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Received 5 Nov 2013 | Accepted 2 Jan 2014 | Published 24 Jan 2014

Ardavan Zandiatashbar1,*, Gwan-Hyoung Lee2,3,*, Sung Joo An2, Sunwoo Lee4, Nithin Mathew1, Mauricio Terrones5,6,7, Takuya Hayashi8, Catalin R. Picu1, James Hone2 & Nikhil Koratkar1,9

It is important from a fundamental standpoint and for practical applications to understand how the mechanical properties of graphene are inuenced by defects. Here we report that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp3-type defects. Moreover, the breaking strength of defective graphene is only B14% smaller than its pristine counterpart in the sp3-defect regime. By contrast, we report a signicant drop in the mechanical properties of graphene in the vacancy-defect regime. We also provide a mapping between the Raman spectra of defective graphene and its mechanical properties. This provides a simple, yet non-destructive methodology to identify graphene samples that are still mechanically functional. By establishing a relationship between the type and density of defects and the mechanical properties of graphene, this work provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.

1 Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA. 2 Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA. 3 Department of Materials Science and Engineering, Yonsei University, Seoul 120-749, Korea. 4 Department of Electrical Engineering, Columbia University, New York, New York 10027, USA. 5 Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. 6 Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. 7 Department of Materials Science and Engineering and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. 8 Faculty of Engineering and Research Center for Exotic Nanocarbons, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan. 9 Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to C.R.P. (email: mailto:[email protected]

Web End [email protected] ) or to J.H.(email: mailto:[email protected]

Web End [email protected] ) or to N.K. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms4186

Effect of defects on the intrinsic strength and stiffness of graphene

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4186

Pristine (that is, defect-free) graphene exhibits ultra-high elastic modulus and unsurpassed strength1. Atomic force microscope (AFM)-based nanoindentation experiments

performed on defect-free graphene has yielded a Youngs modulus of B1 TPa and tensile strength of over 100 GPa (refs 2,3), as theoretically predicted1. However, for various practical applications of graphene, such as composites46, chemical sensors7,8, ultra capacitors9, transparent electrodes10,11, photovoltaic cells12 and biodevices1315, the emergence of defects in the graphene lattice is inevitable either because of the production process used1618 or because of the environmental and operating conditions under which the graphene device operates1923. In addition, in biodevices and DNA-decorated graphene1315, the presence of defects is essential for the desired functionality. Defect engineering of graphene is also used in nanoelectronics for opening a band gap24, DNA-sequencing through nanopores25 and selective molecular sieving through the nanopores of suspended graphene26. Given that defects are ubiquitous in the operational environment of graphene devices, it is important to understand how the defectiveness of graphene has an impact on its elastic properties and intrinsic strength.

Computational work has investigated the mechanical properties of graphene in the presence of vacancies2731, bond reconstruction3235 and functional groups36. Several studies have also shown the formation and structural evolution of defects in graphene using both experimental37,38 and theoretical tools3942. However, on the experimental side, there has been very limited study of how the density and type of defects affect the mechanical properties of graphene. For instance, although the elastic stiffness of graphene oxide (GO), which represents a highly defective state of graphene, was reported by AFM observation of shape changes in GO membranes43, only its elastic modulus was provided, without measurement of breaking strength.

In this study, we use a modied oxygen plasma technique to induce defects in pristine graphene in a controlled manner. We utilize Raman spectroscopy and transmission electron microscopy (TEM) to characterize the defects. We then use AFM nanoindentation to experimentally quantify the stiffness and strength of defective graphene, and use nite element modelling and molecular simulations to understand this behaviour. Our results indicate that graphene sheets with defects are more rugged and structurally robust than what was previously thought. While thermal and electrical transport in graphene is very sensitive to disruptions in the sp2-bonding network, its mechanical properties are far more tolerant of defects and imperfections.

Results

Sample preparation. In our experimental study, a 1 1 cm2

array of circular wells with diameters ranging from 0.5 to 5 mm

was patterned on a Si chip with a 300-nm SiO2-capping layer, by photolithography and reactive ion etching. Graphene was mechanically exfoliated on the patterned substrate2,21 to create suspended membranes. Monolayer graphene akes were identied by optical microscopy and Raman spectroscopy. Elastic stiffness and breaking force were measured by AFM nanoindentation with a diamond AFM tip, as shown in the schematic of Fig. 1a. Figure 1b shows optical micrograph of monolayer and bilayer graphene sheets covering distinct holes of different diameters. Before the indentation testing, non-contact mode AFM imaging was used to conrm that the graphene sheets are well suspended as shown in Fig. 1c.

