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Journal of the American Chemical Society
J Am Chem Soc. 2010 April 28; 132(16): 5672–5676.
Published online 2010 April 1. doi:  10.1021/ja9030243
PMCID: PMC2857913

NMR-Based Structural Modeling of Graphite Oxide Using Multidimensional 13C Solid-State NMR and ab Initio Chemical Shift Calculations


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Chemically modified graphenes and other graphite-based materials have attracted growing interest for their unique potential as lightweight electronic and structural nanomaterials. It is an important challenge to construct structural models of noncrystalline graphite-based materials on the basis of NMR or other spectroscopic data. To address this challenge, a solid-state NMR (SSNMR)-based structural modeling approach is presented on graphite oxide (GO), which is a prominent precursor and interesting benchmark system of modified graphene. An experimental 2D 13C double-quantum/single-quantum correlation SSNMR spectrum of 13C-labeled GO was compared with spectra simulated for different structural models using ab initio geometry optimization and chemical shift calculations. The results show that the spectral features of the GO sample are best reproduced by a geometry-optimized structural model that is based on the Lerf−Klinowski model (Lerf, A. et al. Phys. Chem. B1998, 102, 4477); this model is composed of interconnected sp2, 1,2-epoxide, and COH carbons. This study also convincingly excludes the possibility of other previously proposed models, including the highly oxidized structures involving 1,3-epoxide carbons (Szabo, I. et al. Chem. Mater.2006, 18, 2740). 13C chemical shift anisotropy (CSA) patterns measured by a 2D 13C CSA/isotropic shift correlation SSNMR were well reproduced by the chemical shift tensor obtained by the ab initio calculation for the former model. The approach presented here is likely to be applicable to other chemically modified graphenes and graphite-based systems.


Graphene, a single-atom thick layer of graphite, was first prepared over 30 years ago by thermal chemical vapor deposition on single-crystal metal substrates.(1) Due to the recent revisiting of this system as a new class of carbon nanomaterials having fascinating electronic transport(2) and structural properties,3,4 graphene and other graphene-based materials have gained enormous attention. Chemical modifications of graphene have offered exciting paths to altering its novel functionality.37 As new classes of modified graphenes are discovered, there will be a need for methods to determine their detailed chemical structures. Unfortunately, modified graphenes and graphite-based materials are often heterogeneous, noncrystalline, and insoluble. Conventional methods such as solution NMR and X-ray crystallography are thus limited as sources of structural information for such nanomaterials. Solid-state NMR (SSNMR) is a unique tool that can provide site-specific structural information for heterogeneous noncrystalline solids,813 in some cases, in combination with ab initio calculations.1420 However, distinguishing different structural models of graphite- or graphene-based materials from NMR or other spectroscopic data has not been trivial.

Graphite oxide (GO) has attracted broad attention as a prominent precursor for mass production of single-layer graphene and chemically modified graphene and as an interesting model of single-layer “graphene oxide”;2127 we present a SSNMR-based structural modeling approach for analyzing its structure as a framework that is potentially applicable to a broad range of graphene-based systems. One of the crucial bottlenecks for the application of graphene-based systems in materials science is their mass production. Unlike graphite, GO can be dispersed into single-layer graphene oxide by sonication or simple stirring in water.(3) Since the resulting product can be further chemically modified into graphene or graphene-based systems,(27) a variety of studies on GO have been undertaken.2126,28 GO has also been used as a precursor to make graphene-based nanosheets,(27) graphene-based “paper” materials,4,2931 and polymer composite materials having embedded and modified graphene sheets.(3) Despite its significance, the structure of GO is still debated21,23,25,28,3234 more than 150 years after its first synthesis.(35) In particular, intense modeling efforts were very recently made for oxidized graphite layers,21,23,25,28 yet a conclusive structure model has not been established. Uniformly 13C-labeled GO was recently synthesized, allowing its 13C−13C connectivities to be determined for the first time by SSNMR.(10) Based on such results, a systematic approach to evaluate structural models is here undertaken involving direct comparison of experimental 2D 13C SSNMR spectra with simulated 2D spectra obtained from ab initio calculations. The presented approach offers a novel means of evaluating various structural models by NMR without a priori knowledge of NMR signal assignments for modified graphene having a complex chemical network. This approach is also likely to open an avenue for NMR-based structural studies for a broad range of modified graphenes.


