Oxidative Tearing of Graphene Sheets: Insights into the Probable

Article pubs.acs.org/JPCC

Oxidative Tearing of Graphene Sheets: Insights into the Probable Situations by Computational and Experimental Studies Angana Ray,† Kousik Bagani,‡ Sangam Banerjee,‡ and Dhananjay Bhattacharyya*,† †

Computational Science Division and ‡Surface Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India S Supporting Information *

ABSTRACT: Nanometer size graphene sheet has become a subject of interest both for technological as well as medical applications. In this work, we have focused on the oxidative tearing of nanoscale graphene sheets using ab initio density functional theory. We have geometry optimized several model systems depicting all possible graphene oxide sheets containing either a single or multiple oxygen atoms. We have found that a single oxygen atom prefers to bind to two carbon atoms of the cis-edge by forming an epoxy linkage. Such epoxidation also induces a large curvature into the graphene sheet by breaking the involved C−C bond. This initial epoxidation also favors formation of similar epoxy-linkages at nearby sites in a cooperative manner during the oxidation of a nascent graphene sheet. Such bond breaking, however, is not observed when we try similar epoxidation at the trans-edge. A series of epoxidation starting from the cis-edge thus can cause tearing of the graphene oxide sheet leading to formation of smaller size graphene sheets containing exposed functionalized trans-edges. Because of symmetry in a graphene sheet, we can expect to obtain a smaller functionalized graphene sheet of triangular shape having predominantly trans-edges (cis edges may appear at the corners) during the oxidation process. Our subsequent experiment of magnetic hysteresis compliments the theoretical finding of the tearing pattern.

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INTRODUCTION Graphene is a two-dimensional (2D) planar sheet of sp2hybridized carbon atoms covalently bonded and arranged in a honeycomb lattice, having excellent physicochemical properties.1−4 Because of these properties graphene sheet has various applications in the fields of electronics such as energy storage and conversion, engineering nanocomposites, and so forth. Two-dimensional graphene sheets with dimensions in the order of nanometers have huge bioapplications such as biosensors, drug delivery, cellular imaging, and so forth due to their edges. Bulk scale production of graphene for commercial applications has always been a challenge for the researchers, a perfect solution to which is not known. However, a consecutive oxidation and reduction method appears to be a cost-effective process for obtaining nanoscale graphene sheets.5−9 Upon oxidation, graphite readily exfoliates as single sheets in water, forming graphene oxide (GO) where some of the carbon atoms are oxidized. Chemical or thermal reduction of these GO to obtain graphene is an economical and large-scale production method.7,10−14 The GO contains oxygenated functional groups on its basal plane and edges making it functionalized through covalent interactions, which in turn makes the GO suitable as a building block for synthesizing functional nanomaterials.15−17 The presence of many structural defects and functional groups on reduced GO makes it appropriate for various electrochemical usage.18 During the oxidation procedure, many functional groups (−OH, −O−, −COOH, −CO, etc.) attach onto the © 2014 American Chemical Society

graphene sheet which leads to breaking of its intrinsic C−C π-bonds, causing automatic tearing of the graphene oxide sheet into smaller pieces of random shape and sizes after reduction.13,19 The exact pattern of positions of the functional groups on the graphene skeleton is still unidentified but some NMR studies on GO show that carbonyl (−CO and −COOH) are preferably present at the edges of the GO sheet,15,20 thus, making hydroxyl (−OH) and epoxy (−O−) groups abundant on the faces of the GO sheet. The mechanism for an oxidative breakup of graphene sheet has already been proposed,21,22 where the epoxy groups formed during oxidation were shown to have aligned in a line inducing a rupture in the underlying C−C bonds.23 It is known that an arbitrarily cut graphene sheet has two edges; arm-chair (cis) and zigzag (trans) edge24,25 with distinctly different electronic properties.26 The trans-edge is more hydrophilic as compared to the overall cis-edge, which has been established both experimentally and theoretically.27−29 It was theoretically shown that chain of epoxy groups are responsible for oxidative unzipping of GO sheets22,23,30,31 but none of the studies indicated any preference in generation of cis-edge or trans-edge after reduction A nanoscale graphene sheet has highly hydrophobic faces and slightly polar edges25,29,32 with trans-edge being more polar. Received: November 3, 2014 Revised: December 15, 2014 Published: December 15, 2014 951

