Energetics and Electronic Structure of Encapsulated Graphene

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Energetics and Electronic Structure of Encapsulated Graphene Nanoribbons in Carbon Nanotube Bikash Mandal, Sunandan Sarkar, and Pranab Sarkar J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp4025359 • Publication Date (Web): 15 May 2013 Downloaded from http://pubs.acs.org on May 23, 2013

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The Journal of Physical Chemistry

Energetics and Electronic Structure of Encapsulated Graphene Nanoribbons in Carbon Nanotube Bikash Mandal, Sunandan Sarkar, and Pranab Sarkar∗ Department of Chemistry, Visva-Bharati University, Santiniketan- 731235, India E-mail: [email protected]

Abstract We report results of our total energy electronic structure calculation of encapsulation of graphene nanoribbon (GNR) in the carbon nanotube (CNT). The encapsulation of both coronene and perylene based graphene nanoribbons in zigzag (n,0) carbon nanotubes (where n ranges from 14 to 18 for perylene based nanoribbon and from 16 to 20 for coronene based nanoribbons) are exothermic process. Our study shows that in certain cases arm-chair GNR (aGNR) encapsulated CNT results type II band alignment and may be useful in the application in solar cells. We have also studied the potential of this composites for hydrogen storage. We found that the encapsulated GNR composite systems have higher hydrogen adsorption energies than the individual components of either GNR and CNT. The hydrogen molecules oriented perpendicular to GNR are found to be more stable as compared to hydrogen molecules parallel to GNR.

Keywords: Encapsulated GNR; Stability; Electronic structure; Hydrogen adsorption

∗ To

whom correspondence should be addressed

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1 Introduction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

In carbon family, graphene 1,2 nanoribbons (GNR) are of great interest due to their unique electronic properties which can be tuned by changing their edge structure and width. 3–13 Another allotrope of carbon, which also have immense impact in nanoscience and nanotechnology, is carbon nanotube (CNT), whose electronic properties are function of chirality, diameter and strain. 14–20 Hollow interior of carbon nanotube is nice place for small nanostructured material such as graphene nanoribbons, fullerene, metals, clusters, DNA etc. to be incorporated. The filling of the interior space of the carbon nanotube with nanoscale materials results in a novel nanohybrids with interesting properties which may be very different from the individual components. Very recently a novel composite material, structured as graphene nanoribbons encapsulated in carbon nanotubes, known as encapsulated graphene nanoribbons, was synthesized. 21–23 These authors have shown that the quantum confinement effects provided by one-dimensional tube helps to align coronene and perylene molecules edge to edge to achieve dimerization and oligomerization of those molecules into long nanoribbons. They have also performed a theoretical simulation and have demonstrated the electronic structure of encapsulated GNRs is the same as for free standing ones. However, the details of the electronic structure of this particular class of interesting nanohybrids are still missing. But the detailed understanding of the electronic structure is of immense importance for further exploration and optimization of these nanostructures in device fabrication. Here, we explored the energetics and electronic properties viz. band structure, density of states (DOS), VBT (valance band top), CBM (conduction band minimum) densities of different encapsulated GNRs. We have considered the encapsulation of both perylene and coronene based armchair GNRs in zig-zag CNTs of various radius. We expect the choice of armchair GNRs and zig-zag CNTs will reveal interesting features since armchair GNRs are semiconducting while the zig-zag CNTs are either metallic or semiconducting depending on the chiral indices (e.g. zig-zag nanotube with chiral indices (3n,0) are metallic and others are semiconductor). One of the most challenging research in the recent time, is the development of safe and economically viable hydrogen storage technologies for the widespread use of hydrogen as fuel. The 2


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researchers are searching for several different kinds of materials those include metal, metal alloys, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

metal hydrides etc. for effective hydrogen storage. The nanostructured materials have received considerable attention for this particular purpose due to their potential for a high storage density of hydrogen and have been well studied both at the experimental and theoretical levels. 24–32 Henwood and David Carey 31 investigated the potential of hydrogen physisorption to carbon nanostructures such as graphene and CNTs. As the encapsulated graphene in CNT has been realized experimentally, we explored the the applicability of this new form of composite materials for hydrogen storage. We would like to investigate the possibility of composites as better candidate for hydrogen storage as compared to individual components.