Introduction of defects. A tabletop oxygen plasma etcher was used to induce defects in the suspended graphene sheets (see Methods). Weak oxidation by ion bombardment, oxygen plasma or ultraviolet irradiation has been used to etch graphene or generate defects26,4446. Compared with these techniques, the etch rate of graphene in the oxygen plasma is fast: B9 layers per minute at a chamber pressure of B215 mTorr. To shield the graphene from direct exposure to the plasma, the graphene-deposited Si chips were placed upside down in the plasma chamber between two glass slides (see Supplementary Fig. 1a,b). This reduced the etch rate by a factor of B30 (Supplementary

Fig. 1c,d), and allowed the suspended graphene to survive without breaking or collapse even after plasma exposure of 55 s.

Raman spectroscopy. To quantitatively examine the type and density of defects in the graphene sheets, the graphene was characterized using Raman spectroscopy47,48. Figure 2a shows the evolution of the Raman spectrum with increasing plasma time for a typical monolayer graphene supported on the SiO2/Si substrate, which was repeatedly exposed to oxygen plasma with 3-s periods and then characterized by Raman spectroscopy after each plasma exposure dose. As expected, the D and D0 peaks, indicative of disorder, begin to rise and become more prominent with increased plasma exposure time, while conversely the two-dimensional (2D) peak weakens and broadens49. Interestingly, when Raman spectra were obtained from the suspended graphene, the D peak appeared at shorter exposure times and the peak intensity ratios were different from those in the supported one as shown in Fig. 2b. The peak intensity ratios of DG peaks (I(D)/I(G)), 2DG peaks (I(2D)/I(G)) and DD0 peaks (I(D)/I(D0)) for supported graphene are plotted in Fig. 2c. It is evident that I(D)/I(G) increases with plasma time until it reaches a maximum value of B4 at B27 s and then decreases. On the other hand, I(2D)/I(G) exhibited a slow decrease at the initial stage and then an abrupt decrease around 20 s; such behaviours

b c

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Figure 1 | Nanoindentation experiments and sample preparation. (a) Schematic representation of atomic force microscopy (AFM) nanoindentation test on suspended graphene sheets with defects. Graphene sheet is suspended over a hole with diameters ranging from 0.5 to 5 mm and depth of

B1 mm. (b) Optical micrograph of exfoliated graphene sheets suspended over holes. White-dashed line indicates the boundary of each layer. (c) Non-contact mode AFM image of suspended graphene sheet obtained from the red square box region marked in (b). Scale bars, 3 mm.

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Figure 2 | Evolution of Raman spectra as a function of sheet defectiveness. Raman spectra of (a) supported graphene and (b) suspended graphene samples exposed to oxygen plasma for various numbers of 3-s steps. The evolution of D, G and 2D peaks can be observed as the plasma time exposure increases. Variation of Raman peak intensity ratios of (c) supported graphene and (d) suspended graphene samples as a function of plasma exposure time. For supported graphene, the I(D)/I(G) ratio increases with plasma exposure time, and then reaches a maximum around 27 s and drops back down, while the I(2D)/I(G) ratio shows a sudden drop around 20 s. The suspended graphene exhibits a similar trend. Note that higher I(2D)/I(G) is observed in suspended graphene and maximum of I(D)/I(G) is obtained at shorter plasma exposure time of 20 s, indicating formation of more defects in the suspended graphene at the same plasma exposure time compared with supported graphene. The calculated average distance between defects(LD) is plotted as top x axis. Noted that LD is indicated at the corresponding plasma exposure time without any linear relationship. According to I(D)/I(D)

intensity ratio49 and defect type, the Raman maps of c and d are divided into two regimes of sp3-type and vacancy-type defects. These regimes are indicated by blue and brown areas.

are also observed in the defective graphene induced by other etching techniques4549. Although the Raman spectra (Fig. 2b) and peak intensity ratio (Fig. 2d) of the suspended graphene shows different values at the same plasma exposure time from those of the supported one, they follow a similar trend (Supplementary Fig. 2). Note that these differences in Raman spectra results between supported and suspended graphene sheets may be attributed to the substrate effect on Raman intensity in the supported graphene48, presence of pre-stress2 and etching of both sides50 in the suspended graphene.

