Graphene nanostructures as tunable storage media for molecular hydrogen

Abstract

Many methods have been proposed for efficient storage of molecular hydrogen for fuel cell applications. However, despite intense research efforts, the twin U.S. Department of Energy goals of 6.5% mass ratio and 62 kg/m³ volume density has not been achieved either experimentally or via theoretical simulations on reversible model systems. Carbon-based materials, such as carbon nanotubes, have always been regarded as the most attractive physisorption substrates for the storage of hydrogen. Theoretical studies on various model graphitic systems, however, failed to reach the elusive goal. Here, we show that insufficiently accurate carbon–H₂ interaction potentials, together with the neglect and incomplete treatment of the quantum effects in previous theoretical investigations, led to misleading conclusions for the absorption capacity. A proper account of the contribution of quantum effects to the free energy and the equilibrium constant for hydrogen adsorption suggest that the U.S. Department of Energy specification can be approached in a graphite-based physisorption system. The theoretical prediction can be realized by optimizing the structures of nano-graphite platelets (graphene), which are light-weight, cheap, chemically inert, and environmentally benign.

A recent report on hydrogen clathrate hydrate (1) shows that under high pressure, molecular hydrogen can be trapped in the clathrate cavities reaching a mass ratio close to that defined by the U.S. Department of Energy (DOE) (2). However, the hydrogen clathrate is only stable under high pressure or at very low temperature. Simple sterical considerations suggest that the use of a “help gas” to stabilize the clathrate hydrate under less severe thermodynamic conditions would lead to the deterioration of the hydrogen storage mass ratio and may not be viable for mobile applications. On the other hand, there have also been numerous experimental studies on the binding capacity of molecular hydrogen with graphitic substrates (3, 4). At technologically viable conditions, reliably reproducible results are still far from the DOE goal (3, 4). In the attempt to understand and improve the storage capacity of graphitic materials, calculations have been made on many models. Some of the calculations were based on empirical interaction potentials (5–9), and the others used potentials derived from quantum mechanical calculations (10–16). The role of quantum behavior of molecular hydrogen at low temperatures has also been investigated (6, 8, 17–19). Unfortunately, the binding capacity for hydrogen at near-ambient conditions has not been calculated, including the quantum effects and accurate, ab initio-based interaction potentials. To date, there has not been a reliable theoretical study indicating that the DOE goal of 6.5% mass ratio can or cannot be achieved in pure graphitic materials.

The interaction of nonpolar H₂ molecules with physisorption substrates in graphitic system is mainly the London dispersion. Accurate calculations including treatment of electron correlations on model systems, such as polycyclic aromatic hydrocarbons (PAHs) (e.g., benzene and coronene), indicate that H₂ molecules have adsorption energies between 4 and 7 kJ/mol (12, 14, 16) at an equilibrium distance of ≈3 Å. These binding energies are small and the entropic, and quantum effects cannot be ignored at practical temperatures (≈200–300 K). An adequate description of the motion of light H₂ molecule in the soft, anharmonic potential of a graphitic system is a prerequisite for accurate prediction of the equilibrium constant and, therefore, the binding capacity of molecular hydrogen in these systems (20). Although the thermodynamic behavior of the free H₂ gas in the 200- to 300-K temperature range is essentially classical, this is no longer true in the presence of soft external potentials. Quantum behavior of hydrogen adsorbed in narrow pores manifests itself in the quantum sieving effects (21), which persist up to 300 K (22). Inclusion of the quantum effects in the free energy is a nontrivial computational problem. It involves solving the Schrödinger equation for the motion of the hydrogen atoms on a complicated potential energy surface (PES).

