Site Preferences of Carboyxl Groups on the Periphery of Graphene

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Site Preferences of Carboyxl Groups on the Periphery of Graphene and their Characteristic IR Spectra Tapas Kar, Steve Scheiner, Upendra Adhikari, and Ajit K Roy J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp403728b • Publication Date (Web): 13 Aug 2013 Downloaded from http://pubs.acs.org on August 16, 2013

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The Journal of Physical Chemistry

Site Preferences of Carboyxl Groups on the Periphery of Graphene and their Characteristic IR Spectra Tapas Kar*1, Steve Scheiner1, Upendra Adhikari1 and Ajit K. Roy2 1

Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA 2 Materials and Manufacturing Directorate, Air Force Research Laboratory, OH 45433, USA

ABSTRACT: Energetics of carboxyl groups at the periphery of a graphene sheet are studied using density functional theory (B3LYP) with a 6-31G* basis set, augmented with diffuse functions on O. Corner sites are energetically preferred followed by zigzag edges, and armchair edges are least stable. The energy and geometry of each is attributed to a competition between πconjugation and steric repulsion factors. Vibrational analyses reveal certain features that are characteristic of each site location, which may help in the assignment of experimental spectra of graphene and other polycyclic aromatic hydrocarbons. For example, zigzag sites typically lead to an intense C=O stretching band that occurs below 1700 cm-1, quite uncommon for the carboxyl group. Keywords: Graphene, Carboxylic acid, GO/RGO, DFT-SLDB, Vibrational Frequency

Corresponding Author Email:[email protected], Tel:1-435-797-7230; Fax:1-435-797-33

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1. INTRODUCTION Carboxylic acid, a key oxygen-containing functional group, plays a significant role in a wide range of chemical activities 1 , including industrial and biological chemistry. The structure, stability and reactivity of carboxylated conjugated systems, such as polycyclic aromatic hydrocarbon (PAH), may depend not only on the acid group concentration and locations, but also on just how the carbon networks are extended. Importance of COOH groups, due to further chemical modification to form variety of chemicals, extends beyond the paradigm of organic and biologically relevant molecules to materials chemistry, especially to new allotropes of carbon, viz. carbon nanotubes and graphene. Oxidation processes by various acid treatment techniques to purify prepared carbon nanotubes introduces carboxylic groups (-COOH), along with other oxygen containing functional groups, into the nanotube structure. Unambiguous assignment of acid groups has been complicated by several intermingling factors, such as hydrogen bonding among acid groups or with other oxygen containing groups, coupling with other vibrational modes, and so on. Our recent theoretical studies 2-4 revealed some new features of carboxylated single-wall carbon nanotubes (SWNTs) that had not been envisioned earlier. Some C=O modes of zigzag-COOH tubes exhibit a peak around 1650 cm-1 (normally assigned as quinone C=O or hydrogen bonded COOH in experimental studies for lack of a better guess); such an unusual low-frequency C=O mode for a standalone COOH group can distinguish between zigzag and armchair tubes. Interestingly, we found that these low-frequency peaks occur even in the complete absence of hydrogen bonding acid groups at the tips of SWNTs, a phenomenon which had been previously assumed by experimentalists to explain the spectrum. Thus, the properties of some COOH groups in the carbon nanostructures behave differently depending on their positions, from simple organic molecules. Graphene oxide (GO), created during various oxidation processes, also contains several oxygen containing groups, such as –COOH, -OH, ether, epoxy etc., at both edges and surface 5-11 . Due to strong dependence on the starting materials, oxidation processes, and degree of oxidation, the determination of structures of GO is very complicated. Several structural models of GO, such as that of Hofmann, Ruess, Scholz-Boehm and Nakajima-Matsuo (details in ref 13), had been proposed at an earlier phase of GO research. Based on later results of analytical techniques, those models were found inadequate to correctly describe structures of GO. As work progressed, several new models were proposed, such as those by Lerf-Klinowski 12 and Dékány 13 . Recently Szabó et al. 13 , Dreyer et al. 14 and Zhu et al. 15 have critically analyzed different proposed GO models. However, recent findings suggest some new features, such as the possibility of five- or six-membered lactols 16 and aggregation of oxygen atoms at the edges 17 of GO structures which were not envisioned earlier. In summary, structures of GO and also reduced GO (RGO) are still not well understood and more in depth studies may reveal fruitful new information to define the structural details of these fascinating materials. Understanding of such structures will be essential to control and tune properties in developing application-oriented products. IR spectroscopy, along with other analytical techniques, has been routinely used for determination of GO/RGO structures. Because of various intermingling and coupling factors among different oxygen containing functional groups, complexity arises in analyzing those spectral data, as several C=O/C-O vibration bands appear in the same region. Theoretical vibrational analyses, instrumental in determining structures for a wide range of complicated


