Article pubs.acs.org/JPCC
Amide Functionalization of Graphene and Carbon Nanotubes: Coverage- and Pattern-Dependent Electronic and Magnetic Properties Peng Lu,†,‡ Rulong Zhou,‡,§ Wanlin Guo,*,† and Xiao Cheng Zeng*,‡ †
Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education and Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China ‡ Department of Chemistry and Center for Materials & Nanoscience, University of Nebraska-Lincoln, Lincoln, Nebraska, 68588, United States § School of Science and Engineering of Materials, Hefei University of Technology, Hefei, Anhui 230009, China ABSTRACT: Motivated by successful synthesis of dimethylamide-functionalized graphene (Collins, et al. Angew. Chem. 2011, 123, 9010), we investigate electronic, magnetic, and electron transport properties of covalently functionalized graphene and carbon nanotubes (CNTs) by the amide groups [CON(CH3)2] using density functional theory calculations. We find that when both sublattices of the graphene are evenly functionalized with the amide groups, the band gap of the modified (semiconducting) graphene can be substantially enlarged by increasing the coverage of amide groups. If the modified graphene is metallic, however, its electronic properties are little affected by increasing the coverage. When the two sublattices of the graphene are functionalized unevenly, the decorated graphene exhibits magnetism. As the coverage of amide groups is increased, the electronic properties of the functionalized graphene can be transformed from semiconducting to half metallic and to metallic. Moreover, the electronic structures of functionalized graphene can be regulated by increasing the number of zigzag chains along the supercell edge. For zigzag CNTs (ZCNTs), when the two sublattices are unevenly functionalized by the amide groups, the functionalized CNTs can be either metallic or semiconducting, depending on the pattern of decoration. ZCNTs with large diameters may exhibit magnetism as well. When the two sublattices are unevenly functionalized, the functionalized ZCNTs are always semiconducting with their band gap increasing with the distance between two neighboring amide groups in the radial direction. For armchair CNTs, however, all functionalized systems are metallic without showing magnetism, regardless of the coverage or pattern of amide groups. We also find that the conductivity of the amide functionalized graphene and CNT is lower than that of the pristine counterparts.
1. INTRODUCTION Graphene, a single atomic layer material,1−4 has attracted much interest due to its novel properties, such as the quantum Hall effect,1−4 high thermal conductivity,4−7 and long spin relaxation lengths.8,9 However, pristine graphene itself is a zero-gap semimetal, which prevents its utilization as a logic device and optoelectronic sensor. Many research efforts have been devoted to modulating electronic properties of graphene, for example, by cutting the graphene into nanoribbons with tailored edges,10−14 by doping other elements on the graphene surface,15,16 or by chemical functionalization.17−32 Several experimental studies have shown that chemical functionalization can be an effective approach to modulate properties of the graphene. For example, electronic properties of graphene can be modified by covalently bonding with p-nitrobenzenediazonium tetrafluoroborate,17 hydrogen atoms,18,19 4-mercaptobenzenediazonium tetrafluoroborate,20 pheny,21 aryl moieties,22,32 and 4-nitrobenzene diazonium tetrafluoroborate.23−26 Especially, chemical reaction via Claisen rearrangement, a wellknown carbon−carbon bond-forming chemical reaction, has © 2012 American Chemical Society
been recently realized in oxidizing graphene with the agent N,N-dimethylacetamide dimethyl acetal.32 It has been shown that the carbon-bound N,N-dimethylamide groups [CON(CH3)2] can be covalently bonded with a graphene surface. The aim of this theoretical study is to investigate the electronic, magnetic, and electron transport properties of graphene grown with carbon-bound N,N-dimethylamide, as well as those of functionalized carbon nanotubes (CNTs) with the same dimethylamide groups [CON(CH3)2]. Using density functional theory (DFT) calculations, we find that if the CON(CH3)2 molecules that are bonded with carbon atoms are unevenly distributed over the two sublattices of graphene, the functionalized graphene can exhibit magnetism. As the coverage of CON(CH3)2 increases, the spin polarization can be strengthened, and the functionalized graphene is changed from a metal to a semiconductor. If the CON(CH3)2 molecules are evenly Received: January 30, 2012 Revised: May 28, 2012 Published: June 14, 2012 13722
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Figure 1. (a,b) Atomic structure of graphene covalently bonded with organic molecule CON(CH3)2. Computed electronic structures of functionalized graphene with different supercell size: n = 2 (c), n = 3 (d), n = 4 (e), n = 5 (f) and n = 6 (g). In panels (c)−(f), red and black lines represent spin-down and spin-up bands, respectively. Gray, red, blue, and white balls represent carbon, oxygen, nitrogen and hydrogen atoms, respectively.