Methods

A computationally tractable model of graphene is provided by quantum-mechanical description of H₂–PAH interactions with post-Hartree–Fock treatment of electron correlation (14, 16). We calculate the H₂–benzene PES using second-order Møller–Plessett (MP2) perturbation theory (16). Interaction energies and the PES shape in the H₂–benzene system are sensitive to the choice of the polarization functions and basis set superposition error (BSSE) (16). The BSSE in the interaction energy gradually decreases for larger basis sets, reaching just 0.6 kJ/mol for the aug-cc-pVQZ basis at the global minimum of the H₂/C₆H₆ PES (see Fig. 5, which is published as supporting information on the PNAS web site). The global minimum is found 4.95 kJ/mol below the separated H₂ and benzene. The counterpoise-corrected and uncorrected MP2/aug-cc-pVQZ equilibrium distances differ by only 0.04 Å.

By a fortuitous coincidence, BSSE-uncorrected MP2/cc-pVTZ results for the H₂–benzene model system closely mimic the counterpoise-corrected MP2/aug-cc-pVQZ calculations both at the global minimum and in the asymptotic region. Because MP2/cc-pVTZ calculations are significantly less expensive, this basis was used for the PES exploration in larger models (H₂–coronene below) and for test calculations with coupled-cluster treatment of the electron correlation.

In the global PES minimum, H₂ is aligned along the C₆ symmetry axis of benzene at 3.1 Å between the centres of mass of H₂ and C₆H₆. The energy profile shows a typical London-type ≈r^-6 long-range behavior (16) (Fig. 1). More sophisticated correlation treatment [CCSD(T)/cc-pVTZ] reduces the H₂–benzene interaction by 0.9 kJ/mol (14) (≈20%) compared with MP2/cc-pVTZ, whereas the geometry remains essentially unchanged.

Fig. 1.

H₂/benzene ab initio interaction potentials and fitted Lennard–Jones (LJ) potential. Potential energy E (in kJ/mol) is shown as a function of the distance of the centres of mass of H₂ and benzene (in Å). CP, results with the counterpoise correction applied.

Interaction of H₂ with larger PAHs of higher polarizabilities and smaller ionization potentials leads to stronger binding. For infinitely large graphene platelets, the interaction has been extrapolated to >7 kJ/mol at the MP2 level (16), whereas the intermolecular distance is unchanged with increase of the PAH size (12, 14, 16). The model system H₂/coronene considered here (Fig. 6 and Tables 3 and 4, which are published as supporting information on the PNAS web site) correctly reproduces the expected London-type r^-6 long-range potential tail and only slightly underestimates the extrapolated H₂/graphene physisorption energy (16).

Direct ab initio evaluation of the sufficiently detailed PES of graphene would have been prohibitively expensive. Instead, we describe the H₂/graphene PES by the exp-6 form of the LJ pair potential , where r_i is the distance between H₂ centre of mass and carbon atom i. Parameters A, α, and C₆ are fitted to reproduce the MP2/cc-pVTZ results of the C_6v-symmetric H₂-coronene model system (Table 5, which is published as supporting information on the PNAS web site). The fitted LJ potential shows good agreement with ab initio results for the H₂–benzene system (Fig. 1; and see Figs. 6 and 7, which are published as supporting information on the PNAS web site). The fitted potential slightly underestimates (by 0.4 kJ/mol) the translational barriers between two adjacent minima (Fig. 6). This deviation is small compared with RT and is therefore not expected to affect thermodynamic properties. It is a good approximation to assume the H₂–PAH interaction energy to be additive and independent on the number of H₂ molecules interacting with the PAH (16).

For the evaluation of adsorption potential, we have chosen a two-dimensional, periodic graphite sheet with experimental C–C distance (R_CC). Contributions to the potential from 30 nearest primitive unit cells are included along the in-plane a and b directions. For the double-layer structures, the potential of two layers (“above” and “below” the H₂) is included. For short inter-layer separations, attraction due to the second-neighbor layer may further increase interaction energies. This effect was not considered in our simulations. The potential of the two-dimensionally periodic graphite layer is illustrated in Fig. 8, which is published as supporting information on the PNAS web site.

Free energies of adsorption were calculated in the ideal gas approximation

[1]

where the canonical partition functions q_ads and q_free,

[2]

are obtained from the energy levels ε_i, determined by solving the one-particle Schrödinger equation for H₂ motion in the adsorbing potential (q_ads) and in free space (q_free). Other thermodynamic functions (ΔE, ΔS, etc.) are obtained from ΔF, using standard expressions (23, 24).

