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Hydrogen Storage in Carbon Nanotubes. A Combined Ab-initio and Molecular Dynamic Study

MPOURMPAKIS GIANNIS1, TYLLIANAKIS EMMANUEL2 and FROUDAKIS GEORGE3

1Department of Chemistry, University of Crete, P.O. Box 1470, Heraklion, Crete, GREECE 71409, 2Matterials Science Technological Department, University of Crete, P.O. Box 1470, Heraklion, Crete, GREECE 71409, 3Department of Chemistry, University of Crete, P.O. Box 1470, Heraklion, Crete, GREECE 71409,

Abstract: Combined ab-initio and Molecular Mechanics – Molecular Dynamics calculations have been performed for investigating the hydrogen storage in single-walled carbon nanotubes (SWNTs). The ab- initio calculations at the Density Functional level of Theory (DFT) show the nature of hydrogen adsorption in selected sites of a (5,5) tube walls. On top of this, Molecular Dynamics simulations model large scale nanotube systems and reproduce the storage capacity under variant temperature conditions. Our results indicate that the interaction of hydrogen with SWNT is weak and with a small change in the temperature, hydrogen defuses away from the tube walls.

Keywords: hydrogen storage, carbon nanotubes, physisorption, nanotube bundles, ab-initio, MM-MD calculations

1 Introduction

Among the hydrogen storage technologies we only begin to understand the complexity of the available now, including gas compression at high processes of hydrogen chemi- or physisorption that pressures, liquefaction, metallic hydrides, depend on several, not always well-understood chemisorption and physisorption, the chemisorption factors. and physisorption approaches are the most promising that could meet the goals outlined in the In the theoretical studies of hydrogen DOE Hydrogen Plan. Carbon nanotubes (CNTs) adsorption on CNTs, both chemisorption and have been predicted to be the most promising physisorption were investigated. Similar to the adsorbents in order to meet the DOE standards for experimental studies of hydrogen adsorption on hydrogen application and transportation [1–4]. High CNTs, the theoretical results reported by different values of hydrogen content in the nanotubes have groups also vary. The reason is the difference in the been reported by some research groups. The CNTs models as well as the simulation methods reported experimental data about the capacity of adopted. The chemisorption was studied by DFT- hydrogen storage in CNTs vary greatly, and it seems based methods while the physisorption was analyzed that some exciting results reported fail to be well mainly by Monte Carlo and Molecular Dynamic reproduced. This kind of discrepancy might be due simulations, in which only nonbonding interactions to the differences in quality of CNTs and in the described by the Lennard-Jones potential are adsorption systems adopted. Obviously, more included in the potential functions used. In some systematic work is needed to solve the problem. cases the authors usually treat hydrogen molecules Furthermore, the structures of the different as spherical particles and carry out the calculations carbonaceous materials used as well as the dopant only for, mostly unspecified explicitly, armchair content are very difficult to control [5]. At present nanotubes. 2 Theoretical Approach

The aim of this article is to investigate the nature of the interaction between molecular hydrogen and a (5,5) SWNT using ab-initio calculations together with the hydrogen storage capacity in large scale nanotube systems using Molecular Mechanics and Molecular Dynamics calculations.

Figure 2: a) nanotube sites where molecular hydrogen 2.1 Ab-initio calculations approach, b) three different structural configurations of In order to treat our system with ab-initio methods, hydrogen’s approach (hydrogen bond is set to 0,74 Å), c) we cut several rings of a 5-5 SWNT and treat them carbon atoms described with basis set of high accuracy depending on the case of hydrogen’s approach as an independent cluster. At the end of this system we put hydrogen atoms in order to saturate the We described our system with two different basis set dangling bonds. Our model-nanotube system results depending on the sites A, B and C. Aiming in in C24H12 cluster (Fig1). In the resulting system we accuracy, the carbon atoms closer to the interacting examine three possible sites (A,B and C) where H2 hydrogen, were treated with larger basis set than the can approach the nanotube (Fig 2a). A is considered other atoms of the model. For structural the center of the central phenyl group, B is configurations of A case we described the phenyl considered the middle of a C-C bond and C is carbons (6 bold carbons) (Fig 2c left) and the H2 considered a C atom of the central carbon ring. H2 molecule with the 6-311++G** basis set which adds molecule can approach the nanotube with different polarization and diffusion functions in the triple zeta orientations: inside-outside, vertically or parallel to basis set. The rest of the atoms were described with the tube axis (see Fig 2b). Taking into account all the 3-21G basis set. For structural configurations of the possibilities we examine 12 approaches. (A1in, cases B and C we described the 6 carbons shown in A1out, A2in, A2out, B1in, B1out, B2in, B2out, (Fig 2c right) and the H2 molecule with the 6-311+ B3in, B3out, C1in, C1out). +G** basis set and the rest of the atoms were described with the 3-21G basis set.