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structures 18-20 , may help disentangle the experimental spectra and reveal the source of each adsorption. Since some carboxyl groups at the tips of zigzag tubes exhibit properties different than the acid groups at related armchair tubes, curiosity arises about their structures in graphene sheets as both armchair and zigzag sites are present at the edges of graphene sheets. In fact our preliminary calculations 4 on Gr-COOH asserted the provocative finding that a single COOH group at a zigzag edge of graphene is quite different from one at an armchair edge. Just as in the nanotubes, a low-frequency mode, in this case 1690 cm-1 is observed for the zigzag-edge COOH, as compared to a higher 1724 cm-1 peak for the armchair edge. The intensity pattern is also consistent with the tubes: the zigzag peak is more than three times more intense than the armchair peak. This notion has wide ranging implications, not only for nanotubes and graphenes, but for any molecule containing the prevalent COOH group. It is thus important to understand what sorts of environmental, structural, and chemical factors can lead to such a unique spectroscopic feature, and how what might appear at first sight to be almost nominal differences in structure can lead to what might be described as a new sort of COOH group. The present communication attempts to answer this question. COOH groups are added to a variety of different sites on a graphene sheet: corner, as well as zigzag and armchair. Multiple carboxyl groups are added in order to examine how the presence of one might affect the properties of another. The most stable isomers are identified, as are the energetic separations among various possible isomers. The effects of site selection upon the geometry of the carboxyl groups, as well as the entire graphene sheet, are elucidated. Special emphasis is placed on calculating the IR spectra which offers the hope of allowing experimentalists to distinguish one sort of isomer from another, not only in graphene sheet but also for other PAH systems. And perhaps most importantly, the factors that lead to quite unique structural and spectroscopic features of the carboxyl group are isolated and identified. Lastly, the importance of Gr-COOH structures arises from the activities of carboxyl groups, and similar to SWNT-COOH, such acid groups can be used as anchors for further functionalization. It is hoped that the results and concepts presented here will add to our knowledge of the location and distribution of COOH groups at graphene, particularly since a recent experimental study 21 indicated that carboxyl groups might exist mainly at the graphene edges.

2. METHOD OF CALCULATIONS The B3LYP variant of density functional theory (DFT) 22, 23 was used to include correlation effects. The accuracy of normal mode calculations using the B3LYP method is sufficiently high, and cost-to-benefit ratio optimal, with the 6-31G* basis set 24-27 . This splitvalence double-ζ quality basis with five d-polarization functions was used for all carbon and hydrogen atoms. For proper description of electronegative oxygen atoms, additional diffuse spfunctions were added to the 6-31G* basis; this combined basis set is denoted as 6-31G*(O+). This B3LYP/6-31G*(O+) method was earlier found reliable for predicting energies and vibrational modes of SWNT-COOH 2-4 . Geometries of all carboxylated graphene sheets were fully optimized without any symmetry restriction, followed by vibrational analyses that insure the identification of true minima. Calculated harmonic vibrational frequencies are normally slightly higher than experimental values (even for more accurate methods, such as MP2, CCSD etc, as well as for larger basis sets) and a scale factor is commonly used to better correspond with experimental



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spectra. For example, a value of 0.960 is recommended for B3LYP/6-31G* methods 28 . Since we are interested in the spectra of attached functional groups described by 6-31G* quality basis functions, consideration of a scale factor of 0.960 seems to be a reasonable choice. All calculations were performed using the Gaussian-09 29 code. Models of carboxylated graphene sheets were obtained using Chemcraft 30 software, which was also used to generate GrCOOH figures for geometry and vibrational analyses. 3. RESULTS AND DISCUSSION The general model of single layer graphene sheet is composed of 54 carbons and 20 hydrogen atoms, with hydrogens used to saturate dangling bonds at edges and corners, illustrated in Scheme 1. This idea of H-substitution on a graphene sheet is substantiated by experimental evidence 31, 32 . -COOH groups were placed at various sites on the periphery of the Gr-sheet, first singly and then in groups of two and four. In each case, the geometry was fully optimized with no constraint. All structures discussed below were fully optimized, and were categorized as true minima by the absence of any imaginary frequencies. Addition of zero-point vibrational energies enabled the computation of enthalpies to supplement the electronic energies (E). The possible sites of substitution can be categorized as corner (C), zigzag (Z) and armchair (A), displayed in Scheme 1. A number is added to each site so as to distinguish one from another. The nomenclature used to label each structure begins with n, the number of COOH substituents, followed by the sites occupied. For example, 1-Z2 indicates the placement of a single COOH at position Z2, 2-C1/A2 denotes a pair of COOH groups, one at C1 and the other at A2, and so on.