2 Computational methodology and modelling All simulations were performed by using self-consistent charge density-functional tight-binding (SCC-DFTB) method, considering van der Waals interaction between nanoribbon and nanotube, based on Slater-Kirkwood model. The SCC-DFTB method has been described in detail elsewhere. 33–37 So, here we give a very brief description of the method. In this method, charge density fluctuation is considered and the total energy is expressed as second order expansion of DFT KohnSham 38,39 energy with respect to charge density fluctuations. The total energy including van der Waals interaction in DFTB method can be expressed as follows.

DFT B Etot =

occ

∑ nihΨi|Hˆ 0|Ψii + i

1 N γαβ ∆qα ∆qβ + Erep + Edis 2∑ αβ

= E0 [n0 ] + E2 [n0 , δ n] + Erep + Edis .

(1)

The first term of the above equation is the sum of Kohn-Sham eigenvalues of occupied eigenstates, ψi . We have considered the frozen core approximation i.e the inner electrons are replaced by effective core potential and the valence electrons are treated explicitly. The second term repre-

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sent second-order expansion of total energy with respect to charge density fluctuation. The third 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

term corresponds to internuclear repulsive energy. Finally, the last term is the London-type dispersion energy and has included in the DFTB scheme through Halgren approach. 40 The details of the inclusion the dispersion energy in the DFTB method can be found elsewhere. 41 We considered two different systems, namely perylene based armchair nanoribbon within zigzag nanotube(P-aGNR@z-CNT) and coronene based armchair nanoribbon in zig-zag nanotube (CaGNR@z-CNT). For perylene and coronene based GNRs, the zigzag(n,0) nanotubes were taken with chiral indices varying from 14 to 18 and from 16 to 20 respectively. Graphene nanoribbons were placed at the center of the nanotubes. All the structures were simulated as infinite structures by using periodic boundary conditions and suitably oriented supercells along z axis. The calculations have been performed with a suitable vacuum region of 50 Åsurrounding the structures-along the x and y directions to avoid spurious interactions among consecutive periodic replicas. Geometry optimizations have been performed with the conjugated gradient algorithm, until all forces became smaller than 0.001 eV/Å. Convergence tests on the k-points sampling showed that a (1 X 1 X 8) Monkhorst-Pack grid is appropriate for our calculations. All the structures as well as their lattice constants were optimized using the DFTB+ program, introducing van der Waals interaction, based on Slater Kirkwood model, using previously derived set of parameters for H and C. 42 The total-energy minimized atomic geometries of both perylene and coronene based GNRs encapsulated in the zig-zag (n,0) carbon nanotube are shown in figure 1. From the figure it is clear that both the nanoribbon and the CNT in most of the hybrid aGNR-CNT(n,0) systems almost retain their original shapes. However, the space provided by the CNT(n,0) with n ≤ 14 are not sufficient for the encapsulation of GNR. The structure of the CNT of these systems are substantially distorted from that of isolated one as is evident from the figure. The GNRs are placed horizontally inside the CNTs in the composite systems. Hence, the distance between GNR’s edge hydrogen and CNTs wall is described as Horizontal distance and the perpendicular distance between center of the GNR and CNT wall is the vertical distance. The calculated vertical and horizontal distance (keeping GNR-plane horizontally) between nanotubes and GNRs (for both coronene and perylene based)

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are presented in table I. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3 Results and discussion 3.1 Energetics of GNR encapsulated CNT To understand the stability of different encapsulated GNR in CNT, we have calculated the encapsulation energy, Eenc by subtracting energies of isolated GNRs and CNTs, EGNR , ECNT respectively from that of composite systems, EGNR@CNT :

Eenc = EGNR@CNT − ECNT − EGNR

(2)

