Ab Initio Study of the Vibrational Signatures for the Covalent

Article pubs.acs.org/JPCC

Ab Initio Study of the Vibrational Signatures for the Covalent Functionalization of Graphene Ahmed M. Abuelela,†,‡ Rabei S. Farag,† Tarek A. Mohamed,† and Oleg V. Prezhdo*,‡ †

Department of Chemistry, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt Department of Chemistry, University of Rochester, Rochester, New York 14642, United States

‡

S Supporting Information *

ABSTRACT: The present work reports a theoretical study of the infrared (IR) and Raman spectra of chemical structures that are useful for the description of the surface chemistry of carbon materials. There has been a recent demand in materials science and surface functionalization to couple organic entities with sp2 carbon nanostructures. A slab model of single-layer graphene with its edges terminated by hydrogen atoms containing 82 atoms per unit cell was used in our study. The organic coupling agent, perfluorophenylazide (PFPA), was used according to a recent experiment [Liu, L.-H.; et al.et al. Nano Lett. 2010, 10, 3754]. Two ab initio DFT functionals, B3LYP and ωB97XD, were adopted to calculate the IR and Raman spectra. The computational approach was tested by comparing the calculated IR spectra to those obtained experimentally for various reference compounds. The vibrational features were probed before and after the reaction, and the changes, arising in both PFPA and graphene spectra as a result of the coupling, were identified. B3LYP gave better agreement with the experimental results than ωB97XD for frequency calculations. The stretch modes of the azide group, as well as the fingerprint feature of the CF2 axial stretching vibrations, were used to probe the reaction, and the results were in good agreement with the experimental observations. Special attention was paid to the elucidation of the origins of the G-, D-, and D′-bands in the Raman spectra of graphene. Finally, the predicted assignments were employed to interpret the IR and Raman spectra obtained experimentally for functionalized graphenes. established. Functionalization of graphene by PFPA perturbs πconjugation and opens its band gap, thereby changing its electronic properties from metallic to semiconducting.20 Upon photochemical or thermal activation, PFPA is converted to the highly reactive singlet perfluorophenylnitrene (PFPN) by losing an N2 molecule.21 This highly reactive cation can subsequently undergo CC addition reactions with neighboring molecules.22 Graphene, having a network of sp2 C atoms, could in principle undergo an addition reaction with nitrene to form an aziridine adduct. In fact, PFPAs have been successfully used to functionalize C60,23 carbon nanotubes,24,24 and graphene.21 Obtaining information at the molecular level for surface chemistry on carbon materials is difficult;25 consequently, techniques that can provide direct information about surface functionalization are of primary importance in predicting the state and applications of carbon materials. In particular, vibrational spectroscopy has been widely used over the past four decades to characterize pyrolytic graphite, carbon fibers, glassy carbon, pitch-based graphitic foams,26 nanographite ribbons,27 fullerenes,28 carbon nanotubes,29,30 and graphene.31 However, the vibrational spectra of carbon materials are

1. INTRODUCTION Graphene, one of the allotropes of elemental carbon (other examples include carbon nanotubes, fullerene, and diamond), is a planar monolayer of carbon atoms arranged into a twodimensional (2D) honeycomb lattice. It has been the subject of numerous studies since its discovery in 2004,1 and there are seemingly limitless applications of this form of carbon.2−4 Graphene is a highly stable5 material with unique electronic6,7 and mechanical8,9 properties. Its derivatives have potential applications in many areas: electrochemistry and biosensors,10,11 energy applications (fuel cells, Li-ion batteries, supercapacitors),12,13 solar cells,14 transparent electrodes,8,10 electronics,10,15 among others. In addition, a distinct band gap can be generated as the dimension of graphene is reduced into narrow ribbons with a width of 1−2 nm, producing semiconductive graphene having potential applications in transistors.16,17 Graphene has clearly risen as an important and high value material for scientists searching for new materials in potential electronic and composite industry applications. The chemical modification of graphene by covalently functionalizing its surface potentially allows a wider flexibility by engineering its electronic structure. Numerous methods have been developed to functionalize graphene covalently with other molecular species.18,19 Among these, perfluorophenylazide (PFPA) covalent functionalization of graphene is well © 2013 American Chemical Society

Received: June 12, 2013 Revised: August 28, 2013 Published: August 29, 2013 19489