Figure Figure1a1a shows an experimental two-dimensional (2D) double-quantum/single-quantum (DQ/SQ) 13C-shift correlation spectrum of uniformly 13C-labeled GO (13C > 99%) obtained under magic angle spinning (MAS). In Figure Figure1a,1a, cross peaks are displayed at (ωSQ, ωDQ) = (ωX, ωXY), where ωX denotes the 13C SSNMR frequency of the detected carbon 13CX and ωY is the frequency of a 13CY to which a 13CX is correlated via a through-bond J coupling (i.e., 13CX and 13CY are bonded). In our previous work, we demonstrated that sp2, epoxide (COC), and COH carbons are directly bonded by 2D 13C/13C correlation SSNMR.(10) However, the cross-peaks between 13COH (~70 ppm) and 13COC carbons (~60 ppm) were partially obscured by the diagonal peaks. Since diagonal signals are eliminated in the 2D DQ/SQ spectrum, the two cross peaks at (ωSQ, ωDQ) = (60, 130 ppm) and (70, 130 ppm) (connected by a red line) confirm unequivocally that the COH and epoxide carbons are directly bonded. Other cross peak pairs show connectivities between epoxide and sp2 13C (orange line), 13COH and sp2 13C (pink line), and two kinds of sp2 13C (purple line). This is consistent with our previous results.

Figure 1
(a) Experimental 2D 13C DQ/SQ correlation SSNMR spectrum of uniformly 13C-labeled GO using 13C−13C J coherence transfer. Fast recycling with short recycle delays of 0.3 s and low power (7 kHz) decoupling was used. Signal assignments in (a) are ...

Parts b and c of Figure Figure11 show simulated 2D DQ/SQ SSNMR spectra based on isotropic 13C chemical shifts obtained by ab initio calculations for (b) model A and (c) model B. Models A and B are cluster models based on the Lerf−Klinowski model(33) and Dékány model, respectively.(32) Our previous SSNMR study showed that these two models are the most likely candidates that represent a structure of the GO sample.(10) The geometry-optimized structures of models A and B are shown in parts d and e, respectively, of Figure Figure1.1. Model A represents a primarily flat structure (see the side view in Figure Figure1d,1d, bottom) that is approximately 50% oxidized, with alternating “ribbons” of oxidized and conjugated carbons. Model B is a chairlike structure (see the side view in Figure Figure1e,1e, bottom) with a band of highly oxidized sites. The latter model lacks 1,2-epoxides and incorporates the 1,3-epoxide motif, as proposed in the Dékány model.(32) In model B, two 1,3-epoxides share a carbon−carbon bond. A similar model having 1,3-epoxide was also proposed by a recent ab initio study.(28) Comparison of Figure Figure1b,c1b,c with Figure Figure1a1a shows a much better overall agreement for model A, excluding model B for the present system. In particular, the spectra in Figure Figure1a,b1a,b both show the cross peaks at ωSQ~60 ppm, which are absent in Figure Figure1c1c for model B. The peaks predicted at ωSQ ~115 ppm for 1,3-epoxides in Figure Figure1c1c are missing in Figure Figure1a.1a. Figure Figure1a1a suggests that sp2 13C connected to epoxide (orange line) displays slightly different 13C shifts from those for sp2 13C connected to C−OH (pink line); this is reasonably well reproduced in Figure Figure1b1b for model A. These findings clearly support model A as the model that best reproduces the experimental spectrum in Figure Figure1a.1a. We also attempted geometry optimizations beginning with sp2-conjugated structures containing isolated 1,3-epoxides or 1,4-epoxides, as proposed in the original Dékány model(32) and in a recent transmission electron microscopy study,(34) respectively. However, they were usually optimized to 1,2-epoxides or carbonyl groups. The result is consistent with a recent ab initio study(28) reporting the instability of 1,3-epoxide in graphene in geometry optimization. Since epoxides are often considered to be an unstable species, it is perhaps surprising that our structural modeling approach using SSNMR experiments and ab inito calculations clearly suggested that 1,2-epoxide is likely to be an abundant form in GO.

