Twist-boat conformation in graphene oxides

Abstract

We have investigated the structural, electronic, and vibrational properties of graphene oxide based on first-principles density-functional calculations. A twist-boat conformation is identified as the energetically most favorable nonmetallic configuration for fully oxidized graphene. The calculated Raman G-band blue shift is in very good agreement with experimental observations. Our results provide important insight into structural and electronic characteristics that are useful for further development of graphene-based nanodevices.

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Graphene, a single-layer planar sheet of carbon atoms with chicken wire structure, is being actively explored as a viable candidate for next-generation nanoscale electronics and photonics.^1,2 As a chemically derived configuration, graphene oxide (GO) has recently attracted a great deal of attention due to its solubility in a diversity of solvents and promising potential for large-scale production of graphene-based devices.^2–5 GO can be regarded as graphene with hydroxyl and epoxide functional groups decorating the basal plane and edges.⁶ The sp³ hybridized carbon-oxygen bonds in GO disrupt the extended sp² conjugated network of graphene and induce the formation of an energy gap. The reduction of oxygen can convert the material to a semiconductor and eventually to a graphene-like semi-metal.^2–5 A detailed understanding of the associated energy gap tuning⁶ and the shift in G-band Raman feature⁹ is thus of great importance for practical applications in electronic and photonic devices.

Functional groups of epoxide or hydroxyl on graphene can induce pronounced roughness in the oxide layers. Several first-principles studies have been performed for structural and electronic properties of GO.^6–11 Despite the progress made, some questions remain regarding the characteristic structure of the oxidized phases,^6,10 as well as identifying the mechanisms that promote the blue shifts observed in the experimental Raman G-band.^7–9,12,13 This is, to a large extent, attributed to the composition variations and intrinsic inhomogeneities in the oxidization. Here we present results from first-principles density-functional calculations focusing on the structural, electronic, and vibrational properties of fully-oxidized GO layer. Specifically, we demonstrate that a twist-boat model is capable of accounting for the electronic structure and Raman blue shift characteristics of GO.

Our investigation of the optimal GO structure was built on the current body of knowledge from previous first-principles calculations⁶ encompassing the aggregation of functional groups in GO and various low-energy conformations of graphane—fully hydrogenated graphene.^14,15 The aggregation is attributed to a dwindling of vertical structural distortion when functional groups are chemically bonded on both sides of the sheet,⁶ while the graphane can arrange in a randomly distributed regions consisting of a few low-energy membranes referred to as chair, boat, and twist-boat conformations.^15,22 Specifically, oxygen atoms prefer “epoxy” bonded positions and form epoxide above the middle of a carbon-carbon bond. Hydroxyl groups, on the other hand, reside in the symmetric on-site position above the carbon. A dilute ensemble of epoxide groups on graphene tends to form spatially correlated patterns, which originates from the electron-mediated interaction among epoxides.¹⁶

We have employed first-principles density-functional approach as in our previous study of graphane.¹⁵ The structure and electronic properties of all conformations were investigated using first-principles density-functional calculations. Perdew–Burke–Ernzerhof (PBE) parametrization¹⁷ of the generalized gradient approximation (GGA) was used in majority of the calculations.¹⁸ A kinetic energy cutoff of 340 eV in the plane-wave basis and appropriate Monkhorst-Pack k-points (6 × 6 × 1 for graphene oxide and 10 × 10 × 1 for graphene) were sufficient to converge the grid integration of the charge density. Although the first-principles approach systematically underestimates the band gaps,¹⁹ we are interested primarily in the relative stability of the conformations and the validity of the structural models. Furthermore, we rectified the GGA results by employing Becke 3-parameter and Lee–Yang–Parr (B3LYP) hybrid functional.^20,21 The initial search for stable structures was carried out through semi-empirical molecular dynamics by means of density-functional tight-binding (DFTB) method.^26,27 The obtained local energy-minimum structures were further optimized through first-principles calculations with forces less than 0.01 eV/Å. For GGA structural calculations, Vanderbilt ultrasoft pseudopotentials were employed.¹⁹ The optimization of atomic positions proceeds until the change in energy is less than 1 × 10⁻⁶ eV per cell.

