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Hydrogen adsorption study. Formation of quantum dots on graphene nanoribbons within tightbinding approach
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 175704 (http://iopscience.iop.org/0957-4484/26/17/175704) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.114.34.22 This content was downloaded on 05/04/2015 at 19:40
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 26 (2015) 175704 (4pp)
doi:10.1088/0957-4484/26/17/175704
Hydrogen adsorption study. Formation of quantum dots on graphene nanoribbons within tight-binding approach Alexander G Kvashnin1,2, Olga P Kvashnina3 and Dmitry G Kvashnin4,5 1
Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street, Troitsk, Moscow, 142190, Russia 2 Moscow Institute of Physics and Technology, 141700, 9 Institutskii line, Dolgoprudny, Moscow Region, Russia 3 Pirogov Russian National Research Medical University (RNRMU), 117997, 1 Ostrovitianov st., Moscow, Russia 4 Emanuel Institute of Biochemical Physics RAS, 119334, 4 Kosigin st., Moscow, Russia 5 National University of Science and Technology MISiS, 119049, 4 Leninskiy prospekt, Moscow, Russia E-mail: [email protected] Received 26 November 2014, revised 17 February 2015 Accepted for publication 9 March 2015 Published 2 April 2015 Abstract
Based on the tight-binding model, we investigate the formation process of quantum dots onto graphene nanoribbons (GNRs) by the sequential adsorption of hydrogen atoms onto the ribbon’s surface. We define the difference between hydrogenation processes onto the surface of zigzag (ZGNR) and armchair graphene nanoribbons (AGNR) by calculating the binding energies with respect to the energy of isolated hydrogen atoms for all considered structures. Keywords: hydrogenation, tight-binding, graphene ribbons (Some figures may appear in colour only in the online journal) Introduction
It was observed that the electronic properties of GNRs depend on their width and the type of edges (zigzag or armchair). Depending on the edges, GNRs can be classified either as a zigzag (Z) or an armchair (A) type [6]. The latter NAGNRs, of which the index N is directly related to the ribbon’s width, are semiconductors with index N = 3m and 3m + 1, (m is the integer), but ZGNRs are always metallic. Nowadays, researchers are interested in the possibility of controlled fabrication of graphene quantum dots (GQDs) and antidotes (GADs). Special interest to GQDs has occurred due not only to the features of the electronic spectra but also to the broad area of their applications. For example, due to the superiority in photostability and the brightness of fluorescence of quantum dots they can offer an alternative to traditional luminophores and can be applied where the tunable luminescence is required [7–10]. Thus, the question on the formation of GQDs with desirable properties is still of great relevance.
Carbon graphene-based nanomaterials: fullerenes, nanotubes and ribbons are the hottest topics for investigation nowadays. Graphene was fabricated only a few years ago and still attracts a lot of attention from the scientific community due to its outstanding properties [1]. Nowadays, graphene is one of the most prospective materials for applications in nanoelectronics as a base for transistors, atomic force microscope cantilevers, chemical sensors, etc [2]. Despite the unique properties, the semimetallic nature of graphene’s conductivity makes it difficult to apply graphene directly in nanoelectronics. Lots of attempts have been made to obtain semiconducting material from graphene (to open the band gap). One of the most developed ways to fabricate a graphene-based semiconductor is the fabrication of GNRs— narrow graphene stripes with widths up to 1 nm, which have been paid great interest, especially due to their small size and intriguing electronic and mechanical properties [3–5].