DOI: 10.1021/jp511001f J. Phys. Chem. C 2015, 119, 951−959

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The Journal of Physical Chemistry C

Table 1. Bond Lengths and Bond Orders of −(C−C)− bonds in the different type of linkages are given along with the NBO charges on these C− and H−atoms dimension of graphene sheet 3×3

4×4

5×5

6×6

−C−C− bond length (Å)

−C−C− bond order

NBO charge on terminal H atom

H−(C−C)−H H−C-(C−C)−H

1.381 1.393 (0.02)

1.476 1.373 (0.11)

0.246 (0.00) 0.242 (0.00)

H−C−(C−C)−C−H corner-H−(C−C)−H H−(C−C)−H H−C−(C−C)−H

1.474 1.358 (0.01) 1.387 (0.00) 1.394 (0.02)

1.08 1.626 (0.10) 1.418 (0.00) 1.365 (0.11)

0.239 0.247 0.243 0.242

(0.00) (0.00) (0.00) (0.00)


1.469 1.355 1.376 1.397

(0.00) (0.01) (0.00) (0.00)

1.088 1.643 1.395 1.094

(0.00) (0.09) (0.06) (0.00)

0.240 0.247 0.241 0.242

(0.00) (0.00) (0.00) (0.00)


1.464 1.371 1.380 1.396

(0.00) (0.00) (0.00) (0.01)

1.330 1.523 1.452 1.345

(0.01) (0.00) (0.00) (0.07)

0.240 0.247 0.242 0.242

(0.00) (0.00) (0.00) (0.00)

H−C−(C−C)−C−H corner-H−(C−C)−H

1.462 (0.00) 1.357 (0.01)

edge-typea

1.104 (0.01) 1.628 (0.09)

0.241 (0.00) 0.247 (0.00)

NBO charge on C atoms −0.215 −0.057 −0.185 −0.028 −0.218 −0.209 −0.057 −0.182 −0.028 −0.224 −0.206 −0.064 −0.172 −0.029 −0.223 −0.205 −0.061 −0.179 −0.029 −0.223

(0.00) (0.00)b (0.00)c (0.00) (0.01) (0.00) (0.00)b (0.00)c (0.00) (0.02) (0.00) (0.00)b (0.00)c (0.01) (0.01) (0.00) (0.00)b (0.00)c (0.00) (0.02)

a Four different types of linkages are possible along the two edges of a graphene sheet. The H−C−(C−C)−H linkage has two different types of C atoms, viz., one C atom is attached to two other C atoms and a C atom is attached to a H atom having different charges. bCharge on the C atom that is attached to two other C atoms. cCharge on the C atom that is attached to a H atom.

and all angles equal to 120°. The edges were terminated with hydrogen atoms forming C−H bonds so as to neutralize the valences of all the carbon atoms. There are studies, which report that without such termination at the edges, the graphene sheet with dangling electrons would behave like free-radical, increasing the complexity of the study.37 We successfully optimized all the graphene sheets except the (8 × 8) graphene sheet by standard dispersion corrected density functional theory (DFT-D) based method ωB97XD/6-31g(2d,2p)38 using Gaussian-09 (g09).39 The (8 × 8) GO system containing five epoxy groups was optimized with B3LYP/6-31g(2d,2p)40−42 as it was computationally difficult for such a large system to be optimized by the expensive ωb97XD/631g(2d,2p) method. Considering their overall properties and our available computational power we have considered (5 × 5) graphene sheets as standard miniature model for carrying out further studies. However, in some cases we have also used (4 × 4), (6 × 6), and (8 × 8) models for complete understanding of the processes under study. We modeled several GO sheets of (5 × 5) dimension with different number of epoxy groups placed at desired specific positions on the optimized (5 × 5) graphene sheet with b(C− O) = 1.40 Å and epoxy angles a(C−O−C) = 110°. We also developed some GO sheets of dimension (4 × 4), (6 × 6), and (8 × 8), whenever required, following the same protocol for both modeling and optimization. Completion of geometry optimization was confirmed by calculating the vibrational frequencies of the respective optimized structures. The diagrammatic representations of all the model systems are given in the Supporting Information (Figure S1). Since electron distribution within the highly conjugated graphene sheet is sensitive to its environment, we carried out Natural Bond Orbital (NBO)43,44 analysis to understand the charge distribution on the graphene/GO sheet and thereby effect of

