Article pubs.acs.org/JPCC
Patterned Partially Hydrogenated Graphene (C4H) and Its OneDimensional Analogues: A Computational Study Yafei Li and Zhongfang Chen* Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, Rio Piedras Campus, San Juan, Puerto Rico 00931 S Supporting Information *
ABSTRACT: By means of density functional theory (DFT) computations, we systematically studied the structural and electronic properties of the experimentally just achieved new two-dimensional (2D) hydrocarbon the patterned partially hydrogenated graphene with formula C4H (Adv. Mater 2011, 23, 4497), and in particular its one-dimensional (1D) analogues. The C4H layer is a stable 2D crystal featured with periodic Clar sextet aromatic rings and is semiconducting with a wide band gap; however, this single-sided patterned partially hydrogenated C4H layer can only be obtained when the possibility of double-sided hydrogenation is excluded, since the doublesided graphane-embedded structure is energetically more favorable. The 1D C4H nanotubes, rolled up by the C4H layer, exhibit excellent thermodynamic properties and all have a wide band gap regardless of the tube diameter and chirality. In contrast, cutting the C4H layer into 1D C4H nanoribbons can result in rich electronic characteristics: they can be metallic or semiconducting depending on the chirality and edge configuration.
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INTRODUCTION Graphene, a one-atom-thick planar sheet of sp2-hybridized carbon atoms packed in a honeycomb crystal lattice, has been considered as the “miracle material” of the 21st century since its experimental synthesis in 2004.1 This thinnest two-dimensional (2D) carbon material has extraordinary properties over other allotropes.2 Among others, the carriers in graphene can behave as massless Dirac Fermions3 and have a particular high mobility (106 m/s, close to the speed of light);4,5 graphene has been established as the strongest material ever measured, with a Young’s modulus of >1000 GPa;6 the thermal conductivity of graphene is in excess of carbon nanotubes (CNTs) or diamond.7 These properties endow graphene many exciting applications in numerous fields, such as supercapacitors,8 transparent conducting electrodes,9 and biosensors.10−12 In particular, graphene is expected as a substitutional material for silicon to use in microelectronics.13 However, pristine graphene is a semimetal with zero band gap, which is a principle obstacle limiting the utilization of graphene in electronics,14 such as p-n junctions. Thus an intermediate band gap (e.g., 1−3 eV) must be opened before any graphene-based microprocessor can be realized. Both experimental15 and theoretical studies16,17 have confirmed that cutting 2D graphene into one-dimensional (1D) graphene nanoribbons (GNRs) can generate a nonzero energy gap, irrespective of the width and edge chirality. In particular, the zigzag-edged GNRs have localized edge states18−20 and can be tuned into half-metals under external electric field21−23 or chemical modification.24−26 However, the band gaps in GNRs diminish gradually with increasing ribbon width,16 and so far the large-scale fabrication of GNRs is still a big challenge. © 2012 American Chemical Society
In recent years, many other approaches have been proposed toward engineering a band gap in graphene, such as perpendicular electric field,27−29 periodic antidot lattices,30−34 uniaxial strain,35−37 and covalent38−44 or noncovalent45−47 functionalization. However, the above-mentioned approaches either can only open a tiny band gap ( 5, the stain energy becomes negative while the band gap exceeds that of the C4H layer; all (n,n) tubes have a negative strain energy, while their band gaps are all larger than that of the C4H layer. The above results are not simple coincidences. As we demonstrated above, the electronic properties of the C4H layer and nanotubes are mainly determined by the isolated aromatic rings. For these C4H systems, the aromatic rings are more localized in the energetically more favorable ones and correspondingly present a more pronounced band gap. The stability of C4HNTs can also be hinted at by examining their formation energies. In Figure 6b we present the variation of formation energy of (n,0) and (n,n) C4HNTs as a function of tube diameters. As a comparison, the formation energy of the C4H layer was also computed. The positive formation energy of the C4H layer (0.11 eV/atom) indicates that the reaction between the hydrogen molecules and graphene is endothermic; thus, the C4H layer can only be obtained by exposing graphene to H plasmas (but not molecular H2). The formation energies of (n,0) and (n,n) C4HNTs both increase with increasing tube diameters, and all the tubes examined here have a lower (thus more favorable) formation energy than that of the C4H layer. It is not surprising since CNTs are more reactive than graphene, and these thin tubes have a higher curvature than thick ones, thus possess higher reactivity.91 In particular, (3,0) and (4,0) C4HNTs have negative formation energies, indicating that these two hydrogenated tubes can be realized by direct exposure of (6,0) and (8,0) CNTs to H2 molecules, respectively. Electronic Properties of C4H Nanoribbons. Finally, we investigated the electronic properties of C4HNRs. C4HNRs with zigzag or armchair edges can be obtained by cutting the carbon skeleton of the C4H layer along different directions. Following the convention of GNRs, we define the ribbon parameter N as the number of zigzag chains (Nz) across the ribbon width for zigzag ribbons (Figure 7a), and the number of dimer lines (Na) across the ribbon width for armchair ribbons (Figure 7b). For both zigzag and armchair C4HNRs, due to the ordering distribution of Csp3 atoms in the C4H layer, there exists two kinds of edge configurations: the edge sites occupied with pure Csp2 atoms (I) or alternate Csp3 and Csp2 atoms (II). Obviously, according to our definition, the Nz can only be even