0957-4484/15/175704+04$33.00
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© 2015 IOP Publishing Ltd Printed in the UK
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
Results and discussions In a recent study we explored a pathway of hydrogen adsorption on GNRs with both zigzag and armchair edges. We carried out the atom-by-atom hydrogenation of graphene nanoribbons with both zigzag and armchair edges and found the most favorable pathway of hydrogenation. We considered the ZGNR, 4ZGNR, and armchair nanoribbons with various widths (7AGNR and 13AGNR). Such narrow GNRs may be achieved by covalently bonded molecular segments [11, 12]. It was found that hydrogen adsorption and the formation of hydrogen pathways on GNRs are significantly different from the hydrogen adsorption on graphene (the phase nucleation process [13]) and strongly depend on the type of edges of the nanoribbons. In this study we defined the minimal amount of hydrogen required for favorable formation of quantum dots onto the GNR’s surface. The considered zigzag and armchair nanoribbons consisted of eight and 10 graphene the unit cells in zigzag and armchair directions, respectively, with edges passivated by hydrogen. During the simulation the hydrogen atoms were added one-by-one onto the surface of the GNRs. On each step all possible positions of the subsequent hydrogen atom were considered, and the binding energies were calculated. All of the calculations were carried out by the tightbinding method using periodic boundary conditions in a framework of the dOXON package. The tight-binding method shows good results in calculations of the covalently bonded systems. Such an approach can be applied to calculate atomic geometry, electronic band structures, conductance and ionization energy for both periodic and amorphous solids and for molecular clusters. Earlier, this approach exhibited a good agreement with more accurate ab initio calculations [6, 14]. In these calculations, the minimization of the structures with respect to the total energy was performed with accuracy higher than 0.01 eV. For a structure that consists of n adsorbed hydrogen atoms the binding energy per each adsorbed atom Eb(n) can be evaluated as follows:
Figure 1. Binding energy per hydrogen atom, depending on the
hydrogen concentration. The red dots represent the binding energy of the most favorable configurations. Zero energy corresponds to the energy of the isolated hydrogen atom. The insets show the geometry of GNR structures with 11%, 21.8% and 34% hydrogen concentration.
of the ribbon remains flat, which also states the absence of impact of the width. Due to this fact only 4ZNGR was considered in the paper. Additional test calculations of the adsorption process onto the surface of 10ZGNR display similar behavior during hydrogenation. The first added hydrogen atom prefers to connect with the edges due to the dangling bonds of carbon atoms located on the edges. When the hydrogen concentration approaches 10% the binding energy becomes negative, and the formation of the hydrogen pathway goes along zigzag edges (step 1 in figure 1). Further increasing of hydrogen concentration formed the islands along the edge (step 2 in figure 1). After half of the ribbon’s length is covered by hydrogen, the growth will go to the next zigzag line moving to the opposite edge of the ribbon (step 3 in figure 1). The formed hydrogenated area has zigzag edges, which repeated the type of edges of investigated graphene ribbon. A completely different situation was observed during the hydrogenation of AGNRs (see figure 2). Here, we considered AGNRs with two various widths called 7AGNR and 13AGNR. The supercells of the considered ribbons consist of 70 carbon and 20 hydrogen atoms and 130 carbon and 20 hydrogen atoms, respectively. It was found that the formation of hydrogen pathways onto both armchair ribbons has identical behavior, which does not depend on their width. Moreover, such behavior totally differs from the pathways’ formation onto zigzag nanoribbons, where the pathway goes along zigzag edges and, with the increasing hydrogen concentration, formed the graphene islands along the edge (figure 1). We calculated the binding energy of considered AGNRs, depending on the hydrogen concentration (see figure 2). The atomic structures of partially hydrogenated ribbons at several values of hydrogen concentration are shown in the insets of figures 2(a) and (b). In contrast to the zigzag nanoribbon the binding energy of hydrogen adsorption onto the surface of 7AGNR became
Eb (n) = ( Etotal − EGNR − nEH ) / n ,
where Etotal is the total energy of the graphene nanoribbon with n hydrogen atoms on the surface, EGNR is the total energy of the pristine GNR (without any atoms onto the surface) and EH is the energy of the isolated hydrogen atom. It should be noted that binding energy was calculated with respect to the isolated hydrogen atom. The hydrogenation process is energy favorable in a case of hydrogen adsorption from atomic hydrogen gas. Firstly, we considered the 4ZGNR structure with hydrogenated edges. The structure consists of 56 carbon and 14 hydrogen atoms. In figure 1 the dependence of binding energy per each adsorbed atom on the hydrogen concentration with respect to the energy of the isolated hydrogen atom is shown. It should be noted that in the framework of the tightbinding approach the width of 4ZGNR is enough to avoid the impact of the opposite edges. Moreover, the atomic structure 2
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
hydrogen pathways to the formation of graphene areas, such as onto the graphene surface or ZGNR (figure 1). Such a wide ribbon can be considered as a semi-infinite graphene sheet in which the hydrogenation process will take place in the same manner as for the hydrogenation of the graphene sheet. It is important to note that during the hydrogenation process in a case of narrow AGNRs (7AGNR and 13AGNR) hydrogen atoms form pathways across the ribbons. At the same time small triangular graphene areas divided by hydrogen pathways form onto the AGNR’s surface, whereas in the case of ZGNRs and wide AGNRs hydrogen atoms formed fully hydrogenated islands, which are consistent with phase nucleation [13].