for the functionalized graphene, and 50 k-points are used for the functionalized CNTs.
distributed on the two sublattices, the functionalized graphene can be either metallic or semiconducting. Likewise, if the CON(CH3)2 molecules are unevenly distributed on the two sublattices of zigzag CNTs (ZCNTs), the functionalized CNTs can be either a metal or semiconductor, depending on the location of CON(CH3)2 molecules. Magnetism can arise in certain functionalized ZCNTs with large diameter. If the CON(CH3)2 molecules are evenly distributed on the two sublattices, the functionalized ZCNTs are semiconducting, and the energy gap increases with increasing the distance between the two chemisorbed molecules in the radial direction. In contrast, the functionalized armchair CNTs are always metallic and nonmagnetic. We also find that the conductivity of graphene and CNT cannot be enhanced through covalently bonding with CON(CH3)2 molecules.
3. RESULTS AND DISCUSSION 3.1. Amide Functionalization of Graphene. 3.1.1. Electronic and Magnetic properties of Amide Functionalized Graphene. First, we consider a model system such that the amide groups CON(CH3)2 are only bonded with carbon atoms on the same sublattice of a graphene. As shown in Figure 1a, the rhombic graphene supercell is classified by the number of zigzag lines, n, along the supercell edge. The n can be changed from 2 to 6, which gives rise to different density of the coverage. Here, we focus on the n = 4 case as a typical example to illustrate the atomic structure of the functionalized graphene (Figure 1b). It can be clearly seen from Figure 1b that a CON(CH3)2 molecule is chemically bonded with the graphene through a C−C bond. The sp3 bonded C1 atom is pulled upward, 0.52 Å above the graphene plane. The bond length between C1 and C2 is 1.60 Å, which is slightly larger than the C−C bond length of 1.413 Å in the graphene. Yet, positions of other atoms in the graphene are little affected by the chemisorption of CON(CH3)2. The atomic structures in other cases (n = 2, 3, 5, and 6) are similar to the n = 4 case, for which the C1−C2 distances range from 1.59−1.60 Å, little affected by the supercell size. As n changes from 2 to 5, the functionalized graphene always exhibits magnetism, whereas the system becomes nonmagnetic for n = 6. The computed electronic structures of the functionalized graphene with different supercell sizes (n = 2− 6) are shown in Figure 1c−g, respectively. It can be seen that the Dirac point of the pristine graphene no longer exists due to chemisorption of the amide groups. Meanwhile, the flat bands arise near the Fermi level. Interestingly, we find that the electronic structure of functionalized graphene is strongly dependent on n, the number of zigzag lines along the supercell
2. COMPUTATIONAL METHODS DFT calculations are performed using the Vienna Ab-initio Simulation Package (VASP) 5.2 code.33−35 Ultrasoft pseudopotentials for the core region and local-spin density approximation (LSDA) for the exchange-correlation potential are adopted. A kinetic energy cutoff value of 530 eV is used for the plane-wave expansion. The model system consists of amide groups CON(CH3)2 covalently bonded with graphene or CNTs. The conjugate-gradient method is used for geometric relaxation until the force on each atom is less than 0.02 eV/Å. A vacuum region of 10 Å is implemented to avoid interaction among periodic images. For structure relaxation of functionalized graphenes, two-dimensional Brillouin-zone integration is sampled using 6 × 6 × 1 special k-points, which has been proven to be sufficient even for the smallest supercell of functionalized graphene. For functionalized CNTs, 1 × 1 × 10 special k-points are used to achieve energy convergence. For electronic structure calculations, a total of 48 k-points are used 13723
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edge. When n has a factor of 3 (e.g., n = 3, 6), the two bands around the Fermi level can meet at the Γ point, with shape similar to that near the Dirac point of the pristine graphene (Figure 1d and 1g). Otherwise, an energy gap exists between the two bands that are near the Fermi level, and the gap decreases as increasing n from 2 to 5 (Figure 1c,e,f). It is expected that the conductivity of the graphene may be tunable through changing the coverage of CON(CH3)2 molecules. With the spin polarization for n = 4, the exchange splitting of the flat band located at the Fermi level is 0.13 eV, and the energy of the system is lowered by 68.67 meV (per supercell) compared to the spin unpolarized calculation. As shown in Figure 1e, the flat band at the Fermi level is split into two spin polarized bands, both through the Fermi level. Spatial distribution of the magnetization density is depicted in Figure 2a for the n = 4 case. It is found that the magnetization is
graphene are also changed, from metallic (n = 4−6) to halfmetallic (n = 3), and then to semiconducting (n = 2). The energy gap of the spin-up channel is 0.14 eV for n = 3 (Figure 2c). For n = 2 (Figure 2d), the energy gaps for the spin-up and spin-down channels are 1.88 and 1.85 eV, respectively. As shown in Figure 1e, the magnetism in the functionalized graphene stems mainly from the exchange splitting of the flat bands located at the Fermi level. In Figure 3, we plot the partial
Figure 3. Partial charge density of the flat band (red line) (n = 4).