It has been reported by Eckmann et al.49 that the I(D)/I(D0) intensity ratio can be used to discriminate between sp3-type defects, in which an oxygen atom binds to the graphene and vacancy-type defects. Therefore, we categorize the defects49 as

being predominantly sp3-type (partial oxidation, I(D)/I(D0)47) or predominantly vacancy type (I(D)/I(D0)o7) as shown in

Fig. 2c,d. As the crossover between these two regimes is gradual, the boundary is indicated by the blurred colour in Fig. 2c,d. The crossover region also correlates well to the point at which the I(D)/I(G) intensity ratio achieves a maximum for both the suspended and supported graphene. Our molecular dynamics (MD) simulation results, which will be discussed in detail later, also conrmed the similar evolution of sp3-type and vacancy-type defects with increasing plasma time. To measure the defect density, an average distance between defects (LD), which is used as top x axis in Fig. 2c,d, was calculated using the I(D)/I(G) intensity ratio, as reported46,48 (see Supplementary Discussion for details). Note that for both supported and suspended graphene,

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Figure 3 | Characterization of defective graphene by AFM and nanoindentation. (a) AFM image of a graphene sheet fully covering a hole. High-resolution AFM images of suspended graphene sheet (b) before and (c) after oxygen plasma exposure of 55 s. It is obvious that the plasma treatment leaves the surface pock-marked with a multitude of nanopores that are several nm in size (the dark spots in the image represent the nanopores).(d) Typical force versus displacement curves of AFM nanoindentation test for defective graphene exposed to oxygen plasma for 30 s. Tests are repeated at increasing indentation depths until the sample breaks. The curves fall on top of each other (no hysteresis), which indicates no signicant sliding or slippage between the graphene membrane and the substrate. The AFM images in the inset of d show a graphene sheet before and after fracture. Scale bars, 1 mm (a); 100 nm (b,c).

the I(D)/I(G) intensity ratio increased and reached a maximum at LDB5 nm, and then decreased (Supplementary Fig. 2g). To further characterize the types of defects generated by oxygen plasma, high-resolution AFM imaging was performed with an ultra-sharp diamond-like carbon tip as shown in Fig. 3ac. The membrane appears as a continuous sheet with no pores before plasma etching (Fig. 3a,b). After 55 s plasma etching (Fig. 3c), AFM imaging reveals extended defects, that is, nanopores, which are of the order of several nm in diameter (indicated by black dots in Fig. 3c), as reported elsewhere26,49. Suspended bilayer graphene sheets also showed a uniform distribution of nano-pores (Supplementary Fig. 3), which conrms the homogenous etching of the graphene sheets by the oxygen plasma treatment.

AFM nanoindentation study. To study the evolution of mechanical properties with defect density, a series of samples was prepared and each was exposed to oxygen plasma for a given time (ranging from 0 to 55 s), and was then characterized by Raman spectroscopy. Because of the variability of the oxygen plasma etching, the absolute etch time is not a reliable measure of the defect density. Consequently, the Raman parameters of I(D)/I(G) and I(2D)/I(G) were used to quantify the degree of defectiveness of the graphene sheets. To measure mechanical properties, the suspended sheets were indented by AFM as reported previously2, using a diamond AFM tip with a radius of 80 nm. Figure 3d shows typical forcedisplacement curves for a defective graphene sheet exposed for 30 s. AFM imaging of a defective graphene sheet after fracture (Fig. 3d, inset) indicates that fracture in the defective graphene occurs under the tip, as for pristine graphene. The 2D elastic modulus is determined by tting the force displacement response to a quasi-empirical polynomial form, containing linear and cubic deection terms, as previously used for pristine graphene2 (see Supplementary Discussion for details).

Figure 4a shows the evolution of the 2D elastic modulus (E2D) as a function of the Raman parameters. Remarkably, E2D remains constant (within experimental uncertainty) over the entire sp3-type defect region (that is, when I(D)/I(G)o1, I(2D)/I(G)41 and

I(D)/I(D0)47), indicating that these defects do not appreciably change the stiffness, even at a spacing LD of B5 nm. Once the graphene crosses over into the vacancy-type defect region (that is, when I(D)/I(G)41, I(2D)/I(G)o1 and I(D)/I(D0)o7), E2D decreases with increasing defect density, reaching B30% of the stiffness of the pristine sheet at the maximum exposure time.