In figure 2 we have shown the encapsulation energies of both coronene (a) and perylene (c) based graphene nanoribbon encapsulation in zCNT as a function of the radius of the CNT. The figure reveals that the insertion of ribbons into nanotubes is energetically favorable process and there is an optimum diameter of CNT at which the stabilization is maximum and this optimum diameter also depends on whether the nanoribbon is perylene or coronene based. Thus the most stable perylene based aGNR encapsulated zCNT is (16,0) CNT and that of coronene based aGNR is (18,0) CNT. As coronene based armchair nanoribbons are larger in width than perylene based ribbons, so optimum diameter to gain maximum stabilization increases to (18-0) nanotube and the system, C-aGNR@zCNT(18-0), is stabilized by 0.240 eV/Å of nanotube, as compared to isolated systems. Talyzin et. al 21 in their theoretical simulation also showed that the insertion of the GNRs in CNT is energetically favorable with energy of about 0.2 eV per 1 Å nanotube length with respect to isolated systems. The encapsulation energy consists of many energy terms, namely distortion energies of GNRs and CNTs and energies of van der Waals interaction between GNRs and CNTs and these energies are calculated and plotted as a function of tube radius in figure 2. The energies for van der Waals interaction along with the encapsulation energies are plotted for both coronene(a) and perylene(b)

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based GNRs and the distortion energies of GNR and CNT for both systems are shown in the insets 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(c) and (d). In consistent with figure 1, this figure reveals that distortion is maximum in (16,0) and (14,0) CNTs respectively, for coronene and perylene based systems, and deformation of CNTs gradually decreases with rise of tube radius. In this context it should be noted that distortion of CNTs in coronene based systems is much higher than that of perelyne based systems for a given CNT, due to larger width of coronene based GNR. The figure also reveals that the distortion energy of GNR for all CNTs are very small. Very small deformation energy of GNRs for all CNTs and for both systems indicates that these are not distorted due to encapsulation. The figure shows that the maximum van der Waals interaction energy in C-aGNR@CNT-18-0 and P-aGNR@CNT-16-0, and almost negligible deformation of corresponding isolated systems give rise to highest encapsulation energy for these two different GNR based systems. As radius of CNTs reduces from optimum radius of two different systems, van der Waals interaction for stabilization falls and deformation rises. But the deformation is still smaller than the van der Waals interaction, resulting overall stabilization for encapsulation even in smallest CNT which we have considered. The stability of other encapsulated systems with radius greater than the optimum radius are low due to the wider separation between GNR and CNT and hence weaker van der Waals attraction. The figure also suggests that the encapsulation energy of GNR in CNT will positive beyond certain radius of the CNT and the process will be endothermic. So beyond certain radius, the encapsulation is not favorable. We have also calculated interaction energy between graphene sheet and perpendicularly placed GNR on the sheet and plotted the same as a function of distance between them in fig. 3. The figure reflects that the interaction is maximum when the distance between the sheet and the edge hydrogen is close to 2.60 Å, below this distance the GNR repels the sheet, so stabilization falls down and after that, interaction also decreases due to larger separation. The requirement of 2.60 Å is almost fulfilled in (18,0) CNT for coronene based systems, which results maximum van der Waals interaction in C-aGNR@CNT(18-0). Due to further reduction of CNT’s diameter, GNRs repel CNT’s wall resulting decrement of stabilization energy and distortion of CNTs. The interaction