charge density corresponding to the flat band in the spin unpolarized electronic structure (n = 4). It can be seen that the partial charge density is mainly contributed by the carbon atoms near C1 but on a different sublattice from C1 (Figure 3). This behavior is akin to the magnetization density in functionalized graphene. Due to the sp2 to sp3 transformation for C1, the π bonding of the three carbon atoms around C1 is disrupted. The electrons of the three carbon atoms become more localized upon the transformation, leading to the spin splitting of the flat band. To further support this analysis, we have computed the charge transfer between the graphene and CON(CH3)2 molecule based on Bader charge analysis.40 Only 0.01 e are transferred from the molecule to graphene, suggesting that the magnetization is not induced by charge doping in functionalized graphene. 3.1.2. Stability of Amide Functionalized Graphene. The stability of the functionalized graphene can be evaluated by calculating the Gibbs free energy of formation δG, defined by δG = EGO − nCμC − nOμO − nNμN − nHμH, where EGO is the cohesive energy per atom of the chemically functionalized graphene, and ni is the molar fraction of atom i (i = C, O, N, H) in the functionalized graphene, satisfying the relation nH + nO + nN + nC = 1. The binding energy per atom of O2, N2, and H2 molecules is used for μO, μΝ, and μH, respectively, and μC is the cohesive energy per atom of the graphene. As shown in Figure 4, with n increasing from 2 to 6, δG increases from −0.17 to −0.01 eV per atom, where negative values of the formation energy refer to stable structures with respect to the
Figure 2. (a) Spin density of functionalized graphene (n = 4). (b) Average magnetic moment, net magnetic moment, and energy difference between ferromagnetic and nonmagnetic states, as a function of supercell size n for functionalized graphene. (c) Spin polarized DOS of functionalized graphene (n = 3). (d) Spin polarized DOS of functionalized graphene (n = 2).
mainly contributed by the three carbon atoms near C1, while other carbon atoms in the same sublattice as C1 have little contribution to the magnetization (Figure 2a). We have also examined the nature of magnetic coupling in the functionalized graphene (n = 4). It is found that the C2 atom in the molecule is ferromagnetically coupled with the three carbon atoms around C1. In the graphene plane, the carbon atoms belonging to the same sublattice are ferromagnetically coupled, while those belonging to the other sublattice are antiferromagnetically coupled. The average magnetic moment is 0.07 μB for the three carbon atoms around C1. The net magnetic moment of the system is 0.54 μB. The spatial distributions of the magnetization density in other cases are similar to that in the n = 4 case. For the functionalized graphene, we find that the spin polarization is in inverse proportion to the supercell size n (Figure 2b). As n increases from 2 to 6, the average moment of the three carbon atoms around C1 decreases from 0.21 to 0 μB, and the net moment of the supercell changes from 0.87 to 0 μB (Figure 2b). Meanwhile, the energy difference between nonmagnetic and magnetic states changes from 105.74 to 0 eV as n increases from 2 to 6. The electronic properties of the functionalized
Figure 4. Calculated formation energy as a function of supercell size n for functionalized graphene. 13724
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Figure 5. Atomic structure of functionalized graphene with n = 5 (a) and n = 6 (b). (c) Electronic structure and DOS of functionalized graphene (n = 5) with two molecules bonding with A and A1 carbon atoms, respectively. (d) Electronic structure of functionalized graphene (n = 5) with two molecules bonding with A and B carbon atoms, respectively. (e) Electronic structure and DOS of functionalized graphene (n = 6) with two molecules bonding with A and A1 carbon atoms, respectively. (f) Electronic structure of functionalized graphene (n = 6) with two molecules bonding with A and B carbon atoms. (g) and (h): Partial charge densities corresponding to the two bands located just above and below the Fermi level, respectively, for the functionalized graphene (n = 5) with two molecules bonding on A and B carbon atoms, respectively. Red and black lines in panels (c) and (e) represent spin-down and spin-up bands, respectively. Gray and yellow balls represent carbon atoms with sp2 and sp3 hybridization, respectively.