Compared with the elastic stiffness, the breaking load of Fig. 4b shows greater sensitivity to defects regardless of type. To calculate

the breaking strength of defective graphene from the breaking load, we used the nonlinear nite element method based on ab initio density functional theory calculations (see Supplementary Discussion). This analysis yields a strength of B35 N m 1 for pristine graphene, consistent with previous measurements3.

Because of the highly nonlinear relationship between strength and breaking load, the approximately two-fold decrease in breaking load observed at an I(D)/I(G) ratio of B1.0 corresponds to a decrease in strength of only B14%, to B30 N m 1 (Supplementary Fig. 4). This is a central nding of our study: graphene can maintain a large fraction of its pristine strength and stiffness in the presence of a high density of sp3-type defects. These results can help guide the rational design of graphene-based composite materials because one can now quantify the trade-off that exists between defects (for example, because of crosslinking or processing) and mechanical properties (such as 2D elastic modulus and strength). Once the graphene passes into the vacancy-type region, the linear elastic modulus (and presumably the higher-order elastic moduli as well) changes. Therefore, the nonlinear nite element method3 cannot be applied in this regime. For a rough estimate, we note that in the linear elastic approximation, strength varies as (FbE2D)0.5, where

Fb is the breaking load2. In this simple model, the breaking strength at the highest plasma exposure time in our experiments is roughly four times smaller than that of pristine graphene.

DiscussionThe mapping of the mechanical properties of defective graphene (Fig. 4a,b) to their Raman spectra indicates that, for I(D)/I(G)o1 and I(2D)/I(G)41 (that is, in the sp3-type defect regime), the elastic stiffness of defective graphene is not signicantly diminished in comparison with its pristine counterpart. This is surprising, since an I(D)/I(G) ratio of 1 is generally considered to represent a relatively high state of defectiveness in graphene. For instance, I(D)/I(G) values of B1.0 are typical of graphene that is synthesized by chemical or thermal reduction of GO. Such reduced GO (RGO) sheets are known to offer signicantly lower electrical8 and thermal conductivity51 compared with pristine graphene owing to their defective state. By contrast, for mechanical properties, we nd that graphene is capable of tolerating defects and retaining its ultra-high stiffness properties. As compared with the stiffness, the breaking force (Fig. 4b) of graphene shows greater sensitivity to defects. Nevertheless, owing to the nonlinear elastic behaviour of graphene (Supplementary

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Figure 4 | Measurement of elastic stiffness and breaking load of defective graphene. Measured mechanical properties, (a) 2D elastic modulusand (b) breaking load of the defective graphene as a function of the Raman parameters of I(D)/I(G) and I(2D)/I(G) measured at increasing plasma times. Two regimes of sp3-type and vacancy-type defects are indicated by blue and brown areas. In the sp3-type regime (I(D)/I(G) ratio increases to B4.0), the elastic stiffness was maintained but then dropped precipitously in the vacancy-defect regime. By contrast, the breaking load continuously decreased in both the sp3-type and vacancy-type defect regimes.

Fig. 4), the strength of defective graphene is only B14% smaller than its pristine counterpart in the sp3-type defect regime. Our results provide a simple, non-contact and non-destructive approach to quantifying the mechanical properties of defective graphene samples. This involves measuring the intensities of the Raman D and 2D peaks with respect to the G peak. Using the direct mapping between the Raman parameters and the measured 2D elastic modulus and breaking load that we report (Fig. 4a,b), it is now possible to determine in a quantitative yet non-destructive manner how the mechanical properties of graphene vary as a function of its defectiveness. This has important practical implications for the design of a broad range of graphene-based devices such as chemical sensors7,8, ultra capacitors9, transparent electrodes10,11, photovoltaic cells12, biodevices1315, nanoelectronics24, DNA-sequencing through nanopores25 and selective molecular sieving through the nanopores of suspended graphene26.