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energy decreases with further increase in CNT’s diameter but distortion gets almost disappear. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.2 Electronic structure 3.2.1 Coronene based armchair GNRs encapsulated in zigzag CNT (C-aGNR@zCNT) We show in figure 4 the band structures along with the density of states of three representative encapsulated aGNR in CNT of different radius. To understand the effect of encapsulation in the electronic states of composite systems, we have also shown in the same figure the band structures and density of states of the isolated GNR and CNTs. From the band structures it is clear that states from isolated systems are slightly shifted in composite systems; GNR’s state move towards upward direction and states from CNTs negligibly stepped to downward direction. The movement of energy states may be due to effect of electrostatic potential of individual systems on each other after encapsulation. Band shifting is larger for GNRs compared to CNTs, because of higher electrostatic potential around GNR and it is very interesting to observe that band shifting of GNR decreases with rise of CNT’s diameter due to lowering of perturbation. Few degenerate bands of CNTs become almost separate after encapsulation. Mixing of bands of isolated systems is also observed in (16,0) and (18,0) CNT encapsulated coronene based ribbon. The zCNT(18,0) is metallic and the band structure reveals that the encapsulation of aGNR in (18,0) zCNT retain the metallic behaviour. The other encapsulated systems are semiconducting as that of the isolated CNT however, the electronic band structure near the Fermi level as mentioned earlier has been modified. The band gap also decreases to some extent as compared to isolated CNT. The details of the effect of encapsulation on the electronic energy levels can be gained from the DOS as shown in figure 4. From the figure it is evident that for (16,0), (17,0) and also (19,0) zCNT (not shown here) the encapsulation of aGNR results in type-II band alignment thus, the valance band top (VBT) and conduction band minimum (CBM) are on GNR and CNT, respectively. To have more clear understanding of this type-II behaviour we have plotted the VBT and CBM densities of all five encapsulated systems we studied in figure 5. As it is evident that the VBT and CBM densities of (16,0), (17,0) and (19,0) aGNR@zCNT are on nanoribbons and CNTs respectively, thus confirming the type-II band 7



alignment. The only metallic system aGNR encapsulated(18,0)zCNT has both VBT and CBM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

densities on CNT.

3.2.2 Perylene Based Armchair GNRs Encapsulated in zigzag CNT (P-aGNR@zCNT) We have now considered the electronic structure of perylene based armchair GNR encapsulated zCNT. The electronic band structure of three different encapsulated systems along with the DOSs are shown in figure 6. As can be seen from the figure, the energy bands of individual systems are shifted, but to greater extent, specially for GNRs as compared to coronene based systems. Here also the degeneracy of few CNT’s bands are lifted, but to larger extent relative to previous one. Band mixing of individual components is only noticed in P-GNR@CNT-15-0. The band gap of GNR’s rises in composite system because of lattice contraction. The band structure of P-GNR@CNT-15-0 [6(c)] suggests that it is the most interesting system. From it’s band structure, one can think, there occurs crossing of bands of isolated systems, but close inspection reveals that a degenerate band of isolated CNT splits because of GNR encapsulation, one of it crosses the Fermi level to enter negative energy zone and the other move back to positive energy region from the Fermi level, and the GNR’s band gets back to negative energy from the apparent crossing point along with one of the CNT’s band. The isolated (15,0) and (18,0)(not shown here) CNTs are metallic and in the encapsulation of graphene nanoribbons retain their metallicity character. The other encapsulated systems are semiconducting in nature. From the values of the individual band gap it is seen that the composite systems have lower band gap values as compared to corresponding isolated CNT. Thus the encapsulation of perylene based aGNR in zCNT causes a reduction in the band gap values. From the DOSs plot, we found that the contribution to the valence band top and conduction band minimum comes from GNR and CNT respectively for all encapsulated systems. To have detailed understanding of the contribution of GNR and CNT to VBT and CBM in the composite system we show the VBT, CBM densities in figure 7. The figure clearly reveals the strong localization of VBT on GNRs and CBM on CNTs for all studied systems and thus resulting in type-II band alignment. So, our study reveals that there are encapsulated systems (both Coronene and perylene

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based) where we found type-II band alignment. This type-II band alignment facilitates the charge 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

separation as electrons and holes are residing on different substrates resulting the suppression of charge recombination rate. Thus, we suggest these encapsulated systems may find application in designing solar cell.