constituents. The more negative δG is, the more stable the nanostructure. As such, the functionalized graphene is expected to be stable when the ratio of the number of sp2 to sp3 hybridized carbon atoms (in the graphene) is in the range of 7:1 to 72:1. Moreover, within allowed ratios, the stability of functionalized graphene increases with increasing the number of sp3 hybridized carbon atoms. We have also considered decoration of two molecules on the same sublattice of graphene in one supercell (n = 6). The calculated δG is −0.08 eV/atom, which is more favorable than having one molecule (δG = −0.01 eV/atom) in the same supercell (n = 6). A larger size of supercell with n = 7 has been checked with one molecule per supercell. Indeed, in this case the molecule cannot be covalently bonded with the graphene. The coverage of amide groups on graphene may be controlled by changing experimental conditions. However it is very difficult to attain exactly a specified coverage of amide groups on graphene in an experiment. Note that the stability of functionalized graphene increases with increasing the number of sp3 hybridized carbon atoms. As such, functionalized graphene with a relatively higher coverage of amide group should be more stable. 3.1.3. Effect of Bonding Position on Electronic and Magnetic Properties in Amide Functionalized Graphene. To examine more realistic coverage conditions as in the experiment, we have considered systems with more than one molecule in the supercell. First, we examine two molecules in one supercell for n = 5 and 6, respectively (Figure 5a,b). Due to the bipartite lattice structure of graphene, two possible ways of decorating graphene with two CON(CH3)2 molecules can be
implemented: (1) both molecules are located on the same sublattice (either A or B), or (2) both are located on different sublattices. As shown in Figure 5a, when the two molecules are bonded with the carbon atoms A and A1 located on the same sublattice (for n = 5), the system is a magnetic metal. Compared to the system with only one molecule per supercell (Figure 1f), two additional splitting bands arise near the Fermi level in the electronic structure (Figure 5c). The density of states (DOS) suggests the system is semiconducting with band gaps of 0.79 and 0.81 eV for spin-up and spin-down channels, respectively (Figure 5c). The average magnetic moment is 0.11 μB for the carbon atoms located nearest to the sp3 bonded carbon atoms in graphene. The atoms located at the same sublattice are coupled ferromagnetically; otherwise, they are coupled antiferromagnetically in graphene plane. If the two molecules are bonded with A and B carbon atoms that belong to different sublattice for n = 5 (Figure 5a), the system is semiconducting and nonmagnetic due to the balanced decoration on the bipartite sublattice of graphene. The functionalized graphene has a 0.32 eV band gap with two additional bands arising near the Fermi level (Figure 5d). Similarly, when the two molecules are bonded with carbon atoms located on the A and A1 positions for n = 6, the system is magnetic and metallic (Figure 5e). Due to weakened molecule bonding, the average magnetic moment of the carbon atoms located near the sp3 hybridized carbon atom decreases to 0.07 μB. Yet, when the two molecules are bonded with A and B carbon atoms for n = 6, the functionalized graphene is still metallic (Figure 5f). 13725
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Figure 6. (a) Atomic structure of graphene with n = 7. (b) Electronic structure of functionalized graphene (n = 7) with three molecules bonding with the A, A1, and B atoms, respectively. (c) Electronic structure and DOS of functionalized graphene (n = 7) with four molecules bonding with the A, A1, A2, and B atoms, respectively. Red and black lines represent spin-down and spin-up bands in panel (c), respectively. Gray and yellow balls represent carbon atoms with sp2 and sp3 hybridization character, respectively.