All MP2 and CCSD(T) computations were performed with the nwchem (25) program package. Optimised B3LYP/6–31G^* geometries were taken from previous work (16). Coordinates, corresponding energies, and further details on H₂/PAH computations are given in Tables 3, 4, and 6–8, which are published as supporting information on the PNAS web site.

The time-independent Schrödinger equation is solved for a single featureless particle with the mass of a hydrogen molecule. Calculations employ periodic boundary conditions and a plane wave basis set. To accelerate convergence of the free energies with the plane wave cutoff, identical unit cell dimensions and plane wave cutoffs are used for calculation of q_ads and q_free. The rectangular unit cell is obtained by replicating the primitive unit cell (, b_p = 3R_CC, R_CC = 1.421 Å) in a and b directions. To avoid the attractive artifacts of the exp-6 potential close to the nuclei and reduce the requirements for high-frequency basis set components, the simulation cell extent in the c direction was truncated by d_excl (1.0 ≤ d_excl ≤ 2.0 Å) in the vicinity of the graphene sheet(s). For double-layer structures with interlayer spacing d, the unit cell extent in the c direction is, therefore, c = d - 2d_excl. Single-layer simulations were performed by using the same periodic boundary conditions, but the interlayer spacing d was chosen to be large. The unit cell parameters, plane wave cutoffs, and calculated partition functions are given in Tables 9 and 10, which are published as supporting information on the PNAS web site.

We neglect contributions due to the adsorption-induced changes in the internal motion (rotation and vibration) of the H₂ molecules. The consequences of this approximation can be understood by using the PES of the H₂–benzene complex. Because of the stiffness of the H₂ molecule, only the change in the zero-point energy can contribute at temperatures of interest. At the C_6v minimum of the H₂–benzene PES, we calculate H₂ harmonic vibrational frequency of 4,494 cm^-1, 30 cm^-1 below the free H₂ molecule. [Indeed, the softening of the H₂ vibrational mode appears to be a general trend upon physisorption of this molecule (26).] At 200 K, the (neglected) increase in the adsorption constant is exp(-Δv/2kT) - 1 ≈ 11%, leading to a slight underestimation of the storage capacity.

The assessment of the rotational contribution to the partition function requires knowledge of the anisotropy of the adsorption potential. For the C_6v minimum of the H₂–benzene PES, the MP2/cc-pVTZ binding energy is -395 cm^-1. Binding energies of -261 cm^-1 are found for the corresponding C_2v-symmetric structures with H₂ perpendicular to any of the benzene σ_v symmetry planes. Due to the large rotational level spacing of the H₂ molecule (2B_e ≈ 122 cm^-1) and the effects of the nuclear spin statistics, the explicit treatment of the restricted rotation in this potential leads to a small (≈3%; see Estimation of the Restricted Rotor Contribution to the H₂ Adsorption Free Energy in Supporting Text, which is published as supporting information on the PNAS web site) increase in the adsorption constants, neglected in our calculations.

Dispersive interactions between the graphene layers were not explicitly considered in our simulations. This approach is equivalent to assuming that the layered host structure remains unchanged upon H₂ uptake. Because of the significant free energy cost associated with the graphene layer separation process (27), the “empty” layered structure must be stabilized by other means, such as spacers (see below).

Meaningful calculations of the free energy changes require that K_eq = q_ads/q_free is converged with respect to the volume of the unit cell. From test calculations on the single-layer graphene structure, we find that unit cell a = 3a_p, b = 2b_p leads to K_eq values converged to better than 15%. All calculations reported presently use these unit cell dimensions. Because tunneling of H₂ through the graphene layer is associated with a very high barrier, we do not need to consider unit cells replication in the c direction.