3.3 Hydrogen adsorption of composite system We have also studied the hydrogen adsorption behaviour of encapsulated GNR, considering PaGNR@CNT-16-0 as representative example. We have studied several adsorption sites (Fig. 8) with the axis of the hydrogen molecule aligned either parallel or perpendicular to the graphene surface. Hydrogen molecules are aligned with hydrogen molecular axis perpendicular to the graphene surface on sites A , B and C while the sites D and E are aligned with the hydrogen axis parallel to the graphene surface. On site A, hydrogen molecule is placed above the center of a hexagon of carbon atoms, the molecule is placed above the midpoint a C-C bond(site B) and hydrogen molecule is placed above a carbon atom on site C. For site D, the hydrogen molecule lies across the midpoints of the C-C bonds and for site E, the molecule lies across the two opposing carbon atoms. The binding energies and the separation between different nanosystems such as GNR encapsulated in CNT (composite system), isolated GNR, isolated CNT and hydrogen molecule are shown in Table 2. From the values of the binding energies of the composite and isolated systems it is clear that the hydrogen binding capacity of composite systems are several times larger than the isolated systems. From the table it is also evident that the configurations where the axis of the hydrogen molecule is perpendicular to the graphene surface (adsorption sites A, B and C) have more binding energies as compared to the configurations where the axis of the hydrogen molecule is parallel to the graphene surface (adsorption sites D and E). Our results of hydrogen adsorption on isolated graphene and carbon nanotube are in sharp contrast with that of Henwood and David Carey 31 These authors have shown that the binding energies of parallel configurations are little larger than the perpendicular orientation. This difference in adsorption behaviour is because of the fact that Henwood and David Carey 31 in their study didn’t taken into account the van der Waals 9



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interaction, one of the most important contribution to binding energies. For composite system, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the perpendicular orientation of the hydrogen molecule in the encapsulated GNRs has much better hydrogen adsorption energies as compared to parallel orientation because of the fact that the hydrogen atom in perpendicular orientation experiences van der Waals attraction to carbon atom of the CNT that imparts extra binding energies. Thus the potential well for graphene-hydrogen interaction is deeper for for perpendicular orientation of the hydrogen molecule as compared to parallel orientation. The average graphene-hydrogen separation are smaller for perpendicular orientations of the hydrogen molecule. So our study on hydrogen adsorption in encapsulated GNRs suggests that composite systems have better hydrogen adsorption characteristics as compared to isolated CNT or GNR and the hydrogen oriented perpendicular to the GNRs are found to be more stable than hydrogen oriented parallel to the GNR because of the operation of van der Waals forces between hydrogen atom and the carbon atoms of the CNT. To understand the gas conditions for efficient storage we have calculated and compared the values of GH2 ( = εH2 − µH2 ), for adsorption on different sites. 43 The -ve value of GH2 implies the efficient hydrogen storage. At the absolute temperature T and for a partial H2 pressure, the µH2 is given by

µH2 = H 0 (T ) − H 0 (0) − T S0 (T ) + kB T ln

P P0

(3)

where H 0 and S0 are the enthalpy and entropy at the pressure P0 1 bar and the values are obtained from ref. 44 Using the above equation, one can calculate the chemical potential at different partial pressures of H2 at a certain temperature. We have calculated the chemical potentials at 300K for different partial pressures of H2 and then GH2 at different partial pressures of H2 . We have shown G vs. µ plot for one representative system (H2 adsorbed at site B) in figure 9 and from the figure we found that GH2 is negative only at high hydrogen partial pressure. So, we conclude that hydrogen storage for the composite systems we studied is only efficient at high hydrogen concentrations at normal temperature.

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4 Conclusion 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

To summarize, we have studied the energetics and electronic structure of encapsulation of coronene and perylene based aGNRs in zCNTs. Our study reveals that the process of encapsulation of aGNR in CNT is exothermic, thus such encapsulation is experimentally feasible. However the stability or energy gain very much depends on the radius of the CNT as well as whether the aGNR is of coronene or perylene type. There are optimum radius of CNT where the encapsulation is energetically most favorable. We have found that the encapsulated system aGNR(Coronene)@zCNT(18,0) (the most stable one) retains the metallic character of CNT while other coronene aGNR encapsulated systems are semiconducting. The encapsulation of perylene based aGNR in zCNT results type-II band alignment for CNT of different radius we studied. As the encapsulation of aGNR in zCNT in some cases results in type-II band alignment, the charge recombination rate of these composite systems are expected to be lower and may find application in designing solar cells. We also explored the possibility of using these composites as hydrogen storage devices. Our study reveals that aGNR@zCNT composites have higher hydrogen adsorption characteristics than the individual components and hydrogen adsorption is efficient only at high hydrogen concentration. Acknowledgments This paper is dedicated to Prof. S. P. Bhattacharyya, Ph. D. supervisor of one of the authors (P.S) on the occasion of his 65th birth anniversary. The financial supports from DST, Govt. of India [SR/NM/NS-49/2007 and FIST program ] through research grants are gratefully acknowledged. The authors (B.M.) and (S.S.) are grateful to CSIR , New Delhi, for the award of Senior Research Fellowships(SRF).