In addition to the Raman study, we also carried out aberration-corrected high-resolution TEM (AC-HRTEM) characterization (Fig. 5) of the defective graphene lattice at both low and high oxygen plasma times. Figure 5a is representative of a graphene sheet in the sp3-defect regime (I(D)/I(G)B0.2 and I(2D)/

I(G)B1.5) while Fig. 5b is typical of a graphene sample in the vacancy-defect regime (I(D)/I(G)B2.0 and I(2D)/I(G)B0.2). Both TEM images show the presence of polymer residue (associated with the transfer process3 onto the TEM grid, see Methods). However, it is evident that while Fig. 5b indicates an abundance of nanocavities (that is, etch pits) in the graphene lattice (representative of the vacancy-defect regime), Fig. 5a shows a contrasting absence of such cavities. The black dots (circled in Fig. 5a,b) are sp3 point defects that correspond to oxygen

adatoms52. The upper and lower insets in Fig. 5a show experimentally obtained TEM image and the corresponding simulated image of an oxygen atom attached to sp2 carbon. The settings (Cs: 0.005 mm, Scherzer focus: 53 , operated at

80 keV) in the simulated TEM image is identical to what was used in the experimental image (see Methods). These images conrm that sp3 point defects in the form of oxygen adatoms are generated in the sp3-defect regime, while with increasing plasma exposure carbon atoms are etched from the lattice, resulting in the formation of nanocavities or nanopores in the vacancy-defect regime. Energy dispersive spectroscopy analysis (Supplementary Fig. 5) of the graphene suspended over the holes of the TEM grid also conrmed a signicant increase in the oxygen content even at short plasma times (in the sp3-type defect regime) as compared with pristine graphene.

It should be noted that our AFM nanoindentation technique reveals only the spatially averaged mechanical properties of the defective graphene sheet; the indented area in our testing is at least 4,500 nm2 (67 67 nm2), which contains at least 86,550

carbon hexagons (that is, at least 17,3100 carboncarbon bonds). However, a recent study53 that used topographical AFM imaging on wrinkled GO and wrinkled chemically reduced GO sheets revealed signicant local heterogeneity in the in-plane elastic modulus of such chemically modied carbon nanomaterials. The elastic modulus of GO produced by the chemical oxidation of graphene sheets was found to vary between 0.42 and 0.11 TPa owing to defect concentration or clustering of different functional groups. They determined the average elastic modulus for GO to be B0.23 TPa; this is in reasonable agreement with the samples with the highest plasma exposure (Fig. 4a) that we tested, which showed elastic modulus of B0.3 TPa. For chemical vapour-

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Polymer Residue

Etch pits

Figure 5 | AC-HRTEM characterization of defect structures. Images of a typical graphene sheet in (a) sp3-type and (b) vacancy-type defect regime. Polymer residue associated with the transfer process onto the TEM grid is indicated by arrows. The defective graphene of the vacancy-type defect regime contains an abundance of nanocavities (that is, etch pits), while the defective graphene of the sp3-type defect regime shows a contrasting absence of such cavities. The black dots circled with dashed lines in a and b are oxygen adatoms. The insets of a show the experimentally obtained TEM image (upper) and the corresponding simulated image (lower) of oxygen atoms bonded to carbon forming sp3 point defects. Scale bars, 2 nm (a,b).

deposited graphene, ref. 53 reported far less spatial heterogeneity in elastic properties with an averaged elastic modulus of B0.91 TPa, which shows good agreement with our result (B1 TPa) for pristine graphene (Fig. 4a). Another striking observation in ref. 53 was that the heterogeneities introduced during synthesis of GO were not removed in chemically reduced GO with the material still exhibiting signicant spatial heterogeneity (the elastic modulus of chemically reduced GO varied between B0.82 TPa and B0.36 TPa). This is important because mechanical failure is typically dictated by the weaker (or the more defective) regions. This is consistent with our results for breaking load (Fig. 4b), which indicate a higher sensitivity of the failure load to defects as compared with the elastic modulus.

In addition to the aforementioned experiments and defect characterization studies, we also performed atomistic modelling using the MD simulator, LAMMPS (large-scale atomic/molecular massively parallel simulator). The reactive force eld (ReaxFF) potential used in this study is specially trained for simulation of hydrocarbon oxidation54 and can simulate continuous bond formation and breakage55. In the simulations, oxygen atoms are placed on both sides of the graphene sheet (Fig. 6a) and kept stationary during equilibration. The graphene is equilibrated for 2 ps in the isobaric-isothermal ensemble at 300 K and zero pressure in all directions with a NoseHoover thermostat for temperature control and a time step of 0.2 fs (Fig. 6b). Much longer equilibration periods were run in separate tests to insure that 2 ps would sufciently equilibrate the systems under the given conditions. Post-equilibration, random velocity vectors corresponding to 300 K are assigned to oxygen atoms (Fig. 6c). Microcanonical ensemble with a time step of 0.2 fs is used to run the simulation since the local temperature rise due to collision of carbon and oxygen atoms has a vital role in driving the reactions. Therefore, no external heat bath (that is, thermostat) was used as in ref. 56. Note that the oxygen plasma cleaner used in the experiments generates a cold (or non-thermal) plasma. Since we are simulating cold plasma, the velocity that is given to the oxygen atoms is considered to be equivalent to room temperature (300 K). The simulation ends after the oxygen has completely etched away the entire carbon network (Fig. 6d).