The weak H₂–H₂ interaction is attractive at intermolecular distance >3.1 Å (28, 29). At higher hydrogen guest densities, H₂ can no longer be treated as an ideal gas. Although it is possible to simulate the high-density H₂/graphene system directly, using the grand canonical path integral Monte Carlo approach, such calculations are rather laborious and may be hard to interpret. At the same time, for slowly varying potentials adsorption free energy of an ideal gas is a good approximation to the adsorption free energy of the real gas at the same number density (see Estimation of the Adsorption Free Energy of Nonideal H₂ Gas from the Results of an Ideal Gas Simulation and the Experimental Equation of State in Supporting Text and refs. 23 and 24). We estimate the corrections due to H₂ nonideality at higher densities from an experimental equation of state (30) as follows: Given the external H₂ pressure p_ext, and the equilibrium constant K_eq obtained from the ideal gas simulation, we calculate the effective “internal” H₂ pressure p_int as

[3]

From p_int and the experimental H₂ equation of state (30), we obtain the molar volume v_mol. The apparent molar volume of H₂, characterizing volumetric efficiency of the storage system is then given by

[4]

For dual-layer system, the mass fraction of H₂ in the H₂/graphene system is given by

[5]

where v_mol is in cm³/mol and d, d_excl are in Å. The structural prefactor cm³/mol-Å is calculated from the fixed in-plane carbon–carbon distance R_CC, the atomic masses m_H and m_C of hydrogen and carbon, and the Avogadro constant N_A. Calculated internal pressure, volumetric and mass weight densities for representative temperatures, and external H₂ pressures are collected in Table 1 and Fig. 2.

Table 1. Gravimetric and volumetric H₂ storage capacity of layered graphite structures.

	pext = 5 MPa					pext = 10 MPa
d, Å	pint, MPa	wre, %	wid, %	vre	vid	pint, MPa	wre, %	wid, %	vre	vid
T = 300 K
Free gas*				483	499				248	249
14	22	2.13	2.30	169	157	45	3.63	4.50	98	78
12	27	2.02	2.26	153	137	55	3.38	4.42	90	68
10	40	2.03	2.45	127	105	79	3.25	4.78	78	52
9	54	2.12	2.78	109	83	108	3.28	5.40	70	52
8	91	2.39	3.71	86	55	183	3.47	7.16	59	27
7	167	3.32	6.58	54	26	333	4.54	12.34	39	13
6	273	3.16	7.96	48	18	546	4.17	14.75	36	9
5.75	183	2.41	5.03	61	29	365	3.28	9.58	45	14
5.50	49	1.40	1.79	102	79	99	2.20	3.52	64	40
T = 250 K
Free gas*				387	416				201	208
14	34	3.49	4.10	102	86	68	5.45	7.88	64	43
12	43	3.30	4.12	93	73	85	5.02	7.92	60	37
10	65	3.26	4.68	78	54	129	4.73	8.94	53	27
9	93	3.36	5.56	68	40	186	4.69	10.53	48	20
8	175	3.69	8.13	55	24	349	4.88	15.04	41	12
7	397	5.11	16.74	34	9	794	6.43	29.68	27	5
6	784	4.89	22.95	31	5	1568	6.04	37.33	25	3
5.75	492	3.85	14.63	38	9	984	4.83	25.52	30	4
5.50	112	2.62	4.71	54	29	223	3.60	9.00	39	15

Parameter d is the interlayer distance. Quantities p_ext and p_int are, respectively, the external and internal H₂ pressure (see text), and w_re and w_id are weight fractions of H₂ in the material, estimated from the real (w_re) and ideal (w_id) gas equations of state. Corresponding apparent molar volumes (in cm³/mol) are given by v_re and v_id.

^*Weight fractions of H₂ in the free gas are 100%

Fig. 2.

Gravimetric (Upper) and volumetric (Lower) H₂ storage capacities of layered graphite structures, calculated from the real gas equation of state, as functions of the interlayer separation (see Table 1 and text). The DOE targets for automotive applications (2) (w = 6.5%, v = 31.2 cm³/mol) are indicated by solid horizontal lines.

