NMR Spectral Parameters in Graphene, Graphite, and Related

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NMR Spectral Parameters in Graphene, Graphite and Related Materials: Ab Initio Calculations and Experimental Results Fabio A. L. de Souza, Alan R. Ambrozio, Everson S. Souza, Daniel F. Cipriano, Wanderlã Luis Scopel, and Jair C. C. Freitas J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10042 • Publication Date (Web): 11 Nov 2016 Downloaded from http://pubs.acs.org on November 13, 2016

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The Journal of Physical Chemistry

NMR Spectral Parameters in Graphene, Graphite and Related Materials: Ab Initio Calculations and Experimental Results. Fábio A. L. de Souza,†,‡ Alan R. Ambrozio, † Everson S. Souza, † Daniel F. Cipriano, † Wanderlã L. Scopel, † Jair C. C. Freitas†,* †

Laboratory of Carbon and Ceramic Materials, Department of Physics, Federal University of

Espírito Santo (UFES), Av. Fernando Ferrari, 514, 29075-910, Vitória, ES, Brazil. ‡

Federal Institute of Education, Science and Technology of Espírito Santo, R. Sete de Novembro,

40, 29395-000, Ibatiba, ES, Brazil.

*

Corresponding author. E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT. The shielding tensor in 13C nuclear magnetic resonance (NMR) offers important information about the structural aspects of carbon materials from a local point of view. Not only the symmetry of the carbon site but also the presence of local structural distortions can affect the values of the isotropic shielding constant, the shielding anisotropy and the deviation from axial symmetry. In this report, the

13

C shielding in a single graphene sheet was calculated using

density functional theory (DFT) via the gauge-including projector augmented plane wave (GIPAW) method. After performing convergence tests involving changes of k-sampling and supercell size, the calculations were extended to graphene-based systems, including graphene bilayer and stacked graphene sheets, finally leading to hexagonal graphite. The calculated results showed good agreement with experimental values obtained by

13

C NMR measurements in

different types of carbon materials, evidencing the power of the DFT calculations for predicting NMR parameters in graphene-based nanocarbons.


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Introduction Graphene, consisting of an isolated single atomic layer of carbon atoms with sp2 hybridization as found in graphite, has attracted great attention since it was first experimentally obtained more than 10 years ago.1 This huge interest is motivated both by its unusual physical properties and by the wide range of possible applications of pristine graphene and graphene-based materials.2-5 It is no surprise then that many efforts have been spent on trying to elucidate the theoretical aspects related to the electronic structure of graphene, by employing either analytical or computational methods. In this regard, methods based on the density functional theory (DFT) have proven to be particularly powerful. Examples of successful application of DFT calculations to graphene and related materials include studies of magnetic,6,7 hyperfine,8,9 optical,10 electronic,6,11,12 and mechanical13,14 properties, among many others. The use of DFT methods to predict nuclear magnetic resonance (NMR) spectral features of graphene has been more limited. Although solid-state 13C NMR spectroscopy is largely used for the characterization of nanostructured carbon materials, including nanodiamonds, nanographites, fullerenes, carbon nanotubes, graphite / graphene oxide, etc.,15-19 the theoretical support from ab initio calculations to the interpretation of such spectra is somewhat scarce. For many years the theoretical predictions of NMR chemical shifts were limited to finite systems, such as molecules and clusters,20-22 with some examples of studies of extended systems also treated through cluster methods in a quantum-chemical approach.23 The pioneering approach dealing explicitly with the use of periodic boundary conditions applied to real crystalline solids was proposed in 1996 by Mauri et al., who presented a theory for the ab initio calculation of magnetic susceptibility and NMR chemical shifts in insulators.24,25 The


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pseudopotential approximation was used in these two reports. However, an accurate evaluation of the magnetic response requires a precise description of the core electrons, which are neglected explicitly by using traditional pseudopotential approaches. The projector augmented-wave (PAW) method proposed by Blöchl26 provides a route to recover the shape of all-electron KohnSham (KS) orbitals near the nucleus through pseudopotential-based schemes, but the PAW method is not able to preserve translational invariance in a uniform magnetic field. In 2001, an invariant description in the presence of a magnetic field as an extension of the PAW method was proposed by Pickard and Mauri,27 which became known as the gauge-including projector augmented wave (GIPAW) approach. Therefore, GIPAW is an ab initio method that allows the all-electron calculation of NMR chemical shifts using pseudopotentials. Due to its high accuracy, GIPAW has become a valuable tool for understanding and interpreting experimental NMR spectra, with numerous examples of its application for the calculation of NMR parameters associated with several probe nuclei (including those with spin 1/2 as well as quadrupolar nuclei) in different types of materials.28-39 The continuous improvement of computing capability and the availability of software packages implementing GIPAW calculations are factors that contribute to the expansion of the use of the method for the study of more realistic systems and incorporating important physical issues such as dynamical effects and structural disorder.40 Regarding carbon materials, the most common examples of DFT predictions of NMR parameters are found in studies of amorphous carbon films, fullerenes and carbon nanotubes. Mauri et al. pioneered the application of DFT methods to the calculation of the chemical shifts in 1H and 13C NMR spectra of hydrogenated amorphous carbons, establishing the fractions of sp2 and sp3 carbon atoms bonded or not to hydrogen and thus predicting theoretical spectra in excellent agreement with the experimental solid-state NMR data.41 Deschamps et al. performed DFT


