaica and Sidis18 have published a theoretical study onthe interaction between atomic hydrogen and a C24H12coronene cluster. The results use the local (LDA functional) ofVosko et al. and PW91 generalised gradient corrections.19h22The interaction between atomic hydrogen and a carbon atomsite where the structure is allowed to relax is shown in Fig. 4where the data is taken from ref. 17. We have called thispotential “Chemisorption 1Ï. It is compared with the 10-4-3potential for a site on two-centre Lennard-Jones hydrogenusing the parameters described in part 2.

The “Chemisorption 1Ï potential contains a deep minimumat around 1.5 from the carbon centre and also a secondA�minimum at 2.8 corresponding to dispersion forces.A�

It is important to recognise that the interaction betweenatomic hydrogen and a carbon surface will be very di†erent tothe interaction between a hydrogen atom which is part of ahydrogen molecule and a graphite surface. Indeed the bonddissociation enthalpy of a HÈH bond of 436 kJ mol~1(equivalent to a well depth parameter, u/k \ 52 442 K) is

Fig. 4 Comparison of “10-4-3 Ï potential for interaction of a singlehydrogen site with a single graphitic surface with models for chemi-sorption.

greater in magnitude than the potential well of the atomichydrogenÈcarbon interaction. Using the interaction betweenatomic hydrogen and a carbon surface merely provides astarting point to analysing a hypothetical chemisorption inter-action between molecular hydrogen and graphite. In molecu-lar hydrogen, the bulk of the electron density would becontained in the sigma bond between the two hydrogenatoms, whereas for atomic hydrogen, the electron densitywould be spherically distributed around the proton. Becauseof di†erences in electron polarisability, one might thereforeexpect stronger dispersion forces between atomic hydrogenand a graphitic surface as compared to the interactionbetween an atom on a hydrogen molecule and a graphiticsurface. This is borne out in the depth of the minimum in the10-4-3 potential and the dispersion minimum in the“Chemisorption 1Ï potential. We have deÐned the hypothetical“Chemisorption 2Ï potential such that :

u(z)Chemisorption2\u(z)Chemisorption1

4(5)

The smaller minimum in the Chemisorption 2 potential is ofthe same depth as the 10-4-3 potential. The Chemisorption 2potential could therefore be viewed as a potentially more rea-listic representation of the chemisorption interaction betweena single hydrogen atom on a hydrogen molecule and a graph-ite surface. The further caveat must be added that in a realsituation, the potential energy of the interaction will vary atdi†erent positions within the graphite unit cell, as is the caseeven for dispersion interactions.16 The potential is for presentpurposes treated as being a function merely as distance fromthe wall. The minimum associated with chemisorption islocated at a distance of 0.15 nm from the plane of carboncentres in a graphitic layer. Note that since the separationbetween adjacent stacked layers is 0.335 nm, it is possible (forthis model of the potential) to have intercalation of molecularhydrogen.

Various adsorption isotherms were generated for the Che-misorption 1 and Chemisorption 2 potentials and comparedto a conventional 10-4-3 interaction. The simulations wereconducted using the grand canonical Monte Carlo method asdescribed in section 2. The intermolecular potentials were rep-resented as a series of points in a look-up table and linearinterpolation was used to give particular values during therun.

3.2. Results

Fig. 5 shows simulated adsorption isotherms for a pore ofwidth H \ 0.9 nm at a temperature of 298 K for the three

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Fig. 5 Simulated adsorption isotherms for hydrogen in a pore ofwidth H \ 0.9 nm for 3 models of the gas solid potential. T \ 298 K.

potentials investigated. The chart is plotted as an excess iso-therm in terms of excess grams of hydrogen adsorbed pergram of adsorbent. The excess was calculated by subtractingthe amount of hydrogen that would be present in bulk hydro-gen (at the simulation pressure) in a space of width H@. Theprotocol for calculating the excess isotherm from the rawsimulation results is discussed in section 2.

The Chemisorption 1 potential implies the material couldstore up to 17 wt.% in Fig. 5. Its practical use as a medium forstorage of hydrogen in a pressurised system would be limitedby the fact that the hydrogen does not desorb to any extent at1 bar and ambient temperature. Desorption would require avery signiÐcant heating of the system. Indeed a simulation runat 1 bar for the H \ 0.9 nm pore suggests that 3.7 wt.% stillremains adsorbed at 1000 K. This is not surprising in view ofthe fact that the isosteric heat of adsorption (determined byMonte Carlo integration) for hydrogen in the H \ 0.9 nmpore is 105.9 kJ mol~1 for the Chemisorption 1 potential. Thisis similar to values for chemisorption of molecular hydrogenon metal surfaces.

