Molecular dynamics simulations of hydrogen storage capacity of few-layer graphene
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- Wu, C., Fang, T., Lo, J. et al. J Mol Model (2013) 19: 3813. doi:10.1007/s00894-013-1918-5
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The adsorption of molecular hydrogen on few-layer graphene (FLG) structures is studied using molecular dynamics simulations. The interaction between graphene and hydrogen molecules is described by the Lennard-Jones potential. The effects of pressure, temperature, number of layers in a FLG, and FLG interlayer spacing are evaluated in terms of molecular trajectories, binding energy, binding force, and gravimetric hydrogen storage capacity (HSC). The simulation results show that the effects of temperature and pressure can offset each other to improve HSC. An insufficient interlayer spacing (0.35 nm) largely limits the HSC of FLG because hydrogen adsorbed at the edges of the graphene prevents more hydrogen from entering the structure. A low temperature (77 K), a high pressure, a large number of layers in a FLG, and a large FLG interlayer spacing maximize the HSC.
KeywordsAdsorptionFew-layer grapheneHydrogenMolecular dynamicsPressure
Hydrogen is a potential next-generation clean fuel for replacing fossil fuels. It can reduce CO2 emissions and air pollution due to its high power of combustion, clean combustion, and renewability. Hydrogen-based fuel cells  have been applied to efficiently produce electricity for mobile applications. A critical requirement is hydrogen storage systems that can operate at ambient conditions with sufficient gravimetric and volumetric capacities.
Carbon-based nanomaterials (i.e., carbon nanotubes (CNTs) and fullerences) that comprise carbon atoms with sp2 hybridization are relatively light and inexpensive, and have a high adsorption surface area for hydrogen storage. Graphene, which consists of single-atom-thick sheets of carbon, is the basic structural element of these carbon nanomaterials. Graphene has excellent mechanical (Young’s modulus ∼1.0 TPa), thermal (thermal conductivity ∼3000 W/mK), and electronic properties [2–4]. Several theoretical studies on graphene have demonstrated that it can absorb up to an 8∼9 % mass ratio of hydrogen, which is close to the desired gravimetric capacity set by the US Department of Energy for hydrogen storage (9 wt% by 2015).
Understanding the mechanisms of hydrogen adsorption on graphene under various environments would benefit various fields, including motor vehicles, fusion reactor design, and hydrogen storage . Molecular dynamics (MD) simulations of a graphene–hydrogen interface can be used to explore the nature of surface adsorption. Atomistic simulation can effectively avoid experimental noise and turbulence problems. Many nanosystems have been analyzed using MD, such as metal films , nanowires [7, 8], nanoimprinting , and dip-pen nanolithography [10, 11]. Herrero and Ramirez  studied the diffusion of hydrogen in graphite and found that hydrogen atoms jump from a C atom to a neighboring one with an activation energy of about 0.4 eV. Compared to the adsorption of atomic hydrogen on graphene, molecular hydrogen has a much smaller activation energy and faster diffusion speed due to the interaction of physisorption [13, 14] with graphene. Lamari and Levesque  studied hydrogen adsorption on graphene and found that at a temperature of 77 K and a pressure of 1 MPa, the excess hydrogen physisorption is estimated to be equal to ∼7 wt%, and decreases with increasing temperature. Tozzini and Pellegrini  studied a reversible hydrogen storage process on graphene utilizing density-functional theory. The reversible storage and release of hydrogen are controlled by the extent of graphene buckling, which leads to a high gravimetric capacity of up to 8 wt%. Graphane is a fully saturated hydrocarbon compound derived from a single graphene sheet with formula CH, which has a high gravimetric capacity of 7.7 wt% with great stability .
This work investigates the mechanism of molecular hydrogen adsorption and gravimetric capacity on a few-layer graphene (FLG) structure using MD simulations. To optimize the operation parameters, the effects of pressure, temperature, number of layers in a FLG, and FLG interlayer spacing are studied. The results are discussed in terms of molecular trajectories, binding energy, binding force, and gravimetric hydrogen storage capacity (HSC).