3.1.4. Origin of Different Electronic and Magnetic Behavior for Amide Functionalized Graphene with Different Bonding Positions. To examine the origin of semiconducting characteristics in functionalized graphene (Figure 5d), we plot computed partial charge densities corresponding to the two bands (Figure 5d) near the Fermi level in Figure 5g,h, respectively. It can be seen that the two bands are contributed by atoms belonging to two different sublattices. The charge density of upper band (above the Fermi level) shows antibonding character, while the lower band shows bonding character. By contrast, when the two carbon atoms that are bonded with the molecule belong to the same sublattice, the induced two flat bands almost coincide to each other near the Fermi level, and both flat bands are uniformly contributed by the localized electrons on carbon atoms belonging to the same sublattice (not shown here). The two induced bands will spin split into four bands to lower the system energy. Hence, the differences in electronic properties of functionalized graphene (see Figure 5c,d) are induced by the different stabilization mechanisms of the systems. Notably, if three molecules are bonded with carbon atoms of A, A1, and B in the supercell for n = 7 (see Figure 6a), even though the conjugated balance between different sublattice is broken, the functionalized graphene is still nonmagnetic due to the low density of localized electrons (see Figure 6b). If three molecules are located at A, A1, and A2 positions, and one molecule is at the B position, the system is a magnetic metal with an average moment of 0.02 μB for the nine carbon atoms nearest to A, A1, and A2 positions (see Figure 6c). 3.1.5. Effect of Substrate on Electronic and Magnetic Properties of Amide Functionalized Graphene. Effects of substrate to the functionalized graphene are also investigated, as shown in Figure 7, where the pristine graphene and hexagonal boron nitride (h-BN) layer is the substrate, respectively. The functionalized graphene and the substrates are arranged in AB stacking order (Figure 7). We first choose the graphene as the substrate (Figure 7a), where the bond length of C2−C1 slightly increases to 1.60 Å, and the distance between C1 and the graphene decreases slightly to 0.42 Å (see Figures 7a and 1b). The bond interaction between the pristine graphene and functionalized graphene is increased compared to that between two pristine graphene sheets (bilayer). As such, the distance between the graphene substrate and functionalized graphene decreases to 2.95 Å. Moreover, the magnetization is almost diminished, even though a flat band still arises near the Fermi level, which renders the functionalized graphene metallic (Figure 7b). The weakened magnetism in functionalized graphene when in contact with a graphene substrate can be
Figure 7. (a) Atomic structure of functionalized graphene (n = 4) in contact with a graphene substrate. (b) Electronic structure of functionalized graphene (n = 4) in contact with a graphene substrate (left panel); partial charge density of the flat band (right panel). (c) Atomic structure of graphene (n = 4) in contact with a hexagonal BN monolayer substrate. (d) Electronic structure and DOS of functionalized graphene (n = 4) with an hexagonal BN monolayer substrate. Red and black lines in panel (d) represent spin-down and spin-up bands, respectively. Gray, red, blue, white, and carmine balls represent carbon, oxygen, nitrogen, hydrogen, and boron atoms, respectively.
understood from the bonding character of π bonds. As shown in Figure 7b, the flat band is contributed by both the functionalized graphene and graphene substrate. The broken π bonds and added unpaired electrons in the functionalized graphene can interact with the graphene substrate through π orbitals, thereby making changes in the electronic properties of the graphene substrate. We also consider using a monolayer BN as a substrate for the functionalized graphene (Figure 7c). The bond length of C2− C1 is still 1.60 Å, and the distance between C1 and the graphene is 0.43 Å. The distance between BN sheet and functionalized graphene decreases to 3.09 Å, but is larger than that between the pristine graphene and functionalized graphene, yet smaller than that between the graphene and BN sheet. Due to the weak π orbital interaction between functionalized graphene and the BN sheet, the electronic and magnetic properties of functionalized graphene are little affected by the BN substrate (Figure 7d). Lastly, we have performed additional calculations for an amide group functionalized graphene system (n = 5). As the carbon atom bonding with an amide group can produce a 13726
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dangling p-orbital, we consider a new case such that one carbon atom next to the carbon atom bonded with the amide group is passivated by a hydrogen atom. Electronic structure calculation indicates that the system becomes nonmagnetic and semiconducting with a band gap of 0.52 eV (Figure 8). The electronic structure is similar to that shown in Figure 5d for which two amide groups are bonded with two carbon atoms that belong to different sublattices.