C1

A1

A2

A3

A4

C4

Z1

Z8

Z2

Z7

Z3

Z6

Z4

Z5 C2

A8

A7

A6

A5

C3

Scheme 1. Numbering scheme of different sites. Replacement of a H atom by carboxyl induces certain geometrical changes into the full system. These deformation energies (Edef) were computed by using the carboxyl-substituted molecule as a starting point, then replacing COOH by H. The difference in energy between this system and the fully optimized pristine graphene sheet was taken as the strain energy, providing some estimate of the deformation of the full hexagonal network caused by the functionalization.


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3.1 Single Substitutions. All three different types of site (Z, A and C) of graphene were considered for single COOH functionalized Gr. Optimized structures are shown in Figure 1 and energy data are summarized in Table 1. Relative energies clearly indicate the preferred site for single COOH lies

1-Z2 (1C)

1-Z1 (1B)

1-C1 (1A)

1-A1 (1D)

1-A2 (1E)

Figure 1. Top and side views of graphene-COOH optimized structures. C=O, C-COOH, O--H(C) bond distances in Å.

at the corner (1-C1, 1A). The next lowest energy places COOH at the zigzag edge followed by the armchair edge. In these two sites, location of –COOH at different hexagons of the sheet has a significant effect on the stability. 1-Z1 and 1-A1, where COOH lies closer to the corner of the sheet, is more stable than those where COOH is moved further towards the middle of the sheet, 1-Z2 and 1-A2. For example, 1-Z1 (1B) is higher in energy than the global minimum (1-C1) by



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2.9 kcal/mol, and 1-Z2 (1C) higher by another 3.9 kcal/mol. The energy difference between the two analogous armchair sites (1-A1 and 1-A2) is less pronounced, 9.4 vs 10.9 kcal/mol). Table 1. Relative Electronic Energies (Erel), Relative Enthalpies (Hrel), and Deformation Energies (Edef) of Gr-COOH and R-COOH, all in kcal/mol. R-COOHa 1-C1 (1A) 1-Z1 (1B) 1-Z2 (1C) 1-A1 (1D)

Erel 0.0 2.9 6.8 9.4

1-A2 (1E) 10.9 Benzoic acid (2A) Pyrene-COOH (2B) Anthracene-COOH (2C) Phenanthrene-COOH (2D) a see Figures 1 and 2 for structures

Hrel 0.0 3.1 7.7 9.2

Edef 0.1 1.3 1.2 3.2

10.7

2.5 0.1 0.1 0.9 2.3

One might conceive an alternate situation wherein the COOH might attach itself to a C atom that does not lie along the periphery. However, such a structure would effectively destroy the entire π-network as the hybridization of the linking carbon would change from sp2 to sp3. It is most unlikely that any such an arrangement would be competitive in energy with the molecules examined here; a detailed investigation of such surface carboxylation is in progress and results will be published in a separate article. The acid group at the corner of Gr has little effect on the extended geometry of graphene. This fact is reflected first in the very low deformation energy of only 0.1 kcal/mol of 1-C1. A similarly small deformation energy is also exhibited by smaller carbon networks, like benzoic acid (2A in Figure 2) and pyrene-COOH (2B). The side view of 1-C1 in Figure 1 shows that the COOH group resides in the plane of the graphene sheet, similar to the smaller models (2A and 2B), due to the extension of π-conjugation of COOH with the aromatic ring, as confirmed by the π MOs exhibited in Figure 3. The energy of the π-MO in 1-C1, responsible for the planarity of COOH group with the carbon network in graphene, is also close to that of the smaller models. Such conjugation can be disconnected by an out-of-plane rotation of the acid group. To check the magnitude of this effect, 2A and 2B were re-optimized after fixing dihedral angle φ(1-2-3-4) equal to 90° while relaxing all other geometric parameters. The resulting structures of 2A and 2B are less stable by 6.9 kcal/mol than the global minima. The distorted 1-C1 structure obtained by fixing the same dihedral angle at 90° cost nearly an identical amount 6.8 kcal/mol. Thus, it may be concluded that energy required for breaking π-conjugation between a single acid group and the carbon network is independent of the carbon network size.