Thus, functionality of the graphene sheet depends predominantly on the type of edge, that is, a graphene sheet with higher amount of exposed trans-edges than cis-edges has higher hydrophilicity and in turn might have higher chances of functionalization. Because molecular recognitions in biological systems are based on hydrophobic and hydrophilic interactions, the edge-type of graphene sheet becomes important. We have therefore carried out detail quantum chemical studies on nanoscale GO sheets along with some nascent graphene sheets of same size to address the effect of type of edge on the process of GO formation and tearing. We have extended this scheme for predicting the most probable condition, that is, predicting the positions of epoxy groups on the GO sheets, for tearing. Finally, we have shown that formation of smaller size graphene sheets with predominantly trans-edge is more probable, compared to that of cis-edge, after complete tearing of the GO. It is well-known that there exists narrow electronic density of state at the Fermi level for trans-edge of graphene,33,34 which can lead to large Pauli susceptibility causing the electronic band to split spontaneously giving rise to ferromagnetism (Stoner criterion35). Thus, generation of large number of trans-edges upon reduction will cause increase in magnetism and here we shall support this with experimental magnetization data.

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METHODOLOGY

In our study, we have considered graphene sheets of different dimensions, obtained by varying the number of basic unit, namely benzene ring, (i) 3-ring (3 × 3), (ii) 4-ring (4 × 4), (iii) 5-ring (5 × 5), (iv) 6-ring (6 × 6), and (v) 8-ring (8 × 8) systems. The atomic coordinates of all the carbon and hydrogen atoms arranged in hexagonal lattice with hydrogenterminated trans- and cis- edges were generated by the molecular modeling software MOLDEN36 using standard bond lengths (b(C−C) = 1.421 Å and b(C−H) = 1.009 Å) 952


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Figure 1. (a) A graphene sheet contains trans-edge formed by H−C−(C−C)−H linkage and cis-edge formed by both H−C−(C−C)−C−H and H−(C−C)−H linkages. Also, there exists H−(C−C)−H bonds at the corners, atoms of which have a slightly different property, thus we have labeled these as corner H−(C−C)−H linkage. The NBO charges on terminal C− and H atoms atoms clearly indicate the polarity difference in the two edges. (b) The IR spectra corresponding to a (5 × 5) graphene sheet. Frequencies less than 2000 cm−1 correspond to the −C−C− bond movements in the graphene plane whereas, frequencies above 3000 cmm−1 correspond to the vibrations of terminal −C−H bonds. In the inset plot, the highest intensity peak at 3224.23 cm−1 and other peaks above this frequency correspond to the cis-edge −C−H bond vibrations whereas the trans-edge −C−H bond vibrations are indicated by lower intensity peak at 3206.72 cm−1.

epoxidation. The −C−C− bonds in graphene/GO sheets have extended conjugation and partial double bond character that might have an influence on the tearing pattern. Thus, we calculated bond order of the systems by Wiberg method45 using g09. For our sample preparation, we have synthesized graphene oxide from graphite powder (Sigma-Aldrich) using modified Hummer’s method.46 After drying the GO in vacuum oven at 80°C, we annealed it at 450°C. A detailed synthesis and sample characterization can be found in the literature.47 Magnetic hysteresis curve of GO and Annealed GO (GO-450) was taken at room temperature (300 K) using SQUID magnetometer MPMS XL 7 (Quantum Design).