We considered four different numbers of oxygen atoms: 750, 1,000, 1,500 and 4,500 in the simulations corresponding to varying oxygen pressures. These simulations are representative and have been selected from a large pool of runs of stochastically

similar systems. The number of carbon atoms in the graphene sheet was kept constant at 1,500. In the Supplementary Discussion, we plot the number of carbon atoms removed from the graphene lattice by the oxygen plasma and the number of chemisorbed oxygen atoms normalized by the total number of carbon atoms in the graphene lattice as a function of the plasma time (Supplementary Fig. 6). The result resembles a cumulative Weibull distribution with the following three distinct regimes: (1) incubation period, (2) an intermediate regime and (3) a terminal regime. The incubation period corresponds to before the chemisorption of oxygen sets in. The intermediate regime is when oxygen atoms attach to the graphene lattice and generate defects. The terminal regime corresponds to fast growth, percolation and coalescence of defects resulting in large cavities in the lattice. During the terminal regime the number of carbon atoms removed from the graphene lattice increases sharply culminating in the complete breakup of the graphene structure. The structures formed and evolved during the intermediate regime are of interest for this study.

Let us consider the case of 1,000 oxygen atoms in the simulation. For this case, the incubation period ends and intermediate regime begins at B200 ps, while the terminal region begins after B320 ps of plasma time (Supplementary Fig. 6). The time period from 200 to 350 ps was divided into 10 equal subintervals and 10 structures corresponding to the end of each time interval, and the initial graphene structure at 200 ps were selected for uniaxial tensile testing. The tensile loading simulations were performed at 300 K using a NoseHoover thermostat for temperature control and a time step of 0.2 fs while maintaining zero pressure in the lateral (that is, armchair) direction. The calculated 2D elastic stiffness and ultimate strength for these 11 structures are plotted in Fig. 6e. The results mirror our experimental observations in that the elastic stiffness does not degrade signicantly up to B310 ps (corresponding to sp3-defect regime), after which we see a rapid loss in elastic stiffness in the terminal regime, which corresponds to the vacancy-defect regime of Fig. 4a. The MD simulations qualitatively capture the experimental observations and shed light onto how defects inuence the mechanical properties of graphene. The strength predictions (Fig. 6e) show a gradual decrease in strength up to B310 ps (in the sp3-defect regime) followed by a much more precipitous drop in the vacancy-defect regime (at 350 ps), which is also consistent with our experimental observations. It should be

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equilibration of graphene sheet (time 2 ps). (c) During the plasma treatment (time 6.2 ps). (d) At the end of the simulation (time 400 ps).

(e) Calculated 2D elastic modulus and ultimate strength for the structures generated in the simulation with 1,000 initial oxygen atoms and 1,500 carbon atoms in the graphene sheet. (f) Series of snapshots at various times in the simulation showing chemisorption of oxygen as carbonyl, epoxide and ether groups and structural reorganization of the graphene lattice leading to the removal of carbon atoms in the form of carbon dioxide at 279.2 and 320.6 ps. (g) An example of defect coalescence (at 338.6 ps) initiated by an ether group.

noted that the predicted 2D elastic modulus for pristine graphene is B420 N m 1 (corresponds to B1.2 TPa Youngs modulus), which overestimates the elastic modulus of pristine graphene (B1 TPa). This is because the ReaxFF potential that was used in our study is not fully optimized (calibrated) for mechanical properties prediction. The choice of the ReaxFF potential in our work was dictated by its ability to simulate hydrocarbon oxidation as well as the continuous formation and breakage of bonds.