dx.doi.org/10.1021/jp405819b | J. Phys. Chem. C 2013, 117, 19489−19498

The Journal of Physical Chemistry C

Article

difficult to obtain because of issues in sample preparation, poor transmission, uneven light scattering related to large particle size, etc. Moreover, the electronic structure of carbon materials results in a complete absorption band through the visible region to the infrared. Fortunately, some of these problems can be overcome by improving the sample preparation (e.g., carbon films) and by using more recently developed IR and Raman techniques, such as diffuse reflectance Fourier transform IR spectroscopy and surface enhanced Raman spectroscopy.32 Aside from the technical difficulties in obtaining the vibrational spectra of carbon materials, their interpretation is often problematic because not all of the observed absorption bands can be assigned unequivocally to specific molecular motions of functional groups, most likely because of the overlap of several bands, as well as fundamental coupling. In some cases, it is not uncommon that some band assignments differ substantially among the recent vibrational studies on carbon materials. The current work reports an ab initio analysis of the infrared and Raman spectra of a graphene sheet functionalized with PFPA in the 4000−200 cm−1 range. The calculation of the vibrational spectra is much more time-consuming than electronic and geometric structural optimization,33 since it requires normal-mode analysis involving second derivatives of energy with respect to nuclear displacements. Density functional theory (DFT) calculations are widely used to simulate the vibrational spectra for molecules of relatively moderate size.34,35 The calculations are greatly facilitated by the availability of analytical second derivative techniques,36 which reduce the computational cost, making the vibrational frequency calculations of larger molecules possible.37 In addition, semiempirical dispersion-corrected functionals (DFT-D) have recently been developed to treat the dispersion effects, which have been demonstrated to be a useful and affordable method for studies involving large polynuclear aromatic molecules and molecules on metal surfaces.38 In this work, we test the well-known (DFT) hybrid functional B3LYP against the (DFT-D) dispersion corrected functional ωB97XD in the context of vibrational spectra calculations.

Figure 1. Optimized geometries of (A) 1.14 nm wide graphene nanoribbon with the edges terminated by hydrogen atoms, (B) functionalized graphene with one PFPN at the center, and (C) functionalized graphene with two PFPN, one at the center and one at the edge.

graphene−PFPN systems were optimized. We added one additional PFPN molecule to account for the stability of the coverage ratio on the graphene sheet. Depending on the coverage, the number of atoms in the unit cell fell in the range from 82 (bare graphene) to 120 (graphene with two PFPN species). The VASP simulations were carried out in a cubic cell that was periodically replicated in three dimensions. To prevent spurious interactions between the system’s periodic images, the cell was constructed to have at least 10 Å of vacuum space between the replicas. All atoms in the unit cell were allowed to relax, and the force tolerance was set at 0.0157 eV/Å. The Perdew, Burke, and Ernzerhof (PBE) DFT functional40 and a converged plane-wave basis were used. The core electrons were treated using the projector-augmented wave (PAW) approach.41 The geometries obtained in VASP were optimized further using the hybrid B3LYP functional42 with atomic Gaussian basis sets 6-31g(d,p) for the PFPN−graphene systems using the Gaussian 09 software package.43 To evaluate its performance in the context of simulating the vibrational spectra, ωB97XD57 was also used. The electrons of the elements forming the graphene core were treated via effective core potentials (ECPs), which include relativistic effects that are important in these systems. The energy minima with respect to the nuclear coordinates were obtained by simultaneous relaxation of all geometric parameters using the gradient method of Pulay.44 Full convergence was achieved with the maximum component of the force below 0.000 45 mdyne and the maximum displacement below 0.0018 Ǻ . The optimized structures are shown in (Figure 1). By use of the optimized minima, the theoretical Raman and infrared frequencies were predicted using B3LYP and ωB97XD methods. The calculated Raman spectra were simulated from DFT predicted frequencies and Raman scattering activities. The Raman scattering cross sections (∂σj)/(∂Ω), which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted frequencies for each normal mode.45 To obtain the polarized Raman scattering cross sections, the polarizabilities are incorporated into Sj by [Sj(1 − ρj)/(1 + ρj)], where ρj is the depolarization ratio of the jth normal mode. Sj can be expressed as

2. METHODS The structural optimization of large functionalized-graphene systems presents significant computational challenges, since subtle changes in the initial guess and the subsequent drift in nuclear positions during optimization can lead to saddle points and local energy minima. Imaginary vibrational frequencies assist in identifying saddle points while obstructing the normalmode analysis of the global minima. Trapping in local minima can misrepresent the structure as well as the vibrational signals. Moreover, locating the global energy minimum generally requires a high computational cost. The difficulties of geometry optimization originate from two factors: PFPA is relatively high in flexibility and mobility with respect to the graphene surface, and there is a large conformational space of long PFPA molecules to sample. The initial geometry of the slab model was used for the graphene sheet with an optimized C−C bond length (1.435 Å, Figure 1). We will use the abbreviation PFPA for the coupling agent before it binds to the graphene and the abbreviation PFPN after it binds to the graphene. The geometry was optimized using plane-wave DFT, implemented using the Vienna ab initio simulation package (VASP).39 Then one molecule of PFPN (after eliminating N2) was added to the optimized graphene sheet, and the geometries of the combined

Sj = gj(45αj 2 + 7βj 2) where gj is the degeneracy of the vibrational mode, j and αj are the derivatives of the isotropic polarizability, and βj is that of the anisotropic polarizability. The Raman scattering cross sections and calculated frequencies were used together with a Lorentzian function to obtain the calculated spectrum. Infrared intensities were calculated based on the dipole moment derivatives with respect to the Cartesian coordinates. 19490



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The derivatives were taken from the DFT calculation transformed to the normal coordinates using

The structural parameters for PFPA before and after it is covalently bonded to the graphene sheet are listed in (Table 1).