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(21) Talyzin, A.V.; Anoshkin. I.V.; Krasheninnikov, A.V.; Nieminen, R.M.; Nasibulin, A.G.; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Jiang, H. et al. Synthesis of Graphene Nanoribbons Encapsulated in Single-Walled Carbon Nanotubes. Nano Lett., 2011, 11, 4352-4356. (22) Chuvilin, A.; Bichoutskaia, E.; Gimenez-Lopez, M.C.; Chamberlain, T.W.; Rance, G.A.; Kuganathan, N. et al. Self-assembly of a sulphur-terminated graphene nanoribbon within a single-walled carbon nanotube. Nature Mater., 2011, 10, 687-692. (23) Fujihara, M.; Miyata, Y.; Kitaura, R.; Nishimura. Y.; Camacho, C.; Irle, S. et al. Dimerization-Initiated Preferential Formation of Coronene-Based Graphene Nanoribbons in Carbon Nanotubes. J. Phys. Chem. C, 2012, 116, 15141-15145. (24) Elias, D.C.; Nair, R.; Mohiuddin, T.; Morozov, S.; Blake, P.; Halsall, M. et al. Control of Graphene’s Properties by Reversible Hydrogenation: Evidence for Graphane. Science, 2009, 323, 610-613. (25) Ryu, S.; Han, M.Y.; Maultzsch, J.; Heinz, T.F.; Kim, P.; Steigerwald, M.L. et al. Reversible Basal Plane Hydrogenation of Graphene. Nano Lett., 2008, 8, 4597-4602. (26) Ruffieux, P.; Groning, ¨ O.; Schwaller, P.; Schlapbach, L.; Groning, ¨ P. Hydrogen Atoms Cause Long-Range Electronic Effects on Graphite. Phys. Rev. Lett., 2000, 84,4910-4913. (27) Jeloaica, L.; Sidis, V. DFT investigation of the adsorption of atomic hydrogen on a clustermodel graphite surface. Chem. Phys. Lett., 1999, 300, 157-162. (28) Casolo, S.; Lovvik, O.M.; Martinazzo, R.; Tantardini, G.F. Understanding adsorption of hydrogen atoms on graphene. J. Chem. Phys., 2009, 130, 054704-054714. (29) Hornekaer, L.; Rauls, E.; Xu, W.; Sljivancanin, Z.; Otero, R.; Stensgaard, I. et al. Clustering of Chemisorbed H(D) Atoms on the Graphite (0001) Surface due to Preferential Sticking. Phys. Rev. Lett., 2006, 97, 186102-186106.

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(30) Duplock, E.J.; Scheffler, M.; Lindan, P.J.D. Hallmark of Perfect Graphene. Phys. Rev. Lett., 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2004, 92, 225502-225506. (31) Henwood, D.; David Carey, J. Ab initio investigation of molecular hydrogen physisorption on graphene and carbon nanotubes. Phys. Rev. B, 2007, 75, 245413-245423. (32) Ivanovskaya, V.V.; Zobelli, A.; Teillet-Billy, D.; Rougeau, N.; Sidis, V.; Briddon, P.R. Hydrogen adsorption on graphene: a first principles study. Eur. Phys. J. B, 2010, 76, 481-486. ¨ (33) Porezag, D.; Frauenheim, Th.; KOhler, Th.; Seifert, G.; Kaschner, R. Construction of tightbinding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B, 1995, 51, 12947-12957. (34) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Fraunheim, Th. et al. Selfconsistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268. (35) Niehaus, Th.; Suhai, S.; DellaSala, F.; Lugli, P.; Elstner, M.; Seifert, G. et al. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 2001, 63, 085108-085117. ˘ An Approximate Kohnâ´LŠSham (36) Seifert, G. Tight-Binding Density Functional Theory:âAL’ DFT Scheme. J. Phys. Chem. A, 2007, 111, 5609-5613. (37) Aradi, B.; Hourahine, B.; Fraunheim, Th. DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method. J. Phys. Chem. A, 2007, 111, 5678-5684. (38) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. B., 1964, 136, 864-871. (39) Kohn, W.; Sham, L.J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. A, 1965, 140, 1133-1138.