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calculations to predict the 13C NMR spectrum of C70 fullerene and showed that the calculated parameters can be useful also for the interpretation of the spectra observed for nanoporous carbons.42 Calculations of 13C NMR parameters in carbon nanotubes using GIPAW methods are also fairly common in the literature. Studies on both semiconducting and metallic tubes with different diameters have been reported, including data on isotropic chemical shifts and on shielding tensors.43-46 The effects of the presence of structural defects (e.g., the Stone-Wales defect) on the 13C shielding tensors corresponding to different sites were investigated by Zurek et al.44; large downfield shifts were found for sites taking part of the defect, whereas an overall spectral broadening was also predicted. Graphene and related materials have also been investigated by DFT calculations of NMR parameters. Convergence problems were reported by Vähäkangas et al.47 when using the GIPAW method for calculating the 13C shielding in graphene, which were attributed to the vanishing electronic gap that makes impossible the use of a perturbative approach. Instead, these authors employed cluster calculations to obtain the isotropic chemical shift and the shielding anisotropy of graphene considering it as the infinite limit of concentric aromatic rings with increasing sizes.47 In a related study, Özcan et al. studied the size dependence of the 13C NMR chemical shift in several graphene-like fragments, emphasizing the differences observed between fragments with either zig-zag or armchair edge types.48 Similar calculations have also been performed for polycyclic aromatic systems of varying sizes, 49-51 including a detailed analysis about the effects of curvature on the calculated shielding parameters.51 The above cited convergence problems were not mentioned in other studies also reporting the results of DFT calculations (with use of periodic boundary conditions) of NMR chemical shifts in graphene.45,49 The 13C NMR spectral features of graphene oxide were also calculated using DFT and compared


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to experimental results, allowing the building of a model for the structure of graphene oxide consisting of sp2 carbon clusters embedded into highly oxidized regions.52 It is worth also mentioning some recent reports of calculations of a parameter known as the nucleus independent chemical shift (NICS), using “ghost” probe atoms placed close to graphene-based models or to polyaromatic molecules; NICS is mostly related to ring current effects and can be used as an index of aromaticity, being affected by structural features such as molecular curvature, aromatic cluster size and distance from the cluster.51,53,54 More recently, DFT calculations have been used to study the hyperfine interaction in graphene and related systems containing point defects that give rise to local magnetic moments. Electron spin resonance (ESR) parameters and paramagnetic NMR shieldings were calculated for graphene sheets containing H or F adatoms, as well as for hydrogenated or fluorinated graphenes with a H or F missing atom, respectively.55 The hyperfine magnetic field was also calculated for graphene-based systems presenting a ferromagnetic ground state, including systems containing single atomic vacancies and graphene nanoribbons with oxygen-containing edge sites; good agreement was observed between the results of hyperfine magnetic field calculations and the NMR signal observed in zero-field NMR experiments performed in bulk samples of ferromagnetic graphite.9 In this work, DFT-based first-principles calculations were carried out to predict the 13C NMR shielding tensor components for different carbon sites in pristine graphene, in graphene bilayer and in graphite. Given the above mentioned existence of convergence issues in graphene, particular attention was paid to the convergence of the calculated values with respect to the sampling of the first Brillouin zone in the reciprocal space; also, the effects associated with interlayer spacing and layer to layer orientation (AA or AB stacking type56,57) were analyzed. The


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calculated shielding tensors were then used to simulate the powder patterns corresponding to each system, which were compared to experimental 13C NMR spectra obtained for carbon materials.

Methods Computational details The DFT calculations were carried out using the GIPAW approach as implemented in the Quantum Espresso package (version 5.1).58 The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) scheme was employed for these calculations. 59 The interaction between ion cores and valence electrons was described by norm-conserving TroullierMartins pseudopotentials.60 The van der Waals interaction was taken into account following the semi-empirical approach described by Grimme et al.61 All structures were relaxed until Hellmann-Feynman forces acting on each atom were smaller than 0.01 eV/Å and the energy cutoff was set to be 1088 eV. From the relaxed atomic structure of the studied systems, the GIPAW method was used to determine the components ij of the shielding tensor corresponding to each carbon site. The calculations were performed to determine the 13C NMR shielding tensors of the following model systems: a perfect graphene sheet (single layer); graphene bilayers with AA or AB stacking order; and 3D graphite structures also with AA or AB stacking orders, corresponding to simple and Bernal-type hexagonal structures, respectively.56,57 In the case of a single graphene layer and a graphene bilayer, a vacuum region of 15 Å was introduced at each side of the planar system