The Chemisorption 2 potential can store up to about 8wt.% of hydrogen at 112 bar. At atmospheric pressure andambient temperature about 2.5 wt.% of hydrogen would beretained by the material. For a practical system operatingbetween 1 and 20 bar, the system would yield approximately4.5 wt.% over the adsorption/desorption cycle. This is some-what less than the DOE hydrogen plan for fuel cell vehicles,although it might be possible to use waste heat in the vehicleto enable more hydrogen to desorb at ambient pressure. Aswas seen in section 2, a physisorption model based on a 10-4-3potential provides only up to 1.5 wt.% adsorption.

Fig. 6 shows the structure of the adsorbate within the poreat P\ 112 bar, T \ 298 K, H \ 0.9 nm for various potentialmodels. The distance r is the distance from the centre of thepore. The orientation of the hydrogen molecule is describedby the ensemble average of cos2 / for a given position withinthe pore of the centre of mass of the hydrogen molecule, where/ is the angle between the HÈH axis and the normal to thegraphitic layers in the slit-like pores. Thus cos2 /\ 0 impliesthat the hydrogen molecule lies parallel to the pore walls andcos2 /\ 1 would imply a molecule perpendicular to the walls.

Both chemisorption potentials (a and b in the Ðgure) giverise to a single layer of molecules adjacent to the pore wallswith negligible density within the remainder of the pore. In theregion of the strongly adsorbed layer, the molecular orienta-

Fig. 6 Density (dashed line) and orientation proÐles (solid line) forP\ 112 bar, T \ 298 K and H \ 0.9 nm for (a) chemisorption 1, (b)chemisorption 2, (c) 10-4-3.

tion is such as to reduce the average value of cos2 / so as tohave both the hydrogen atoms on a molecule within a poten-tial well of one wall. For the Chemisorption 1 potential, thepotential well is such that there is an almost negligible densityin the repulsive region between the chemisorption potentialwell and the smaller physisorption potential well. Unfor-tunately, this absence of particles has led to poor statistics inthe ensemble average of cos2 / within this region. This hasmanifested itself in a series of anomalous spikes in Fig. 6a.

In the 10-4-3 potential (Fig. 6c), the density of particles isrestricted to the centre of the pore. There is no density of par-ticles at the positions corresponding to the layers in Fig. 6aand b because the potential is strongly repulsive in this region.Note that the value of Scos2 /T in the centre of the pore isclose to 0.333 for all the potentials. This is the value thatwould be expected if the orientation of the hydrogen moleculewas random and implies the inÑuence of conÐnement isminimal on a molecule in the pore centre.

Fig. 7 shows simulated adsorption isotherms for a pore ofwidth H \ 1.2 nm at a temperature of 298 K for the threepotentials investigated. The results are almost identical to Fig.5. Since Fig. 6 implies that signiÐcant adsorption hydrogenoccurs only in a single layer adjacent to the surface andadsorption in subsequent layers is minimal, one would notexpect a signiÐcant change in adsorption in wider pores. Thispoint is borne out strongly in Fig. 8 which shows the“Chemisorption 2Ï potential at T \ 298 K for various porewidths. The smallest pore width studied is H \ 0.335 nm,

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Fig. 7 Simulated adsorption isotherms for hydrogen in a pore ofwidth H \ 1.2 nm for 3 models of the gas solid potential. T \ 298 K.

which is commonly taken as the interlayer spacing within gra-phitic sheets and demonstrates that if the hydrogen atoms ona hydrogen molecule could interact with the surface accordingto a chemisorption type of interaction, then it would be pos-sible for molecular hydrogen to intercalate. Fig. 9 shows theparticle density and orientation for various positions with thepore. It can be seen that only a single strongly adsorbed layeris formed for the smaller pore. In the isotherms, the adsorp-tions for H \ 0.9, 1.2 and 2.0 nm are approximately doublethat for the H \ 0.335 nm pore reÑecting 2 strongly adsorbedlayers rather than one.