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1

4

1

2

2 4

3

3

2A 2

2C

1

1

3

2

6

4

5

4

3

2D

2B

Figure 2. Two views of each R-COOH optimized structure; benzoic acid (2A), pyrene-COOH (2B), anthracene-COOH (2C) and phenathrene-COOH (2D). C=O, C-COOH, shortest nonbonded O---H(C) distances in Å.

3A

3B

3C

3D

Figure 3. Top and side-view of π-MO (contour value = 0.025 au) of benzoic acid (3A), pyreneCOOH (3B), 1-C1 (3C) and 1-Z1 (3D). Eigenvalues of this π-MO are -0.4566 au (3A), -0.4567 au (3B), -0.4554 au (3C) and -0.4467 au (3D).



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The second preferred site for COOH group is at the zigzag edge of graphene (1-Z1, 1B in Figure 1), less stable than 1-C1 by 2.9 kcal/mol. Moving the acid group further towards the middle of the sheet, as in 1-Z2, costs 3.9 kcal/mol. In both cases, the deformation energies are around 1.2 kcal/mol indicating the distortion of the graphene sheet is a bit higher in zigzag sites compared to a corner site. From the side views it may be seen that the COOH group becomes progressively more twisted as it moves from the corner towards the middle of the hexagonal network. On the other hand, the side-views also clearly show the planarity of the carbon network is preserved. The situation is different in the armchair sites where both 1-A1 and 1-A2 produce significant distortion of the hexagons near the attached acid group. Side views indicate this deformation is more pronounced in 1-A1 than 1-A2, also reflected in their respective deformation energies of 3.2 and 2.5 kcal/mol. These quantities are a bit larger than the deformation energies in the small-molecule analogue phenathrene-COOH (2D). In both 1-A1 and 1-A2, a pair of carbons of the armchair site is moved out of the plane and adjacent carbon pairs are displaced in the opposite direction. In fact, such displacement of carbons from the overall molecular plane occurs up to two hexagon layers. A disruption of the π-conjugation is thus felt not only between COOH and its attached hexagon, but also among the hexagonal rings at the functionalized site. Key geometric parameters of the functionalized sites of Gr-COOH and smaller representative organic acids are reported in Table 2. In the case of corner site, all relevant bond parameters (C=O, linking C-COOH, C-O and O-H) of 1A are identical to those of the smaller models 2A and 2B. Thus extension of carbon network has no effect on the structural parameters Table 2. Bond Lengths (in Å) of Gr-COOH and Smaller Models of Carboxylic Acids Modelsa R(C=O)

R(C-O)

1A 2A 2B

1.218 1.218 1.218

1B 1C 2C

1.224 1.221 1.217

R(O-H)

R(O----H-C)

R(=O----H-C)

1.362 1.362 1.362

R(CCOOH) 1.485 1.484 1.484

0.975 0.975 0.975

2.381 2.423 2.414

2.532 2.533 2.525

1.365 1.366 1.362

1.482 1.486 1.494

0.976 0.977 0.977

2.071 2.279 2.342

2.336 2.211 2.332

1D 1.219 1.371 1.482 1E 1.215 1.365 1.494 2D 1.215 1.364 1.494 a See Figures 1 and 2 for structures.

0.976 0.977 0.977

2.362 2.459 2.503

2.555 2.678 2.506

when COOH group is linked at the corner of Gr. However, minor changes in these distances occur when COOH is moved to zigzag or to armchair sites. Among all these systems, the C=O distance is longest (1.224 Å) in 1-Z1 (1B). This C=O lengthening lessens when COOH is moved away from the corner, e.g. 1.221 Å in 1-Z2. Armchair sites yield only a very modest C=O stretch: 1.219 and 1.215 Å in 1-A1 and 1-A2, respectively, compared to 1.215 Å in 2D. The COH bond length is less susceptible to change, as may be noted in the next column of Table 2. As