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(either a single layer or a bilayer), in order to minimize the interaction between the main system and its periodic image along the direction perpendicular to the layers. The lattice parameter for graphene obtained from structural optimization was 2.46 Å, which is in good agreement with previous experimental results62 as well as DFT calculations.63 The interatomic distances were freely allowed to change during structural relaxation for all studied systems, while keeping fixed the supercell size. The Brillouin zone integration in the case of graphene was performed using the Monkhorst-Pack64 scheme with k × k × 1 grids, where the number k was varied together with the supercell size in order to investigate the convergence of the calculated NMR parameters (see below). Following these convergence tests, a supercell with 18 atoms (corresponding to 3 × 3 unit cells) and a 20 × 20 × 1 k-space sampling grid were adopted for the graphene single layer; in all other cases, a single unit cell was adopted, with 35 × 35 × 1 and 25 × 25 × 1 sampling grids for graphene bilayer with AA and AB stacking types, respectively, and a 30 × 30 × 10 sampling grid for graphite with both stacking types. No correction due to sample shape and bulk magnetic susceptibility effects was included in the calculations; these contributions are not expected to be significant except in the case of oriented samples,49 which is not the case of the samples studied experimentally in this work. From the calculated components of the shielding tensor ( ij ) in its principal axis system ordered as 11  22  33 , the parameters isotropic shielding ( iso ), span () and skew () were computed as follows:65,66

iso 

1  11  22  33  , 3   33  11 ,

(1)

(2)


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

3  iso  22  

.

(3)

The isotropic shielding defines the average position of the NMR line associated with a given site; in liquids (and gases), it is the only shielding component that survives after the averaging process induced by the rapid molecular tumbling motion.15 The span defined in Eq. 2 corresponds to the total breadth of the powder pattern observed experimentally, whereas the skew (Eq. 3) reflects how the local arrangement around the nuclear site deviates from axial asymmetry:  = ±1 for axial symmetry (+1 for a prolate and 1 for an oblate ellipsoid representing the shielding tensor);  = 0 for a site with 22 halfway between 11 and 33 .65 The definitions presented above for the span and the skew are related to the shielding anisotropy and shielding asymmetry, respectively, which are parameters used in other commonly employed shielding tensor conventions.65,66 From a practical point of view, in order to compare the calculated values with experimental results, it is necessary to convert the calculated shielding parameters in chemical shifts, which means that a convenient compound must be chosen as a reference standard to define the shift scale.15,66 As discussed in detail in previous studies43,67, benzene (with all its carbon atoms taking part of sp2 bonds, similarly to graphene) is an appropriate choice to be used as an intermediate reference for the calculation of chemical shifts in carbon materials, since the electronic similarity between the studied system and the reference molecule is expected to lead to the cancelation of systematic errors present in the calculations. Thus, following this approach, benzene was chosen as an intermediate reference, with the chemical shift calculated as follows: iso )   Benzene / TMS . G / TMS   G  (Benzene

(4)


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iso ) In this expression, G and (Benzene correspond to the shielding parameters calculated for a given

system (e.g., graphene) and for an isolated benzene molecule, respectively; the parameter Benzene / TMS is the experimental chemical shift of benzene (in the gas phase) with respect to liquid

tetramethylsilane (TMS), which is the common primary reference used in

13

C NMR

spectroscopy. The experimental value Benzene / TMS  126.9 ppm 43,68 and the calculated value iso ) (Benzene  38.8 ppm were adopted in this work; by using these numerical values in Eq. 4, all

calculated shielding parameters were then converted to chemical shifts (with respect to liquid TMS) and a direct comparison of calculated and experimentally-derived spectral parameters was thus possible.

Experimental methods 13

C NMR experiments were conducted at 9.4 T (100.52 MHz frequency) at room temperature

with static samples of the following materials: milled graphite, obtained by milling a high-purity graphite rod (Alfa Aesar) for 40 min, as described in detail by Vieira et al.;19 and a commercial sample of fullerene soot (Sigma-Aldrich). A spin-echo sequence with /2 and  pulses with durations of 4.3 and 8.6 s, respectively, an inter-pulse delay of 40 or 800 s (allowing the recording of a half-echo or a whole echo, respectively) and a recycle delay of 15 s were used in the experiments. The powder patterns were obtained by Fourier transform of the echoes. The chemical shifts, expressed in parts per million (ppm), were referenced to tetramethylsilane (TMS), using hexamethylbenzene (HMB) as external reference (methyl peak at 17.3 ppm).


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The experimentally-obtained powder patterns were simulated using the DMFIT software,69 with numerical determination of the parameters characterizing the chemical shift anisotropy (CSA) tensor: iso (isotropic chemical shift),  (span) and  (skew).65,66 The experimental isotropic chemical shifts can be compared to the results of the DFT calculations by using Eq. 4 to convert the calculated shielding values into chemical shifts, as described before; on the other hand, the span and skew derived from the spectra are directly comparable to the calculated values defined in Eqs. 2 and 3, which are independent on the reference choice.