Conclusions Here, the detailed investigation of the hydrogenation process onto the GNRs’ surface depending on the type of edges and the width was carried out in the framework of the tightbinding approach. The binding energy, depending on the hydrogen concentration, was calculated with respect to the energy of the isolated hydrogen atom. It was found that the hydrogenation process onto the ZGNR’s surface has the nucleation behavior. With the increase of the hydrogen concentration atoms formed small graphene islands onto the surface beginning from the ribbon’s edge. In contrast with ZGNR completely different behavior has the hydrogenation process onto the surface of narrow AGNR. Hydrogen atoms formed the pathways from one edge to the opposite edge of the ribbon. Formation of isolated grapheme areas took place. With further increasing of the width of AGNR hydrogenation process changed the behavior to the nucleation with the formation of graphene islands beginning from the edge.
Figure 2. (a) Dependence of the binding energy on the hydrogen
concentration for 7AGNR and its atomic structure with hydrogen concentrations of 5.7%, 14.3%, 30%, 45.7% and 57.1%; the inset displays the binding energy dependence in a range of concentrations from 10% to 60%; (b) dependence of the binding energy on the hydrogen concentration for 13AGNR and its atomic structure with hydrogen concentrations of 5.3%, 13.1% and 21.5%. Zero energy corresponds to the energy of the isolated hydrogen atom.
negative, even at a low concentration (5.7% for 7AGNR compared with 10% for 4ZGNR), which corresponds to only a few hydrogen atoms onto the surface (see step 1 of figure 2(a)). When the hydrogen covering exceeds 5.7% the binding energy still remains the constant value. In the inset of figure 2(a) the dependence of binding energy on hydrogen concentration is shown in a range of concentration from 10% to 60%, allowing one to see the actual behavior with the varying concentration. As the hydrogen concentration increases the pathway grows to the opposite edge along the zigzag direction (see step 2 in figure 2(a)). After the edge has been reached the hydrogen pathway starts to grow from the starting point and reaches the opposite edge by the other zigzag way (see step 3 in figure 2(a)). The formed hydrogenated line divided the GNR surface into small separate graphene areas. Further growing has a similar tendency as in the previous three steps. In figure 2(b) the dependence of binding energy on the hydrogen concentration for 13AGNR is shown. Similar behavior of the hydrogenation process onto the surface of 13AGNR was found. With further increasing of the ribbon’s width up to 27AGNR the behavior of the hydrogenation process changed from the formation of
Acknowledgments We are grateful to Moscow State University for the use of the ‘Chebishev’ and ‘Lomonosov’ cluster computers and to the Joint Supercomputer Center of the Russian Academy of Sciences for the possibility of using a cluster computer for our quantum-chemical calculations. AGK acknowledges the Scholarship of President of Russia for Young Scientists and PhD Students (competition SP-2013). DGK also acknowledges the support from the Russian Ministry of Education and Science (No. 948 from 21 November, 2012).