To explain why the elastic stiffness of the graphene sheet shows lower sensitivity to defects as compared with its breaking strength, we considered the structure of the chemisorbed oxygen and the processes of carbon atom removal from the graphene lattice. During the simulation, carbonyl groups are initially formed because of the chemisorption of oxygen (Fig. 6f). Increasing numbers of chemisorbed oxygen atoms then result in the formation of epoxide and ether groups. This

functionalization of the graphene lattice with carbonyl, epoxide and ether groups involves rupture of some CC bonds that introduces discontinuities in the graphene lattice as indicated in Fig. 6f. Breaking of CC bonds lowers the strength of the graphene sheet, which explains why the strength gradually drops in the experiments and in the simulations with the chemisorption of oxygen functional groups. Unlike strength, localized disruptions to the carbon bonding network does not signicantly lower the elastic stiffness of the 2D graphene structure. However, the situation changes beyond 320.6 ps of plasma time when signicant numbers of carbon atoms are physically removed (Fig. 6f) from the graphene lattice. More importantly, as the density of defects increases (332.6 ps in Fig. 6g), adjacent defects coalesce to form bigger voids or extended cavities (338.6 ps in Fig. 6g). At this stage large numbers of carbon atoms are rapidly removed from the graphene lattice, which results in a precipitous drop in elastic stiffness and strength as the graphene structure

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4186

breaks apart. The formation of nanocavities in the graphene lattice in the vacancy-defect regime is also corroborated by ACHRTEM imaging of the graphene sheet (Fig. 5b).

To summarize, over the entire sp3-type defect region, the 2D elastic modulus and strength of graphene is relatively insensitive to defects, even at a spacing LD of B5 nm. This has important implications for design of graphene-based composite materials since it indicates that graphene can be covalently bonded to polymer matrices without sacricing its reinforcing abilities. Only in the vacancy-defect regime, when the plasma begins to etch the graphene sheet and remove large numbers of carbon atoms, does the elastic modulus and strength of graphene begins to degrade signicantly. The direct mapping between the Raman signature of defective graphene and its mechanical properties that we provide allows for a simple and non-destructive methodology to predict the 2D elastic modulus and breaking strength of defective graphene without actually testing it. These results could enable the rational design of graphene composites as well as mechanically stable graphene membranes for a variety of applications.

Methods

Sample preparation. To fabricate array of holes with various diameters of0.5B5 mm, a Si wafer with 300 nm SiO2-capping layer was patterned by conventional photolithography and reactive ion etching. The depth of hole is B1 mm for indentation test. The graphene sheets were deposited on the patterned substrate by the well-established Scotch tape method2,18. A benchtop radio frequency oxygen plasma cleaner (Plasma Etch Inc., PE-50 XL, 100 W) was utilized for introducing defects in graphene. To increase the controllability of defect generation, the chip was ipped and placed upside down on two carefully cleaned glass slides in the oxygen plasma chamber (Supplementary Fig. 1). For the AC-HRTEM imaging, the pristine samples were transferred to a TEM grid using poly(methyl methacrylate) transfer method3. After removal of poly(methyl methacrylate) by annealing, the samples were then exposed to oxygen plasma irradiation in the same manner.

Characterization of defects. The type and density of defects in the graphene sheets were characterized using Raman spectroscopy (Renishaw, invia with 532 nm wavelength laser and 0.7 mm spot size). For high-resolution imaging of vacancy-type defects, suspended graphene samples exposed by the oxygen plasma were carefully scanned by AFM with ultra-sharp diamond-like carbon tip (NT-MDT, NSG01_DLC) with a small tip radius of o1 nm. HRTEM instruments (JEOL, JEM-2100F with double Cs correctors, operated at 80 keV and JEOL, JED-2300T) were used for high-resolution imaging and energy dispersive spectroscopy, respectively. TEM image simulation of oxygen adatom (an oxygen atom attached to sp3 carbon) was conducted using settings (Cs: 0.005 mm, Scherzer focus: 53 , operated at

80 keV) that are identical to that used in the experiments to acquire the images.

AFM nanoindentation. The precise nanoindentation on the suspended graphene was performed using AFM (Park Systems, XE-100). Before each indentation, the samples were scanned in non-contact mode to nd graphene sheets fully covering a hole. After scanning, the diamond AFM tip (MicroStar Tech) was centred in the middle of the circular hole. Mechanical testing was performed using force displacement mode. When non-trivial hysteresis was observed (presumably due to slippage of the graphene on the substrate), their corresponding data were discarded. The nonlinear force versus displacement curves obtained from the AFM nanoindentation tests were used to quantitatively determine the elastic stiffness and breaking load of defective graphene following the model described in refs 2 and 3.