band gaps. This is in stark contrast to the conventional (n,m) CNTs, which are metallic only if (n − m)/3 is an integer; otherwise, they are semiconducting.86,90 The uniform semiconducting property of the C4HNTs is attributed to the fact that all the Csp2 atoms are in the Clar sextet aromatic rings. For (n,0) C4HNTs, the band gap increases monotonically with the increase of n, indicating that the quantum confinement effect is not pronounced here. In particular, when n > 5, the bands gaps of (n,0) tubes are even larger than that of the C4H layer. In comparison, the band gaps of (n,n) tubes initially increase as n increases, and then from (5,5) tube converge to a constant value of 3.62 eV. Interestingly, even the smallest (n,n) tube has a larger band gap than that of the C4H layer. Overall, the uniformity of electronic properties would be a key advantage for the application of C4HNTs in nanotechnology. Stability of C4H Nanotubes. The stability of C4HNTs is a very important issue since it indicates the feasibility of experimental realization. To estimate the stability, we first examined the strain energies of both (n,0) and (n,n) C4HNTs as a function of n and compared them with their corresponding (2n,0) and (2n,2n) CNTs. Note that the strain energy only reflects the relative stability, and to some extent, the synthesis difficulty, but not the absolute stability. The strain energy of (n,0) C4HNTs decreases as the increase of n (Figure 6a), similar to single-walled carbon nanotubes. In particular, the negative strain energies for the nanotubes with n > 5 indicate that these thick (n,0) C4HNTs are energetically even more favorable than the C4H layer. In comparison, all the (n,n) C4HNTs we considered herein, including the thinnest (3,3) tube, have negative strain energies. The strain energy of (n,n) C4HNTs initially decreases with increasing tube diameter and then approaches a value of −0.02 eV at (8,8) and is expected to converge to zero (as that of the C4H layer) with the further increase of the tube diameter. The negative strain energies of the above studied C4HNT nanotubes (except (3,0) and (4,0)) strongly indicate that the C4H monolayer may easily bend to form nanotubes under appropriate conditions. The above results can be understood by considering the fact the Csp3 atoms in C4HNTs are closer to ideal sp3 hybridization than those of the C4H layer. Generally speaking, rolling the C4H layer into C4HNTs could release the strain of basal plane, and thus make C4HNTs energetically more favorable than the C4H layer. However, this reasoning is not valid for (3,0) and (4,0) tubes: their Csp3 atoms are closer to ideal sp3 hybridization than the thick tubes, but these two very thin nanotubes still have positive strain energies. Why? This is also not difficult to understand. Although the strain due to the deviation from ideal sp3 hybridization is much more released in very thin tubes, 4530
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I-8-ZC4HNR is metallic with two energy levels crossing over from conduction band to valence band across the Fermi level in the band structure. The two energy levels are mainly contributed by the pz orbitals of edge Csp2 atoms which are not in the Clar sextet ring. In contrast, II-8-ZC4HNR is semiconducting with a 3.48 eV indirect band gap. The VBM and CBM are both localized at the Csp2 atoms of Clar sextet aromatic rings throughout the ribbon (see Figure S3 in Supporting Information). Both having edge Csp2 atoms, why is I-8-ZC4HNR metallic while II-8-ZC4HNR is semiconducting? Careful examination of the locations of the unhydrogenated Csp2 atoms gives us the answer. In II-8-ZC4HNR, all the Csp2 atoms are in Clar sextet rings, the same as these of C4H layer. In contrast, the edge Csp2 atoms in I-8-ZC4HNR do not belong to any Clar sextet ring, thus, it is the residual pz electrons of the edge Csp2 atoms that contribute to the metallicity of I-8-ZC4HNR. Both I-9-AC4HNR and II-9-AC4HNR are semiconducting, with a 3.74 and 2.78 eV direct band gap, respectively. For I-9AC4HNR, the VBM is mainly contributed by the two inner aromatic rings, while the CBM is localized at the Clar sextet aromatic rings throughout the ribbon (Figure S3, Supporting Information). Therefore, the edge states are not found in I-9AC4HNR, though in each edge there are two Csp2 atoms which do not belong to any Clar sextet ring. In contrast, in the band structure of II-9-AC4HNR, several new levels are at the top of the valence band and at the bottom of the conduction band, which shrink the band gap correspondingly. Both VBM and
Figure 7. The optimized geometric structures of (a) I-8-ZC4HNR, (b) II-8-ZC4HNR, (c) I-9-AC4HNR, and (d) II-9-AC4HNR.