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for the C=O bonds, the C-COOH linking distances are also unaffected by attachment to a corner site. However, the two zigzag sites cause this bond to contract, from 1.494 in small molecule 2C, down to 1.486 in 1-Z2 and to 1.482 Å in 1-Z1. In addition to changes in the internal bond lengths, the site of attachment has a large effect upon the orientation of the COOH and structural distortion within the graphene sheet. Much of this perturbation may be attributed to steric repulsions between the COOH O atoms and neighboring C-H bonds of the graphene sheet. The pertinent–O---H and =O---H distances are summarized in the last two columns of Table 2. In 1-C1 for example, these distances are 2.381 and 2.532 Å, close to the corresponding distances of the smaller 2A and 2B models. Any potential steric repulsions are clearly outweighed by the stabilizing π-conjugation factor, since all of these systems maintain planarity. In 1-Z1 hydrogen atoms are much closer (2.071 and 2.336 Å) to oxygen atoms of COOH than that in 1-C1. In this structure the COOH is twisted slightly out of the plane of the sheet (by about 5°). Consequently the π-MO of 1-Z1 is higher in energy by about 0.01 au than the corresponding π-MO of 1-C1. This weakening of π-conjugation, coupled with enhancement of steric repulsion, in addition to slight deformation of the sheet appears to be the root of the higher energy of 1-Z1 as compared to 1-C1. In the case of 1-Z2, the steric repulsion is reduced by the rotation of the COOH group. In fact, if the acid group is forced into the plane of the sheet, the resulting –O---H and =O---H distances of 1.54 and 1.83 Å, respectively, raise the energy by 26 kcal/mol. The COOH rotation of 45° in 1-Z2 minimizes the steric repulsion without much distortion of the carbon network, reflected in the deformation energy of 1.2 kcal/mol in 1-Z2. The cost of maintaining π-conjugation between the acid group and carbon hexagons in armchair sites 1-A1 and 1-A2 is more than 250 kcal/mol in the planar structure, due to closeness of O---H distances (less than of 1.0 Å). Such repulsion not only pushes the acid group out of plane but also displaces attached carbon rings from planarity. In summary, the structure and stability of edge-functionalized Gr-COOH strongly depends on two opposite forces – stabilizing π-conjugation and repulsive steric effects. The corner site is the preferred, followed by zigzag edge and then armchair edge. 3.2 Multiple Substitutions. It is expected that oxidized graphene commonly contains more than a single acid group and a larger number of such groups may influence the preference, stability and IR spectra, due to several factors, such as hydrogen bonding among the COOH units. In order to examine such effects, a second acid group was added at various sites. The results obtained for some of the lower energy structures are depicted in Figure 4 (with higher energy structures displayed in supplementary documents, S1), which includes C=O and linked C-COOH distances. The relative energies along with deformation energies are summarized in Table 3. Three possible combinations that place both COOH units at corners of the graphene sheet (4A-4C) were considered and all three structures can be considered equally stable with energies clustered within 0.2 kcal/mol of one another. The side-views is Figure 4 indicate that all three structures retain full planarity, reflected in negligible deformation energies. These structures echo the observation obtained for the single substitutions that the corner is the preferred site of COOH placement. The C=O and C-COOH bond lengths are almost the same for all three structures and unchanged upon addition of a second COOH group.



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Table 3. Relative Electronic Energies (Erel), Enthalpies (Hrel) and Deformation Energies (Edef) of Doubly Substituted Graphene, all in kcal/mol. Modelsa Erel Hrel 2-C1/C3 (4A) 0.0 0.2 2-C1/C2 (4B) 0.1 0.1 2-C1/C4 (4C) 0.2 0.2 2-C1/Z4 (4D) 3.2 3.3 2-Z1/Z4 (4E) 4.9 5.1 2-C1/Z3 (4F) 8.0 8.1 2-C1/Z2 (4G) 8.1 8.2 2-C1/A4 (4H) 9.9 9.7 2-C1/Z1 (4I) 10.6 10.3 2-Z1/Z3 (4J) 12.0 11.9 2-Z2/Z6 (4K) 15.9 15.8 2-A2/Z3 (4L) 18.8 18.5 2-A2/A4 (4M) 19.5 19.1 2-A1/A4 (4N) 20.9 20.5 2-A2/A6 (4O) 21.4 20.9 2-Z2/Z3 (4P) 22.3 22.0 2-A2/A3 (4Q) 28.0 27.4 a see Figure 4 and S1 for structures.