Figure 9. Computed electronic structure of (a) (7,0) CNT, (b) (8,0) CNT, (c) (9,0) CNT, (d) (5,5) CNT, (e) (7,7) CNT, and (f) (9,9) CNT. Partial charge density of the flat band near the Fermi level of (g) (8,0) CNT and (h) (7,7) CNT. Gray, red, blue, and white balls represent carbon, oxygen, nitrogen, and hydrogen atoms, respectively.
Figure 8. Atomic and electronic structures of graphene functionalized by a hydrogen atom and an amide group with an n = 5 per supercell.
In summary, depending on the coverage and pattern, the functionalized graphene can show different electronic and magnetic properties induced by the localized π orbital of C atoms. The mechanism is different from that in aryl groupfunctionalized graphene,39 where the electronic properties of graphene are changed by the charge transfer between graphene and the aryl group. 3.2. Amide Functionalization of CNTs. 3.2.1. Electronic and Magnetic properties of Amide Functionalized CNTs. Since CNTs have similar sp2 bonding characters as the graphene, it is expected that the Claisen rearrangement can be realized between a CNT and the organic molecule CON(CH3)2 as well. We first consider binding of the CON(CH3)2 molecules on the same sublattice of single-walled CNTs. The DFT calculations show that all the functionalized ZCNTs [(4,0)−(10,0)] and armchair CNTs [(3,3)−(10,10)] are stable and exhibit metallic properties, regardless of their chirality. Figure 9a−c displays computed electronic structures of (7,0), (8,0), and (9,0) CNTs, respectively. Due to the bonding interaction between CON(CH3)2 and CNT, the geometric structure of the CNT exhibits slight deformation along the radial direction (inset of Figure 9b). An additional band arises near the Fermi level. Moreover, the spin polarized DFT calculations suggest that functionalized ZCNTs are magnetic if their diameter is larger than that (0.55 nm) of (7,0) CNT. The magnetization becomes stronger with increasing the diameter of the CNTs, and the two splitting flat bands can still cross the Fermi level. To examine the origin of magnetism in a functionalized (8,0) CNT, the partial charge density corresponding to the flat band near the Fermi level is plotted in Figure 9g. It can be seen that the partial charge density is mainly distributed over the carbon atoms on a different sublattice from the sp3 bonded carbon atom in CNT since the π bonds are disrupted by the sp3 bonded atom in the (8,0) CNT. Due to the curvature effect, the residual unpaired π electrons on the C1 and C2 atoms can interact with each other. For functionalized CNT with a larger diameter, the distance between C1 and C2 atoms becomes longer, thereby decreasing the interaction between unpaired electrons on C1 and C2 atoms
and enhancing the spin polarization of the functionalized ZCNT. For the functionalized armchair CNTs, their electronic properties are quite similar to the ZCNTs (Figure 9d−f). Near the Fermi level, an additional band arises, contributed by the carbon atoms on a different sublattice from the sp3 bonded atom (Figure 9h). All functionalized armchair CNTs are metallic regardless of their diameter. Furthermore, all functionalized armchair CNTs are nonmagnetic, even if the diameter is as large as 1.22 nm [(9,9) CNT]. The dramatically different magnetic behavior between zigzag and armchair CNTs can be understood from their differences in atomic structures (Figure 10). For functionalized ZCNTs, there are two atoms located in the radial direction, and one atom located in the axial direction per unit cell. Because the ZCNT is prone to deform along the radial direction rather than in the axial direction, the C1−C2 distance is shorter than those of C1− C3 and C2−C3 (Figure 10a). As such, the π interaction between
Figure 10. Partial atomic structure of (a) (8,0) CNT and (b) (7,7) CNT. Gray and yellow balls represent carbon atoms with sp2 and sp3 hybridization character, respectively. 13727