The procedure outlined above is equivalent to treating graphene structure as a “nanopump,” increasing the hydrogen pressure inside the structure, but otherwise leaving H₂ guest gas unaffected. Although approximate, this treatment allows us to completely sidestep the (still controversial) question of the choices H₂–H₂ interaction potentials, treatment of the quantum effects for H₂–H₂ interactions, and the associated convergence issues.

It is important to understand the approximations made in the nonideal gas estimation of the storage capacities v_re and w_re. Eq. 3 requires the use of fugacities f, rather than gas pressures p. As the f/p ratio decreases with pressure (at temperatures and pressures considered presently), Eq. 3 is expected to underestimate the internal pressure p_int. At the same time, using the free gas equation of state to calculate the molar volume neglects changes in H₂–H₂ radial distribution function due to the adsorption potential and, thus, overestimates the compressibility of the guest. Although these two defects may be expected to partially offset each other, the overall nonideality correction is at best semiquantitative. To illustrate the effect of the nonideality corrections, Table 1 also includes v_id and w_id values calculated from the ideal gas equation of state. When the real and ideal gas values are close, the residual error in the storage capacity is determined by the remaining uncertainties in the ab initio H₂/graphene interaction potential and the corresponding LJ fit. Based on the basis set and method convergence, we estimate this error at ±25% in v_re and w_re. When the real and ideal gas values deviate significantly from each other, the real gas result is clearly more reliable but should still be treated only as a semiquantitative estimate.

Results and Discussion

The spatial distribution of molecular hydrogen adsorbed on graphene is very delocalized (Fig. 3). This observation is in agreement with previous path-integral and Monte Carlo simulations (5, 15, 18) and indicates an essentially free lateral motion of H₂. Our calculations indicate a slightly attractive (-1.2 kJ/mol) H₂-graphene free reaction energy at 300 K (see Table 2). The entropic contribution to the free energy is significant (ΔS₃₀₀). The physisorption free energy corresponds to an equilibrium constant of K_eq = exp(-ΔF/RT) ≈ 1.6. In other words, at room temperature a single graphite layer increases the H₂ abundance by only ≈60%. The enhancement factor does not significantly change at lower temperatures (Fig. 4) or higher pressures. Considering the volume taken up by graphene itself, graphite surfaces are unsuitable for practical H₂ storage.

Fig. 3.

Probability densities for selected lowest eigenstates of the translational nuclear Hamiltonian. The lowest in-phase (Top to Bottom: first, second, and fifth) eigenstates for the double-layer structure are shown (d = 8 Å).

Table 2. Free energy of H₂ adsorption on graphite surfaces and in graphite layered structures.

d, Å	ΔE0,* kJ/mol	ΔF300, kJ/mol	ΔE300, kJ/mol	ΔS300, J/mol-K	K300
∞†	–6.2	–1.2	–2.4	–4.0	1.6
12.0	–6.4	–4.2	–5.3	–3.7	5.5
10.0	–6.7	–5.2	–6.0	–2.9	7.9
9.0	–7.1	–5.9	–6.7	–2.5	10.8
8.0	–8.1	–7.2	–8.1	–2.7	18.3
7.0	–11.0	–8.7	–10.8	–6.7	33.3
6.0‡	–13.0	–10.0	–13.1	–10.4	54.6
5.5‡	–10.1	–5.7	–10.1	–14.7	9.9
5.0‡	+1.2	+7.2	+1.7	–18.2	0.06

Results for quantum computations of ideal-gas H₂ in external graphite potentials. Parameter d is the interlayer distance. ΔF₀ = ΔE₀ and ΔF₃₀₀ are free energies of H₂ adsorption at 0 K and 300 K, respectively. The energy and the enthropy of adsorption at 300 K are given by ΔE₃₀₀ and ΔS₃₀₀, and K₃₀₀ is the equilibrium constant.

