Unprecedented Strength in Centimeter-Scale Single-Crystal Monolayer Graphene

Unprecedented Strength in Centimeter-Scale Single-Crystal Monolayer Graphene | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Unprecedented Strength in Centimeter-Scale Single-Crystal Monolayer Graphene Anirban Kundu, Seyed Kamal Jalali, Minhyeok Kim, Meihui Wang, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5223363/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Despite extensive microscale studies, the macroscopic mechanical properties of monolayer graphene remain underexplored. Here, we report the Young’s modulus (E = 1.11 ± 0.04 TPa), tensile strength (σ = 27.40 ± 4.36 GPa), and failure strain (ε f = 6.01 ± 0.92 %) of centimeter-scale single-crystal monolayer graphene (SCG) ‘dog bone’ samples with edges aligned along the zigzag (zz) direction, supported by an ultra-thin polymer (polycarbonate) film. For samples with edges along the armchair (ac) direction, we obtain E = 1.01 ± 0.10 TPa, σ = 20.21 ± 3.22 GPa, ε f = 3.69 ± 0.38 %, and for chiral samples whose edges were between zz and ac, we obtain E= 0.75 ± 0.12 TPa, σ = 23.56 ± 3.42 GPa, and ε f = 4.53 ± 0.40 %. The SCG is grown on single crystal Cu(111) foils by chemical vapor deposition (CVD). We used a home-built ‘float-on-water’ (FOW) tensile testing system for tensile loading measurements that also enabled in situ crack observation. The quantized fracture mechanics (QFM) analysis predicts an edge defect size from several to tens of nanometers based on chirality and notch angle. Through Weibull analysis and given that the fatal defects are confined on the edges of macroscale samples, we projected strength ranging from 13.67 to 18.43 GPa for an A4-size SCG according to their chirality. Our findings demonstrate exceptional mechanical performance of macroscale single crystal graphene (SCG) and pave the way for its widespread use in a very wide variety of applications. Nanoscience Single Crystal Graphene High Tensile Strength Near-ideal Stiffness Chiral Dependency Damage Evolution Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction There are very few materials that exhibit particularly high strength at macroscale (centimeter and larger), whereas many materials can exhibit ‘ideal strength’ at microscale (microns and smaller) 1 . Ideal strength refers to the theoretical maximum stress a material can withstand without failure when it is free of any defects or imperfections. As one example, ‘ultrahigh strength’ commercial carbon fibers have tensile strength of 7 GPa 2 , but the ‘ideal’ in-plane strength of defect free graphite, (and graphene and carbon nanotubes), is ~ 120 GPa 3 , 4 . It is important not to confuse strength with modulus, which measures the material's stiffness (or resistance) to deformation, rather than the maximum stress it can endure. We note that strength is a kinetic, not thermodynamic, parameter. The ‘ideal tensile strength’ of graphene could be thus taken as a well calculated value of the stress-at failure (at 0K or around room temperature, no reactive species present in such a calculation). It comes as no surprise that exfoliated (or CVD grown) graphene samples can exhibit ‘ideal’ strength values when tested at the micron length scale 5 , 6 : at this length scale a reasonably high fraction of samples will have no defects. At larger length scale (millimeters, centimeters, and up) it is much more likely that graphene ( or any other material ) will have defects, referred to as “flaws” by the solid mechanics community 7 . Such defects are ‘stress concentrators’, and the far field tensile stress on a sample can be much larger very close to flaws 8 , thus failure of macroscale samples of almost all materials occurs at a much lower stress than the ideal strength 9 . This is the influence of length scale on the fracture strength of real materials 10 , 11 . To the best of our knowledge, only ultralong (few millimeter of gauge length) carbon nanotubes (CNT) 4 , 12 exhibit “macroscale” ideal tensile strength . A few types of glass fiber also show macroscale tensile strength close to their ideal limit 2 . If graphene had high strength at large length scales and was produced at large scale (such as A4-size sheets in great quantity) and moderately inexpensive, it would have a very wide range of applications where it finds no use now . Nanoindentation on exfoliated graphene of micron-scale size led to reported values of \(\:E\) ~ 1.0 TPa and \(\:\sigma\:\) of ~ 130 GPa 5 . Theoretical calculations based on density functional perturbation theory (DFPT) had predicted \(\:E\) and ideal strength \(\:\) values as 1 ± 0.1 TPa and 100–130 GPa, respectively 3 . Advances in chemical vapor deposition (CVD) of graphene 13 – 15 have enabled the production of large-scale, single-crystal monolayer graphene (SCG) 16 , 17 . The mechanical properties of CVD graphene have been characterized by atomic force microscopy (AFM) nanoindentation 6 , 18 , indentation in scanning electron microscopy (SEM) 19 , and push-to-pull (PTP) tensile tests in SEM 20 : these studies were on microscale sized samples. While microscale CVD-grown graphene has demonstrated high \(\:E\) values, its tensile strength can be lower than ideal due to point defects, grain boundaries, and edge defects 21 – 24 . But many samples at the micron length scale are readily achieved that show ideal strength by, e.g., nanoindentation. The tensile loading response of centimeter-scale single-layer graphene using dynamic mechanical analyzer (DMA) in conjunction with a camphor-assisted transfer process 23 , yielded \(\:E\) values up to 737 GPa. Recently, SCG was fabricated using the CVD method, which has a large area (centimeter scale) defect-free, adlayer-free graphene 16 , 17 . Transferring