References [1] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V and Geim A K 2005 Proc. Natl Acad. Sci. 102 10451 [2] Novoselov K S, Fal′ko V I, Colombo L, Gellert P R, Schwab M G and Kim K 2012 Nature 490 192 [3] Ao Z M, Hernández-Nieves A D, Peeters F M and Li S 2010 Appl. Phys. Lett. 97 233109 3
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
[10] Dreoscher S, Knowles H, Meir Y, Ensslin K and Ihn T 2011 Phys. Rev. B 84 073405 [11] Franc G and Gourdon A 2011 Phys. Chem. Chem. Phys. 13 14283 [12] Chen Y C, Cao T, Chen C, Pedramrazi Z, Haberer D, de Oteyza D G, Fischer F R, Louie S G and Crommie M F 2015 Nat. Nanotechnology 10 156 [13] Lin Y, Ding F and Yakobson B I 2008 Phys. Rev. B 78 041402(R) [14] Zhang X, Kuo J L, Gu M, Baic P and Sun C Q 2010 Nanoscale 2 2160
[4] Gallagher P, Todd K and Goldhaber-Gordon D 2010 Phys. Rev. B 81 8 [5] Cresti A, Lopez-Bezanilla A, Ordejn P and Roche S 2011 ACS Nano 5 9271 [6] Son Y W, Cohen M L and Louie S G 2006 Phys. Rev. Lett. 97 216803 [7] Kamat P V 2008 J. Phys. Chem. C 112 18737 [8] Li Y H, Zhang L, Huang J, Lianga R P and Qiu J D 2013 Chem. Commun. 49 5180 [9] Gupta V, Chaudhary N, Srivastava R, Sharma G D, Bhardwaj R and Chand S 2011 J. Am. Chem. Soc. 133 9960
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Hydrogen adsorption study. Formation of quantum dots on graphene nanoribbons within tightbinding approach
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 175704 (http://iopscience.iop.org/0957-4484/26/17/175704) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.114.34.22 This content was downloaded on 05/04/2015 at 19:40
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 26 (2015) 175704 (4pp)
doi:10.1088/0957-4484/26/17/175704
Hydrogen adsorption study. Formation of quantum dots on graphene nanoribbons within tight-binding approach Alexander G Kvashnin1,2, Olga P Kvashnina3 and Dmitry G Kvashnin4,5 1
Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya Street, Troitsk, Moscow, 142190, Russia 2 Moscow Institute of Physics and Technology, 141700, 9 Institutskii line, Dolgoprudny, Moscow Region, Russia 3 Pirogov Russian National Research Medical University (RNRMU), 117997, 1 Ostrovitianov st., Moscow, Russia 4 Emanuel Institute of Biochemical Physics RAS, 119334, 4 Kosigin st., Moscow, Russia 5 National University of Science and Technology MISiS, 119049, 4 Leninskiy prospekt, Moscow, Russia E-mail: [email protected] Received 26 November 2014, revised 17 February 2015 Accepted for publication 9 March 2015 Published 2 April 2015 Abstract
Based on the tight-binding model, we investigate the formation process of quantum dots onto graphene nanoribbons (GNRs) by the sequential adsorption of hydrogen atoms onto the ribbon’s surface. We define the difference between hydrogenation processes onto the surface of zigzag (ZGNR) and armchair graphene nanoribbons (AGNR) by calculating the binding energies with respect to the energy of isolated hydrogen atoms for all considered structures. Keywords: hydrogenation, tight-binding, graphene ribbons (Some figures may appear in colour only in the online journal) Introduction
It was observed that the electronic properties of GNRs depend on their width and the type of edges (zigzag or armchair). Depending on the edges, GNRs can be classified either as a zigzag (Z) or an armchair (A) type [6]. The latter NAGNRs, of which the index N is directly related to the ribbon’s width, are semiconductors with index N = 3m and 3m + 1, (m is the integer), but ZGNRs are always metallic. Nowadays, researchers are interested in the possibility of controlled fabrication of graphene quantum dots (GQDs) and antidotes (GADs). Special interest to GQDs has occurred due not only to the features of the electronic spectra but also to the broad area of their applications. For example, due to the superiority in photostability and the brightness of fluorescence of quantum dots they can offer an alternative to traditional luminophores and can be applied where the tunable luminescence is required [7–10]. Thus, the question on the formation of GQDs with desirable properties is still of great relevance.