⎛ ∂μu ⎞ ⎟L ⎜ = ⎜∑ ⎟ ij ∂Q i ⎝ j ∂Xj ⎠ ∂μu

Table 1. Geometrical Parameters of PFPA and PFPN Obtained with B3LYP and ωB97XD Using 6-31G(d,p)a ωB97XD

B3LYP

where Qi is the ith Cartesian displacement coordinate and Lij is the transformation matrix between the Cartesian displacement coordinates and normal coordinates. The infrared intensities were then calculated with

bond length/angle r(C7−C14) r(C14−N16) r(C14O15) r(N16−C17) r(N16−H18) r(C17−H21) ∠(C7−C14−N16) ∠(C7−C14−O15) ∠(C14−N16−C17) τ(C−C−N−C) τ(C−C−O−N)

2 ⎡ ⎛ ∂μy ⎞2 ⎛ ∂μ ⎞2 ⎤ Nπ ⎢⎛ ∂μx ⎞ ⎟⎟ + ⎜⎜ z ⎟⎟ ⎥ ⎟⎟ + ⎜⎜ Ii = 2 ⎜⎜ 3c ⎢⎣⎝ ∂Q i ⎠ ⎝ ∂Q i ⎠ ⎥⎦ ⎝ ∂Q i ⎠

3. RESULTS AND DISCUSSION One advantage of the covalent functionalization of graphene with polymers is that the addition of long polymer chains can facilitate the solubility of graphene in a wide range of solvents, even at a low degree of functionalization.21 The resulting soluble graphene can further undergo in situ polymerizations with immobilized functional groups. Although it is important for solubility, the side chains of PFPA are not crucial to the vibrational properties of this nanocomposite. As such, we replaced the side chains of PFPA with methyl (−CH3) groups in order to simplify the vibrational spectra calculations. 3.1. Stability and Geometric Structures of the Graphene−PFPN Systems. The adsorption energy of the functionalized graphene has been calculated for the sheet with a PFPN in the center (Figure 1B) and for the sheet with two PFPN species, one in the center and one at the edge (Figure 1C). The adsorption energy for the graphene−one-PFPN system was calculated according to the equation

r(CC) r(C−F) ∠(C5−C−C9) ∠(C4−C5−F) r(N1N2) r(N2N3) ∠(N−NN) τ(C−NNN) r(C−C) τ(C−C−C−C)

PFPA

PFPN

Methylaminocarbonyl 1.516 1.512 1.363 1.366 1.223 1.224 1.454 1.452 1.008 1.008 1.090 1.090 115.5 115.5 120.7 121.1 121.5 121.7 176.8 −176.9 178.3 −178.4 Benzene Ring 1.388 1.387 1.338 1.354 117.0 116.0 119.7 119.8 Azide Group 1.137 1.245 10.79 179.8 Graphene Sheet 1.435 1.591 0.001 13.39

PFPA

PFPN

1.513 1.357 1.217 1.449 1.006 1.090 115.4 121.0 120.7 176.1 178.1

1.510 1.359 1.218 1.447 1.006 1.090 115.1 121.2 121.5 −176.1 −178.3

1.385 1.341 117.2 119.7

1.385 1.343 116.7 120.0

1.129 1.241 10.27 179.6

0.002

1.577 14.69

The bond lengths and angles are in Ǻ and degrees, respectively. The atom numbers are defined in Figure 4.

a

Eads(sheet/PFPN)

The PFPA undergoes a CC addition reaction; two single bonds are generated between it and the sheet, owing to the conversion of a conjugated CC bond of graphene to a single bond. According to the calculated structural parameters, the bond length between the C atom of graphene and the N atom of the adduct is approximately 1.43 Å, typical of a single C−N bond, indicating covalent bond formation. The C atom and its nearest neighbors in graphene is approximately 1.591 Å, notably larger than the C−C bond length of 1.47 Å of graphene with sp2 hybridization, which indicates bond breaking. The C− C bond lengths in graphene beyond its nearest neighbors are found to be negligibly affected by the functionalization. On the other hand, the plane of the sheet is largely affected after binding to PFPA. For example, the τ(C−C−C−C) of the benzene ring was ∼0.001−0.002° (Table 1); however, it becomes 13.39° after binding, showing that the binding causes a curvature in the plane of benzene ring. For the second addition, this value shifts to −14.4° for the central PFPN, while the one at the edge causes a change of only −9.24°. 3.2. Vibrational Assignment. The vibrational spectrum can be studied from two different perspectives, and we will therefore divide this part into two sections. 3.2.1. Probing Changes Relative to the PFPA Spectrum. The vibrational spectra of organic azides have been investigated previously, both experimentally and computationally.47,48 However, a brief discussion of the vibrational assignments is required for the sake of comparison of the PFPA spectra before

= E(sheet/PFPN) − E(sheet) − E(PFPN)

The values obtained using the B3LYP and ωB97XD functionals were 1.48 and −19.64 kcal/mol, respectively. After the addition of the second PFPN to the edge site of the sheet, the adsorption energy was calculated according to the equation Eads(sheet/(2 PFPN)) = E(sheet/(2 PFPN)) − E(sheet) − E(2 PFPN)

The B3LYP and ωB97XD functionals gave −26.92 and −72.16 kcal/mol, respectively. The adsorption energy decreased by 25.4/52.5 kcal/mol (B3LYP/ωB97XD) after the addition of the second PFPN. This indicates that the second addition is easier, and the system stability is raised by increasing the coverage of the graphene surface. The first attack is much more difficult because the graphene sheet is intact. After this first attack, the geometry of the graphene sheet is distorted, and the sheet is no longer fully planar. The created defects facilitate the second attack. Here, ωB97XD gives qualitatively better results than B3LYP. B3LYP predicts that ligand adsorption onto the graphene sheet is energetically unstable, in contradiction with the experimental data. On the contrary, ωB97XD favors adsorption. Although ωB97XD was originally proposed to include atom−atom dispersion corrections for noncovalent interactions, it performs noticeably well for covalent systems as well.46 19491