while the Na can only be odd. Each edge atom is passivated with a hydrogen atom to ensure that the atom coordination of nanoribbons is the same as that of the C4H layer. Figure 7 presents the optimized structures of two representative zigzag and armchair C4HNRs, and their corresponding band structures are shown in Figure 8. Our computations demonstrated that these C4HNRs all have a nonmagnetic ground state.
Figure 8. Electronic band structures of (a) I-8-ZC4HNR, (b) II-8-ZC4HNR, (c) I-9-AC4HNR, and (d) II-9-AC4HNR. Panels (e) and (f) are the variations of the band gaps of zigzag (6 ≤ Nz ≤ 18) and armchair (5 ≤ Na ≤ 17) C4HNRs as a function of ribbon widths, respectively. 4531
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CBM are localized at the edge Csp2 atoms, indicating that the electronic properties of II-9-AC4HNR are determined by these edge states. We also investigated the electronic properties of zigzag and armchair C4HNRs with two types of edge configurations as a function of ribbon widths (Figure 8e,f). All the I-ZC4HNRs are metallic regardless of the ribbon width, while the II-ZC4HNRs are all semiconducting, and due to the quantum confinement effect, their band gaps decrease slightly with increasing ribbon width, and gradually approach that of the C4H layer. In comparison, both I- and II- ACH4NRs are semiconducting, the band gap of I-ACH4NRs decreases from 4.06 eV at Na = 5 to 3.62 eV at Na = 15, which shows the quantum confinement effect, while due to the presence of edge states, II-AC4HNRs all have a lower band gap than that of the C4H layer. With the increase of ribbon width, the edge states get less and less pronounced and the band gap could be enlarged correspondingly; at the same time the quantum confinement effect essentially lowers the band gap. As a result, the band gap of IIAC4HNRs converges to a constant value of 2.80 eV as ribbon width increases.
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Article
ASSOCIATED CONTENT
S Supporting Information *
The band structure of the C4H layer computed using HSE06 functional, electronic profiles of VBM and CBM for C4H nanotubes and C4H nanoribbons, and the structural properties of a series of C4H nanotubes. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support by NSF Grant EPS-1010094 is gratefully acknowledged.
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REFERENCES
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CONCLUSION
In summary, we systematically investigated the structural and electronic properties of the recently achieved 2D C4H layer and its 1D derivatives: C4HNTs and C4HNRs by means of DFT computations. Structurally, the C4H layer is rather unique: all its Csp2 atoms are benzenoid while the Csp3 atoms slightly deviate from the ideal sp3 hybridization. Electronically, the C4H monolayer is semiconducting with a sizable band gap. However, this singlesided patterned partially hydrogenated C4H layer can only be obtained when we prevent the double-sided hydrogenation, since the double-sided graphane-embedded structure is energetically more favorable. Rolling up the C4H layer into C4HNTs can make the Csp3 atoms even closer to ideal sp3 hybridization. Consequently, the majority of C4HNTs (except (3,0) and (4,0)) have negative strain energies, and all the C4HNTs have more favorable formation energies than the C4H layer. These energetic evaluations indicate that C4HNTs can be feasibly realized. In contrast to carbon nanotubes whose band gap depends on the chirality and diameter, all C4HNTs have wide energy gaps regardless of the tube chirality and diameter. C4HNRs present much richer electronic properties than C4HNTs. ZC4HNRs can be either metallic or semiconducting: those terminated with Csp2 atoms not associated in Clar sextet rings are metallic due to the residual pz electrons of edge atoms, while those terminated with alternate Csp2 and Csp3 atoms are wide-gap semiconductors. AC4HNRs are always semiconducting: those terminated with pure Csp2 atoms all have a larger band gap than that of the C4H layer; in contrast, due to the presence of edge states, those terminated with alternate Csp2 and Csp3 atoms all have a lower band gap than that of the C4H layer. The above unique structural and electronic properties endow the C4H layer and its 1D analogues many promising applications in optics and opto-electronics devices, besides others. We hope our theoretical studies will help promote more experimental and theoretical studies of these novel materials and exploration of their applications in various fields. 4532
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The Journal of Physical Chemistry C
Article
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