Carbon graphene-based nanomaterials: fullerenes, nanotubes and ribbons are the hottest topics for investigation nowadays. Graphene was fabricated only a few years ago and still attracts a lot of attention from the scientific community due to its outstanding properties [1]. Nowadays, graphene is one of the most prospective materials for applications in nanoelectronics as a base for transistors, atomic force microscope cantilevers, chemical sensors, etc [2]. Despite the unique properties, the semimetallic nature of graphene’s conductivity makes it difficult to apply graphene directly in nanoelectronics. Lots of attempts have been made to obtain semiconducting material from graphene (to open the band gap). One of the most developed ways to fabricate a graphene-based semiconductor is the fabrication of GNRs— narrow graphene stripes with widths up to 1 nm, which have been paid great interest, especially due to their small size and intriguing electronic and mechanical properties [3–5].
0957-4484/15/175704+04$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
Results and discussions In a recent study we explored a pathway of hydrogen adsorption on GNRs with both zigzag and armchair edges. We carried out the atom-by-atom hydrogenation of graphene nanoribbons with both zigzag and armchair edges and found the most favorable pathway of hydrogenation. We considered the ZGNR, 4ZGNR, and armchair nanoribbons with various widths (7AGNR and 13AGNR). Such narrow GNRs may be achieved by covalently bonded molecular segments [11, 12]. It was found that hydrogen adsorption and the formation of hydrogen pathways on GNRs are significantly different from the hydrogen adsorption on graphene (the phase nucleation process [13]) and strongly depend on the type of edges of the nanoribbons. In this study we defined the minimal amount of hydrogen required for favorable formation of quantum dots onto the GNR’s surface. The considered zigzag and armchair nanoribbons consisted of eight and 10 graphene the unit cells in zigzag and armchair directions, respectively, with edges passivated by hydrogen. During the simulation the hydrogen atoms were added one-by-one onto the surface of the GNRs. On each step all possible positions of the subsequent hydrogen atom were considered, and the binding energies were calculated. All of the calculations were carried out by the tightbinding method using periodic boundary conditions in a framework of the dOXON package. The tight-binding method shows good results in calculations of the covalently bonded systems. Such an approach can be applied to calculate atomic geometry, electronic band structures, conductance and ionization energy for both periodic and amorphous solids and for molecular clusters. Earlier, this approach exhibited a good agreement with more accurate ab initio calculations [6, 14]. In these calculations, the minimization of the structures with respect to the total energy was performed with accuracy higher than 0.01 eV. For a structure that consists of n adsorbed hydrogen atoms the binding energy per each adsorbed atom Eb(n) can be evaluated as follows:
Figure 1. Binding energy per hydrogen atom, depending on the
hydrogen concentration. The red dots represent the binding energy of the most favorable configurations. Zero energy corresponds to the energy of the isolated hydrogen atom. The insets show the geometry of GNR structures with 11%, 21.8% and 34% hydrogen concentration.