Given the preferred on-site and epoxy site adsorption for hydroxyl and epoxide functional groups, respectively, the fully-oxidized phases can be modeled through a graphene sheet randomly decorated with hydroxyl and epoxy groups.^23–25 The geometry optimization of the decorated graphene sheet was performed using DFTB method with self-consistent charges.²⁶

The fully-oxidized GO with randomly decorated hydroxyl and epoxy groups closely resembles the fully hydrogenated graphene in that there exist broad distribution of corrugated membranes that can be classified in accordance to the chair, boat, and twist-boat conformations of graphane (see Fig. 1).¹⁵ However, there exist crucial differences from graphane due to the existence of predominantly randomly-oriented epoxides along zigzag or armchair directions and a paucity of on-site hydroxyl groups forming a chair membrane. The boat conformation (Fig. 1a), recognized as the fully oxidized structure in previous calculations,⁶ is free from angle strain. In the boat conformation parallel bonds along the zigzag direction lift out alternatively from the graphene plane with two of six bonds being eclipsed, which have severe steric crowding on the “bow” and “stern” of the boat conformation.

Fig. 1 Prospective views of GO atomic structures for selected phases. (a) Fully-oxidized epoxide-only boat phase C₂O with oxygen rows on both sides of the plane along the zigzag direction; (b) C₈O₂(OH)₄ structure with hydroxyl-epoxide strips separated by twist-boat epoxide conformations; (c) and (d) Fully-oxidized epoxide-only twist-boat C₂O phase along zigzag and armchair directions, respectively. The twisted bonds are indicated with yellow. Carbon, oxygen, and hydrogen atoms are colored with green, red, and white, respectively.

In the presence of both hydroxyl and epoxide functional groups, the local epoxide configuration typically assumes a twist-boat form adjacent to chair membranes of hydroxyl groups (see Fig. 1b for a prototype twist-boat-chair structure).¹⁵ By twisting the boat structure, the steric hindrance can be partially relieved with completely eclipsed bonds. A twist-boat conformation of fully-oxidized GO (C/O = 2) can be constructed along either zigzag or armchair directions. The twist-boat-zigzag conformation (Fig. 1c) is locally stable but converts to boat under cell optimization. Careful examination of various structures indicates that the twist-boat along the armchair direction (Fig. 1d) is the lowest-energy conformation for fully-oxidized GO.

Summarized in Table 1 are the calculated binding energy, energy gap, and unit cell dimensions for boat and twist-boat conformations, along with those for low-energy epoxy-pair (EP) structures. EP chain conformations (Figure S1), although higher in energy than the twist-boat-armchair, are relevant to the oxidative breakup process.¹¹ Closer scrutiny of the energy contributions from various conformations reveals that EP prefers to aggregate together such that the EP chains can break up into carbonyl pairs through “twisting boat” process, in conformity with the conclusion obtained from previous studies.¹¹

Table 1 Calculated binding energy per oxygen atom E_B with use of PBE and B3LYP functionals, band gap E_g and the associated unit cella × b for boat, twist-boat, and epoxy-pair (EP) conformations (Table S2 and Figure S1), respectively

Structure	E ^PBE B (eV)	E ^B3LYP B (eV)	E g (eV)	a × b (Å^2)
Boat	−23.39	23.29	2.95	2.52 × 4.49
Twist-boat	−23.65	23.33	4.40	5.10 × 4.28
EP-zigzag	−23.06	22.79	0.40	2.52 × 4.50
EP-alt	−23.54	23.27	1.85	5.47 × 4.60

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An important ramification of our simulation results is that the epoxide twist-boat membranes represent as a realistic model for describing the structure of GO. As can be seen from Table I (and Table S1), among various fully-oxidized structures,⁶ the effective periodicity of 2.55 Å × 4.28 Å for twist-boat conformation has the best agreement with experimentally observed local periodicity of 2.73 Å × 4.06 Å.^28,29 In view of the experimentally observed fully-oxidized GO does not have well-ordered structures,^23–25 we investigated the randomly distributed carbonyl and hydroxyl groups using DFTB approach (see Fig. 2). As is readily observable from Fig. 2, there exists a paucity of regular-ordered patterns, while local membranes have prominent corrugations with twisted bonds. This suggests that the corrugations built intrinsically in the twist-boat model capture the essential structural features of the randomly distributed membranes.²²

Fig. 2 Top and side views of randomly distributed, fully oxidized GO conformation functionalized by carbonyl and hydroxyl using DFTB method.

We illustrate in Fig. 3 the calculated band structures for boat and twist-boat conformations, along with the extracted charge density distribution of valence and conduction states, respectively. The extracted gap for optimized twist-boat structure is 4.4 eV while the boat counterpart has a gap of 3.0 eV. By contrast, all EP structures have much smaller gap, which is attributed to the coexistence of sp² and sp³ configurations. As seen from insets of Fig. 3, the charge density follows the epoxide chains, which is more apparent for the conduction state of the twist-boat-armchair.