1a): H−C−(C−C)−H, H−C−(C−C)−C−H, H−(C−C)−H, and corner-H−(C−C)−H. The trans-edge is composed only of H−C−(C−C)−H bonding, whereas the cis-edge contains both H−(C−C)−H and H−C−(C−C)−C−H types of bonds. The corners of the graphene sheet also have similar H−(C−C)−H linkage but its properties are slightly different (Table 1), hence are named corner-H−(C−C)−H. Along with difference in bond length, bond orders, and NBO charges, these bonds can also be distinguished on the basis of infrared (IR) frequencies (Figure 1b). The normal-mode analysis for the (5 × 5)graphene sheet showed higher IR intensity for the cis-edge C− H bond stretching, which appear between 3220 and 3240 cm−1 frequencies, as compared to the trans-edge C−H bonds (Figure 1b). Thus, for a graphene sheet having two distinct edges viz., cis-edge and trans-edge with different electrostatic and structural properties, epoxidation might lead to placement of epoxy groups at either of the two edges or both the edges simultaneously. During epoxidation the epoxy groups are certainly placed on both the two faces and all the edges of a graphene sheet, but during oxidation of graphitic material, the edges are far more accessible than the faces. In our study we have thus started to mimic epoxidation by considering the edges and then moved onto the faces. The −C−C− bonds of the trans-edge retained the length of 1.40 Å after optimization of the (5 × 5)-nascent graphene sheet but some of the cis-edge −C−C− bond lengths were increased to 1.464 Å and some decreased to 1.376 Å. This difference in −C−C− bond length along the cis-edge indicated an increase in the number of possible epoxidation sites giving rise to three possibilities as positions for epoxidation along the edges, viz., one along the trans-edge and two along the cis-edge (Figure 1a). Thus, with the expectation that tearing of GO may be influenced by the position of the epoxy group on the graphene sheet we first generated three GO models. Each of these models had one

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RESULTS AND DISCUSSION Graphene is generally an infinite 2D sheet, but since we were interested in understanding the changes in its structural features during the fragmentation of GO, we adopted dispersion corrected-DFT formalism suitable for small molecules without periodicity, using localized atomic orbitals as basis set instead of plane wave pseudopotential method. We started by optimizing (3 × 3), (4 × 4), (5 × 5), and (6 × 6) graphene sheets and observed that all the sheets retained their geometric planarity and a consistency in −C−C− bond length, bond order, and NBO charges was maintained (Table 1). In our previous work,29 we observed that hydrogen bond interaction between a water molecule and a graphene sheet is stronger at the transedge. This is in accordance with our present NBO charge analysis that the trans-edge has comparatively higher net positive charge that can attract the partially negatively charged oxygen atom of water molecule. Hence, we decided to consider the (5 × 5)-sheet as a standard for proceeding with our work. As discussed earlier, a graphene sheet has two edges but the edges involve four different types of −C−C− linkages (Figure 953


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The Journal of Physical Chemistry C epoxy group placed along the edges of the optimized (5 × 5)nascent graphene sheet. As already discussed, there were two distinct possibilities of placing an epoxy group along the cisedge, shown in [model 1] where an epoxy group is linked to the C*-atoms of the H−C−(C*−C*)−C−H linkage and; [model 2] where the epoxy group is linked to the two C*atoms of H−(C*−C*)−H linkage. After optimization of both these GO models we found that [model 1] was energetically favorable over [model 2] by 10.60 kcal/mol, that is, epoxidation is preferred at the H−C−(C*−C*)−C−H linkage along the cis-edge. Also, when an epoxy group was placed along the transedge involving C*-atoms of the H−C−(C*−C*)−H linkage [model 3], we observed that [model 1] was favored by 7.99 kcal/mol over this situation, too. In the optimized structure of [model 1], the −C−C− bond involved at the epoxidation site was completely broken and a huge bending was introduced in the GO sheet indicating an initiation of the tearing process (Figure 2a). There was a small increment in the −C−C− bond

Table 2. Comparison of the Three Models: [Model 1], [Model 2], and [Model 3] on the Basis of Molar Heat Capacities at Constant Volume for the Corresponding Optimized Structures along with NBO Charges on the Atoms Involved in Epoxidationa charge of the atoms forming epoxy linkage model [model 1] [model 2] [model 3]

C*

O

C*

CV (molar heat capacity at const. vol.) (Cal/mol-K)