of the ribbon remains flat, which also states the absence of impact of the width. Due to this fact only 4ZNGR was considered in the paper. Additional test calculations of the adsorption process onto the surface of 10ZGNR display similar behavior during hydrogenation. The first added hydrogen atom prefers to connect with the edges due to the dangling bonds of carbon atoms located on the edges. When the hydrogen concentration approaches 10% the binding energy becomes negative, and the formation of the hydrogen pathway goes along zigzag edges (step 1 in figure 1). Further increasing of hydrogen concentration formed the islands along the edge (step 2 in figure 1). After half of the ribbon’s length is covered by hydrogen, the growth will go to the next zigzag line moving to the opposite edge of the ribbon (step 3 in figure 1). The formed hydrogenated area has zigzag edges, which repeated the type of edges of investigated graphene ribbon. A completely different situation was observed during the hydrogenation of AGNRs (see figure 2). Here, we considered AGNRs with two various widths called 7AGNR and 13AGNR. The supercells of the considered ribbons consist of 70 carbon and 20 hydrogen atoms and 130 carbon and 20 hydrogen atoms, respectively. It was found that the formation of hydrogen pathways onto both armchair ribbons has identical behavior, which does not depend on their width. Moreover, such behavior totally differs from the pathways’ formation onto zigzag nanoribbons, where the pathway goes along zigzag edges and, with the increasing hydrogen concentration, formed the graphene islands along the edge (figure 1). We calculated the binding energy of considered AGNRs, depending on the hydrogen concentration (see figure 2). The atomic structures of partially hydrogenated ribbons at several values of hydrogen concentration are shown in the insets of figures 2(a) and (b). In contrast to the zigzag nanoribbon the binding energy of hydrogen adsorption onto the surface of 7AGNR became
Eb (n) = ( Etotal − EGNR − nEH ) / n ,
where Etotal is the total energy of the graphene nanoribbon with n hydrogen atoms on the surface, EGNR is the total energy of the pristine GNR (without any atoms onto the surface) and EH is the energy of the isolated hydrogen atom. It should be noted that binding energy was calculated with respect to the isolated hydrogen atom. The hydrogenation process is energy favorable in a case of hydrogen adsorption from atomic hydrogen gas. Firstly, we considered the 4ZGNR structure with hydrogenated edges. The structure consists of 56 carbon and 14 hydrogen atoms. In figure 1 the dependence of binding energy per each adsorbed atom on the hydrogen concentration with respect to the energy of the isolated hydrogen atom is shown. It should be noted that in the framework of the tightbinding approach the width of 4ZGNR is enough to avoid the impact of the opposite edges. Moreover, the atomic structure 2
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
hydrogen pathways to the formation of graphene areas, such as onto the graphene surface or ZGNR (figure 1). Such a wide ribbon can be considered as a semi-infinite graphene sheet in which the hydrogenation process will take place in the same manner as for the hydrogenation of the graphene sheet. It is important to note that during the hydrogenation process in a case of narrow AGNRs (7AGNR and 13AGNR) hydrogen atoms form pathways across the ribbons. At the same time small triangular graphene areas divided by hydrogen pathways form onto the AGNR’s surface, whereas in the case of ZGNRs and wide AGNRs hydrogen atoms formed fully hydrogenated islands, which are consistent with phase nucleation [13].
Conclusions Here, the detailed investigation of the hydrogenation process onto the GNRs’ surface depending on the type of edges and the width was carried out in the framework of the tightbinding approach. The binding energy, depending on the hydrogen concentration, was calculated with respect to the energy of the isolated hydrogen atom. It was found that the hydrogenation process onto the ZGNR’s surface has the nucleation behavior. With the increase of the hydrogen concentration atoms formed small graphene islands onto the surface beginning from the ribbon’s edge. In contrast with ZGNR completely different behavior has the hydrogenation process onto the surface of narrow AGNR. Hydrogen atoms formed the pathways from one edge to the opposite edge of the ribbon. Formation of isolated grapheme areas took place. With further increasing of the width of AGNR hydrogenation process changed the behavior to the nucleation with the formation of graphene islands beginning from the edge.