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from the azide group (see Figure 4 for a few selected vibrational modes). It is worth mentioning that vibrational frequencies obtained by quantum chemical calculations are typically larger than their experimental counterparts, and thus, empirical scaling factors are often used to match the experimental data.49 It is emphasized that the theoretical data reported herein were not scaled, since the current work focuses on the changes in the PFPA spectra induced by binding to the graphene sheet rather than on the absolute values of the frequencies. 3.2.1.1. Assignment of Methylcarbamoyl (Methylaminocarbonyl). The methylcarbamoyl group could be in either cis or trans configuration, depending on the orientation of the hydrogen and oxygen atoms with respect to each other, which in turn affects the frequencies positions. We adopted the most stable trans configuration (see Figure 4). The hydrogen-bonded NH stretch appears strong and fairly broad, in the region of 3315 ± 45 cm−1.50 The calculated spectra (Figures 2 and 3) of the B3LYP functional show a weak band at 3663 cm−1, which was predicted at 3706 cm−1 using the ωB97XD functional. This calculated absorbance is assigned to the free NH stretching vibration, which is relatively higher than the observed absorbance because of the absence of hydrogen bonding interactions, since our calculation is for an isolated molecule, presumably in the gas phase. The antisymmetric methyl stretching vibrations, often observed in the region of 2995−2900 cm−1,50,51 are in good agreement with those predicted at 3175/3198 cm−1 and 3107/ 3154 cm−1 using the B3LYP and ωB97XD functionals (Table 2), while the symmetric stretch is observed in the region of 2870 ± 45 cm−1, clearly separated from the antisymmetric counterpart.52 The high frequencies usually corresponds to the trans-RC(O)NHMe rather than to the cis configuration, which explains the good agreement with the recorded value of 2915 cm−1 52 and our calculated values of 3040/3067 cm−1 using B3LYP/ωB97XD functionals, which favor the trans configuration (Table 2). The CO stretching vibration gives rise to a strong band in the region of 1680 ± 60 cm−1.50 The frequencies tend to be the

and after binding to the graphene sheet in order to probe the effects of the attachment. Figures 2 and 3 represent the

Figure 2. Calculated infrared spectra (4000−200 cm−1) of PFPA using B3LYP functional (green line) and ωB97XD functional (blue line).

Figure 3. Calculated Raman spectra (4000−200 cm−1) of PFPA using B3LYP functional (green line) and ωB97XD functional (blue line).

simulated infrared and Raman spectra of PFPA before and after binding in the spectral range of 4000−200 cm−1. The normal modes for perfluorophenylazide can be distributed between three sets of fundamental vibrations, those arising from the methylcarbamoyl group, from the fluoro-substituted ring, and

Figure 4. Atom numbering and selected normal modes of the PFPA: (A) atom numbering of the optimized structure at B3LYP/6-31g(d,p); (B) CO stretch; (C) ring stretch; (D) azide stretch. The normal mode displacement vectors are shown in blue, and the dipole-derivative unit vectors are shown in orange. 19492



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Table 2. Selected Vibrational Frequencies (cm−1) of PFPA and PFPN ωB97XD

B3LYP assignment

exptl50−52

PFPA

νNH νaMe νaMe νsMe νCO δNH/νCNa δaMe δsMe (umbrella) νC−N/δNHa ρMe (rock) ρMe (twist) νN−C γNH/COa δCO γCO δ−C(O)−N δ−C−N−C

3360 2995 2900 2915 1740 1550 ± 50 1480 1425−1375 1270 ± 55 1155 ± 30 1100 ± 65 1015 735 ± 60 695 ± 75 600 ± 70 450 ± 100 315 ± 55

3663 3175 3107 3040 1782 1582 1520 1445 1315 1182 1150 1103 815 764 746 428 282

νaC−F νsC−F ring stretch

1195 ± 90 1195 ± 90 1600 1580 1490 1440 1315 ± 65 1000

1171 1023 1678 1631 1533 1441 1340 1020

2169−2080b 1343−1177b

2283 1377

PFPN

PFPA

Methylaminocarbonyl 3664 3706 3175 3198 3097 3154 3036 3067 1777 1834 1581 1597 1523 1529 1449 1470 1290 1348 1179 1199 1152 1162 1106 1128 812 831 763 776 742 758 436 436 277 293 Benzene Ring 1158 1199 995 1039 1677 1719 1626 1677 1523 1569 1436 1482 1359 1348 1023 1038 Azide Group 2339 1403

PFPN

IR intensityc

Raman activityc

3718 3197 3142 3064 1832 1607 1527 1468 1356 1198 1156 1132 839 774 754 444 300

5.96/6.06 0.33/38.8 3.78/9.28 9.40/15.9 45.8/31.3 30.2/65.4 45.8/60.0 3.81/12.3 59.3/60.8 4.92/28.5 3.09/8.86 1.83/7.42 0.84/7.42 3.81/12.6 1.98/14.5 1.14/7.33 0.57/1.11

9.40/0.00 8.59/41.0 20.5/0.84 50.4/0.99 11.3/0.22 5.89/19.9 42.8/46.0 50.9/10.0 35.4/81.7 1.53/4.65 2.10/0.87 4.92/0.93 0.99/1.08 2.52/1.65 0.84/1.26 1.26/0.87 0.96/0.48