Edef 0.0 0.2 0.2 1.3 2.0 1.2 1.3 3.2 0.3 1.6 2.1 3.8 5.7 4.6 5.0 6.2 6.2

The next most stable structure moves one of the COOH groups from the corner to the zigzag edge, leading to 2-C1/Z4. This system is higher in energy by 3.2 kcal/mol. Its deformation energy of 1.3 kcal/mol matches that of 1-Z1, so can be attributed primarily to the zigzag location of the COOH group. The side-view of 2-C1/Z4 indeed verifies a slight twist of COOH from the graphene plane, similar to that of 1-Z1. When the COOH is moved from the corner to the Z1 site, the energy of 2-Z1/Z4 rises by 1.7 kcal/mol. Interestingly, the Z1 COOH maintains its planarity while the Z4 group is slightly twisted. Another significant increment in energy occurs when one COOH remains at a corner and the second group moved from Z4 to Z3. 2-C1/Z3 is higher in energy by 4.8 kcal/mol, relative to 2-C1/Z4. The 2-C1/Z2 structure, where the second group lies closer to the corner is comparable in energy to 2-C1/Z3, as are their deformation energies. An additional increment of 2.6 kcal occurs if the second group is moved closer to the occupied corner, placing both COOH of 2C1/Z1 on the same corner hexagon, ortho to one another. The close proximity forces a rotation of the Z1 COOH, as is evident in its side view (4I). In fact, comparison of side views of 2C1/C2, 2-C1/Z4, 2-C1/Z3, 2-C1/Z2, and finally 2-C1/Z1, where one group is fixed at a corner and the other moved step-by-step from the opposite corner towards the first one along the zigzag edge, clearly shows progressive twisting of the second group. There would thus appear to be an energetic preference for separation of the COOH groups, which minimizes steric repulsion and maximizes π-conjugation. The lesser favorability of the armchair site is repeated in the doubly substituted graphenes. Structures where an armchair edge is occupied by one or both COOH group(s) are


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2-C1/C3 (4A)

2-C1/Z4 (4D)

2-C1/Z2 (4G)

2-C1/C2 (4B)

2-Z1/Z4 (4E)

2-C1/C4 (4C)

2-C1/Z3 (4F)

1-C1/A4 (4H)

2-C1/Z1 (4I) Figure 4. Two views of each graphene-(COOH)2 optimized structure, C=O and C-COOH distances are in Å. Rest of the structures studied are given in Figure S1.

less stable by at least 10.0 kcal/mol, compared to the global minimum 2-C1/C3. This high energy is attributed to distortions due to steric repulsion either between COOH and neighboring C-H bonds, or between themselves. For example, the energy of 2-C1/A4 is 9.9 kcal/mol higher than 2-C1/C3 and Erel increases further as groups come closer as in 2-A2/A4, 2-A1/A4, and 2-A2/A3. A structure where both zigzag and armchair sites are carboxylated simultaneously, as in 2A2/Z3, lies 19 kcal/mol higher in energy than the global minimum.



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The addition of a second acid group has practically no effect on the key geometric parameters of carboxylated graphene. For example, the C=O bond length at any corner site(s) is 1.218 Å, whether or not a second acid group is added, and similarly for the C=O bond length at any armchair site. Maximal variation of C=O bonds is found at different locations of the zigzag sites. As the acid group moves from Z4 to Z1, this bond contracts from 1.224 to 1.213 Å. The shortest carbonyl bond occurs when both acid groups are located on the same hexagon (2C1/Z1). In summary, the first preference of a pair of COOH groups is occupation of corner sites , preferably at opposite corners of the sheet. Comparing the two edge sites, zigzag is preferred over armchair.