Results and Discussion DFT calculations – pristine graphene and convergence issues The DFT calculations were first carried out for pristine graphene, using different supercell sizes and changing the k-sampling accordingly. With all carbon sites chemically equivalent in the single graphene layer, the calculations yielded a unique shielding tensor for all sites. Figure 1 shows how the calculated 13C NMR isotropic shielding ( iso ) changes as a function of the number of k-points in the first Brillouin zone, for several choices of supercell sizes. For each supercell, the value of iso was calculated by increasing k-sampling until achieving convergence. As it can be observed in Fig. 1, the oscillations in the iso values that are observed for low k-sampling become smaller as the supercell size is increased. Thus, a faster convergence is achieved for larger supercells, as expected. With use of a 3 × 3 supercell (with 18 atoms, which was the final choice in the present work), no significant oscillation is observed for k = 20 (i.e., for a 20 × 20 × 1 k-point grid).


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As mentioned before, a strong oscillatory behaviour of iso with increasing k-sampling in graphene has been previously reported,47 similarly to what has been observed for semimetallic nanotubes.67 However, the present results clearly indicate that good convergence can be achieved with a moderate k-sampling, provided a reasonably large supercell is chosen. Thus, these findings show that the calculation of the 13C NMR shielding tensor in graphene using periodic boundary conditions is indeed feasible, in agreement with some previous reports;45,49 therefore, the DFT calculations of NMR parameters in graphene-based systems are not restricted to finite molecular clusters.

Figure 1. 13C NMR isotropic shielding in graphene as a function of k-sampling for different supercell sizes. Dashed lines are guides to the eyes. The inset shows an illustration of the 3 × 3 supercell. The converged values of the components of the 13C NMR shielding tensor for graphene are given in Table 1, along with the results obtained for the other studied systems (to be discussed later). From these results, the corresponding values of isotropic chemical shift, span and skew were


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calculated using Eqs. 1-4; these values are informed in Table 2, where other calculated and experimental results are also compiled, for comparison. Table 1. Calculated components of the shielding tensors for the systems studied in this work.

11

22

33

iso

(ppm)

(ppm)

(ppm)

(ppm)

Graphene – single layer

20.1

20.1

154.4

38.1

Graphene bilayer (AA stacking)

28.1

28.1

156.9

33.6

Graphene bilayer (AB stacking) – site C1

18.6

18.6

155.9

39.6


23.9

23.9

154.9

35.7

Graphite (AA stacking)

29.5

29.5

156.3

32.5

Graphite (AB stacking) – site C1

20.4

20.4

156.5

38.6


35.0

35.0

153.9

28.0

System


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Table 2. Summary of calculated and experimentally-derived 13C NMR shielding parameters for the systems studied in this work.a System

δ iso (ppm)



Ref.

Observations

(ppm) Graphene – single layer

a

127.6

174.5

This work

DFT calculation

127.4

n.d.

b

45

DFT calculation

118.0

n.d.

49

DFT calculation

127.1

n.d.

70

DFT calculation

117

n.d.

71

Experimental result obtained for reduced graphene oxide

123

n.d.

72


122, 119

n.d.

73

Experimental result obtained for reduced graphene oxide after two chemical treatment stages

118

n.d.

74


122

170

75


128

163

16

Result derived indirectly from experiments performed with a HOPG sphere

Graphene bilayer (AA stacking)

132.1

185.0

This work

DFT calculation


126.1

174.5

This work

DFT calculation


130.0

178.8

This work

DFT calculation

Graphite (AA stacking)

133.3

185.8

This work

DFT calculation


127.2

177.0

This work

DFT calculation


137.8

188.9

This work

DFT calculation


124.3

n.d.

49

DFT calculation


134.9

n.d.

49

DFT calculation

Graphite

119

178

76

Static 13C NMR experiment

Graphite

119.5

180.8

77


Milled graphite

121(2)

173(5)

This work


sp2 carbons in fullerene soot

126(2)

183(5)

This work


The informed parameters are the isotropic chemical shift with respect to TMS (  iso ) and the span (); the skew

value  = +1 was found for all carbon materials investigated in this work, as expected for systems with axial symmetry around the axis perpendicular to the graphene planes (known as c-axis in the case of graphite). b

n.d. = not determined.