large-scale graphene remains challenging, as defects can be introduced in atomically thin monolayer graphene during the multistep transfer process 25 , 26 . However, we can transfer centimeter scale graphene/polymer films on target substrate, especially on silicon wafer 16 or liquid surface. The “float on water” (FOW) tensile test techniques have been used to measure tensile loading response of millimeter-scale ultrathin polymer films 27 , 28 . We have tested this method on single- SCG as we describe further below- and it has worked very well for macroscale SCG supported by thin polymer film. We report tensile loading of 1 cm long, 2 mm wide, SCG with graphene adhered to a 200 nm thick polycarbonate (PC) layer, and analysis of stress-strain curves to obtain the Young’s modulus ( \(\:E\) ), and stress ( \(\:\sigma\:\) ) and strain at failure ( \(\:{\epsilon\:}_{f}\) ). We discovered that crack initiation and subsequent propagation within graphene is controlled by the graphene crystal orientation, armchair (ac) or zigzag (zz). Through modeling we anticipate the mechanical response of stacked graphene-polymer layers with a model system that mitigates the impact of edge defects. We elucidate the fracture mechanics of macroscale SCG, and the exceptionally high tensile strength values observed open avenues for its wide application in automobile and transportation (trains, planes) sectors, large scale optoelectronic devices, straintronics, etc. Results and Discussions Tensile Test Measurements in FOW System We conducted uniaxial tensile measurements on SCG films utilizing the FOW system. The primary objective of our study was to investigate the mechanical response in macroscale SCG films. We used a thin layer of Poly(bisphenol-A-carbonate) (PC) as the support material for our SCG films because the inherent ultrathin nature (~ 0.34 nm) and brittleness of SCG have, to date, made it challenging to prepare a freestanding macroscale sample suitable for tensile measurement. This choice was made due to three key factors: First, PC exhibit high optical transparency, a crucial property for the FOW system’s accurate measurement capabilities. Second, the PC possesses considerable mechanical strength, ensuring minimal interference with the SCG film’s intrinsic behavior during the tensile testing process 29 . Third, PC’s higher tensile failure strain than SCG ensures full support until its failure point. This allows us to isolate the effects of the SCG film’s properties on its mechanical response. SCG was synthesized on Cu(111) foils using thermal CVD. Raman spectroscopy of as-grown SCG on Cu (111) showed an \(\:{I}_{2D}/{I}_{G}\) ratio of 2.56 and a 2D full width at half maximum (FWHM) of 35.16 cm − 1 (Fig. S12) 16 . SCG on the SCG-PC films was verified using Raman spectroscopy (Fig. 1 c). In the Raman spectra of SCG-PC, the intense G (~ 1584.9 cm − 1 ) and 2D (~ 2667.1 cm − 1 ) peaks with negligible D peak confirm the high quality of this single crystal graphene. We observed a blueshift in G (~ 3.3 cm − 1 ) and 2D (~ 15.1 cm − 1 ) band after removal of PC film, which is attributed due to the removal of strain generated at the interface between the PC and SCG. PC/chloroform solutions were spin-coated onto the as-grown SCG/Cu(111) samples, with thickness variation controlled by adjusting the spin speed. AFM was used to determine film thickness (Fig. S13 and S14). PC and SCG-PC samples were designated based on their PC film thickness, as detailed in Tables S2-S3. A “dogbone’ cutter (model no. SDMP-1000 and JISK 6251-7) was then used to cut out dog bone specimens (with gauge length 10 mm, width 2 mm, see Fig. S15), from which the Cu(111) was etched away, as described in Fig. S16. Thus, the dog bone 200 nm SCG-PC samples were floated on water and attached to the FOW system components that apply tensile loading with van der Waals type adhesion clamping. The tensile tests were done on samples floating on the water surface at room temperature under constant displacement rates of 0.002 mm/s, equivalent to a strain rate of 0.0002 (mm/mm)/s (Fig. 1 a-b). The mechanical properties of similar 200-nm thick PC films (with no graphene) were characterized independently using the FOW system. Figure 1 d shows the stress-strain curves for 200 nm PC and SCG-PC films. Complete stress-strain curves are presented in Fig. S17c and S18c. Monochromatic imaging showed wrinkles in bare PC films even at 0% strain (Fig. 1 e) due to their intrinsic flexibility 30 , while SCG-PC films were smooth (Fig. 1 f), indicating uniform contact with the water surface facilitated by the SCG’s flatness. At 5% strain, both films displayed horizontal lines perpendicular to the displacement direction within the gauge area, indicating stress concentration zone(s) (Fig. 1 e-f, detailed analysis in Fig. S19 and Fig. S20). The higher density of such lines in the SCG-PC film suggests greater stress than the bare PC film due to SCG’s higher strength, leading to earlier failure (~ 7.69%) compared to bare PC (> 20%) films. Mechanical properties of PC and SCG-PC films are summarized in Tables S4-S5. The SCG-PC films exhibited roughly 1.5 times higher \(\:E\) and \(\:\sigma\:\) compared to bare PC films. By using these values, we extracted \(\:E\) and \(\:\sigma\:\) values for SCG using the rule of mixtures according to the following equation: $$\:{E}_{SCG-PC}={E}_{PC}\frac{{t}_{PC}}{{t}_{PC}+{t}_{SCG}}+{E}_{G}\frac{{t}_{SCG}}{{t}_{PC}+{t}_{SCG}}$$ 1 where \(\:{E}_{SCG}\) and \(\:{E}_{PC}\) are the Young's modulus values for SCG and PC, respectively, and \(\:{t}_{SCG}\) and \(\:{t}_{PC}\) are the thicknesses of graphene and PC, respectively. Figure 1 g compares the \(\:E\) , \(\:\sigma\:\) , strain at maximum stress, and failure strain of SCG, SCG-PC, and PC