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(40) Halgren, T.A. The representation of van der Waals (vdW) interactions in molecular mechanics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

force fields: potential form, combination rules, and vdW parameters. J. Am. Chem. Soc., 1992, 114, 7827-7843. (41) Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. J. Chem. Phys, 2001, 114, 5149-5155. (42) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th. et al. Selfconsistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 1998, 58, 7260-7268. (43) Wassmann, T.; Seitsonen, A. P.; Saitta, A. M.; Lazzeri M.; Mauri, F. Structure, Stability, Edge States, and Aromaticity of Graphene Ribbons. Phys. Rev. lett., 2008, 101, 096402-096405. (44) Chase, M. W., Jr.; Curnutt, J. L.; Downey, J. R., Jr.; McDonald, R. A.; Syverud, A. N.; Valenzuela, E. A. JANAf Thermochemical Tables, 1982 Supplement. J. Phys. Chem. Ref. Data, 1982, 11, 695-940.

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Table 1: Horizontal and vertical distances between CNT and GNR. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

GNR

CNT

(16,0) (17,0) Coronene based (18,0) (19,0) (20,0) (14,0) (15,0) Perylene based (16,0) (17,0) (18,0)

Distance between GNR and CNT(Å) Horizontal Vertical 2.36 5.75 2.41 6.38 2.61 7.00 2.78 7.37 3.20 7.74 2.46 5.22 2.65 5.83 2.90 6.40 3.33 6.71 3.69 7.10

Table 2: Separation and binding energies of molecular hydrogen on Perylene-aGNR@(16,0)CNT on different adsorption sites of GNR. Site A B C D E

Composite D (Å) Ead (meV) 2.76 48.861 2.78 51.237 2.77 50.858 3.02 9.9210 3.06 9.6270

Systems GNR D (Å) Ead (meV) 2.36 16.166 2.44 20.470 2.46 21.571 3.13 3.9450 3.03 4.0540

D (Å) 2.49 2.51 2.53 3.10 3.18

17


CNT Ead (meV) 18.303 19.953 20.001 6.7730 6.2100


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Optimized structures of coronene (first row) and perylene (second row) based armchair graphene nanoribbon encapsulated in zig-zag nanotube. Carbon and hydrogen atoms are colored cyan and white respectively.

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0 0.04

0.02

GNR CNT

(c)

-0.1

D (eV/Å)

0.015

0.02

0.01

0.01

0.005

0

-0.15

GNR CNT

(d)

0.03

D (eV/Å)

-0.05

E (eV/Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 6.5

7

7.5

r (Å)

5.5

6

r (Å)

6.5

7

-0.2

-0.25

(a) 6.5

7

E(enc)

(b)

E(van der Waals)

7.5

5.5

6

r (Å)

6.5

E(enc) E(van der Waals)

7

r (Å)

Figure 2: Calculated encapsulation energy (Eenc in eV/Å of nanotube) and different contribution to encapsulation energy of coronene, (a), (c) and perylene, (b), (d), based armchair graphene nanoribbon encapsulated in different zig-zag CNTs as a function of the radius(r) of the CNT. Black circles and red triangle represent distortion energy (D) of CNTs and GNRs relative to isolated CNTs and GNRs respectively. The encapsulation energy and van der Waals interaction energy are shown by blue circles and cyan triangle consecutively.