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C1 and C2 is slightly stronger than that between C1−C3 or C2− C3 in the ZCNTs. The unbalanced interactions among C1, C2, and C3 atoms induce the magnetic moments of C1 and C2, both being 0.02 μB, while the moment of C3 is 0.04 μB in functionalized (8,0) CNT. As the diameter of ZCNT increases, the magnetic moments of C1 and C2 increase to 0.03 μB, and the moment of C3 is still 0.04 μB in the functionalized (10,0) CNT. However, for the functionalized armchair CNTs (Figure 10b), there are two atoms located in the axial direction, and one located in the radial direction. The π interactions between C1− C3 and C2−C3 are slightly stronger than that between C1 and C2 due to the atomic structure of armchair CNT. Therefore, the π interactions among the three carbon atoms in armchair CNTs are balanced, rendering the functionalized armchair CNTs nonmagnetic. 3.2.2. Stability of Amide Functionalized CNTs. To examine stability of the functionalized CNTs, again, we compute the Gibbs free energy of formation δG defined as δG = ECNTO − nCμC − nOμO − nNμN − nHμH, where ECNTO is the cohesive energy per atom of the functionalized CNT, and μC is the cohesive energy per atom of the corresponding pristine CNT. As shown in Figure 11, with increasing the diameter from 0.31
Figure 12. (a,b) Electronic structure of functionalized (8,0) CNT with two molecules per supercell and both molecules belonging to the same sublattice. (c,d) Electronic structure of functionalized (8,0) CNT with two molecules per supercell and both molecules belonging to different sublattice. (e,f) Electronic structure of functionalized (7,7) CNT with two molecules per supercell and both molecules belonging to the same sublattice. (g,h) Electronic structure of functionalized (7,7) CNT with two molecules per supercell and both molecules belonging to different sublattice. Insets display the partial charge density of the nearly flat bands close to the Fermi level.
(2.41 Å). In this case, two nearly flat bands meet at the Fermi level (Figure 12b), and the magnetization of the functionalized (8,0) CNT is enhanced , with the magnetic moment of C1 and C2 (Figure 10a) being 0.06 μB. When the two CON(CH3)2 molecules belong to different sublattices and are located at the opposite sides of the functionalized (8,0) CNT (inset of Figure 12c), the CNT is semiconducting with an energy gap of 0.06 eV (Figure 12c). If the two molecules are located closer to each other along the radial direction (inset of Figure 12d), the energy gap increases to 0.28 eV (Figure 12d). Further calculations show that the energy gap of the functionalized ZCNTs can increase as the CNT diameter increases. For example, if two molecules are located at the positions of (10,0) and (6,0) CNTs, respectively, as shown in the inset of Figure 12d, the energy gaps become larger (0.53 eV) and smaller (0.13 eV), respectively, compared to that of (8,0) CNT. For the armchair (7,7) CNT, as shown in Figures 11e−h, all the functionalized (7,7) CNTs are metallic, independent of the location of the two molecules. As shown in the insets of Figure 12, the flat bands near the Fermi level are mainly contributed by the π electrons of the carbon atoms that are nearest to the sp3 carbon atoms. In summary, the amide functionalized CNTs might be synthesized using the same method for achieving the Claisen rearrangement chemical reaction on graphene. Moreover, the electronic and magnetic properties of functionalized CNTs are also dependent on the coverage of amide groups on the sidewall of CNTs. 3.3. Transport Properties of Amide Functionalized Graphene and CNTs. Finally, we have investigated electron transport properties of the functionalized and pristine graphene, (5,5) CNT and (7,0) CNT, respectively. The
Figure 11. Calculated formation energy as a function of CNT diameter.