0.32

−0.521

0.315

169.747

0.045

−0.517

0.045

169.971

0.071

−0.518

0.179

170.059

C*-atoms are the C atoms connected via epoxy linkage −C*−O− C*−. a

edge involved in the process of GO formation and ultimately leading to tearing of graphene sheets. Apart from these situations there existed two more possibilities for positioning of an epoxy group; one along the cis-edge [model 4] and another along the trans-edge [model 5]. In both these situations an oxygen atom replaces two hydrogenatoms. We developed [model 4] by connecting the two C*atoms of the H−C*−C−C−C*−H linkage and removing the terminal H atoms for maintaining valency. It was expected that optimization might give stability to the five member ring, that is, decreasing the associated −(C−C)− bond lengths causing breaks in some of the nearby −(C−C)− bonds. However, optimized geometry of [model 4] showed only slight increase in −(C−C)− bond length of the bonds adjacent to fivemember ring. The [model 5] was not studied as it seemed to be possible only theoretically because a four-member ring formation on a graphene plane would be energetically too unstable. Usually under experimental conditions the epoxidation of graphene sheet leads to placement of a number of epoxy groups on the sheet48 and obtaining smaller graphene sheets from tearing larger ones requires a GO sheet with a number of epoxy groups. The NBO charges and bond order calculations on [model 1] indicated that the −C−C− bonds next in parallel to the first epoxidation site have the lowest bond order along with corresponding C atoms having the lowest negative charge making them susceptible to further epoxidation (Figure 3). In order to confirm this, we developed two more models by placing another epoxy group on the optimized [model 1] structure but at different positions. The optimized [model 6a] containing two epoxy groups at parallel positions proved to be energetically favorable by 44.52 kcal/mol compared to [model 6b] containing the two groups in nearly adjacent positions. Thus, with the aim to clarify the influence of number of epoxy groups on tearing of GO, we optimized two more model systems where four epoxy groups were placed, starting from the cis-edge [model 7a] and trans-edge [model 7b], respectively. All the epoxy groups were placed on the same side of the sheet for both the models and only the H−C−(C*−C*)−C−H linkage of the cis-edge was considered while building [model 7a] as it was arguably more favored. Optimized geometries of both [model 7a] and [model 7b] (Figure 4a,b) showed breakage in the −C−C− bonds at the epoxidation sites along with a bending in the sheet, although a detail analysis gave up a clear picture that tearing of GO sheet was favored by an

Figure 2. (a) The optimized geometry of a (5 × 5)-GO sheet containing an epoxy group at the cis edge linked to two C*-atoms of H−C−(C*−C*)−C−H linkage has the −C−C− bond broken at that site whereas, (b) the optimized geometry of the same GO sheet with epoxy group at the trans edge has the −C−C− bond intact with slight increase in bond length.

distance at epoxidation site at the trans-edge of the optimized [model 3] structure (Figure 2b) with small bend in the GO sheet. Both of these scenarios elucidate that during epoxidation of graphitic material initially the exposed graphene layers were oxidized first, introducing a bend/kink in that sheet that readily exposes the lower sheets to oxidation ultimately leading to tearing and exfoliation into individual graphene/GO sheets. In the following discussion, we have tried to reason out why the optimized [model 1] is energetically most favored. The NBO charges for the three atoms (C*, O, and C*) forming the epoxy linkage (−C*−O−C*−) indicated that in [model 1] the partially negatively charged oxygen was attached to two partially positively charged carbon atoms; however, in [model 2] and [model 3] the concerned carbon atoms have very low positive charge. Also, the molar heat capacity at constant volume for optimized [model 1] is the lowest confirming that it is energetically easier to obtain (Table 2). Moreover, the NBO charges calculated for the (5 × 5)-nascent graphene sheet clearly showed that the C*-atoms of the H−C−(C*−C*)−C− H linkage have lowest negative charge making them most suitable for initiation of epoxidation (Figure 1a) and the bond orders indicated that the −C−C− bonds formed by the same C*-atoms of H−C−(C*−C*)−C−H linkage is weak with low partial double bond character, making these bonds a preferable tearing site (Table 1). Thus, the GO sheet with epoxy group at the H−C−(C*−C*)−C−H position of the cis-edge seemed to be the best model by far for addressing the effect of type of 954


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Figure 5. Schematic representation of possibilities leading to tearing of GO sheet. The two black-colored lines indicate direction of tearing when epoxidation at two available types of linkages along the cis-edge are compared. Epoxidation initiating at H−C−(C*−C*)−C−H linkage favors tearing (solid line) over epoxidation involving C*atoms of H−(C*−C*)−H linkage (dotted line). Tearing after epoxidation is favored when epoxidation is initiated at the cis-edge and followed thereafter. The red lines indicate tearing conditions requiring high energy.