MD simulations. LAMMPS was used for MD simulations as it has been extensively tested and successfully used for modelling solid, liquid and gaseous systems using different force elds and boundary conditions. For the purpose of atomistic modelling of graphene and its chemical reactions with oxygen, ReaxFF potential was used. The ReaxFF used in this study is specially trained for simulation of hydrocarbon oxidation54 and is able to bridge the gap between quantum chemical and empirical force eld-based computational chemical methods54,55. In the initial state, the oxygen atoms are placed not closer than 1 nm from the graphene sheet surface. This distance is intentionally selected to be larger than the nearest neighbour cutoff distance (0.45 nm) to avoid initial interactions between oxygen atoms and the graphene sheet. To remove the in-plane pressure from graphene (pressure components along x and y directions), graphene is equilibrated for 2 ps in the isobaric-isothermal ensemble at 300 K and zero pressure in all directions with a NoseHoover thermostat (Tstart, Tstop of 300 K and Tdamp of 10 K) for temperature control and a time step of 0.2 fs. After equilibration, random velocity vectors corresponding to 300 K are assigned to the oxygen atoms. The carbon atoms already have velocities corresponding to 300 K. This is followed by running

the simulation in the microcanonical ensemble with a time step of 0.2 fs and without coupling the system to an external heat bath using a thermostat56. Additional information is provided in the Supplementary Discussion.

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Acknowledgements

N.K. and C.R.P. acknowledge the funding support from the US Ofce of Naval Research (Award Number: N000140910928) and the US National Science Foundation (Award Number: 1234641). N.K. also acknowledges support from the John A. Clark and EdwardT. Crossan endowed chair professorship at the Rensselaer Polytechnic Institute. J.H. acknowledges support from AFOSR MURI Program on new graphene materials technology, FA9550-09-1-0705, and G.-H.L. acknowledges the support from Samsung-SKKU Graphene Center. We thank Ryan Cooper and Jeffrey W. Kysar for fruitful discussion.

Author contributions

A.Z. and G.-H.L. contributed equally to this work. A.Z. and G.-H.L. jointly designed the AFM, plasma and Raman characterization tests. A.Z., G.-H.L., S.L. and S.J.A. jointly prepared the samples, performed the AFM and Raman characterization tests, and analysed the data. A.Z. and N.M. designed and prepared the LAMMPS simulation set-ups and post-processing scripts. M.T. and T.H. performed the HRTEM, energy dispersive spectroscopy characterization and analysis. N.K. and C.R.P. supervised the study at Rensselaer Polytechnic Institute. J.H. supervised the study at Columbia University. A.Z., G.-H.L., C.R.P., J.H. and N.K. wrote the manuscript.

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How to cite this article: Zandiatashbar, A. et al. Effect of defects on the intrinsic strength and stiffness of graphene. Nat. Commun. 5:3186 doi: 10.1038/ncomms4186 (2014).

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Abstract

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It is important from a fundamental standpoint and for practical applications to understand how the mechanical properties of graphene are influenced by defects. Here we report that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp(3)-type defects. Moreover, the breaking strength of defective graphene is only ~14% smaller than its pristine counterpart in the sp(3)-defect regime. By contrast, we report a significant drop in the mechanical properties of graphene in the vacancy-defect regime. We also provide a mapping between the Raman spectra of defective graphene and its mechanical properties. This provides a simple, yet non-destructive methodology to identify graphene samples that are still mechanically functional. By establishing a relationship between the type and density of defects and the mechanical properties of graphene, this work provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.

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Title

Effect of defects on the intrinsic strength and stiffness of graphene

Author

Zandiatashbar, Ardavan; Lee, Gwan-hyoung; An, Sung Joo; Lee, Sunwoo; Mathew, Nithin; Terrones, Mauricio; Hayashi, Takuya; Picu, Catalin R; Hone, James; Koratkar, Nikhil

Pages

3186

Publication year

2014

Publication date

Jan 2014

Publisher

Nature Publishing Group

e-ISSN

20411723

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1038/ncomms4186

ProQuest document ID

1491277851

Effect of defects on the intrinsic strength and stiffness of graphene

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