Following this methodology we perform a scan of the potential energy of these different approach pathways (Fig. 3). From our results the following conclusions can be made:

- From distances between 0,5-2,5 angstroms from the nanotube, the potential of hydrogen interaction is repulsive. The attractive potential starts at larger from 2,5 Å distances and varies according to the site.

- There are mainly three groups of pathways and each one follows its own behavior:

The first one (Fig.3 group A) consists of A1in, B2in, Figure 1: The procedure of CNT cut and the resulting B1in, C1in, A2in and B3in pathway, which are model-system. pathways that approach the nanotube from inside

The method we used is the Density Functional The second group (group B) consists of B1out, Theory with the B3LYP functional and the C1out and A1out. These are pathways of H2 calculations were performed using the Gaussian 98 approaching the nanotube from outside with program package [6]. perpendicular orientation to the tube axis. temperature changes? This question can only be answered by Molecular Dynamics calculations. 2.2 Molecular Mechanics – Molecular Dynamics calculations

Two systems were studied in this part of our work: (a) a (5,5) armchair, carbon nanotube with hydrogen molecules and (b) nanotube bundle composed of seven (5,5) armchair nanotubes with hydrogen molecules. In the literature, results of molecular mechanics (MM) [8], together with molecular dynamics (MD) simulations [9] for both systems are reported. Nevertheless, unlike the previous works, in which the hydrogen molecules Figure 3: Potential energy scan of molecular hydrogen interacting with 5-5 CNT in different sites and with were treated as single point structureless spherical different structural conformations. particles, explicit atom model was used in the present study. In addition, the force fields applied The third group (group C) consists of A2out, take into account not only the Lennard-Jones B2out and B3out. These are also pathways of H2 potential describing nonbonded interactions but approaching the nanotube from outside but parallel allow for the deformations of the nanotubes. In all to the tube axis. cases, the length of CNT was 2.68 nm. Hydrogen atoms were used to saturate the dangling bonds of Consequently to the previous, the stronger CNTs, which is a common practice for saturating the interaction takes place inside the nanotube (group boundaries, yielding C220H40. A). The inner positions of molecular hydrogen possess larger binding energies than the equivalent MM and MD calculations have been performed outer positions. Due to the opposite curvature of the by the Discover program in Materials Studio two sites, in the inner positions, the molecular program package [10] and with Compass hydrogen interacts with more carbon atoms. The parameterizations. It should be noted that in most favorable binding (-0,937 Kcal/mole) of COMPASS force field most parameters were hydrogen was observed in pathway A1in where H2 derived from ab-initio data. For each system studied symmetrically interact with the most possible carbon in the present atoms.