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The converged value of 13C NMR iso in graphene for all supercell sizes is 38.1 ppm (Table 1 and Fig. 1). Using Eq. 4, the value iso  127.6 ppm is thus obtained (see Table 2), which is in good agreement with the calculated values of 127.4 and 127.1 ppm reported by Lai et al.45 and Skachkov et al.,70 respectively, but is somewhat higher (by ca. 10 ppm) than the result obtained by Thonhauser et al.49 Currently, there are no available NMR experimental results obtained directly for a single graphene layer, which is understandable due to the low sensitivity intrinsic to 13C NMR and to the difficulties with the instrumental setup required for such experiments. On the other hand, there are 13C NMR experimental data reported for bulk materials somewhat similar to graphene, such as reduced graphene oxide (rGO) – which is a material actually composed by many sets of crumpled and randomly aggregated graphene-like sheets.71 The 13C NMR spectra of these rGO samples generally exhibit a broad line attributed to sp2 carbons, with reported average iso values falling into the range 117-123 ppm (see Table 2).71-75 Another indirect evidence for the 13C NMR features of graphene was achieved by analyzing the NMR results obtained for a sphere of highly oriented pyrolytic graphite (HOPG).78 By applying a nearly empirical correction due to macroscopic effects associated with the largely anisotropic magnetic susceptibility of graphite, the value iso  128 ppm was then determined for a single graphene plane.16,78 These experimental values are thus in quite reasonable agreement with the calculated isotropic chemical shift here reported for a single graphene sheet. As for the other shielding parameters, the calculated span and skew are 174.5 ppm and +1, respectively (see Table 2). The value of the skew is perfectly consistent with an axial symmetry around the axis perpendicular to the graphene plane, as expected; this finding is common to all


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carbon systems investigated in this work (i.e., 11  22 for all systems, as shown in Table 1). To the best of our knowledge, there are no previous reports of DFT calculations of parameters related to the shielding anisotropy (e.g., the CSA span) in graphene. On the other hand, span calculations performed for clusters of concentric aromatic rings yielded values approaching a limit close to ca. 200 ppm as the cluster size was increased.47 Similar span values have also been obtained in calculations involving polycyclic aromatic systems of different sizes.50,51 The span value here calculated also compares well with the experimental estimate of 163(5) ppm for a graphene plane derived from NMR results obtained in HOPG16,78 and with the value of 170 ppm directly achieved for reduced graphene oxide.75

DFT calculations – graphene bilayer Having established the appropriateness of the DFT/GIPAW approach for 13C NMR shielding calculations in graphene and in order to evaluate the influence of interlayer interactions on the shielding parameters, further calculations were next performed for a graphene bilayer. Two stacking possibilities were considered: In the so-called AA stacking, all carbon atoms in the top layer lie exactly on top of the corresponding sites in the layer underneath. On the other hand, in the AB stacking (see Figure 2), half of the carbon atoms in the top layer are aligned with carbon atoms in the layer underneath, whereas the atoms in the other half are located directly above the centres of the hexagons in the adjacent layer.57 This latter stacking type corresponds to what is experimentally observed in hexagonal graphite (known as Bernal structure).56 The interlayer spacing values achieved after structural relaxation were equal to 3.52 and 3.25 Å for AA and AB stacking, respectively, values that are comparable to the actual interlayer spacing observed in


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graphite (3.34-3.35 Å, depending on the temperature62) and to previous calculations carried out for graphene bilayers.79-81

Figure 2. Graphene bilayer with AB stacking type. The two chemically distinct carbon sites are indicated.

The 13C NMR shielding tensor components corresponding to AA and AB stacking order in the graphene bilayer were then calculated, with the results shown in Table 1 and Table 2; from these data, the corresponding 13C NMR spectra were simulated, as exhibited in Figure 3 (which also includes, for comparison, the spectra obtained for graphene single layer and for graphite, to be discussed later). Two types of carbon sites are discernible in the AB case: the C1 site corresponds to atoms in a given plane exactly below the hexagon centres in the adjacent plane, whereas the C2 site corresponds to atoms directly aligned with other atoms in the adjacent plane (see Figure 2). In the case of the AA bilayer, the calculated values of isotropic chemical shift and span ( iso  132.1 ppm and   185.0 ppm ) were somewhat larger than the values found for graphene single layer (see Table 2), pointing to a significant role played by interlayer coupling


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(as it will be further discussed later in connection with the analysis of the results obtained for graphite). As for the AB bilayer, a difference of ca. 4 ppm between the isotropic chemical shifts associated with the two chemically distinct sites was achieved, with C1 site presenting isotropic shielding and shielding anisotropy (span) closer to the values obtained for graphene single layer; on the other hand, the numerical values corresponding to C2 site in the AB bilayer are comparable to the ones found for AA bilayer, which is understandable due to the proximity between atoms in the two layers in both cases. It is worth observing that, in the AB bilayer case, the difference between the shielding parameters associated with the two carbon sites is larger for the 11 and 22 components (~5 ppm) than for the 33 component (~1 ppm), as shown in Table 1; consequently, the distinction between these sites is more clearly observed at the high frequency edge (i.e., for chemical shifts close to 200 ppm) of the simulated spectra in Figure 3.