^*H₂ ground state energy in the adsorbing potential

^†The infinite distance is computed in a box with interlayer spacing d = 43 Å

^‡Values at these interlayer separations may be affected by the shape of the repulsive part of the potential, leading to an increase in the error bars

Fig. 4.

Equilibrium constants K_eq (Upper) and reaction free energies ΔF (Lower; in kJ/mol) are plotted as a function of the interlayer distance d (Left; in Å, at T = 300 K) and temperature T (Right; in K, at d = 8 Å), respectively.

To improve the binding capacity, it is possible to sandwich H₂ between graphite layers. Binding energies of up to 30 kJ/mol have been reported for H₂ inside carbon nanotube tips (11). We have calculated quantum-mechanical physisorption free energies for interlayer distances d, between two graphite layers ranging from 4 to 14 Å. As can be seen from the results in Table 2, at separations above 7 Å the zero-temperature enthalpy of the H₂–graphite interaction is very similar for bi- and monolayer structures (12). Even at these separations, the free energy is strongly affected by the presence and position of the second layer (Table 2 and Fig. 4). We predict an increase in H₂ binding free energy with decreasing layer separation up to a maximum of ≈10 kJ/mol for an interlayer distance of ≈6 Å. For smaller separations, exchange repulsion reduces the free energy considerably (Fig. 4), which becomes positive for interlayer separations <5 Å. The thermodynamics of the H₂/graphite system at shorter separations is purely repulsive (31). The calculated equilibrium constant shows a sharp “peak” at 6–7 Å (Fig. 2 Upper). Consequently, experimental fine-tuning of K_eq should be taken with care; too small a separation could readily lead to a collapse in the adsorption free energy. At ambient conditions (T = 298 K, P = 0.1 MPa), we estimate maximum equilibrium constant of ≈30, for a graphite–graphite interlayer distance of 7 Å. The very favorable adsorption free energies for d = 6–7 Å effectively creates a “nanopump,” increasing the internal H₂ pressure inside the layered structure (see Table 1). As a result, the target of 62 kg/m³ (≈31 cm³/mol) volumetric storage density, set by the DOE, can be approached at a moderate external H₂ pressure (≈10 MPa) even at room temperature.

At the same time, our simulations indicate that a pure carbon-based storage system cannot achieve the DOE gravimetric storage target (6.5 wt % H₂) at room temperature and moderate pressures. Due to the increasingly nonideal behavior of H₂ at high internal pressures, room-temperature storage capacity is limited to 2–3 wt % at 5 MPa, and 3–4 wt % at 10 MPa. Although not yet achieving the DOE target, this storage capacity is already competitive with best known physisorption substrates. We calculated similar room-temperature gravimetric storage capacities for a wide range of interlayer spacing (d = 7–12 Å; see Fig. 2), which should simplify practical design of the storage material.

Lower but still technologically acceptable temperatures can increase the equilibrium constant by at least one order of magnitude. Fig. 4 illustrates the temperature dependence of the equilibrium constants for a bilayer with d = 8 Å. Although our treatment of H₂–H₂ interactions becomes increasingly uncertain at lower temperatures (see Methods), the simulations indicate that gravimetric storage capacities of 5.0–6.5 wt % of H₂ should be achievable at technologically acceptable conditions, e.g., at T = 250 K, P_ext = 10 MPa or T = 200 K, P_ext = 5 MPa (Table 1 and Fig. 2). Because these storage capacities are only weakly sensitive to the graphite interlayer separation, the design of the necessary layered graphite structure does not appear to be an insurmountable challenge.

Caution should be applied in interpreting the results of our simulations for small interlayer distances (d ≤ 9 Å). At low pressures, van der Waals close-packing arguments suggest that at most two H₂ monolayers (6.6 wt %) can fit between the graphene layers separated by d = 9 Å. For d = 6 Å, just one monolayer can fit in the structure, indicating a maximum H₂ storage capacity of 3.3 wt % (3, 4). Although this argument holds at low pressures, the large adsorption free energy calculated for small interlayer spacing can drive the internal pressure beyond 2 kbar (1 bar = 100 kPa), even at moderate external pressures (Table 1). In the free hydrogen gas, the density at such pressures exceeds the close-packing limit (30). At the same time, our approach to H₂–H₂ interactions is crude, so that the pronounced maximum in H₂ storage capacity we find at interlayer spacing 6 Å ≤ d ≤ 7.5 Å should be considered only as a tantalizing possibility. Confirming or disproving its existence would require further, more elaborate simulations (or experiment).