Figure 3. After breaking of −C−C− bond due to epoxidation, the properties like charge on C atoms and bond order of −C−C− adjacent to the epoxidation site changes. The values given in parentheses are NBO charges of the corresponding C atoms and the values in italics and blue color are the bond order of the −C−C− bonds.

analysis of optimized structures corresponding to these two models showed that [model 8a] was energetically favored over [model 8b] by 15.96 kcal/mol, generalizing the earlier result that tearing is easier with epoxidation involving the influence of cis-edge types. In order to clearly understand the directionality involved in tearing, we have constructed and optimized two (4 × 4) GO models each containing two epoxy groups, namely [model 9a] and [model 9b] with the average −C−C− distance and −C−O−C− angles at the epoxidation sites for [model 7a], [model 7b], [model 9a], and [model 9b] (Table 3) emphasized Table 3. Comparison of the Following Four Models: [Model 7a], [Model 7b], [Model 9a], and [Model 9b] on the Basis of −C−C− Bond Distance and −C−O−C− Angle at the Epoxidation Site

Figure 4. (a) Optimized geometry of [model 7a] showing the −C− C− bonds broken at all the epoxidation sites, tearing the sheet to the maximum possible. (b) Optimized geometry of [model 7b] containing some −C−C− bonds unbroken even after epoxidation.

amount of 50.39 kcal/mol, when the oxidation takes place involving the cis-edge. Another significant observation was that an increase in number of epoxy groups increases the possibility of tearing GO sheet. The −C−C− bond of trans-edge was not broken in [model 3] with only one epoxy group whereas the same −C−C− bonds were elongated when four epoxy groups were lined up from the trans-edge. We also tried to probe into directionality of the tearing pattern by developing two model systems, [model 8a] and [model 8b] with (4 × 4) graphene sheet as the basic unit to capture the directional influence with more clarity but with lower computational cost. Optimized geometry of [model 8a] was energetically favored over optimized [model 8b] geometry by 30.54 kcal/mol establishing that tearing is favored in a particular direction (Figure 5) starting from H−C−(C−C)−C−H edge toward H−(C−C)− H edge. Until now we optimized only systems involving epoxy groups at the edges but epoxydation only in the plane and away from the edges of the graphene sheet may be important. Hence, we developed [model 8a] and [model 8b] by removing epoxy groups from the cis-edge of [model 7a] and trans-edge of [model 7b] respectively. Only three epoxy groups were taken this time to reduce the computational expense as the effect of number of epoxy groups had already been addressed. The

model [model 7a] [model 7b] [model 9a] [model 9b]

C−C distance at epoxy site (Å) [distance between C*-atoms in C*− O−C* link]

C−O−C angle at epoxy site (deg) [C*−O−C* angle]

2.317 (0.05)

115.775 (3.35)

1.913 (0.37)

87.148 (24.94)

2.287(0.06)

113.450 (3.84)

2.230 (0.08)

109.710 (4.97)

that tearing is favored only by breaking-up of particular type of bonds (Figure 5). This allows us to conclude that tearing is most favored by breaking the C*−C* bonds of H−C−(C*− C*)−C−H and moving toward H−C*−C*−H. We modeled and optimized two (8 × 8) GO sheets containing five epoxy groups on the plane of each sheet but none at the edges with only the difference in the position of the epoxy groups; [model 10a] was found energetically favorable to [model 10b] by 33.04 kcal/mol, thus generalizing the above stated hypothesis for GO sheets of all sizes. The tearing of GO sheets produces smaller graphene sheets having functionalization at the edges.49 These smaller graphene sheets may have either only cis- or trans-edge or both the edges. The following part of our study involved prediction of the type 955