1189 1042 1721 1672 1562 1476 1336 1042

2.94/8.14 19.1/4.23 12.5/32.7 3.51/12.4 24.8/70.3 3.66/12.8 4.35/16.7 19.2/14.0

1.50/1.26 0.39/1.65 99.3/4.38 2.61/28.6 23.1/43.1 52.9/7.90 13.2/11.0 0.51/0.48

99.8 3.51

17.4 4.14

The first fundamental has a major contribution that is coupled to a small extent to the second fundamental. bInfrared bands only, taken from ref 51. Normalized infrared intensity and Raman activity multiplied by 102. We have chosen B3LYP to account for the intensities before and after binding, as ωB97XD would be relatively similar by comparison. a c

Similarly, the mixed νC−N/δNH vibration usually appears in the region of 1270 ± 55 cm−1 with moderate to strong infrared intensities, although the C−N stretch is dominant in secondary amides.51,53 Therefore, the calculated absorbance at 1315/1348 cm−1 (B3LYP/ωB97XD) is assigned for this mixed mode. The γNH/CO or ωNH/CO wagging mode is moderately but broadly observed in the infrared region of 735 ± 60 cm−1, in which the O and H atoms move simultaneously out of the plane in the same direction.54 It is yet unknown whether the γNH or the γCO groups contribute to a great extent to this vibration; this deformation could be compared to that of ωNH2/CO in primary amines.52 Therefore, the calculated B3LYP/ωB97XD frequency at 815/831 cm−1 could be attributed to this mode. Methyl antisymmetric deformations are usually observed between 1480 and 1410 cm−1.50,53 The calculated spectra (Figures 2 and 3) show a band at 1520/1529 cm−1 (B3LYP/ ωB97XD), which could be assigned to the antisymmetric (inplane) deformation of the methyl group. The symmetric methyl deformation appears between 1425 and 1375 cm−1,54 which was calculated at 1445/1470 cm−1 (B3LYP/ωB97XD) (Table 2) and is assigned to the umbrella mode of the methyl group (Figures 2 and 3). The methyl rocks and twists are coupled to N−CMe stretches, and they absorb weakly rather than moderately in the IR region. The rock occurs at 1155 ± 30

same when using both the infrared and Raman techniques, although the intensities differ. In the infrared spectra, νCO tends to be among the strongest bands present, while its band is considerably weaker in the Raman spectra.51 The calculated spectrum shows good agreement in both the expected position and intensity of the CO stretch, at 1782/1834 cm−1 (B3LYP/ωB97XD), in both the infrared and Raman spectra (Figures 2 and 3), with a higher intensity in the IR than in the Raman spectrum (Table 2). The CO in-plane deformation is observed with a moderate to strong intensity in the region of 695 ± 75 cm−1. The CO out-of-plane deformation, γCO/NH or γNH/CO, absorbs moderately in the region 600 ± 70 cm−1. With this vibration, the O and H atoms move simultaneously out of the plane in opposite directions.52 The band calculated at 764/776 and 746/758 cm−1 (B3LYP/ωB97XD) could be assigned to the inplane and the out-of-plane deformations, respectively (Table 2). The NH in-plane deformation is coupled to the C−N stretch (δNH/νC−N), which absorbs only in the range 1550 ± 50 cm−1 for the trans configuration,50 although for most of the secondary amides the δNH makes a larger contribution.52 The calculated B3LYP/ωB97XD absorbance at 1582/1597 cm−1 is characteristic for a noncyclic monosubstituted amide; therefore, it can be assigned to the above-mentioned mixed mode. 19493