films (a total of 25 combinations as summarized in Table S6). The highest \(\:E\:\) value for SCG was 970.5 GPa (Table S6), approaching microscale monolayer graphene’s modulus measured by a push-to-pull (PTP) micromechanical device 20 . In our initial investigations, the edge orientation (zigzag or armchair) of SCG was not controlled during the preparation of dog bone samples, resulting in chiral SCG edges. The maximum tensile strength we observed was 30.48 GPa (Table S6), representing a nearly tenfold increase compared to the yield strength of previously reported macroscale graphene 23 . However, this value remains lower than the theoretical tensile strength of graphene. This is likely due to edge defects in SCG introduced during mechanical cutting, as observed by SEM (Fig. S21) and TEM (Fig. S22a-b) analyses. TEM imaging shows the presence of nanometer-sized defects or cracks along the SCG edge. The average \(\:E\) and \(\:\sigma\:\) across 25 combinations (of five chiral SCG-PC and 5 bare PC samples) were 748.9 ± 121.9 GPa and 23.56 ± 3.42 GPa, respectively (Fig. 1 g). The ideal strength of monolayer graphene, approximately 130 GPa, has been observed at an applied strain reported as 25% 5 . In our study here, the failure of chiral SCG occurred at an average strain of 4.53%, which corresponds to an estimated strength of 41.2 GPa at this strain (with \(\:E=\) 1 TPa and the third order modulus, \(\:D=\) 2 TPa) 5 . While the average \(\:E\) is comparable to previous macroscale results obtained using a DMA system on free-standing graphene/polymer films 23 , increased strength and failure strain is observed showing our approach (FOW measurement system and SCG) yields significantly higher values. While the DMA test 23 , reported a yield strain of 0.6% and the corresponding strength of 3.33 GPa, our chiral SCG samples carry substantially higher stress of 5.58 GPa at a strain of 0.6%. This improvement can be attributed to the absence of grain boundaries and adlayers in our single-crystal SCG, and utilizing an optimal polymeric substrate with a 200 nm thickness compared to 100 nm 23 (see the supplementary section 4 on role of polymer thickness). Note that defining the strength of a centimeter-scale SCG solely by its yield stress underestimates its capacity. Although microcrack initiation can cause a deviation from linearity, our chiral SCGs smoothly continued to bear loads at stress levels up to 23.56 GPa, demonstrating their full failure strength—7.08x greater than the previously reported yield stress. This highlights the well-known concept of damage tolerance , where macroscale SCG, like many materials, can redistribute stress after the initiation of damage, thereby delaying total failure 31 , 32 . The crack initiation and propagation were visualized such as shown in supplementary Video S1. This video correlates the mechanical response with the formation and growth of a notch on the SCG-PC film. We observed that the strain at maximum stress of a SCG-PC sample denotes the failure strain of the SCG. The measured failure strain of macroscale SCG (~ 4.53%) was comparable to microscale measurements by the push-to-pull method (~ 5.8%) 20 . Lower SCG failure strain compared to the theoretical limits (that are reported to be approximately 13–19% along the armchair and 20–26% along the zigzag direction) 33 – 35 likely originated due to the existence of critical edge defects as discussed (through QFM analysis) in the model prediction section later. The similarity between the SCG failure strain and the strain at maximum stress of bare PC (Table S4-S5) suggests that the failure strain of SCG is influenced by the strain at the point of maximum stress in the PC layer. Mechanical property variation of SCG with PC thicknesses (with different \(\:E\) and \(\:\sigma\:\) ) are discussed in supplementary section 4. Identification of Crack Initiation and Propagation in Macroscale SCG The transparent PC substrate in SCG-PC films allows direct visualization of crack initiation and propagation within the SCG layer (Fig. 2 a-f). At 2% applied strain, stress concentration zones (SCZ) become evident, primarily at the edges (see Fig. 2 c). The reason for observing the SCZs at ~ 2% can be attributed due to the transition from linear to non-linear response in the polymer’s stress-strain curve (see Fig. S16c). With increasing strain, the SCZs intensity manifests as horizontal lines to the loading direction (Fig. 2 c-d). At 3% strain, a significant increase in the density of horizontal lines at SCZs shows the initiation of macrocrack propagation (Fig. 2 g-h). An observed crack appears in SCG at 3.5% strain, originating from an existing SCZ (Fig. 2 h). Simultaneously, new SCZs emerge at other edges on the top of the SCG-PC film (Fig. 2 i), serving as potential sites for further crack initiation. This process continues, ultimately leading to complete failure of the SCG layer. Crack identification is facilitated by the distinct contrast between SCG (bright white lines) and the PC layer (Fig. 2 i-k). A crack that initiates at one edge appears to trigger the formation of a complementary crack on the opposite edge. These cracks then propagate in opposite directions, culminating in complete SCG failure (Fig. 2 l). Even after SCG failure, the PC layer with fragmented SCG on its surface continues to elongate under tensile stress, and the SCG-PC film (Fig. S20) exhibits a faster breakdown compared to the bare PC films (Fig. S19) due to its higher ultimate stress. To further analyze crack characteristics, tensile testing was interrupted at various strain points, and the SCG films were transferred to a Si/SiO 2 wafer for SEM analysis. Chloroform treatment removed the PC layer, exposing the SCG morphology. Fig. S23 compares the effect of