The qualitative difference in the H₂ storage capacity of mono- and bilayer graphite is easily understood by comparing the density-of-states (DOS) (Fig. 9, which is published as supporting information on the PNAS web site) for the two models. The single-layer graphite potential creates relatively few H₂ bound states, which are localized at the graphite surface. For the majority of states, the DOS is very similar to the DOS of free H₂, reflecting the short-range nature of the binding potential. For the double-layer structure, DOS has many binding states, with the bulk of the available states shifted to low energies. In other words, whereas free H₂ can move away from a single layer and hence on average experiences little attraction, H₂ inside a double-layer structure is always in an attractive potential. Fig. 3 shows probability densities of H₂ in between two graphite layers, for a few lowest states. Even low-energy modes are delocalized on the surface. The abundance of low-energy surface modes on graphite and in sandwiched structures suggests the presence of a two-dimensional H₂ gas. The lateral modes should facilitate diffusion inside the storage material, thus ensuring easy loading and unloading.

The estimated limit of accuracy of our calculations at d ≥ 8 Å is within ±25% (see Methods). Even considering this large margin of error, we conclude that an H₂ storage enhancement material approaching, or possibly even exceeding, the DOE specification can be produced by encapsulating molecular hydrogen in graphite layers with an appropriate interlayer spacing. The significant dependence of the equilibrium constant on the graphite interlayer distance indicates that the H₂ abundance of a nanostructured graphite system is intimately controlled by the nano- and mesoscopic structure. Together with the pronounced temperature dependency, the controversial issue of the qualitatively different amounts of H₂ adsorption in the literature of the last decade (5, 10, 32–34) on graphite systems may well arise from slight microstructural variations both within and between different samples.

It is hence an experimental challenge to provide a synthesis of nanostructured graphite with sufficiently uniform and reproducible interlayer distances suitable for H₂ storage. One possibility is to introduce well defined spacers. Aside from the tuning possibilities, the spacers may provide additional benefits, such as an increase in the stability of the storage media. Spacers can also act as molecular sieves, preventing penetration of larger gas molecules such as N₂, CO, and CO₂, which typically have a higher graphene binding energy than H₂ and may reduce storage capacity (21). For example, we compute the binding energy of the N₂/benzene model system to be two times larger than the comparable H₂/benzene model.

One possibility for the experimental realization of the layered graphene storage system is provided by graphite intercalation compounds, which exhibit a wide range of interlayer separations (35). Achieving the optimal H₂ storage capacity requires a stage-1 intercalation compound, with guest molecules appearing after each graphene sheet. Stable stage-1 species with interlayer separations from 3.7 to 12 Å are known (35), offering almost unlimited possibilities for chemical tuning. One of the experimental challenges in synthesizing our storage system lies in minimizing the interlayer volume, excluded by the spacers. This goal can be achieved by preparing a mixed intercalation compound with two guests of a different size. The larger guest can be chemically or photochemically cross-linked to the graphene host, followed by elimination of the weakly bound smaller guest. Chemical cross-linking may partially disrupt the graphene π-system, somewhat decreasing the van der Waals interactions and the adsorption free energy. At the same time, sufficiently polar spacers can increase electrostatic interactions enough to more than compensate for this loss (15).

Another prototype for the storage system is carbon foam (36) with the structure based on rigidly interconnected segments of graphite. In principle, the interlayer separation can be adjusted by extending the interlayer carbon skeleton. The resulting “foam” structures cover the structural phase space extending from hexagonal diamond to graphite. A previous theoretical study (36) has shown that this hybrid system possesses unusually high structural stability and low mass density.