In previous SSNMR studies of GO, signal assignments were based on solution NMR data for small model compounds.10,33,36 It is noteworthy that no signal assignment information on GO was utilized in the above analysis to select the best structural model. In fact, in the proposed 2D NMR-based modeling approach using ab initio calculations, prior knowledge on signal assignments is not a prerequisite. A fingerprint matching of experimental and simulated 2D spectra allows for the selection of the best-fit structural model, and then calculated shifts for the best model yield assignments with the connectivity information from 2D SSNMR. Thus, this assignment-free modeling approach provides a rigorous basis to test signal assignments as well as various structural models for GO and probably other graphite-based systems. This will be particularly useful for the development of new modified graphene/graphite materials, for which signal assignments or NMR shift data for suitable small model compounds may not be easily available.

Multiple quantum (MQ) spectroscopy using J coupling such as one in this study has been successfully employed for solids in order to highlight correlations without diagonal signals.(37) However, the requirement of high-power decoupling during the long mixing times generally imposes the use of long recycle delays in order to avoid probe arcing in this method. In our experiments, use of low-power decoupling and the short 1H T1 relaxation time of this sample allowed for fast repetition (~0.3 s/scans) for higher sensitivity (or a better signal-to-noise ratio for a given time).(38) As a result, the 2D spectrum was attained after only 4.5 h for 12 mg of the 13C-labeled sample, rather than 2 days, which would be required by a standard approach with slow recycling. Although systems having slower relaxation times may require more sample quantity, the present approach is likely to be applicable for a broad range of graphite-based systems.

In Figure Figure2,2, we further confirm the validity of our NMR-based structural model of GO by examining 13C chemical shift anisotropies (CSA). Three principal values of CSA (δ11, δ22, δ33), which can be extracted from these lineshapes, sensitively reflect asymmetry in the local electronic environments.3941 Thus, it is possible to test the proposed structural model more rigorously by comparing the principal values calculated at each different carbon site with those from the experimental CSA patterns. Figure Figure22 shows a 2D spectrum of the 13C-labeled GO correlating isotropic shift and 13C CSA powder patterns, the latter of which was obtained by a ROCSA “recoupling” sequence under MAS.(42) Slices along the indirect dimension show experimental CSA patterns, each of which show singularities (i.e., peaks or shoulders) at principal values. In Figure Figure3,3, these slices were compared with powder patterns calculated from the principal values obtained from the ab initio calculations for models A (blue) and B (green) for (a) sp2, (b) COH, (c) COC. For model B, the powder pattern of 1,3-epoxide 13C does not reproduce the experimental pattern. Although for COH the pattern shows slight deviation probably due to the finite nature of the model, the overall agreement between calculated and experimental spectra is reasonable for model A. Chemical shift calculations including periodic boundaries are ongoing in our laboratory. The results in Figure Figure33 confirm that model A is likely to present a representative structure of the GO sample analyzed here. On the other hand, for GO oxidized under different conditions, structures such as model B may be present. For such systems, the CSA data for model B can be utilized for future analysis.

Figure 2
(a) 2D 13C anisotropic chemical shift/isotropic shift correlation spectrum for GO obtained by the ROCSA sequence(42) at 15 kHz MAS with (b−d) 1D slices along the indirect ω1 dimension showing experimental chemical shift anisotropy (CSA) ...
Figure 3
Comparison of the experimental 13C chemical shift anisotropy (CSA) spectrum (black) with simulated CSA powder patterns from ab initio chemical shift calculations (blue, model A; green, model B) for (a) sp2 and (b) COH (c) COC carbons. The simulated powder ...

Figure Figure44 shows our preliminary data of a 2D triple-quantum/single-quantum (3Q/SQ) correlation spectrum for the same 13C-labeled GO sample. In this experiment, cross peaks are displayed at (ωSQ, ω3Q) = (ωY, ωX + ωY + ωZ), where ωY denotes the 13C SSNMR frequency of the detected carbon 13CY and ωX and ωZ are the frequencies of 13CX and 13CZ, to which 13CY is connected via a through-bond J coupling (i.e., connected as CX−CY−CZ). Strong signal intensities were observed for the cross peak correlating three oxidized 13C sites such as 1,2-epoxide and COH (red arrows). The cross peaks clearly demonstrate that a cluster of three oxidized 13C sites is likely to have a considerable population in the GO sample. On the other hand, the presence of 3Q connecting three sp2 groups seems to indicate that networked sp2 groups are still retained in this sample. Although further studies are needed, more quantitative analysis of the signal intensities is likely to reveal detailed distributions of the oxidized sites or possible clustering of the oxidized sites in GO and other graphite- and graphene-based systems, including graphene oxide.