Fig. 3 Calculated band structure for fully-oxidized epoxide-only C₂O: (a) boat and (b) twist-boat along armchair direction, respectively. Insets: extracted charge density (isovalue of 0.05 au) at the band center (Γ point) for conduction band minimum (CBM) and valence band maximum (VBM), respectively. Dashed rectangles indicate unit cells (Table S2).

It is worth mentioning that energy order for various GO conformations remains intact based on calculations using hybrid B3LYP functional^20,21 (see Table 1). The energy gap for the twist-boat conformation is 6.42 eV using B3LYP as compared to 4.40 eV using GGA. Notwithstanding the corrections to the band gaps, the overall band structures are qualitatively similar. On the other hand, there exists specially-patterned GO EP-structures that are metallic and low in energy (see Table S1).³⁰ Those structures are separated from the twist-boat conformation with a much larger barrier than from the simple EP-models as shown in Table 1. The low-energy metallic phase may be relevant to the experimentally observed flash reduction and patterning of GO.³¹

The stretching of the carbon-carbon bond in graphene gives rise to the G-band Raman feature at ∼1582 cm⁻¹.^7,9,32 Our calculation yields a dominant peak at 1589 cm⁻¹ associated with the E_2g mode, in very good agreement with experimental and other first-principles calculation results.^7,9,12,13 For Raman spectrum calculations, the norm-conserving potentials and GGA were used. The calculation was based on the linear-response scheme.^33,34

When the bond lengths and angles of graphene are modified by the oxidization, the hexagonal symmetry of graphene is broken. As a result, the G-band is highly sensitive to strain effects and can be used to probe the degree of oxidization.⁹ In the experimental work on the transformation from graphene to GO, there is a blue shift of the graphene G-band in GO, while the converse is observed after partial reduction of GO.^9,12,13

Shown in Fig. 4 are the calculated Raman spectrum of the twist-boat-armchair conformation along with that for graphene. We also summarize in Table 2 the corresponding vibrational frequency at the band center (Γ point). The effects of epoxides give rise to one dominant peak in the G-band spectrum around 1650 cm⁻¹, which is attributed to two vibrational modes at 1652 and 1662 cm⁻¹ with A_g and B_2g symmetry, respectively. As is readily observable in the insets of Fig. 4, contrary to in-plane motions of the Raman G-band for graphene, both A_g and B_2g modes in the Raman G-band for GO engage out-of-plane motions as well. The in-phase and out-of-phase stretching among the epoxide bonds correlates with the differences between these Raman-active modes. The calculated G-band blue shift in GO (∼50–70 cm⁻¹) is in very good agreement with experimental observations,^9,12,13 supporting the validity of the twist-boat model for GO.

Fig. 4 Calculated Raman spectrum for the twist-boat GO and graphene, respectively. The vibrational frequencies are displayed as blue bars (Table 2). Insets: vibrational motions of GO at 1652 and 1662 cm⁻¹, and the vibrational motion for graphene at 1589 cm⁻¹, respectively.

Table 2 Calculated vibrational frequencies in cm⁻¹ for graphene and the twist-boat-armchair conformation of GO

	Odd	(IR active)	Even	(Raman active)
Graphene	A 2u	928	B 2g	162
				928
	E 1u	1589	E 2g	252
				1589
GO	A u	452	A g	655
		985		1184
		1173		1471
		1599		1652
	B 1u	335	B 1g	458
		576		566
		1058		900
		1230		1200
				1455
	B 2u	755	B 2g	429
		1133		1151
		1543		1285
				1662
	B 3u	135	B 3g	277
		408		524
		648		777
		1112		1093
				1339

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In summary, we have demonstrated that the twist-boat model accounts for the structural and vibrational characteristics of GO, in good agreement with experimental observations. Our findings are useful for developing effective graphene manipulation means and for understanding the GO structure. We remark, before closing, that it is straightforward to employ the first-principles approach to partial reduction in GO, as the structural relaxation plays a vital role in “debundling” of oxygen from the twist-boat conformation. The investigation of the relevant electronic structures will provide an important tool for developing future graphene-based nanodevices.

Acknowledgements

This work was supported by the National Science Foundation (Grant DMR-0934142), Army Research Office (Grant W911NF-06-1-0442), and Air Force Office of Scientific Research (Grant FA9550-10-1-0254).