tensile loading on SCG at the crack initiation point and the failure strain of SCG. Smaller microcracks parallel to the main macrocrack were observed at initiation, likely contributing to its propagation until complete SCG failure. Further analysis (Fig. S23c-d) revealed that the crack angles were multiples of approximately 30 o , reflecting that the crack in SCG propagates along armchair or zigzag directions. Microcracks were parallel to each other and perpendicular to the elongation direction, while larger macrocracks tended to align with the armchair or zigzag edges of graphene (Fig. S23e-f). These observations suggest that crack propagation in SCG is influenced by both stress concentration points at opposing edges and the intrinsic defects of graphene. Mechanical Properties of SCG along armchair (ac) and zigzag (zz) directions The zigzag (zz) edge of SCG grown on Cu(111) preferentially aligns with the Cu direction, while the armchair (ac) edge aligns with the Cu(112) direction (see Fig. 3 a) 36 . The Cu direction can be optically identified from rolling marks on the Cu foil (Fig. 3 b) as confirmed by electron backscatter diffraction (EBSD) data (Fig. S35). To determine the orientation of graphene edges relative to Cu rolling marks, hexagonal SCG islands were grown on Cu(111) (Fig. 3 c, Fig. S36). The angle between the edge of SCG islands and rolling marks was calculated from optical and SEM images as 90.79 ± 0.27 o and 90.14 ± 2.06 o , respectively (Fig. S36). Polarized Raman spectroscopy performed on marked (black dotted line) graphene edges on Cu(111) foil (Fig. 3 c) showed an increase in the G peak intensity with the angle between incident and scattered light (varied using the analyzer), which also confirmed that the edge perpendicular to the rolling marks corresponds to the zz edge of SCG 37 (Fig. 3 d). Polymer coated SCG/Cu(111) foils were aligned with the rolling marks and cut to prepare dogbone-shaped SCG-PC samples with zz (perpendicular) and ac (parallel) edges. The perpendicular orientation (~ 89.24 ± 0.82 o ) denotes the dogbone sample with zz edge, while the parallel orientation (~ 0.63 ± 1.27 o ) denotes the ac edge; see supplementary Fig. S37. Polarized Raman spectra at these perpendicular and parallel edges are shown in Fig. S38. We performed TEM imaging at the edge of SCG parallel to the rolling marks. The diffraction pattern (Fig. S21c) and high resolution TEM image (Fig. S21d) confirms the ac direction along the edge 38 . Stress-strain curves were obtained from tensile loading in the FOW system along the zigzag (Fig. 3 e) and armchair (Fig. 3 f) direction for these different dogbone samples. The average \(\:E\) values for ac and zz SCG-PC samples were 3.53 GPa and 3.68 GPa, respectively, while the average \(\:\sigma\:\) values were 99.8 MPa and 110.7 MPa, respectively. We thus observed 1.12 times (99.8 to 110.7 MPa) enhanced strength for zz SCG-PC samples, and similar \(\:E\) values. The ac SCG-PC samples showed a higher average failure strain of 10.10% compared to 7.79% for zz SCG-PC samples. The mechanical response of zz and ac SCG-PC samples are summarized in supplementary Table S10. The mechanical properties ( \(\:E\) and \(\:\sigma\:\) ) of zz-SCG and ac-SCG were obtained by comparing the stress strain curves in Fig. 3 e-f (and supplementary Fig. S39) with those of bare PC films (200 nm thick). \(\:E\) values for zz- and ac-SCG were 1.11 ± 0.04 TPa and 1.01 ± 0.10 TPa, respectively. The average strength for zz-SCG was 27.40 ± 4.36 GPa, while that for ac-SCG was 20.21 ± 3.22 GPa. Chiral SCG (with edge orientations not aligned to zz or ac) samples exhibited an average strength of 23.56 ± 3.42 GPa (Fig. 3 g), falling between the average strength for zz- and ac-SCG. The mechanical properties ( \(\:E\) , \(\:\sigma\:\) and failure strain) of ac, zz, and chiral SCG are compared in Fig. 3 g. These results align with previously reported theoretical findings from density functional theory (DFT) and molecular dynamics (MD) simulations. 3 , 39 We compared the previously reported theoretical and experimental results with our experimental values in supplementary Table S13. Failure strains of ~ 3.69% and ~ 6.01% for SCG were observed for the ac and zz direction, respectively. Observation of higher strength and failure strain along the zz direction compared to the ac direction can be attributed to the larger bond angle variation along the zz direction. 39 , 40 Theoretical Model Predictions We now consider scaling from our current dimensions of 1 cm along the tensile loading axis with an area of 0.2 cm², to an A4-sized sheet. This results in scale ratios of \(\:R\) = 29.7 for length and 3118.5 for the area. According to the Weibull scale law provided in the Section 1 of supplementary information, the strength of a reference sample, \(\:{\sigma\:}_{0}\) (here our current samples), is related to the scaled strength, \(\:\sigma\:\) , (such as of an A4-sized sheet) by the power law, \(\:\sigma\:={\sigma\:}_{0}{\left(R\right)}^{-\frac{1}{\alpha\:}}\) , where \(\:\alpha\:\) is the Weibull modulus, which characterizes the material's statistical strength distribution 41 . To perform strength scaling, we fitted a Weibull distribution (Fig. S1) on the measured strengths of chiral, zz, and ac SCGs listed in Tables S6, S11, and S12. From this, the reference strengths of \(\:{\sigma\:}_{0}\) were determined to be 25.00, 29.24, and 21.54 GPa for chiral, zz, and ac SCGs, respectively. The Weibull moduli \(\:\alpha\:\) were 8.22, 7.35, and 7.46, corresponding to chiral, zz, and ac. When scaling by length, we assume the critical flaws are edge-confined, consistent with our experimental findings where failure initiates at the edge. For an A4-size SCG sample with \(\:R\) = 29.7, the predicted