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0

-0.004

E (eV/Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-0.008

-0.012 2.2

2.4

2.6

2.8

3

d (Å)

Figure 3: The interaction energy (E, in eV per Å of GNR in periodic direction of the GNR) between graphene sheet and perpendicularly placed GNR on the sheet, as a function of distance (d) between them.

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2

1

E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-1

-2

Γ

Z PDOS (arb. unit)

(a)

(b)

Γ

Z PDOS (arb. unit)

(c)

(d)

Γ

Z PDOS (arb. unit)

(e)

(f)

Figure 4: Electronic structure of C-GNR@CNT-16-0 (a,b), C-GNR@CNT-17-0 (c,d) and CGNR@CNT-18-0 (e,f). In band structures (a, c and e), solid black lines are bands of composite systems while dotted red (blue) lines are bands of corresponding isolated CNTs (GNR). In figures (b), (d) and (f), the shaded region indicates total DOS where as PDOS from CNTs (GNR) is shown by red (blue) lines. (The Fermi energy of overall system is set to zero.)

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5: VBT (red) and CBM (blue) of composite systems consisting of C-aGNR and (a) (16,0) (b) (17,0) (c) (18,0) (d) (19,0) and (e) (20,0) CNT.

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2

1

E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

-1

-2

Γ

Z PDOS (arb. unit)

(a)

(b)

Γ

Z PDOS (arb. unit)

(c)

(d)

Γ

Z PDOS (arb. unit)

(e)

(f)

Figure 6: Electronic band structures (a, c and e) and PDOS (b, d, f) of encapsulated perylene based armchair graphene nanoribbon in (14,0), (15,0), (16,0) CNTs ,respectively. Black solid lines represent bands of total systems and dotted red (blue) lines are for bands of free standing CNTs (GNR) in band structures. In PDOS figures, the shaded zone shows total DOS and red (blue) line exhibits PDOS of corresponding CNTs (GNR). (The Fermi energy of composite system is set to zero.)

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 7: VBT (red) and CBM (blue) of (a) (14,0), (b) (15,0), (c) (16,0), (d) (17,0), and (e) (18,0) CNT encapsulated P-GNR.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 8: Adsorption sites for a hydrogen molecule on GNR.

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2

1

2

GH (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

-1

-2 -2 300 K pH

2

-1

-20

10

0 µΗ (eV) 2 -10

1

2

0

10

10

Figure 9: GH2 versus chemical potential(µH2 ) plot for most stable hydrogen adsorbed composite system. The alternative bottom axis shows the pressure (in bar) of molecular H2 gas corresponding to the chemical potentials at T=300 K

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 10: TOC Graphic

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E (eV/Å)

0 0.04

0.02

GNR CNT

(c)

-0.1

0.03

0.015

0.02

0.01

0.01

0.005

0

0

-0.15

GNR CNT

(d) D (eV/Å)

-0.05

D (eV/Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


6.5

7

7.5

r (Å)

5.5

6

r (Å)

6.5

7

-0.2

-0.25

(a) 6.5

7

E(enc)

(b)

E(van der Waals)

7.5

5.5

6

6.5

r (Å)

r (Å) ACS Paragon Plus Environment

E(enc) E(van der Waals)

7


0

-0.004

E (eV/Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

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-0.008

-0.012 2.2

2.4

2.6

2.8

d (Å)


3

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2

1

E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


0

-1

-2

Γ

Z PDOS (arb. unit)

(a)

(b)

Γ

Z PDOS (arb. unit)

(c)

(d)


Γ

Z PDOS (arb. unit)

(e)

(f)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


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2

1

E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


0

-1

-2

Γ

Z PDOS (arb. unit)

(a)

(b)

Γ

Z PDOS (arb. unit)

(c)

(d)


Γ

Z PDOS (arb. unit)

(e)

(f)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


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2

1

2

GH (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

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0

-1

-2 -2 300 K pH

2

-1

-20

10

0 µΗ (eV) 2 -10

10

1

0

10


2

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Energetics and Electronic Structure of Encapsulated Graphene

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