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cm−1, and the twist is more extensive at 1100 ± 65 cm−1.51−53 Moreover, these modes are very sensitive to the immediate environments, so the frequencies and intensities vary considerably.51 The calculated spectra show identical agreement at 1182/1199 and 1150/1162 cm−1 (B3LYP/ωB97XD) for the rock and twist modes, respectively (Table 2). The N−CMe stretch, essentially, the symmetric counterpart of the amide vibration, can be found in the region of 1015 ± 95 cm−1. The intensity fluctuates between weak and moderate in the infrared spectrum. Disregarding the high values around 1106 cm−1, which is coincident with the methyl rock, the majority of the investigated molecules display the νC−N around 1050 ± 45 cm−1.50,52 Nevertheless, the calculated band at 1103/1128 cm−1 (B3LYP/ωB97XD) could be assigned to this mode, taking into consideration that it is in good agreement with a higher value recorded around 1106 cm−1. The external −C(O)−N skeletal deformation appears to have weak to moderate intensities within a wide range of 450 ± 100 cm−1, similar to the skeletal C−N−CH3 deformation in the region of 315 ± 55 cm−1.52 Thus, the bands calculated at 428/ 436 and 334/340 cm−1 (B3LYP/ωB97XD) can be assigned to the δ−C(O)−N and γC−N−CH3 modes, respectively (Table 2). 3.2.1.2. Assignment of the Fluoro-Substituted Ring. Benzene, belonging to the point group D6h, has 20 normal modes of vibrations, of which four are infrared active. After substitution of an H atom by an F atom, the symmetry is lowered from D6h to either C2v or Cs. The stretching and bending fundamentals of the substituent bond not only give rise to phenyl−CF stretching vibrations and a Ph−CF in-plane and a Ph−CF out-of-plane deformation but also influence the ring stretches in-plane and out-of-plane ring deformations. In fact, there is no pure C−F stretching vibrational motion in fluorobenzene; it is primarily accompanied by some vibrational motion of the benzene ring. These coupled ring/Ph−CF vibrations make it difficult to determine which wavenumber can be attributed to either the Ph−CF stretch or ring vibrations (bending and stretching).52,55 According to Varsányi and Szöke,56 absorption in the region of 1195 ± 90 and 1090 ± 30 cm−1 is primarily due to a C−X stretch in substituted benzenes with atomic masses of X < 25 (light atom) and X > 25 (heavy atom), respectively. In addition, benzenes with multiple substituents were found to absorb at lower wavenumbers.52 Therefore, calculated bands at 1171/1199 and 1023/1039 cm−1 (B3LYP/ωB97XD) could be assigned to the C−F symmetric and antisymmetric vibrations, respectively (Table 2). The benzene ring possesses six ring stretches; the four with the highest wavenumbers occur near 1600, 1580, 1490, and 1440 cm−1.51,52 With heavy atom substituents, these bands tend to shift to somewhat lower wavenumbers. A larger number of substituents on the ring results in broader observed bands. The B3LYP/ωB97XD calculated bands at 1678/1719, 1631/1677, 1533/1569, and 1441/1482 cm−1 could be assigned to the ring group vibrations (Figures 2 and 3). The fifth ring stretching vibration (Kekulé vibration) is active near 1315 ± 65 cm−1,51,52 which agrees well with the calculated band at 1340/1348 cm−1 (B3LYP/ωB97XD). The sixth ring stretch (ring breathing) is substituent-sensitive; it appears as a weak infrared band near 1000 cm −1 in mono-, 1,3-di-, and 1,3,5-trisubstituted benzenes.54 The calculated wavenumber at 1020/1038 cm−1 (B3LYP/ωB97XD) could be assigned to this mode. On the other hand, three or more ring deformations are substituentsensitive and their utility for identification purposes is very

limited for the organic functionalities attached to graphene. The ring deformations are strongly coupled to the (Ph)−CF stretching vibration, and an interchange with the stretch cannot be excluded. The ring twist deformation occurring near 695 cm−1, on the contrary, is a beneficial group vibration. 3.2.1.3. Assignment of Azide Group. The group frequencies of organic azides have been studied extensively by Lieber et al.57 The asymmetric NNN group’s stretch falls in the region of 2169−2080 cm−1 (IR, vs), and the corresponding symmetric mode appears in the region of 1343−1177 cm−1 (IR, w). Typically, other bands with weaker infrared intensities near 2400 and 2200 cm−1 are observed in the case of an unsaturated moiety (e.g., Ph, CC, CO) adjacent to the azide group.58 The observed splitting of the NNN asymmetric bands is attributed to the Fermi resonance of the NNN asymmetric stretch with the combination tones of NNN and C−N stretches, along with other low-lying frequencies. However, because of the four highly electronegative fluorine atoms in the aryl ring, the splitting disappears in the perfluorophenylazide spectra (Figure 2). We calculated a very strong IR band at 2283/2339 cm−1 and a weak band at 1377/ 1403 cm−1 (B3LYP/ωB97XD), which could be assigned to asymmetric and symmetric stretching vibrations, respectively. The asymmetric NNN stretching mode exhibits medium to strong Raman intensity. Not only is the symmetric mode much weaker, but it also appears to be more variable in position than the asymmetric mode. Accordingly, it appears to be of negligible analytical use in the current study. 3.2.1.4. Assignment of the PFPA Fundamentals after Functionalization. By comparison of the vibrational spectrum of the PFPA before and after binding, a vibrational signature that confirms an attachment can be obtained. Liu et al.21 compared a graphene infrared spectrum before and after binding to PFPAs bearing a perfluoroalkyl group. Some of the PFPA vibrational frequencies, which were absent in the IR spectrum of the pristine graphene, appeared in the spectrum after binding. Intense absorption bands at 1340 and 1140− 1200 cm−1 were assigned to CF2(axial) symmetric and asymmetric stretches, respectively. These fingerprints were used by Liu to confirm the functionalization. However, those vibrations should be observed for the PFPA whether it has bound to the sheet or not. A more powerful confirmation would be the absence of the azide group stretching vibration from the PFPA spectrum after binding to graphene, owing to the liberation of an N2 molecule. The very strong IR band of the azide asymmetric stretch at 2283/2339 cm−1 (B3LYP/ ωB97XD) disappeared after binding with graphene (Figures 5 and 6 for comparison). A similar result was observed for the weak (IR) band of symmetric stretching at 1377/1403 cm−1 (B3LYP/ωB97XD). The region of 1600−600 cm−1 is referred to as the fingerprint region, where many vibrational modes are not localized, making it useful for molecular characterization before and after binding. Thus, we can refer to the hypothetical localized motions as being coupled; the delocalized vibrational motion involves more atoms in the investigated molecule. The most relevant region to examine the effect of graphene vibrations on PFPA vibrations is the region between 200 and 2000 cm−1 where both graphene and PFPA vibrations strongly overlap. It is noted that hydrogen vibrations strongly mix with the motion of the carbon skeleton, and because of their “artificial presence” in our models, these spectra can only provide a qualitative picture of the effects of functionalization. 19494



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contributions arise from the PFPA atoms, implying that the HOMO and LUMO are localized on the graphene sheet rather than the PFPA molecule. This result can also be determined from charge density calculations for the HOMO and LUMO (Figure 7). The sheet has 82 atoms, while the functionalized

Figure 5. Calculated infrared spectra (4000−200 cm−1) of PFPA (green line) and graphene−PFPN system (blue line) using B3LYP/631g(d,p).