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was preferred over [model 11a-2], the epoxy group placement pattern in [model 12a] was similar to that of [model 11a-1]. The energies of the optimized geometries showed that [model 12a] is unfavored over [model 12b] by 21.32 kcal/mol but unlike in [model 11a-1] or [model 11a-2] the bonds were intact at the epoxidation sites of both [model 12a] and [model 12b] with slight change in the −C−C− bond lengths. Thus, on comparing energies of all the five models, [model 11a-1], [model 11a-2], [model 11b], [model 12a], and [model 12b], it was clear that [model 11a-1] was energetically the most favorable situation for tearing of GO. With the aim to cover up all possible aspects we finally developed two more models: [model 13a] and [model 13b], which had (6 × 6) dimension of the GO sheet and 10 epoxy groups randomly placed. In [model 13a], epoxy groups were arranged in a way that upon tearing it may lead to either cis- or trans-edge smaller sheets or both simultaneously. After its optimization, the −C−C− bonds at the epoxidation sites were broken in such a way that if extrapolated it will lead to formation of only trans-edge smaller sheets (Figure 7a). In

of edge formation after the process of tearing is completed, that is, to theoretically predict which edge formation is more plausible after complete tearing (Figure 6). Keeping in mind

Figure 6. Schematic diagram indicating that tearing of a large-size graphene sheet would lead to formation of smaller sheets having either trans-edge or cis-edge.

that it was impossible to place four epoxy groups on a (5 × 5) graphene sheet along the most preferred position (cis-edge H− C−(C*−C*)−C−H influence) without involving the edges, we developed [model 11a-1] which had somewhat H−C− (C*−C*)−C−H influence. The bond length, bond−order, IR frequency of C−H stretching, and NBO charges on C atoms of the corner-H−(C−C)−H bonds were intermediate between the cis-edge and the trans-edge. Hence we developed [model 11a-2] containing four epoxy groups on a (5 × 5) graphene sheet but with H−(C*−C*)−C−H linkage influence from the trans-edge. Thus, we modeled three GO sheets each with four epoxy groups placed on the same side of the sheet in such a way that tearing of one leads to formation of cis-edged sheets [model 11b] and the other two gives a trans-edged sheet. After optimization we obtained that the tearing of both [model 11a1] and [model 11a-2] GO sheets were preferred over [model 11b] by 35.33 and 29.86 kcal/mol of energy respectively, indicating that formation of cis-edge upon tearing is not favorable. This was in accordance with the observation that the optimized geometries of only [model 11a-1] and [model 11a-2] showed breaks in C−C bonds eventually suggesting formation of trans-edged sheet after tearing of GO. The average −C−C− distance and −C−O−C− angle at the epoxidation sites in optimized geometry of [model 11b] were seen to be 1.866 Å (0.39) and 86.007° (25.13), respectively, the same in the case of optimized [model 11a-1] geometry being 2.089 Å (0.35) and 100.034° (22.06) eventually making up for the fact that ultimate tearing of GO will lead to formation of smaller graphene sheets with trans-edge. This is in accordance with the experimental report that thermal reduction favors unzipping process that leads to increase in exposed zigzag edges.50 Furthermore, experimentally the positioning of epoxy groups can be random; hence the four epoxy groups might not line-up on the same side of the GO sheet. This aspect was tackled by optimizing two more model systems, [model 12a] and [model 12b], where the alternate epoxy groups were placed on the opposite faces of the graphene sheets. Because [model 11a-1]

Figure 7. Optimized structure of (a) [model 13a] and (b) [model 13b]. The highlighted broken −C−C− bonds at some epoxidation site indicate that tearing will always lead to trans-edge sheets.