References

1. A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183.
2. T. Ohta, A. Bostwick, T. Seyller, K. Horn and E. Rotenberg, Science, 2006, 313, 951.
3. M. Y. Han, B. Ozyilmaz, Y. B. Zhang and P. Kim, Phys. Rev. Lett., 2007, 98, 206805.
4. X. Li, X. Wang, L. Zhang, S. Lee and H. J. Dai, Science, 2008, 319, 1229.
5. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen and R. S. Ruoff, Nature, 2006, 442, 282.
6. J.-A. Yan, L. Xian and M. Y. Chou, Phys. Rev. Lett., 2009, 103, 086802.
7. J.-A. Yan, W. Y. Ruan and M. Y. Chou, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 125401.
8. J. L. Li, K. N. Kudin, M. J. McAllister, R. K. Prudhomme, I. A. Aksay and R. Car, Phys. Rev. Lett., 2006, 96, 176101.
9. K. N. Kudin, B. Ozbas, H. C. Schniepp, R. K. Prud'homme, I. A. Aksay and R. Car, Nano Lett., 2008, 8, 36.
10. D. W. Boukhvalov and M. I. Katsnelson, J. Am. Chem. Soc., 2008, 130, 10697.
11. Z. Y. Li, W. H. Zhang, Y. Luo, J. L. Yang and J. G. Hou, J. Am. Chem. Soc., 2009, 131, 6320.
12. L. Liu, S. Ryu, M. R. Tomasik, E. Stolyarova, N. Jung, M. S. Hybertsen, M. L. Steigerwald, L. E. Brus and G. W. Flynn, Nano Lett., 2008, 8, 1965.
13. D. C. Kim, D.-Y. Jeon, H.-J. Chung, Y. Woo, J. K. Shin and S. Seo, Nanotechnology, 2009, 20, 375703.
14. D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim and K. S. Novoselov, Science, 2009, 323, 610.
15. D. K. Samarakoon and Wang, ACS Nano, 2009, 3, 4017.
16. R. J. W. E. Lahaye, H. K. Jeong, C. Y. Park and Y. H. Lee, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 125435.
17. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
18. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Payne, Z. Kristallogr., 2005, 220, 567.
19. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias and J. D. Joannopoulos, Rev. Mod. Phys., 1992, 64, 1045.
20. A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
21. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter, 1988, 37, 785.
22. S. B. Legoas, P. A. S. Autreto, M. Z. S. Flores and D. S. Galvão, Nanotechnology, 2009, 20, 465704.
23. N. R. Wilson, P. A. Pandey, R. Beanland, R. J. Young, I. A. Kinloch, L. Gong, Z. Liu, K. Suenaga, J. P. Rourke, S. J. York and J. Sloan, ACS Nano, 2009, 3, 2547.
24. D. W. Lee, L. De Los Santos V., J. W. Seo, L. Leon Felix, A. Bustamante D., J. M. Cole and C. H. W. Barnes, J. Phys. Chem. B, 2010, 114, 5723.
25. L. B. Casabianca, M. A. Shaibat, W. W. Cai, S. Park, R. Piner, R. S. Ruoff and Y. Ishii, J. Am. Chem. Soc., 2010, 132, 5672.
26. M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai and G. Seifert, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 58, 7260.
27. C. Z. Wang, K. M. Ho and C. T. Chan, Phys. Rev. Lett., 1993, 70, 611.
28. C. Gomez-Navarro, J. C. Meyer, R. S. Sundaram, A. Chuvilin, S. Kurasch, M. Burghard, K. Kern and U. Kaise, Nano Lett., 2010, 10, 1144.
29. D. Pandeya, R. Reifenberger and R. Piner, Surf. Sci., 2008, 602, 1607.
30. H. J. Xiang, S.-H. Wei and X. G. Gong, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 035416.
31. L. J. Cote, R. Cruz-Silvaand and J.-X. Huang, J. Am. Chem. Soc., 2009, 131, 11027.
32. M. S. Dresselhaus, A. Jorio, M. Hofmann, G. Dresselhaus and R. Saito, Nano Lett., 2010, 10, 751.
33. S. Baroni, S. de Gironcoli, A. dal Corso and P. Giannozzi, Rev. Mod. Phys., 2001, 73, 515.
34. D. Porezag and M. R. Pederson, Phys. Rev. B: Condens. Matter, 1996, 54, 7830.

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Footnote

† Electronic supplementary information (ESI) available: The optimized atomic coordinates, binding energies, and vibrational modes. See DOI: 10.1039/c0nr00710b

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