strengths for zz, chiral, and ac orientations are 18.43 GPa, 16.55 GPa, and 13.67 GPa, respectively. However, when scaling by area ( \(\:R\) = 3118.5), assuming surface-distributed flaws, the predicted strengths drop to 9.78 GPa, 9.39 GPa, and 7.32 GPa, indicating a significant reduction in strength due to the increased number of critical flaws; however as noted, the flaws were always identified at the edges, and not in the interior. To estimate the size corresponding to theoretical strength, we inversely scaled down by setting \(\:\sigma\:\) = 130 GPa and solving for \(\:R\) . For zz SCGs, the theoretical strength would correspond to a length of 0.174 µm and an area of 350 µm². Using the same approach, ac SCGs yield lengths of 0.015 µm and areas of 30.2 µm², while chiral samples result in 0.013 µm and 26 µm². These scaling estimates, from theoretical strength to A4-size sheets, are illustrated in Fig. 4 a. We did a fracture mechanics analysis using QFM (quantized fracture mechanics), which extends linear elastic fracture mechanics by introducing a fracture quantum 42 , as detailed in the Section 2 of supplementary information. This fracture quantum is calculated such that a crack length of zero exhibits an ideal strength of 130 GPa. Accordingly, we determine critical lengths of 6.23, 8.53, and 11.70 nm for a sharp crack at the edge of zz, chiral, and ac SCGs with the strength 27.40, 23.56, and 20.21 GPa, respectively. By substituting the sharp crack with a V-notch as the critical defect on the SCG edge 43 and assuming a notch angle of 30°, we find critical notch depths (perpendicular to the edge) of 13.43, 19.65, and 28.87 nm for zz, chiral, and ac SCGs, respectively. Figure 4 b illustrates the variation of the critical edge defect against the SCG strength. Finally, we used a damage evolution model to capture the softening behavior of SCG on an ultra-thin polymer substrate, as detailed in Section 3 of supplementary information. The calibrated nonlinear stress-strain curves, derived from the constitutive laws presented in Eqs. S30-S32, are plotted in Fig. 4 c. We also applied this model to a stack created by folding a SCG-PC sample, allowing us to predict the stack's stress-strain response, as shown in Fig. S9. We find that the folded SCG-PC sample with 100 layers of SCG-PC stacking can sustain a stress of 125.15 MPa at 4.53% strain, which is 1.80 times higher than the PC sample and 1.19 times higher than the SCG-PC sample. Conclusion We found near-intrinsic tensile loading mechanical properties in centimeter-scale single crystal monolayer graphene (SCG) measured with a float on water testing system. We report average values of \(\:E\) = 1.11 TPa and \(\:\) = 27.40 GPa along the zigzag edges of SCG, approaching the theoretical limits for graphene. Loading along the armchair edges yielded \(\:E\) = 1.01 TPa and \(\:\) = 20.21 GPa while chiral SCG exhibits had \(\:E\) and \(\:\sigma\:\) of 0.75 TPa and 23.56 GPa, respectively. Fitting a Weibull distribution on the experimental data set of the current sample size, i.e., 10 x 2 mm, we predict that if the fatal damage is initiated solely on the edges of a macroscale sample (as we observed in all samples), the strength of an A4-size SCG can range from 13.67 to 18.43 GPa depending on chirality with zigzag as the maximum, armchair the minimum, and chiral in between. Although edge defects and supporting layer slightly impact tensile strength, our findings confirm that optimizing the support layer thickness enhances stiffness. This study establishes the remarkable mechanical resilience of large-scale single crystal monolayer graphene , demonstrating a failure strain of up to 6.01% for tensile loading along the zigzag edge. The developed methodology of macroscale graphene mechanics, characterized by uniform and well-controllable tensile loading, offers potential for studying the mechanical properties of other 2D materials and their heterostructures. This work could advance graphene-based straintronics, large-scale optoelectronic devices through strain engineering, and industrial applications, particularly in the transportation sector. Experimental Methods Growth of Large-Area Single-Crystal Graphene To grow single-crystal single-layer graphene (SCG), 35 mm × 50 mm Cu(111) foils were loaded into a 40 mm diameter quartz tube with a uniform heating zone around 100 mm and placed at the center of the heating zone. First, the furnace was heated to 1060°C within 60 min in a 300 sccm Ar and 40 sccm H 2 atmosphere at 30 Torr pressure, followed by introducing 34 sccm 0.1 mol% CH 4 for 60 min while the temperature was held at 1060°C. The sample was then rapidly cooled to room temperature under the same gaseous conditions (300 sccm Ar, 40 sccm H 2 , and 34 sccm 0.1 mol% CH 4 ). The as-prepared SCG on Cu(111) was characterized using Raman spectroscopy and SEM to confirm the uniformity and quality of graphene. Preparation of Polycarbonate-Graphene Film (SCG-PC) Poly(bisphenol A carbonate) [PC] from Sigma-Aldrich (average Mw ~ 45000) was dissolved in chloroform, and 0.5-5 wt% solutions were prepared. PC/chloroform solution was spin-coated at a speed of 3000 RPM on bare Cu(111) foil to prepare PC films and on Gr/Cu(111) foil to prepare SCG-PC films. The thicknesses of the PC and SCG-PC films were measured by AFM after transferring the sample onto Si/SiO 2 wafers. Tensile Test Measurement Setup : The Float-on-Water (FOW) measurement setup was built by assembling two critical components: (i) a force sensor (model no. LTS-100GA from the Kyowa Electronic Instruments Co. Ltd.) and (ii) a displacement motor (model no. C863 from Physik Instrumente (PI)). The force exerted upon the samples due to displacement was recorded using a Kyowa sensor interface (Model No: