B

configuration. In this case the tube wall is not flat toward the tube axis but shows a zigzag shape (Fig. 4a, middle). In the case of the "all rings together" configuration the tube wall is changing shape only in the beginning and at the end, while in between it stays flat (Fig. 4a, right). The flat wall shape that was favorable when carbon atoms had sp2 hybridization is not favored after the hydrogen adsorption because carbon atoms changed hybridization to sp3. Extending this configuration to an infinite atom tube will end up to 50% coverage since one C-zigzag ring has hydrogens and the next does not, periodically. This procedure will cause a 15% enlargement of the tube volume (half of the rings gain 30% in volume).

Bauschlicher in [34] reported also 50% hydrogen coverage in a (10,0) SWNT. He tested with the ONIOM approach a lot of random and prefixed bonding configurations of hydrogen in the tube walls. The "pairs of lines" configuration is presented in Figure 5 and found to be energetically more favorable. This result is not in disagreement with that previously mentioned for a (4,4) SWNT by Froudakis [35] since the (10,0) tube is significantly larger than the (4,4), and the curvature was found to play an important role in the adsorption procedure to SWNTs [37-39]. Furthermore Froudakis has not calculated a "pair of lines" configuration in the (4,4) SWNT.

The second question we tried to answer in [35] is what happens after the adsorption of hydrogens to the tube walls. Is it easier to fill up the tube with hydrogens? In

Figure 5. The most stable configuration of 50% hydrogen coverage in a (10,0) SWNT calculated by Bauschlicher. Modified from [34], C. W. Bauschlicher, Jr., Nano Lett. 1, 223 (2001). © 2001, American Chemical Society.

Figure 4b we report the potential curves when atomic hydrogen approaches the center of three tube-wall hexagons which differ only in the adsorption rate. The first has no hydrogen, the second is half filled with hydrogen, and the third is full of hydrogen. Analyzing these potential curves we see two competing forces in the approaching procedure. In one hand it is clear that the more hydrogen we have in the C hexagon, the larger the hexagon is and the easier the outgoing H passes. This can be easily observed by lowering the barrier at the tube wall as the number of hydrogens in the hexagon increases. On the other hand, the hydrogen in the hexagon is screening the attraction of the carbon atom to the external hydrogen. This screening, in the case of a fully hydrogenated hexagon, inserts a barrier in- the outgoing hydrogen at a distance of 1 A from the tube wall (where the bonded hydrogens are actually located). As a result, the energetically favorable H approach is when the tube wall is half filled with hydrogens. This happens because in the first part of the approach there is no barrier caused by steric repulsion of the bonded hydrogens, while in the entrance of the tube wall the barrier is smaller by almost 0.3 eV than the case of the bare tube.

Comparing the QM/MM results of Froudakis [35] with those of Seifert et al. [32] and Kudin et al. [40] obtained with periodic boundary condition models, we find an agreement concerning the stoichiometry (C: 2 ligand: 1) and the deformation of the tube that take place during the adsorption. Nevertheless there is a disagreement about the ligand orientation around the tube wall that could be a consequence of the different approach used (QM/MM versus periodic box) and/or from the different ligand (H versus F) and/or from the different tube examined (4,4 versus 10,10 that have almost double diameter).

5.4. Molecular Hydrogen Interaction with Doped Carbon Nanotubes

After 1999 when Chen et al. [9] reported that alkali-doped carbon nanotubes possess high hydrogen uptake a lot of experimental work has been performed trying to investigate the hydrogen adsorption in SWNTs and to improve the storage capacity of the tubes by doping them [15]. On the other hand, there was no sufficient theoretical explanation of this phenomenon.

All the theoretical calculations reported so far can be divided in two categories. Either they are empirical [23-29] or they are based on first principle methods but deal only with atomic hydrogen [30-35]. The first category cannot give an understanding of the elementary steps in the adsorption process. Since these methods are not ab initio but based on parameters, they cannot provide insight into the chemical bond. The first principle methods can, but they deal only with atomic hydrogen while the most important interaction for the storage, which is the molecular hydrogen interaction with SWNTs, remains untouched. The reason ab initio studies of the H2 interaction with SWNTs do not exist is obvious. The interaction is weak and the system is large.

In [41] we tried to investigate the nature of the H2 adsorption in alkali-doped SWNTs and to compare it with the adsorption in pure SWNTs. Only in this way it is possible to answer why alkali doped carbon nanotubes have high H2

uptake. In order to compromise the large size of the system together with an accurate ab initio method without ending up in a prohibitively large calculation we applied the QM/MM mixed model as described earlier (Section 4.2) in a closed (5,5) SWNT with 150 carbon atoms. K atoms dope the tube in a 2 x 2 pattern as suggested by Gao et al. [42]. In this pattern the K atoms were placed on "hollow" positions above the center of the C hexagons of the tube in such a way that if one hexagon has potassium, all the neighboring ones do not (Fig. 6). A geometry optimization confirmed that these positions were optimum for our model, too. Twenty-four carbon atoms together with two potassium atoms and all the H2 molecules that were interacting with these two K atoms were kept in the QM region, while the rest of the atoms were treated by MM.

The first case considered (Fig. 6, left) was a doped tube where a single H2 molecule was interacting with each K atom. After the geometry was optimized, the binding energy of the H2 to the Kwas 3.4 Kcal/mol/H2. The distance of the K atom from the center of the C6 hexagon of the tube was 3.0 A while the distance of the closer H of the H2 molecule from the K was 3.0 A, too. In the next case (Fig. 6, middle) two hydrogen molecules were interacting with each K and finally three (Fig. 6, right). The binding energies were 2.5 and 1.8 kcal/mol/H2 respectively. The H2 distance from the K was found to be 3.3 and 3.5 A while the K-tube distance remained the same (3.0 A).

From these results is clearly showed that at least three hydrogen molecules can bound each K atom of a doped tube even though the binding energy is consistently decreasing with the number of ligands. The two questions that immediately arise are: How many H2 can be accommodated to each alkali of the doped tube? And why do the doped tubes have larger hydrogen uptake that the pure carbon nanotubes?

For answering the first question we also calculated in [41] the case where five H2 molecules were attached at each K of the doped tube. The binding energy was 1.1 kcal/mol/H2. Then the binding energy per hydrogen molecule was plotted with respect to the number of the H2 molecules. As can be seen from Figure 7 the binding energy decays exponentially. This result has to be considered together with the

Figure 6. Three of the alkali metal doped (5,5) SWNTs used by Froudakis [41] to study the interaction with molecular hydrogen. The first has one H2 per K, the second two, and the third three. A magnifying part of all pictures is also presented.

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