nm [(4,0) CNT] to 0.78 nm [(10,0) CNT], δG changes from −0.21 to −0.06 eV per atom. For armchair CNTs, with increasing the diameter from 0.41 nm [(3,3) CNT] to 1.22 nm [(9,9) CNT], δG changes from −0.15 to −0.04 eV per atom. With similar diameter, the armchair CNT appears to be more stable than the ZCNT. Similar to the functionalized graphene, increasing the coverage of molecule on the CNT surface can make the functionalized CNT more stable. For example, the formation energies are 0.11 to 0.16 eV/atom for the (6,0) CNT supercells functionalized with one and two molecules, respectively. 3.2.3. Effect of Bonding Position on Electronic and Magnetic Properties of Amide Functionalized CNT. We have also considered functionalized (8,0) and (7,7) CNTs with two CON(CH3)2 molecules per supercell. When the two molecules belong to the same sublattice, the magnetic and electronic properties of functionalized CNT are strongly dependent on the radial distance between two molecules. If the two molecules are located at the opposite sides of the (8.0) CNT (inset of Figure 12a), deformation of the CNT is the strongest, and the distance between C1 and C2 (Figure 10a) decreases to 2.40 Å. The enhanced hybridization between C1 and C2 π orbitals induces an energy gap of 0.08 eV for the functionalized (8,0) CNT (Figure 12a). If the two molecules are closer to each other along the radial direction as shown in the inset of Figure 12b, weaker deformation is induced, with the distance between C1 and C2 (Figure 10a) being slightly longer 13728
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carbon atoms is within a certain range. In general, the stability of amide-functionalized graphene or CNTs becomes higher by increasing the portion of sp3 hybridized carbon atoms. However, the conductivity of the amide functionalized graphene and CNT is lower than that of the pristine counterparts, and the turn-on voltage for the functionalized graphene and CNTs is apparently higher than that for the pristine ones. This feature is contrary to the functionalized graphene by aryl groups, which shows increased conductivity due to functionalization.
electron transport properties are performed using the TRANSIESTA program implemented in the SIESTA 3.0 package.36 The local density approximation and single-ζ plus polarization (SZP) basis set are selected.37 A real-space grid with an equivalent energy cutoff of 200 Ry is adopted to expand the electron density for numerical integration. The pseudopotentials of C, H, O, and N are all generated in the Troullier− Martins scheme.38 Graphene and CNT electrodes are selected in the calculation of functionalized graphene and CNT, respectively (Figure 13a). The computed I−V curves for the
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AUTHOR INFORMATION
Corresponding Author
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[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS W.L.G. is supported by grants from the 973 Program (2012CB933403) and NSFC (10732040, 91023026) of China. X.C.Z. is supported by the NSF (DMR-0820521 and EPS-1010674) and ARL (W911NF1020099).
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Figure 13. (a) Two-probe systems for electron transport calculations of the functionalized graphene and CNT. (b) Calculated I−V curves of the pristine and functionalized graphene and CNT. Gray, red, blue, and white balls represent carbon, oxygen, nitrogen, and hydrogen atoms, respectively. Brown balls represent carbon electrode.
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pristine and functionalized graphene, (5,5) and (7,0) CNTs are shown in Figure 13b. In contrast to the functionalized graphene by aryl groups,39 which shows increased conductivity, the conductivity of the amide functionalized graphene and CNT is decreased compared to the pristine counterparts. As shown in Figure 13b, the functionalized (5,5) CNT shows marked conductivity once the bias voltage is greater than 0.6 V, while the pristine (5,5) CNT is already conductive under a bias voltage near zero. For the (7,0) CNT, both pristine and functionalized CNTs are not conductive under a low bias voltage. The turn-on voltage for the functionalized (7,0) CNT is apparently higher than that for the pristine (7,0) CNT. Similar results are also found for the functionalized graphene. Hence, although the chemisorption of amide groups can introduce new bands near or crossing the Fermi level, the electron transport properties appear to be little improved because the electronic states corresponding to the induced bands are highly localized.
4. CONCLUSIONS We have investigated electronic, magnetic and electron transport properties of the covalently functionalized graphene and CNTs by the amide groups [CON(CH3)2] using DFT calculations. Particular attention is placed on how the properties and stabilities of chemically modified carbon systems are affected by the decoration pattern and coverage of the dimethylamide groups. Most importantly, we find that the functionalized graphene and ZCNTs can exhibit coverage- and pattern-dependent electronic and magnetic properties, in addition to the chirality dependence in the case of CNTs. The functionalized armchair CNTs are always metallic and nonmagnetic. The amide-functionalized graphene or CNTs can be highly stable when the ratio between sp2 and sp3 hybridized 13729
dx.doi.org/10.1021/jp3009578 | J. Phys. Chem. C 2012, 116, 13722−13730
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