Figure 4
Experimental 2D 13C 3Q/SQ correlation SSNMR spectrum of uniformly 13C-labeled GO using 13C−13C J coherence transfer. Short recycle delays of 0.3 s and low power (7 kHz) decoupling were used. The carrier frequency was set at 211.17 ppm. In the ...


We have shown that a combination of multidimensional SSNMR experiments and chemical shift calculations offers a powerful approach to construct a structural model that well reproduces SSNMR spectra for GO. There are primarily three novel aspects in this study. First, the presented approach permits us to fully utilize excellent resolution and connectivity information from multidimensional 13C SSNMR, which has been rarely utilized for graphene/graphite related materials. Without requirements of prior knowledge of NMR chemical shift assignments, this approach will offer a novel means to evaluate structural models of a variety of graphite/graphene-based systems. Based on the results of 3Q/SQ correlation, extending this approach to 3D/4D SSNMR for more detailed structural information is promising with the excellent sensitivity offered by fast recycling under very fast MAS for 13C-labeled GO. Second, the present study on GO is the first example demonstrating that reasonable accuracy in 13C chemical shift calculations can be obtained for infinitely conjugated modified graphene by ab initio calculations for cluster models. As found in the present and previous examples,14,16,19,20,43 establishing ab initio chemical shift calculations for a new class of materials will open novel opportunities for structural analysis. Chemical shift anisotropy line shapes will offer an additional basis to distinguish different structural models of modified graphene. Third, our results suggest that model A in Figure Figure1d1d (based on the Lerf−Klinowski model) convincingly reproduced the 2D DQ/SQ-correlation SSNMR and CSA powder patterns found in our experimental spectra for 13C-labeled GO. Thus, among various models proposed in the previous studies, model A based on the Lerf−Klinowski model is the most plausible structural model for the GO system investigated here. Recently proposed structural models involving 1,3- or 1,4-epoxide moieties, thus, seem not likely to represent the GO system. It is also noteworthy that this study based on the NMR data has revealed the primary structural features for major chemical species in GO, and other kinds of structures may be present at a lower population(44) in the highly heterogeneous sample. Such detailed structural features can be also studied by the present approach if sufficient sensitivity is obtained in NMR data for the minor species. In addition, it is probable that a different degree of oxidization or different oxidization methods may result in GO of different molecular structures; such structural differences will be easily examined by the method presented here. The characterization of molecular structures of precursors in chemical synthesis often provides a basis to understand the nature of reactions and discover new paths for synthesis. Since the SSNMR approach presented here yields detailed structural information on GO, a precursor for graphene-based systems,(3) and will also be relevant for analysis of other chemically modified graphenes, this approach has value for the synthesis of chemically modified graphene systems and for optimization of such synthesis protocols.


Solid-State NMR Experiments

Uniformly 13C-labeled graphite oxide was prepared in the Ruoff laboratory as described previously.(10) SSNMR experiments were conducted at 9.4 T using a Varian InfinityPlus 400 NMR spectrometer and a home-built 2.5 mm MAS probe. The pulse sequence and phase cycling used for 2D MQ/SQ correlation experiments through J transfer in Figures Figures11 and and44 are shown in Figure S1 (Supporting Information). All chemical shifts were referenced to TMS using adamantane as an external reference. 2D MQ/SQ correlation spectra in Figures Figures1a1a and and44 were collected using a MAS spinning speed of 20000 ± 10 Hz, and the cooling air temperature for a Varian variable-temperature (VT) stack was set at −10 °C. For the spectra of GO shown in Figures Figures1a1a and and4,4, fast recycling with short delays of 0.3 s and low power (7 kHz) decoupling(38) was used. During the CP period, the 13C RF field amplitude was linearly swept from 52 to 70 kHz during a contact time of 2.0 ms, while the 1H RF amplitude was kept constant at 82 kHz.

For the 2D DQ/SQ-correlation experiment in Figure Figure1a,1a, 200 t1 points were collected using a mixing time of 1.5 ms with 28 scans for each real or imaginary t1 data point during a total experimental time of 4.5 h. The t1 increment was 12.5 μs. The spectra were processed with 150 Hz line Gaussian broadening in each dimension. The carrier frequency for 13C was set at 211.17 ppm. The carrier frequency in the DQ dimension is displayed as 422.34 ppm in Figure Figure1a1a so that the DQ frequency simply exhibits the sum of chemical shifts for two correlated 13C groups.