[model 13b], the epoxy groups were far more randomly placed, yet after optimization only those −C−C− bonds were broken (Figure 7b) which in future will lead to tearing in a way that theoretically confirms the higher probability of forming smaller sheets with enhanced trans-edges. We have tabulated the calculated relative energies (Table 4) of all the model systems from which the most feasible model becomes clear. We support the above tearing model indirectly by magnetic measurements. From Figure 8, it is clearly seen that the magnetization of GO increases after annealing. Earlier we had reported similar types of behavior50 where we showed that the magnetization increases drastically after annealing the GO at 600°C temperature. Acquiring the thermal energy during annealing, the epoxy groups arranged themselves as discussed above to form a long chain of epoxy groups. After annealing, the epoxy groups are removed from the surface, exposing many zigzag (trans) edges. Role of zigzag edges in magnetic property of graphene is now well established by both theoretically and experimentally.51 At the zigzag edge, the π-electrons are highly localized. To minimize Coulomb repulsion energy, the edge states are occupied with same spins, which leads to ferromagnetic ordering at the zigzag edge. This is another way of looking at magnetism in graphene apart from Stoner criterion. Our observation of increase in magnetization of GO after annealing at 450°C indicates formation of large number of smaller graphene sheets with more zigzag edges during the annealing process. 956


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The Journal of Physical Chemistry C Table 4. Comparison of the Optimized Model Structures on Based on Their Energiesa total number of set

dimension of GO sheet

C atoms

H atoms

O atoms

1

(5 × 5)

64

22

1

2

(5 × 5)

64

22

2

3

(5 × 5)

64

22

4

4

(5 × 5)

64

22

3

5

(4 × 4)

48

18

2

6

(8 × 8)

160

34

5

7

8

(8 × 8)

(5 × 5)

64

64

22

22

4

4

models [model 1] [model 2] [model 3] [model 6a] [model 6b] [model 7a] [model 7b] [model 8a] [model 8b] [model 9a] [model 9b] [model 10a] [model 10b] [model 11a-1] [model 11a-2] [model 11b] [model 12a] [model 12b]

Δ (kcal/mol) 0.00 10.60 7.99 0.00 44.52 0.00 50.39 0.00 30.54 0.00 15.96 0.00

Figure 9. (a) All possible tearing patters are indicated. Red (bold) lines indicate the tearing directions/pattern that is not possible. Red (dotted) lines indicate possible tearing pattern but at the cost of high energy, whereas black lines represent the most favorable tearing pattern. (b) The expected smaller size graphene sheet after complete tearing of a line size GO-sheet.

33.04

to smaller graphene sheets with a gradual increase in the percentage of trans edge, that is, −(C−C−C)− bonding predominant at the edges with some functionalization at the terminal C atoms. A closer look at the expected tearing patterns also indicates that there exists a possibility of obtaining triangular graphene sheets containing n2-number of carbon atoms, that is, 9, 16, 25, 36, and so forth. It would be interesting in the future to experimentally detect the existence of such a pattern in the number of C atoms forming the nanographene sheets. However, as a conclusion to our study, we would like to state that it is possible to obtain a functionalized graphene sheet containing only exposed hydrophilic trans-edge (zigzag edge) (Figure 9b) making the sheet highly exploitable in biological systems.

−35.33 −29.86 0.00 21.32 0.00

a

Similar models having the same number of atoms and similar pattern of epoxidation have been grouped in one set. Energy of one model system in each group is set to zero and the energies of the rest are specified relative to that.

■

ASSOCIATED CONTENT

S Supporting Information *

Figure S1 showing the schematic representation of all the models studied in detail; complete Author List for refs 13, 15, 19, and 39. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-332337 0379, extn. 2252. Fax: +91-33-2337 4637. Notes

The authors declare no competing financial interest.

■ ■

Figure 8. Magnetic hysteresis curve of as-prepared and annealed graphene oxide (GO) annealed graphene oxide measured at room temperature (300 K).

ACKNOWLEDGMENTS A.R. and D.B. are thankful to BARD project of Department of Atomic Energy, Government of India for support.

■

CONCLUSION In this investigation, we could narrow down the type of edges possible to obtain after tearing of a graphene sheet. Along with this a preference in the tearing pattern was also observed. The tearing of a graphene sheet prefers to happen along the cis-edge with −C−C− bonds of H−C−(C−C)−C−H type breaking at the lowest cost of energy. This was indicated by the energies obtained from quantum chemical calculations and supported by the NBO charges obtained. On analyzing all possible tearing patterns (Figure 9a), we could say that progressive tearing of a large graphene sheet into smaller and smaller ones would lead

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