4-C1/C2/C3/C4 (5A)

4-C1/C3/Z4/Z8 (5D)

4-C1/C4/Z4/Z5 (5B)

4-Z1/Z4/Z5/Z8 (5E)

4-C1/C2/Z5/Z8 (5C)

4-Z1/Z4/A2/A4 (5F)

Figure 5. Two views of each graphene-COOH optimized structure, C=O and C-COOH distances in Å, relative energies (relative enthalpies) of graphene-(COOH)4. Rest of the structures studied are given in Figure S2. In order to insure that the conclusions are not limited to only mono and di-substitution, a number of systems were examined in which four COOH groups were added to graphene. Based on the earlier results, it was not surprising to find the most stable such molecule places an acid group at each of the four corners: 4-C1/C2/C3/C4 (5A), illustrated in Figure 5. The deformation energy of this tetrasubstituted system is quite small, only 0.5 kcal/mol, as may be seen by the first row of Table 4. Three possible structures (5B to 5D), where two acid groups were kept at


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corners and two others were moved to zigzag edges, are less stable. Of this subset, a higher energy is found when the two corners, and two zigzag sites, are diametrically opposite one Table 4. Energetics (in kcal/mol) of Tetra-Substituted Graphene. 4-C1/C2/C3/C4 (5A) 4-C1/C4/Z4/Z5 (5B) 4-C1/C2/Z5/Z8 (5C) 4-C1/C3/Z4/Z8 (5D) 4-Z1/Z4/Z5/Z8 (5E) 4-Z1/Z4/A2/A4 (5F) 4-Z3/Z7/A2/A6 (5G) 4- A2/A4/A5/A8 (5H) 4-Z2/Z3/Z6/Z7 (5I) 4-Z2/Z3/A2/A3 (5J) 4-A2/A3/A6/A7 (5K) a see Figure 5 and S2 for structures.

Erel 0.0 3.4 3.4 6.4 10.8 24.8 36.9 42.6 46.0 48.9 57.1

Hrel 0.0 3.6 3.6 6.7 11.2 24.5 36.3 41.7 45.2 48.9 55.9

Edef 0.5 1.8 1.8 2.5 3.7 7.6 7.4 11.9 10.5 11.3 11.7

another, as in 4-C1/C3/Z4/Z8 (5D). Side views indicate a slightly more twisted COOH in 5D than 5B or 5C. The next jump up in E occurs when all four carboxyls are added to zigzag sites, in 4-Z1/Z4/Z5/Z8 (5E), with two on each side of the graphene. As armchair sites become occupied, as in the other structures listed in Table 4, the energy rises dramatically, and introduces clear evidence of geometrical distortion. For example, replacing the two zigzag sites of 4Z1/Z4/Z5/Z8 by armchair locations increases the energy of 4-Z1/Z4/A2/A4 (5F) by 14.0 kcal/mol. Thus, the preferences in evidence for the singly and doubly substituted graphenes persist when the number of acid groups increases to four, and presumably beyond. 3.3 Vibrational Spectra. A workhorse of experimentalists in identifying synthesized oxidized graphenes and RGO is IR spectroscopy. In an effort to aid these efforts, the vibrational spectra of the various carboxylated graphenes were computed and analyzed. Lorentzian broadening with fwhm of 20 cm−1 was applied to each spectrum to better simulate an experimental result. Since C=O and O-H stretching modes are, in general, used as two characteristic bands of carboxyl groups, an emphasis is placed on those modes, besides other modes at the 1000-1600 cm-1 range. The calculated spectra of the most stable isomers of Gr-(COOH)n, n = 1, 2 and 4 , viz. with carboxyl groups in the corners, are superimposed in Figure 6, along with the spectrum of the pristine graphene as the bold black line. The most characteristic C=O peak of COOH appearing at 1718 cm-1 is blue-shifted by 2 cm-1 by each successive increase in the number of acid groups. Consistent with the larger number of these C=O groups, the intensity of the peak increases along with n, as do the intensities of other prominent bands around 1300 and 1150 cm1 . The former peak is normally assigned as C-OH bending and the latter as C-O stretching of COOH. However, according to our vibrational analyses, none of these two modes are pure, but rather represent a mixture of C-OH bending, C-O and C-COOH stretching motions. In fact, only formic acid itself exhibits such pure modes; mixing occurs even for benzoic acid. In any case, the peak around 1300 cm-1 is blue-shifted and the band around 1140 cm-1 red-shifted with increasing



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number of COOH units. The O-H and C-H peaks (not shown) appearing around 3551 and 3100 cm-1, respectively, are unaffected by n. Two peaks at 1548 and 1589 cm-1 with low intensity are identified as C=C, coupled with C-H bending of Gr, and are also little affected by n.

Gr 1-C1 (1A) 2-C1/C3 (4A) 4-C1/C2/C3/C4 (5A)

C-O 1139 1142 1143

C=O 1722 1720

Site Preferences of Carboyxl Groups on the Periphery of Graphene

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