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Figure 3. Simulated 13C NMR spectra (CSA powder patterns) of graphene single layer, graphene bilayer (AA and AB stacking types) and graphite (AA and AB stacking types), constructed from the results of the DFT calculations. The crystallite orientations corresponding to the magnetic field parallel or perpendicular to the c-axis of the hexagonal graphite structure (corresponding to the directions perpendicular or parallel to the graphene planes, respectively) are indicated.

DFT calculations – graphite Also two stacking possibilities were considered in the calculations involving the 3D structure of graphite. The AA stacking gives rise to a simple hexagonal structure, whereas the AB stacking (see Figure 2) corresponds to what is experimentally observed in hexagonal graphite (known as Bernal structure).56 Again in this case the equilibrium interlayer spacings (equal to 3.47 and


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3.22 Å for AA and AB stacking, respectively) are in reasonable agreement with previous experimental and calculated results.56,57,62,79 The 13C NMR shielding tensor components in graphite for the single site in the case of AA stacking and for the two chemically distinct sites (C1 and C2) in the case of AB stacking are given in Table 1, whereas the corresponding chemical shift parameters are shown in Table 2 and the simulated 13C NMR spectra are exhibited in Figure 3. Similarly to the previously discussed case of graphene bilayers, it can be observed from the simulated spectra that there is a sizeable difference (~15 ppm) between the in-plane ( 11  22 ) shielding components of C1 and C2 sites, whereas the out-of-plane components ( 33 ) are less dissimilar (difference ~3 ppm) for the same sites. These results show then that the crystallites oriented with the magnetic field parallel to the graphene planes (for which the 11 and 22 components define the chemical shift) are the most sensitive to the type of plane stacking, in terms of shielding effects on 13C nuclei, leading to observable differences at the high-frequency edge (shifts ~185-200 ppm) of the powder patterns shown in Figure 3 (for AB graphite). On the other hand, the chemical shifts are much closer for C1 and C2 sites at the other extreme of the powder pattern (shifts close to 9-12 ppm), corresponding to crystallites oriented with the magnetic field perpendicular to the graphene planes. As expected, the chemical shifts associated with the C2 site (for AB stacking) are pretty close to the value observed for all sites in the case of AA stacking (where there is only one type of site, since all atoms have neighbours along the c direction in the adjacent planes). In order to evaluate the influence of interlayer interactions on the 13C NMR shielding parameters in graphite (for AB stacking), further DFT calculations were conducted with a systematic change in the interlayer spacing. In these calculations, the interplanar spacing was varied, while keeping


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fixed the carbon atomic positions in each layer. Then, for each established value of the interplanar spacing, electronic relaxation was performed in order to determine the NMR shielding parameters. Figure 4 shows how the isotropic chemical shifts corresponding to C1 and C2 sites in the graphite structure change as a function of the interlayer spacing. For small values of the interlayer spacing, a significant difference was observed between the iso values associated with C1 and C2 sites, with a difference of ca. 10 ppm obtained at the calculated value of the equilibrium interlayer spacing of 3.22 Å (indicated by the dashed vertical line in Figure 4). This difference was found to increase indefinitely as the interlayer spacing was reduced. On the other hand, when the interlayer spacing was increased from ca. 5 Å upward, the distinction between the chemical shifts of the two sites was no longer observed and both isotropic chemical shifts approached the value corresponding to a single graphene layer (indicated by the dashed horizontal line in Figure 4) as the interlayer spacing grew above ca. 14 Å. This behaviour can be qualitatively interpreted in terms of the van der Waals interaction between the layers and the orbital overlap between the  orbitals of the adjacent layers, which are the main interactions that determine the equilibrium spacing and the preferred stacking type in graphite and also in graphene bilayer.79-81 In fact, previous calculations81 have shown that the total energy of a graphene bilayer with AB stacking changes little with the interlayer spacing for separation distances above ca. 5 Å, which is a value close to the range where the distinction between the isotropic chemical shifts associated with C1 and C2 sites ceases to be observable according to the present results. The same work81 established the value of 6.9 Å as the critical spacing above which no interlayer interaction would be significant in the graphene bilayer. It is interesting to observe, however, that the isotropic chemical shift corresponding to the graphene


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single layer was only achieved for the two sites in graphite when the interlayer spacing was far above this critical value, as shown in Figure 4.

Figure 4. Change of the isotropic chemical shifts corresponding to C1 and C2 sites in the graphite structure (for AB stacking) as a function of the interlayer spacing. The dashed horizontal line indicates the value obtained for graphene single layer; the dashed vertical line indicates the calculated equilibrium value of the interlayer spacing in AB graphite.