PCD-430A). Monochromatic images of the thin films were captured using the Allied Vision camera (Model No: Manta G-146B). Mechanical Cutter PC-coated graphene films and bare PC films on Cu foil were transferred into the mechanical cutter (model no. SDMP-1000 and JISK 6251-7 from Dumbell Co. Ltd.) and cut into "dumbbell" or "dogbone" shapes (gauge length × gauge width) conforming to the international ISO-34-1 standard. The optical image of the mechanical cutter and a schematic of the shape were presented in Fig. S8. Armchair and zigzag SCG-PC dogbone sample preparation Rolling marks of as grown SCG-Cu(111) foil were identified using the optical microscope. The orientation of armchair (ac) and zigzag (zz) direction of SCG with respect to the rolling marks were recognized by polarized Raman spectroscopy. The variation in edge (ac or zz) orientation were further measured by optical and SEM images. PC coated graphene films were aligned with the mechanical cutter in parallel and perpendicular direction to the rolling marks of Cu(111) to obtain the ac or zz edge in the dogbone sample. The orientation of rolling marks was further measured from the optical images after preparation of dogbone samples. Transferring SCG-PC Film onto Water Surface The PC and SCG-PC films on Cu foil were floated on an aqueous etchant (0.5 M (NH 4 ) 2 S 2 O 8 ) to remove Cu(111). The floated films were then transferred to a water bath (repeated three times) to remove excess etchant and were further used for FOW measurements. As per requirements, the films were transferred onto Si/SiO 2 wafers for AFM and Raman spectroscopic characterizations. The floated SCG-PC films were transferred on the Qunatifoil Cu TEM grid (200 mesh) followed by removal of PC layer for TEM samples preparation. Characterization A Bruker Dimension Icon atomic force microscope (AFM) was used to measure the surface morphology and thickness of the PC and SCG-PC films studied in this work. Raman spectroscopy was performed using a WiTec micro-Raman instrument with a 488 nm (for SCG on Cu(111)) and 532 nm (for SCG/SCG-PC on Si/SiO 2 ) laser line. A Zeiss optical microscope (OM, AxioCamMRc5) was used to characterize the morphology of the specimens. A scanning electron microscope (SEM, Verios 460, FEI) was used to image the morphologies of the samples and the graphene structures. TEM imaging was done using an aberration corrected TEM (JEM-ARM300F) at an acceleration voltage of 80 kV. Declarations Acknowledgements: This work was supported by the Institute for Basic Science (IBS-R019-D1). We thank J. H. Lee of the UNIST Center Research Facilities for the TEM imaging. Author contributions: R.S.R. supervised the project. R.S.R., W.K.S. and A.K. conceived the experiments. A.K. and M.H.K. did the SCG and Cu(111) growth experiments. A.K. characterized the SCG samples. W.K.S. designed, assembled and built the FOW tensile test measurement system. A.K. prepared the PC and SCG-PC dogbone samples and performed the tensile test measurement in the FOW system. S.K.J. and N.P. performed the theoretical calculations. M.W. helped in performing the initial graphene sample preparation and measurements. D.L. contributed through discussion about the growth of graphene and suggested the orientation of graphene on Cu(111) foil. S.H.L contributed through discussion in optimizing the choice of polymer and understanding polymer mechanics. A.K. and S.K.J. wrote a draft manuscript and R.S.R., W.K.S., N.P., S.K.J., and A.K. revised it. All co-authors commented on the manuscript before its submission. References Wang G et al (2023) Recent advances in the mechanics of 2D materials. Int J Extreme Manuf 5. https://doi.org/10.1088/2631-7990/accda2 Inc. TI (2014) Toray Develops High Tensile Strength and Modulus Carbon Fiber TORAYCA® T1100G and High-performance TORAYCA® Prepreg Liu F, Ming P, Li J (2007) Ab initiocalculation of ideal strength and phonon instability of graphene under tension. Phys Rev B 76. https://doi.org/10.1103/PhysRevB.76.064120 Bai Y et al (2021) Mechanical Behavior of Single and Bundled Defect-Free Carbon Nanotubes. Acc Mater Res 2:998–1009. https://doi.org/10.1021/accountsmr.1c00120 Lee C, Wei X, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–388. https://doi.org/10.1126/science.1157996 Gwan-Hyoung, Lee et al (2013) High-Strength Chemical-Vapor – Deposited Graphene and Grain Boundaries. Science 340:1073–1076. https://doi.org/10.1126/science.1235126 Krajcinovic D (1996) Damage mechanics. Elsevier, Amsterdam, New York Kachanov ML (2003) Handbook of Elasticity Solutions . 1st. edn, (Dordrecht: Springer Netherlands : Imprint: Springer, 2003) Anderson TL (2005) Fracture mechanics: fundamentals and applications, 3rd edn. Taylor ༆ Francis, Boca Raton, FL Zhu T, Li J (2010) Ultra-strength materials. Prog Mater Sci 55:710–757. https://doi.org/10.1016/j.pmatsci.2010.04.001 Abernethy RB (1996) The New Weibull Handbook. R.B., Abernethy Bai Y et al (2020) Super-durable ultralong carbon nanotubes. Science 369:1104–1106. https://doi.org/10.1126/science.aay5220 Xuesong Li et al (2009) Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324:1312–1314. https://doi.org/10.1126/science.1171245 Zhang Y, Zhang L, Zhou C (2012) Review of Chemical Vapor Deposition of Graphene and Related Applications. Acc Chem Res 46:2329–2339. https://doi.org/10.1021/ar300203n Li X, Colombo WCL, Rodney S (2009) Ruof. Evolution of Graphene Growth on Ni and Cu by Carbon Isotope Labeling. Nano Lett 9:4268–4272. https://doi.org/10.1021/nl902515k Wang M et al (2021) Single-crystal, large-area, fold-free monolayer graphene. Nature 596:519–524. https://doi.org/10.1038/s41586-021-03753-3 Luo D et al (2019) Adlayer-Free Large-Area Single Crystal Graphene Grown on a Cu(111) Foil. Adv Mater 31:e1903615. https://doi.org/10.1002/adma.201903615 