Figure 7. Isosurface plot of charge densities of (A) highest occupied molecular orbital (HOMO) and (B) lowest unoccupied molecular orbital (LUMO).

sheet has 101 atoms. In the sheet, both the HOMO and LUMO are formed primarily from pz orbitals from the carbon atoms (Figure S1). The carbons lie in the XY-plane, so the pz orbitals lie above and below the CC bonds. In both the HOMO and LUMO, the orbitals have opposite signs. However, in the HOMO, a few opposite signs are not equal, indicating that the HOMO has a bonding character, unlike the LUMO. The orbitals suggest no significant differences in the frequencies for the two systems, which would explain the similarity between the experimental spectra of the sheet and the sheet + PFPN.21 3.2.2. Probing the Changes Relative to the Graphene Spectrum. For sp2 nanocarbons such as graphene and carbon nanotubes, Raman spectroscopy can give additional information such as crystallite size, clustering of the sp2 phase, the presence of sp2−sp3 hybridization, as well as the presence of chemical impurities, the magnitude of the mass density, the optical energy gap, elastic constants, doping, defects and other crystal disorders, edge structure, strain, number of graphene layers, nanotube diameter, chirality, curvature, and metallic vs semiconducting behavior. In this article, we consider three aspects of calculated Raman spectra, which are sensitive enough to provide unique information about the changes in graphene structure. The first spectral feature is called the G-band, and it arises because of the E2g vibrational mode of sp2 bonded carbon in graphitic materials, which is common to all sp2 carbon systems. When the bond lengths and angles of graphene are modified by strain caused by the interaction with a substrate or other graphene layers (external perturbations), the hexagonal symmetry of graphene is broken.59 The G-band is therefore highly sensitive to strain effects in sp2 nanocarbons and can be used to probe any modification to the flat geometric structure of graphene, such as the strain induced by external forces. Usually, a single Raman peak is observed for a 2D graphene sheet at 1582 cm−1. In order to locate the calculated frequency associated with the G-band, we analyzed the normal modes with respect to the nuclei displacement over the range from 1595.8 to 1621.6 cm−1 (Figure S2). The vibrations arising from both C−C and C−H bonds are highly mixed in this region, so this procedure is important for resolving these vibrations. The displacement of the normal modes takes place in the XY-plane. In the standard orientation, the Z coordinates for all atoms are zero. When normal modes are interpreted, the signs and relative values of the displacements of the different atoms have more relevance to the interpretation than their exact

Figure 6. Calculated Raman spectra (4000−200 cm−1) of PFPA (green line) and graphene−PFPN system (blue line) using B3LYP/631g(d,p).

Because of the complex nature of these vibrations, it is very difficult to assign a one-to-one correspondence of modes for pristine and functionalized graphene. Accordingly, we have selected major vibrational features for the PFPA and its corresponding modes after binding for comparison (see Table 2). A further change that is notable is the increase in the infrared intensities and Raman activities. Figures 5 and 6 clearly show that the IR intensities and the Raman activities increase after functionalization by a factor of approximately 1.5−45.5 (km/mol) and 1.26−46.3 (Å4/amu), respectively. Another notable difference in frequency is the red-shift of the fingerprint C−F vibrations (Table 2) by 13 and 28 cm−1 for symmetric and antisymmetric modes, respectively. These shifts can be explained by changes in the charge distribution upon the graphene−PFPN binding. Interaction with graphene decreases the polarization of the C−F atoms. The Mullikan charges on the C11−F16/C13−F18 bonds are (0.302 to −0.262)/(0.310 to −0.277) before binding and (0.285 to −0.274)/(0.278 to −0.273) after binding. As a result, the electrostatic interaction that contributes to bond strength decreases and νC−F undergoes red frequency shifts, in good agreement with experimental data.21 Other than the absence of the azide fundamentals, C−F bond shift, and the increase in intensities, the location of the rest of the bands does not change by more than 10 wavenumbers. When the orbital coefficients are examined, the most important factor is their relative magnitudes with respect to one another within that orbital, regardless of sign. The molecular orbitals correspond essentially to the atoms with the highest magnitudes. In Figure S1 in Supporting Information, it is evident that the highest magnitudes come from the carbon atoms, even after functionalization. Low 19495