Comparison to experimental results As mentioned above, to the best of authors’ knowledge there are no available experimental 13C NMR results obtained directly in graphene single layer or bilayer. As for graphite, it is difficult to find experimental 13C NMR results that can be appropriately compared to the theoretical


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predictions. The reason for this is the occurrence of large internal fields in macroscopic graphite samples, due to the previously mentioned strong and anisotropic magnetic susceptibility of graphite. In the two most detailed studies dealing with 13C NMR experiments performed with oriented HOPG macroscopic samples,78,82 the distinction between the C1 and C2 sites was solely observed when the sample was oriented with the magnetic field perpendicular to the graphene layers; a doublet was observed for this orientation, with chemical shift separation of ca. 40 ppm, whereas a singlet was detected when the magnetic field was oriented parallel to the graphene layers. However, if, on the one hand, the chemical shift of the single peak corresponding to the parallel orientation was indeed close to 200 ppm (and thus in good agreement with the present results, as shown in the simulated spectra of Figure 3), the doublet recorded for the perpendicular orientation appeared extremely shifted to low frequencies (i.e., with large upfield shift), reaching values around 300 or 380 ppm for HOPG samples with ellipsoidal82 or spherical78 shapes, respectively. The reason for this large upfield shift is related to the severely anisotropic diamagnetic susceptibility of graphite, which introduces additional strong magnetic fields (demagnetizing and Lorentz fields) inside the sample; these internal fields are shape-dependent and affect in a crucial way the experimentally observed NMR chemical shifts.16,78,82 After taking these extra fields into account and applying the appropriate corrections, the shielding values expected for a single graphene plane (i.e., with no magnetic susceptibility-related effects) can be determined, as indicated in Table 2.16 Thus, the direct comparison of the present calculations performed for graphite to the experimental results obtained for HOPG samples is not possible. It is worth observing, furthermore, that the magnitude of the chemical shift differences here predicted for C1 and C2 sites in graphite is much smaller than the values observed for HOPG


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samples; in fact, the large broadening present in spectra recorded for actual non-oriented graphitic samples is expected to make difficult the direct detection of differences in the chemical shifts associated with the two inequivalent sites in the graphite structure, which can explain why this difference is not usually observed in 13C NMR experiments performed with non-oriented graphitic (or related) samples.15-17,19,76,77,83-86 There are few well documented examples of 13C NMR powder patterns obtained for graphite and graphitic materials. As indicated in Table 1, Resing et al. obtained iso  119 ppm and

  178 ppm using HOPG samples, but no detail was given regarding the sample shape.76 In a study dealing with carbon blacks, Darmstadt et al. determined the values iso  119.5 ppm and

  180.8 ppm for a graphite powder, by means of spectral simulation considering a CSA powder pattern.77 The isotropic chemical shift can also be obtained in experiments performed with magic angle spinning (MAS); a 13C MAS NMR experiment using a graphite powder resulted in a spectrum composed of an ill-defined and severely broadened resonance, with maximum around 112 ppm.85 The magnetic susceptibility effects found in graphite can be reduced by means of boron doping, which causes a change in the Fermi level and a decrease in the magnetic susceptibility component corresponding to the magnetic field parallel to the c-axis (i.e., perpendicularly to the graphene layers).16 A graphite sample with 0.54 at. % boron doping yielded the values

iso  128 ppm and   155 ppm , thus in reasonable agreement with what is expected for a single graphene layer (see Table 1).16


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Another process that leads to the reduction of the mentioned magnetic susceptibility effects is the introduction of defects that disturb the structural order and consequently reduce the large and anisotropic magnetic susceptibility typical of graphitic materials. Thus, carbonaceous materials containing sp2-hybridized carbon atoms and with deprived crystallinity are good candidates for NMR experiments aiming at determining the 13C NMR shielding parameters associated with graphene-like local arrangements. Charcoal83, carbon blacks77 and soot84,86 constitute some examples of materials for which 13C NMR spectra have been reported, exhibiting the typical CSA powder patterns characteristic of graphene-based materials. Two examples of experimental 13C NMR spectra obtained for materials of this type are shown in Figure 5, including a sample of milled graphite (Figure 5a) and a sample of fullerene soot (Figure 5b); the shielding parameters obtained by spectral fitting (using the CSA powder patterns also shown in Figure 5) are given in Table 1. In the case of graphite, milling for moderate times cause the introduction of structural defects and the reduction of crystallite sizes, leading to a diminishing of the effects associated with the circulation of electrons through the graphene layers.19 As a result, the 13C NMR powder pattern obtained for milled graphite is somewhat narrower and the isotropic chemical shift is displaced to higher frequencies (downfield shift) in comparison to the results previously reported for graphite.76,77 For fullerene soot, the spectrum exhibits similar isotropic chemical shift and a slightly higher span; a single narrow line at 144 ppm is also present, corresponding to the signal due to rapid-rotating C60 fullerene molecules,84,86 which at room temperature present mobility high enough to cause motional averaging of the powder pattern.15 In both spectra, the high-frequency edge (close to 200 ppm and associated with crystallites oriented with the magnetic field perpendicular to the c-axis) is better defined than the other extreme of the powder pattern (close to 0 ppm and associated with