Lennard-Jones potential parameters 
ε (J mol−1)
2.385 × 10−3
2.233 × 10−3
Results and discussion
Effects of pressure and temperature on HSC of single-layer graphene
The effect of temperature is studied using temperatures of 100, 200, 300, and 400 K. The system pressure is fixed at 10 MPa. Figure 3 (b) shows the variation of gravimetric hydrogen with time for these temperatures. The gravimetric hydrogen largely decreases with increasing temperature due to an increase in the kinetic energy of hydrogen molecules. Due to a weak C-H2 binding energy (approximately units of kcal mol−1) , the hydrogen molecules adsorbed on graphene are easily desorbed when their kinetic energies increase with temperature, which is in agreement with previous reports [15, 21]. At stage I, high-speed adsorption appears. The gravimetric hydrogen then gradually slows down with time (stages II and III). The gravimetric hydrogen obtained at 77 K (Fig. 3(a) and (b)) is higher than that obtained at higher temperatures. The gravimetric hydrogen increases 1.27-, 1.45-, and 1.71-fold when the system temperature is decreased from 400 K to 300, 200, and 100 K, respectively. The results indicate that HSC has a strong dependence on pressure and temperature. The effects of the two parameters are expected to partially offset each other to improve HSC. HSC is optimal in a system with a high pressure and a low temperature.
Effect of number of layers in a FLG
Effect of interlayer spacing
Effects of pressure and temperature on HSC of FLG
Comparison of various carbon-based systems for hydrogen storage
Hydrogen storage on various bare carbon-based systems has been studied theoretically and experimentally. The HSCs of single-walled carbon nanotubes (SWCNTs) obtained by experiments are about 4 wt% (at 0.1 MPa and 77 K)  and 1 wt% (at 0.1 MPa and 295 K) . For double-walled carbon nanotubes (MWCNTs), the HSCs are close to 5 wt% (at 10 MPa and 300 K)  and 0.25 wt% (at 0.1 MPa and 300 K) . The HSC of MWCNTs depends on their size of shells and number of shells. Studies have shown that the HSC of SWCNTs is better than that of MWCNTs. Graphite nanofibers are layered graphite nanostructures which have high HSCs of 6.5-10 wt% (at 12 MPa and 300 K) [29, 30]. The HSC of graphene is 0.9 wt% (at 10 MPa and 298 K) . These results reveal that for carbon-based systems, higher HSCs are obtained at higher pressures and lower temperatures, and for systems with a larger adsorbable surface area. However, for a given carbon-based system, the theoretical HSCs are much larger than those obtained by experiments due to the assumption of an ideal crystalline material and an ideal environment. For example, SWCNTs and graphene have theoretical HSCs of 11.2 wt% (at 10 MPa and 77 K)  and 7.0 wt% (at 1 MPa and 77 K) , respectively. The maximum (theoretical) HSC might thus be achieved by properly designing the material and controlling the environment.
Some metal decorated systems are attractive for hydrogen storage materials at room temperature. They have higher hydrogen wt% capacity than bare carbon materials due to a larger bond strength interacting with hydrogen and hydrogen absorption ability. Transition metal-ethylene complexes formed by laser ablation exhibit a high HSCs of 12.0 wt% (at 0.1 MPa and 298 K) . The HSCs of multi-functionalized naphthalene with Ti and Li metal atoms are 6.72 and 3.73 wt% (at 0.1 MPa and 298 K), respectively . Nanoscale titanium-benzene complexes have a HSC of 6.0 wt% (at 0.1 MPa and 298 K) . The HSC of C2H2Ti and C2H2Li complexes are 12.0 and 19.65 wt% (at 0.1 MPa and 300 K) , respectively. The HSC of C2H4V and C2H4V+ organometallic compounds are 11.32 and 13.28 wt% (at 0.1 MPa and 298 K) , respectively. The HSCs of Ti-acetylene (C2H2Ti) and Li-acetylene (C2H2Li) complex are 12.0 and 19.65 wt% (at 0.1 MPa and 298 K) , respectively.
MD simulation was used to investigate hydrogen adsorption on a FLG structure. The effects of pressure, temperature, number of graphene layers, and FLG interlayer spacing on HSC were analyzed. For the effect of temperature, high-speed adsorption appears in the first 325 ps, whereas for the effect of pressure, it appears in the time period of 325∼910 ps. The effects of temperature and pressure can offset each other to improve HSC. The hydrogen adsorbed on graphene is sensitive to temperature due to a weak C-H2 binding energy. The hydrogen molecules adsorbed on graphene are easily desorbed when their kinetic energies increase with temperature. The HSC of FLG can be improved by increasing the FLG interlayer spacing, which significantly increases the adsorbable area and storage space. A low temperature (77 K), a high pressure, a large interlayer spacing, and many layers maximize the HSC of FLG.
This work was supported by the National Science Council of Taiwan under grants NSC 100-2628-E-151-003-MY3 and NSC 100-2221-E-151-018-MY3.