The 2D 3Q/SQ-correlation spectrum on uniformly 13C-labeled GO in Figure Figure44 was collected with the same pulse sequence used for the 2D DQ/SQ experiment, but with a different phase cycle (see Figure S1, Supporting Information). With a mixing time of 3 ms, 60 t1 points were collected with 384 scans for each real or imaginary t1 data point during a total experimental time of 4.5 h. The t1 increment was 6.25 μs. The carrier frequency for 13C was set at 211.17 ppm. The carrier frequency in the 3Q dimension is displayed as 633.51 ppm in Figure Figure44 so that the 3Q frequency simply exhibits the sum of chemical shifts for three correlated 13C groups. Other conditions are the same as those for 2D DQ/SQ correlation.

The recoupling of chemical shift anisotropy (ROCSA) pulse sequence developed by Chan and Tycko(42) was used to measure the 13C powder patterns due to chemical shift anisotropy (CSA) of three different chemical groups for GO under magic angle spinning conditions. We used the C221 symmetry sequence with the time period before the first rotor-synchronized pulse (a period as defined in ref (42)) and the duration of the composite pulse (b period) equal to 0.0329τR and 0.467τR, respectively, where τR denotes a rotation period. The experiment was performed at a spinning speed of 15000 ± 10 Hz. A 13C rf nutation frequency of 64 kHz was used for the ROCSA recoupling period. High-power TPPM 1H decoupling (100 kHz) was used. The cooling air temperature for the VT stack was controlled at −10 °C. For this experiment, 40 t1 points with 64 scans each were collected using a recycle delay of 2 s, for a total experimental time of 2.85 h.

Ab Initio Geometry Optimization and Chemical Shift Calculations

Chemical shift calculations were performed using Gaussian 03 (Revision D.01)(45) on a Beowulf PC cluster at the Academic Computing and Communications Center at UIC. Each of the models shown in Figure Figure11 were geometry optimized at the B3LYP/6-31G* level of theory.4648 Chemical shielding tensors were calculated using GIAO(49) with B3LYP and a 6-311G basis set. Chemical shieldings for the three principal components of the tensor were converted to chemical shifts as follows. Methane was used as the theoretical reference compound. The isotropic chemical shielding of 13C in methane was calculated at the B3LYP/6-311G level of theory, after geometry optimization at the same level of theory. The calculated shielding was converted to TMS shielding by adding the difference (−11.0 ppm) between the chemical shift of methane in the gas phase and TMS with susceptibility correction.(50) This gave the calculated shielding of TMS, which is 185.0 ppm for B3LYP/6-311G. The calculated shielding tensor values of each carbon were then subtracted from the calculated isotropic shielding of TMS at the same level of theory in order to give the calculated chemical shifts. The principal values of the chemical shift tensors obtained for models A and B are found in the Supporting Information (Table S1). The simulated CSA patterns in Figure Figure33 were obtained by a superposition of the powder patterns for all 13C sites belonging to the same chemical group.

To create a cluster model from an infinite graphene sheet, we used structures containing 54 carbons terminated with C−H bonds in models A and B. To test whether the conclusion would vary depending on model type, the same calculations were done on alternative models of 43 carbons that were terminated with C−H bonds and C=O groups (models X and Y in Figure S3d,e, Supporting Information). Model X is a model based on the Lerf−Klinowski model, while model Y is that based on the Dékány model. For these slightly smaller models, we simulated 2D DQ/SQ spectra (Figure S3b,c, Supporting Information). A comparison of the experimental spectrum (Figure S3a, Supporting Information) with the simulated spectra supports the conclusion that the model based on the Lerf−Klinowski model (model X in Figure S3d, Supporting Information) best reproduces the experimental spectrum compared to other suggested models.


This work was supported by the NSF CAREER program (CHE 449952) and also in part by the Dreyfus Foundation Teacher−Scholar Award program and the NIH RO1 program (AG028490) for Y.I. W.W.C., S.P., R.P., and R.S.R. appreciate support from NSF 0742065, the DARPA CERA and DARPA iMINT Centers, and SWAN-NRI.

Funding Statement

National Institutes of Health, United States

Supporting Information Available

Supporting Information Available

Full author list of ref (45), evaluation of 13C chemical shifts for alternative models, and additional details of experimental conditions and ab initio calculations. This material is available free of charge via the Internet at

Supplementary Material


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