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crystallites oriented with the magnetic field parallel to the c-axis). The spectral fitting is always more accurate close to the high-frequency edge. On the other hand, as commonly found in other types of carbonaceous materials,16,17,77,83,86 the low-frequency edge is somewhat broad and illdefined due to residual magnetic susceptibility effects that can cause a distribution of shifts and can even preclude a completely random distribution of crystallite orientations when the powdered sample is placed under the strong magnetic field used in NMR experiments.16 These features can be qualitatively compared to the predicted 13C NMR powder patterns described above. First, a comparison of the spectra experimentally obtained for the carbonaceous materials here analyzed (Figure 5) with the simulated spectra theoretically constructed from the results of the DFT calculations for the graphene-based systems (Figure 3) shows that there is a reasonable agreement in terms of the general spectral features (shape of the powder patterns, isotropic chemical shifts and approximate edge positions). Also, it is interesting to note the good agreement between the calculated chemical shifts and the experimental values (obtained by spectral fitting) for the case of crystallites oriented with the magnetic field parallel to the graphene planes (or perpendicular to the c-axis), which corresponds to the high-frequency edge of the powder patterns. For all theoretically studied systems, the shift values obtained from the in-plane shielding components ( 11  22 ) fall into the range 185-200 ppm, which agrees reasonably well with the values obtained by fitting the 13C NMR spectra obtained for fullerene soot ( 11  22  187 ppm ) and for milled graphite ( 11  22  179 ppm ). It is clear from the calculated spectra (Figure 3) that the distinction between the two inequivalent sites in graphite and the effects due to stacking order affect mostly the high-frequency edge of the spectra (shift close to 200 ppm). Even though, these differences are not observed in the


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experimental powder patterns commonly reported for carbonaceous materials (including the ones shown in Figure 5), which are supposed to be formed by a superposition of contributions from graphene-like planes containing structural defects and aggregated in a turbostratic way. 15 It is also apparent from this analysis that the low signal to noise (S/N) ratio of the 13C NMR spectra recorded in routine experimental conditions makes difficult the detection of individual contributions due to, for example, different stacking possibilities (as discussed here) or structural defects present in the material.44 These contributions might be possibly observable for carbon materials derived from 13C-isotopic enriched precursors, similarly to what has been done for carbon nanotubes87 and graphite oxide,88 where the recorded 13C NMR spectra exhibited much improved S/N ratio and allowed a much more detailed analysis of spectral features.


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Figure 5. Experimental 13C NMR spectra of milled graphite (a) and fullerene soot (b), obtained for static samples. The simulated CSA powder patterns obtained by spectral fitting are also exhibited in each case. The narrow peak in (b), which was not included into the fitting, is due to rapid-rotating C60 fullerene molecules.


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Conclusions DFT calculations were used in this work to predict the shielding parameters and to simulate the 13

C NMR spectra of a number of graphene-based systems (graphene single layer, graphene

bilayer and graphite). A satisfactory convergence of the calculated values was achieved with appropriate choices of k-sampling and supercell sizes. The influence of the stacking order of the layers on the spectral features was studied in the case of graphene bilayer and graphite. In both cases and considering the AB stacking type, it was observed that the differences between the chemical shifts associated with the two inequivalent carbon sites were more readily detectable in the case of crystallites oriented with the magnetic field parallel to the graphene planes (or perpendicular to the c-axis). The effect of changing the interlayer spacing was also addressed in the case of AB graphite; for interlayer spacings above ca. 5 Å, the distinction between the chemical shifts of the two inequivalent sites was no longer observed, with the isotropic chemical shifts approaching the value corresponding to a single graphene layer for spacings above ca. 14 Å. The comparison of the calculated spectral features with experimental results was somewhat difficult because of the large magnetic susceptibility effects known to occur in graphite and also due to the low S/N ratio of the 13C NMR spectra ordinarily obtained for carbon materials. Nevertheless, the simulated 13C NMR spectra theoretically predicted for the graphene-based systems showed good agreement with the general features present in the spectra recorded for carbon materials under static conditions, including the shape of the powder patterns, the isotropic chemical shifts and the approximate edge positions. The comparison was especially favourable regarding the chemical shifts measured at the high-frequency edge of the powder patterns – where the fitting of the experimental spectra to theoretical CSA powder patterns was more


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satisfactory. However, the low S/N noise ratio and the large broadening of the experimental spectra did not allow the direct observation of subtle effects such as the distinction between the two inequivalent sites in graphite or the influence of stacking order, suggesting that methods aimed at enhancing the sensitivity of 13C NMR experiments might be useful for more detailed structural studies of nanocarbons.

AUTHOR INFORMATION Corresponding Author * Corresponding author e-mail: [email protected].

Author Contributions All authors have equally contributed to the manuscript and have given approval to its final version.

ACKNOWLEDGMENT The support from Brazilian agencies CNPq, CAPES, FINEP and FAPES is gratefully acknowledged.


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NMR Spectral Parameters in Graphene, Graphite, and Related

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