The difference of the energies between the group B and group C hydrogen pathways can be attributed to charge induced dipoles. In our previous work [7] we explained why alkali metal doped carbon nanotubes possess high hydrogen uptake and we attributed that to the fact that hydrogen interacted stronger with the alkali doped nanotubes rather that the pure nanotubes due to charge induced dipoles that were created on the molecular hydrogen. In this Figure 4: Projections of (5,5) carbon nanotube with work we observe the same phenomenon only in hydrogen molecules after molecular mechanics. smaller scaling since the dipole in H that is induced 2 work, the structure was optimized before the main from the nanotube’s π electrons is smaller. In the B2out case, no dipole can be induced due to the MD simulations. Contrary to the former calculations parallel orientation of the hydrogen molecule to the in which only nonbonded interactions described by tube walls. The highest binding energies of group’s the Lennard-Jones potential have been taken into B configurations varies from -0,45 to -0,32 account, the nanotubes are not treated as rigid. Thus, Kcal/mole while of group’s C binding energies the energy increments associated with the bond varies from -0,20 to -0,10 Kcal/mole. length and bond angle deformations as well as those pertaining to torsional distortions and electrostatic It is obvious that the interaction of molecular interactions are included in the force field used. In hydrogen with a nanotube is weak. What does it addition, nonbonded interactions involving really happen when we have a slightly change on the hydrogen atoms, not those of the hydrogen system’s condition and especially when the molecules treated as spheres, enter explicitly our calculations. The stabilization energy of a complex temperature is favourable to the hydrogen was calculated as a difference between the total adsorption. energy of the complex and the sum of the energies of its constituent parts. All MD simulations were Interestingly, the bundle of seven armchair (5,5) performed at constant volume (NVT ensemble) with nanotubes and hydrogen molecules, we found that it 1 fs time step in order to study the effect of is more stable with the hydrogen sheath remaining temperature on the hydrogen adsorption in CNTs, intact at least up to 50 K (Fig. 5). The calculations where N represents the number of atoms, V is presented indicate that the total amount of the volume and T is temperature. The energy of the hydrogen inside the nanotubes is very small and H2 systems was minimized then and the main MD molecules outside the nanotubes do not ‘stick’ to simulation was performed after equilibration. MD them at higher temperatures. This result agrees with was carried out for the entire systems at 10, 50 and the conclusions of other groups using different 100 K. models [11–14]. Therefore, it seems that the very high hydrogen uptake of carbon nanotubes that even 2.2.1 Molecular mechanics study could surpass the US Department of Energy requirements of the gravimetric (6.2wt %) and All MM calculations were performed with volumetric (65 kg/m3) densities for storage and hydrogen molecules being outside the CNTs. As transportation cannot be obtained by physisorption shown in Fig. 4, H2 molecules are arranged in process. concentric with the tube ring outside the nanotube. No hydrogen molecules enter the tube which may be due to its small diameter. The molecular mechanics calculations on the single armchair (5,5) nanotube and hydrogen molecules revealed that the system is stabilized in comparison with the isolated nanotube and hydrogen molecules. The stabilization energy is defined as the difference between the steric energy of the system of nanotubes with hydrogen molecules and that of the sum of the energies of its constituent parts.

2.2.2 Molecular dynamics study

It is known that the physisorption of a given sorbate is governed by several factors such as the potential energy surface of the sorbate–sorbent interactions, and temperature. For a given system made of specific CNTs and hydrogen molecules, temperature is a factor that needs to be taken into account. Taking this into account and following the Figure 5: Bundle consisting of seven (5,5) carbon minimized structures of hydrogen-involved CNT nanotubes with hydrogen molecules after 500 ps of discussed above, MD simulations were further molecular dynamics at 50 K. carried out to examine adsorption behaviours of hydrogen molecules at different temperatures.

The concentric ring is stable only up to 10 K. At 3 Conclusions higher temperatures the ring is destroyed, resulting Using both ab-initio and MM/MD calculations in the scattering of H molecules in all directions. 2 we investigated the hydrogen storage in (5,5) The attractive energy of nonbonding interactions is SWNTs. The ab-initio results revealed the exact too small to counteract the destruction caused by binding energy when molecular hydrogen interacts thermal vibrations. This happens due to the kinetic with different sites of the sidewalls of the nanotube energy of H molecules that increases greatly at 2 and with different structural conformations. The higher temperatures. When the kinetic energy is high nature of this very weak interaction was enough, the H molecules would escape from the 2 characterized by charged induced dipoles. On top of attraction of the tube. It should be noted here that the this, MM/MD simulations showed that hydrogen hydrogen molecules diffuse with lower speed at 50 molecules adsorbed on (5,5) CNTs via a K than at 100 K, suggesting that the lower physisorption mechanism are very limited even at low temperatures. Acknowledgements

The present work is supported through grants from the IRAKLITOS-Fellowship for research of University of Crete and the O.P. Education ‘Pythagoras’.

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