3.3. Discussion

These “ChemisorptionÏ calculations can be criticised on anumber of fronts :(i) Hydrogen is treated classically.(ii) The potentials used are somewhat arbitrary, being derivedas they are from the potential of interaction of atomic hydro-gen with graphite. There is no evidence to suggest that inreality molecular hydrogen would chemisorb on to graphite.

Fig. 8 Simulated adsorption isotherms for hydrogen in a pores ofvarious widths for “Chemisorption 2Ï model of the gas solid potential.T \ 298 K.

Fig. 9 Density (dashed line) and orientation (solid line) of hydrogen(Chemisorption 2 potential) in pores of width H \ (a) 0.335, (b) 0.9, (c)1.2, (d) 2 nm (P\ 112 bar, T \ 298 K).

(iii) Even if chemisorption did occur in some way, the poten-tial would depend strongly on position relative to the graphiteunit cell. This would mean that the adsorbate would possess alateral structure, something that is not modelled here at all.(iv) The current analysis assumes that the interactionsbetween adsorbed molecules will not be a†ected by strongchemisorption to the surface. Three body and higher forceshave been neglected.The defence against the Ðrst point is that the results obtainedusing our classical approach are consistent with the resultsobtained in the path integral Monte Carlo calculations ofJohnson and Wang.10,11

The defence against the second and third points is to acceptthat we are just asking a ““what if ÏÏ question based on hypo-thetical potential functions and have no wish to imply from atheoretical standpoint the actual existence of a chemisorption.

The fourth point is perhaps harder to answer. Clearly if ahydrogen molecule could be chemisorbed to the surface andperhaps integrated within the delocalised electron system,then it might be possible for more hydrogen molecules to

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become involved in a resonance structure at the same time. Allwe can do is to Ñag that this is an area requiring extra study.

What the calculations do show is that even with the mostplausible mechanism for chemisorption that we can devisethat maximum uptake is around 8 wt.% and in a practicalsystem the maximum amount of hydrogen that could bedelivered is much less than this. On this basis, it is difficult tosee any kind of mechanism (physisorption or chemisorption)that could give rise to the levels of uptake (40%) suggested byBaker and Rodriguez. The much more moderate levels ofuptake suggested by Turpin5 for a GNF and Heben et al.8 fora SWNT might however be consistent with the results pre-sented here.

4. Conclusions and future workAn elongated model (two centre Lennard-Jones) for hydrogenmakes little di†erence to the simulated adsorption as com-pared to a spherical model of hydrogen. This predictedadsorption agrees with previous PIMC calculations for aspherical model of hydrogen and suggests that at ambienttemperatures quantum mechanical e†ects make relatively littledi†erence to the simulation results.

The level of hydrogen adsorption predicted by a simulationmodel with hydrogenÈcarbon potentials based purely on dis-persion forces model suggests a maximum uptake of 1.5 wt.%for an optimal material. The uptake is less than that reportedby Baker and Rodriguez by more than an order of magnitude.

However even a hypothetical model for strong chemisorp-tion of hydrogen suggests that it is unlikely that uptakebeyond 16 wt.% could be obtained. This is still much lowerthan the experimental results of Baker and Rodriguez.However, even if this strength of chemisorption was possible,it would also mean that a practical system for on-boardhydrogen storage could not be based on pressure swings atambient temperature since almost all of the material remainsadsorbed at ambient pressure.

A more plausible (although still hypothetical) model forchemisorption gives uptakes of up to 8 wt.% with some 2.5%remaining adsorbed at ambient pressure.

Although the substrate is not allowed to relax during thesimulation, the e†ects of relaxation on the potential is alreadyimplicitly accounted for in chemisorption potentials based onthe DFT calculations. Neverthless, this could form the subjectof future study.

A deÐciency in this modelling approach and that of othersis that the inÑuence of three body forces and higher has notbeen investigated fully. Apart from experimental error, thepossibility of multiple hydrogen atoms being incorporatedinto some kind of massive stable resonance structure incorp-orating the graphitic sheets seems the only possible remaining

explanation for the high levels of uptake reported by Bakerand Rodriguez.

AcknowledgementsThe author wishes to thank Hans Geerlings and Heiko Oos-terbeek of Shell Global Solutions International for their helpand support during this work. The author also wishes tothank Shell Hydrogen for permission to publish.

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