Figure 2. (a) Dependence of the binding energy on the hydrogen
concentration for 7AGNR and its atomic structure with hydrogen concentrations of 5.7%, 14.3%, 30%, 45.7% and 57.1%; the inset displays the binding energy dependence in a range of concentrations from 10% to 60%; (b) dependence of the binding energy on the hydrogen concentration for 13AGNR and its atomic structure with hydrogen concentrations of 5.3%, 13.1% and 21.5%. Zero energy corresponds to the energy of the isolated hydrogen atom.
negative, even at a low concentration (5.7% for 7AGNR compared with 10% for 4ZGNR), which corresponds to only a few hydrogen atoms onto the surface (see step 1 of figure 2(a)). When the hydrogen covering exceeds 5.7% the binding energy still remains the constant value. In the inset of figure 2(a) the dependence of binding energy on hydrogen concentration is shown in a range of concentration from 10% to 60%, allowing one to see the actual behavior with the varying concentration. As the hydrogen concentration increases the pathway grows to the opposite edge along the zigzag direction (see step 2 in figure 2(a)). After the edge has been reached the hydrogen pathway starts to grow from the starting point and reaches the opposite edge by the other zigzag way (see step 3 in figure 2(a)). The formed hydrogenated line divided the GNR surface into small separate graphene areas. Further growing has a similar tendency as in the previous three steps. In figure 2(b) the dependence of binding energy on the hydrogen concentration for 13AGNR is shown. Similar behavior of the hydrogenation process onto the surface of 13AGNR was found. With further increasing of the ribbon’s width up to 27AGNR the behavior of the hydrogenation process changed from the formation of
Acknowledgments We are grateful to Moscow State University for the use of the ‘Chebishev’ and ‘Lomonosov’ cluster computers and to the Joint Supercomputer Center of the Russian Academy of Sciences for the possibility of using a cluster computer for our quantum-chemical calculations. AGK acknowledges the Scholarship of President of Russia for Young Scientists and PhD Students (competition SP-2013). DGK also acknowledges the support from the Russian Ministry of Education and Science (No. 948 from 21 November, 2012).
References [1] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V and Geim A K 2005 Proc. Natl Acad. Sci. 102 10451 [2] Novoselov K S, Fal′ko V I, Colombo L, Gellert P R, Schwab M G and Kim K 2012 Nature 490 192 [3] Ao Z M, Hernández-Nieves A D, Peeters F M and Li S 2010 Appl. Phys. Lett. 97 233109 3
A G Kvashnin et al
Nanotechnology 26 (2015) 175704
[10] Dreoscher S, Knowles H, Meir Y, Ensslin K and Ihn T 2011 Phys. Rev. B 84 073405 [11] Franc G and Gourdon A 2011 Phys. Chem. Chem. Phys. 13 14283 [12] Chen Y C, Cao T, Chen C, Pedramrazi Z, Haberer D, de Oteyza D G, Fischer F R, Louie S G and Crommie M F 2015 Nat. Nanotechnology 10 156 [13] Lin Y, Ding F and Yakobson B I 2008 Phys. Rev. B 78 041402(R) [14] Zhang X, Kuo J L, Gu M, Baic P and Sun C Q 2010 Nanoscale 2 2160
[4] Gallagher P, Todd K and Goldhaber-Gordon D 2010 Phys. Rev. B 81 8 [5] Cresti A, Lopez-Bezanilla A, Ordejn P and Roche S 2011 ACS Nano 5 9271 [6] Son Y W, Cohen M L and Louie S G 2006 Phys. Rev. Lett. 97 216803 [7] Kamat P V 2008 J. Phys. Chem. C 112 18737 [8] Li Y H, Zhang L, Huang J, Lianga R P and Qiu J D 2013 Chem. Commun. 49 5180 [9] Gupta V, Chaudhary N, Srivastava R, Sharma G D, Bhardwaj R and Chand S 2011 J. Am. Chem. Soc. 133 9960
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