Liu K et al (2014) Elastic properties of chemical-vapor-deposited monolayer MoS2, WS2, and their bilayer heterostructures. Nano Lett 14:5097–5103. https://doi.org/10.1021/nl501793a Suk JW, Mancevski V, Hao Y, Liechti KM, Ruoff RS (2015) Fracture of polycrystalline graphene membranes by in situ nanoindentation in a scanning electron microscope. Phys status solidi (RRL) – Rapid Res Lett 9:564–569. https://doi.org/10.1002/pssr.201510244 Cao K et al (2020) Elastic straining of free-standing monolayer graphene. Nat Commun 11:284. https://doi.org/10.1038/s41467-019-14130-0 Zhang X, Beyer A (2021) Mechanics of free-standing inorganic and molecular 2D materials. Nanoscale 13:1443–1484. https://doi.org/10.1039/d0nr07606f Lopez-Polin G, Gomez-Navarro C, Gomez-Herrero J (2022) The effect of rippling on the mechanical properties of graphene. Nano Mater Sci 4:18–26. https://doi.org/10.1016/j.nanoms.2021.05.005 Wang B et al (2018) Camphor-Enabled Transfer and Mechanical Testing of Centimeter-Scale Ultrathin Films. Adv Mater 30:e1800888. https://doi.org/10.1002/adma.201800888 Wang C, Wang J, Barber AH (2017) Stress concentrations in nanoscale defective graphene. AIP Adv 7. https://doi.org/10.1063/1.4996387 Liu F et al (2022) Achievements and Challenges of Graphene Chemical Vapor Deposition Growth. Adv Funct Mater 32. https://doi.org/10.1002/adfm.202203191 Zhang J et al (2017) Clean Transfer of Large Graphene Single Crystals for High-Intactness Suspended Membranes and Liquid Cells. Adv Mater 29. https://doi.org/10.1002/adma.201700639 Zhang S, Galuska LA, Gu X (2021) Water-assisted mechanical testing of polymeric thin‐films. J Polym Sci 60:1108–1129. https://doi.org/10.1002/pol.20210281 Kim JH et al (2013) Tensile testing of ultra-thin films on water surface. Nat Commun 4:2520. https://doi.org/10.1038/ncomms3520 Choi WJ, Bay RK, Crosby AJ (2019) Tensile Properties of Ultrathin Bisphenol-A Polycarbonate Films. Macromolecules 52:7489–7494. https://doi.org/10.1021/acs.macromol.9b00835 Miyagawa A, Korkiatithaweechai S, Nobukawa S, Yamaguchi M (2013) Mechanical and Optical Properties of Polycarbonate Containing p-Terphenyl. Ind Eng Chem Res 52:5048–5053. https://doi.org/10.1021/ie302035e Toor PM (1973) A review of some damage tolerance design approaches for aircraft structures. Eng Fract Mech 5:837–880. https://doi.org/10.1016/0013-7944(73)90054-4 Ritchie RO (2011) The conflicts between strength and toughness. Nat Mater 10:817–822. https://doi.org/10.1038/nmat3115 Cadelano E, Palla PL, Giordano S, Colombo L (2009) Nonlinear elasticity of monolayer graphene. Phys Rev Lett 102:235502. https://doi.org/10.1103/PhysRevLett.102.235502 Wei X, Fragneaud B, Marianetti CA, Kysar JW (2009) Nonlinear elastic behavior of graphene:Ab initiocalculations to continuum description. Phys Rev B 80. https://doi.org/10.1103/PhysRevB.80.205407 Wei Y, Yang R (2019) Nanomechanics of graphene. Natl Sci Rev 6:324–348. https://doi.org/10.1093/nsr/nwy067 Nie S, Wofford JM, Bartelt NC, Dubon OD, McCarty KF (2011) Origin of the mosaicity in graphene grown on Cu(111). Phys Rev B 84. https://doi.org/10.1103/PhysRevB.84.155425 Cong C, Ting Yu, Wang H (2010) Raman Study on the G Mode of Graphene for Determination of Edge Orientation. ACS Nano 4:3175–3180. https://doi.org/10.1021/nn100705n Yu Q et al (2011) Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition. Nat Mater 10:443–449. https://doi.org/10.1038/nmat3010 Zhao H (2009) Aluru. Size and Chirality Dependent Elastic Properties of Graphene Nanoribbons under Uniaxial Tension. Nano Lett 9:3012–3015. https://doi.org/10.1021/nl901448z Traian Dumitrica M Hua, Yakobson BI (2006) Symmetry-, time-, and temperature-dependent strength of carbon nanotubes. Proceedings of the National Academy of Sciences 103, 6105–6109 https://doi.org/10.1073/pnas.0600945103 Pugno NM, Ruoff RS (2006) Nanoscale Weibull statistics. J Appl Phys 99:024301. https://doi.org/https://doi.org/10.1063/1.2158491 Pugno NM, Ruoff RS (2004) Quantized fracture mechanics. Phil Mag 84:2829–2845. https://doi.org/10.1080/14786430412331280382 Carpinteri A, Pugno N (2005) Fracture instability and limit strength condition in structures with re-entrant corners. Eng Fract Mech 72:1254–1267. https://doi.org/10.1016/j.engfracmech.2004.09.008 Additional Declarations The authors declare no competing interests. Supplementary Files FinalSupplementaryFile20241007.docx Supplementary Information File SupplementaryVideoS1.mp4 Supplementary Video_Crack Propagation Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5223363","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":363527580,"identity":"ac82330e-3c8d-41e7-b599-bb6f2dd4770e","order_by":0,"name":"Anirban Kundu","email":"","orcid":"https://orcid.org/0000-0002-5025-7555","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":false,"prefix":"","firstName":"Anirban","middleName":"","lastName":"Kundu","suffix":""},{"id":363527581,"identity":"5a92b2c0-609c-4850-9085-0d205ed0cc7b","order_by":1,"name":"Seyed Kamal Jalali","email":"","orcid":"","institution":"Laboratory for Bioinspired, Bionic, Nano, Meta Materials \u0026 Mechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano, 77, 38123 Trento, Italy.","correspondingAuthor":false,"prefix":"","firstName":"Seyed","middleName":"Kamal","lastName":"Jalali","suffix":""},{"id":363527582,"identity":"b1131011-fbc5-4575-9c8c-0eb61da3eed4","order_by":2,"name":"Minhyeok Kim","email":"","orcid":"","institution":"Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea.","correspondingAuthor":false,"prefix":"","firstName":"Minhyeok","middleName":"","lastName":"Kim","suffix":""},{"id":363527583,"identity":"e5e6d212-1782-4c0b-9d56-c96b7af2d6b5","order_by":3,"name":"Meihui