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A blue-shift in the G-band also takes place after functionalization, from 1595.8 to 1621 cm−1 (25 cm−1) (Figure 8), which agrees fairly well with experimental functionalization using nitrophenyl.62 In these experimental results, a blue shift was found from 1580 to 1585 cm−1 to the exfoliated graphene and a red shift from 1586 to 1564 cm−1 to the epitaxial graphene. It is worth noting that the shift direction (blue or red) of the G-band is difficult to discern when modeling graphene. Kudin et al.63 investigated this issue intensively for different models of graphene. Computationally, among all of the structures that they have considered, only the alternating pattern of single−double carbon bonds within the sp2 carbon ribbons, as well as the Stone−Wales (SW) defects and the double vacancy (C2) defects, which is composed of two pentagonal rings and one octagonal ring (5−8−5), yields Raman bands of high enough intensity that are blue-shifted compared to the G-band of graphite. Also, to obtain single− double bond alternation within extended sp2 carbon areas, it is necessary to have sp3 carbons on the edges of the carbon ribbon. Termination of the edges with hydrogen atoms leads to the same result and sufficiently mimics the experimental results that we have adopted. The product of the perfluorophenylazide functionalization on graphene indicates that the introduction of the azide groups leads to saturated sites in the graphene lattice that may be viewed as internal edges to the conjugated regions, taking 1392.6 cm−1 for the D-band as the frequency of a structural defect in pristine graphene and graphitic materials with longrange crystalline order and 1652.7 cm−1 for the D′ band, along with the blue shift in the G-band.

magnitudes. Figure S2 shows that the C−C bonds contribute to the vast majority of the vibration at 1595.8 cm−1. It has the lowest oscillation for hydrogen atoms at the equilibrium positions, while the C−C bonds oscillate correspondingly and most effectively among the other vibrations in both positive and negative directions. In our treatment, we illustrate the motion by showing the paths of the nuclei in both directions; therefore, this vibration could be assigned to the G-band signature (Figure 8). This is in reasonable agreement with the experimental value.

Figure 8. Calculated Raman spectra (4000−200 cm−1) of graphene− PFPN system (upper panel) and graphene sheet (lower panel) using B3LYP/6-31g(d,p). Inset is the experimental spectra61 of (A) defected graphene and (B) bare graphene.

The presence of disorder in sp2-hybridized carbon systems leads to rich and intriguing phenomena in their resonance Raman spectra. Because of this and the fact that Raman spectroscopy is one of the most sensitive and informative techniques to characterize disorder in sp2 carbon materials, it has become an instrumental tool and is widely used to identify disorder in the sp2 network of different carbon structures, such as diamond-like carbon, amorphous carbon, and nanostructured carbon.60 When graphene is attacked, point defects are formed and the Raman spectra of the disordered graphene exhibits two new sharp features appearing at 1345 and 1626 cm−1 (see the inset in Figure 8, taken from ref 61). These two features have been termed the D- and D′-bands, respectively, to denote disorder. Quantifying disorder in a graphene monolayer is usually determined by analyzing the ID/IG intensity ratio between the disorder-induced D-band and the Raman-allowed G-band. The D-band is ring breathing (A1g mode) and becomes Raman active after neighboring sp2 carbons are converted to sp3 hybridization in graphitic materials. In order to assign the Dband in the spectrum of graphene attached to the PFPN, we analyzed the normal modes in the range between 1363 and 1392.6 cm−1 (Figure S3). We found that the calculated frequency at 1392.6 cm−1 has the lowest contribution from the hydrogen atoms around the equilibrium position rather than the carbon atoms of the graphene; therefore, this vibration is attributed to the D-band. Using the same procedure for the analysis of normal modes (Figure S4), we assigned the calculated band at 1652.7 cm−1 to the D′-band (Figure 8). It is notable to find that the frequency 1677 cm−1 has no contribution to the graphene sheet, as it is attributed to the ring of PFPN, in agreement with PFPN-modes interpretations after binding (see Table 2 for this particular assignment). We excluded the PFPN atoms to facilitate the normal-mode analysis; otherwise, the contribution would fluctuate strongly around equilibrium in the PFPN atoms region.

4. CONCLUSIONS We performed density functional (both DFT and DFT-D) geometry optimization and frequency calculations on a model of single layer graphene and its functionalized form to gain insight into the changes that take place in geometries and vibrational spectra upon graphene functionalization. We adopted a slab model of 82 atoms for the graphene, terminated by hydrogen atoms and functionalized by one (G-PFPN) and two (G-2PFPN) perfluorophenylazide units. G-2PFPN was found to be much more stable than G-PFPN. This finding can be explained by structure defects and symmetry breaking in the intact graphene plane, as reflected in the geometrical parameters. Introducing sp3 centers in the ring causes a sharp kink in the local structure, which makes the second attack much easier. Significant spectral changes are observed upon functionalization: the azide fundamental of the PFPA at 2283 and 1377 cm−1 disappears and the C−F antisymmetric and symmetric stretches undergo a red-shift in the fingerprint region (13 and 28 cm−1). The B97XD functional tends to produce higher vibrational frequencies than B3LYP, overestimating the values relative to the experimental frequencies. Bending defects introduced in graphene by chemical functionalization reveal themselves in the Raman spectrum of graphene as a blue-shift in the G-band accompanied by appearance of the D- and D′-bands. The normal-mode analysis provides detailed information regarding the modes involved in the IR and Raman signals, characterizing the specific types of nuclear motions generating the spectroscopic data. According to current model calculations, chemical functionalization of graphene introduces sp3-type defects, leading to significant changes in the nanostructure. 19496



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ASSOCIATED CONTENT

S Supporting Information *

Molecular orbital coefficients and normal mode analysis. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 585-276-5664. Fax: 585-276-0205. E-mail: oleg. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support of the U.S. National Science Foundation, Grant CHE-1300118, is gratefully acknowledged.

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Ab Initio Study of the Vibrational Signatures for the Covalent

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