Wang","email":"","orcid":"","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":false,"prefix":"","firstName":"Meihui","middleName":"","lastName":"Wang","suffix":""},{"id":363527584,"identity":"05a906f3-5b19-4b1b-914e-a8e625d2a57e","order_by":4,"name":"Da Luo","email":"","orcid":"","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":false,"prefix":"","firstName":"Da","middleName":"","lastName":"Luo","suffix":""},{"id":363527585,"identity":"d19c5ca0-2a82-441a-886b-c9b97d1dd8f8","order_by":5,"name":"Sun Hwa Lee","email":"","orcid":"","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":false,"prefix":"","firstName":"Sun","middleName":"Hwa","lastName":"Lee","suffix":""},{"id":363527586,"identity":"1f7a33bc-448e-43db-b360-55a2439c067b","order_by":6,"name":"Nicola M. Pugno","email":"","orcid":"","institution":"Laboratory for Bioinspired, Bionic, Nano, Meta Materials \u0026 Mechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano, 77, 38123 Trento, Italy.","correspondingAuthor":false,"prefix":"","firstName":"Nicola","middleName":"M.","lastName":"Pugno","suffix":""},{"id":363527587,"identity":"e265102b-8b4b-4473-aa03-c31ccd24c5b6","order_by":7,"name":"Won Kyung Seong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYHACxgcgkh9EJBQQp4XZAERKNoC0GBCnhU0CRBocAJNEqOeXbj4gXVFzx27z+dWJHx4YMMjzix3Ar0VyzrEEwzPHniVvu/F2swTQYYYzZyfg12JwI8cgsYHtcLLZjbMbQFoSDG4T1JL/4WDDv8PJxjPObv5BpJYcxsbGtsN2Bvy924izRXJGmjFjY9/hBIkbvNssEgwkCPuFXyL5+c+Gb4ft+fvPbr75o8JGnl+agBYYSGyQAKuUIE45CNgz8B8gXvUoGAWjYBSMLAAA3/VIkwZR5aIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0004-8914-8622","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":true,"prefix":"","firstName":"Won","middleName":"Kyung","lastName":"Seong","suffix":""},{"id":363527588,"identity":"3320946e-4888-40fc-ac20-0dfeb0cadeba","order_by":8,"name":"Rodney S. Ruoff","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYJCCDxUFDAn8IFZCAXE6GGecMWBIkGwAaTEgRYvBARCbGC3mM5IPNhwwsMszPr868cMDAwZ5frED+LXI3EhLBGpJLja78XazBNBhhjNnJ+DXIiGRY/74gwFz4rYbZzeAtCQY3CasxRBoS33i5hlnN/8gRcvhxA38vduItIXnGcgvx4slbvBus0gwkCDCL+ygEKuozuPvP7v55o8KG3l+aQJakDSDVUoQqxwE+A+QonoUjIJRMApGEgAAwKJITcKbdsQAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-6599-6764","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","correspondingAuthor":true,"prefix":"","firstName":"Rodney","middleName":"S.","lastName":"Ruoff","suffix":""}],"badges":[],"createdAt":"2024-10-08 08:23:58","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5223363/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5223363/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":66284825,"identity":"dd10d7cc-1c72-49fc-afce-82e1a29f3289","added_by":"auto","created_at":"2024-10-09 16:40:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2277267,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTensile testing of macroscale single-crystal graphene using a float-on-water (FOW) measurement system. \u003c/strong\u003e(a,b) An experimental setup illustrating the FOW system with the dogbone-shaped SCG-PC specimen. The white arrow shows the displacement direction. (c) Raman spectra of PC, SCG-PC film, and SCG on Si/SiO\u003csub\u003e2\u003c/sub\u003e wafer. The presence of strong G and 2D bands in SCG on PC was observed, and no D peak wea detected, confirming the quality of SCG. (d) Stress-strain curves of 200 nm PC and 200 nm SCG-PC films, each recorded from five different samples. The red and blue curves present the average stress-strain curves. Representative images of (e) 200 nm PC and (f) 200 nm SCG-PC samples at 0% and 5% applied strain showcasing graphene failure at 5% strain, whereas no breakage is observed in PC at 5% applied strain. (g) Comparison of average Young's modulus, tensile strength, strain at maximum stress, and failure strain values of PC, SCG-PC samples, and SCG (extracted from SCG-PC and PC curves).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/ec39ce50890b8606a8569bfc.png"},{"id":66284826,"identity":"505af164-c504-4b79-8933-77404f5d0863","added_by":"auto","created_at":"2024-10-09 16:40:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2003681,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEvolution of SCG-PC films under tensile loading, illustrating crack initiation and propagation in graphene. \u003c/strong\u003eMonochromatic images of the SCG-PC films at various strain levels (a-f) are shown under tensile loading. No cracks are observed for (g) 2% and (h) 3% strain, and crack initiation occurs at approximately (i) 3.5% applied strain, followed by crack propagation (i-k), SCG failure (l), and complete failure of SCG-PC at around 8% strain (m). Scale bar: ~2.0 mm. The yellow and white arrows indicate the cracks in SCG and notches in the SCG-PC film, respectively. The blue and red outlines denote the bottom and top edge, respectively.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/93948b5d782039caa1cd2cf7.png"},{"id":66284926,"identity":"0411e50c-3df3-4a6e-aa21-24136e5b62e6","added_by":"auto","created_at":"2024-10-09 16:48:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1634254,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMechanical properties of SCG along armchair (ac) and zigzag (zz) direction. \u003c/strong\u003e(a) Preferred orientation of SCG on Cu(111). (b) Identification of rolling marks of Cu(111) on as grown SCG on Cu(111) sample. (c) Optical image of hexagonal SCG. (d) Polarized Raman spectra of zz-SCG edge on Cu(111) as marked in (c) by black dotted line. Stress strain curve of SCG for tensile loading along (e) zigzag and (f) armchair direction. (g) Comparison of mechanical properties of SCG for armchair, chiral and zigzag direction.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/69ff8c21844b4d812336485b.png"},{"id":66284828,"identity":"2e7fd8e1-69fb-495a-a7e9-7b20f277a162","added_by":"auto","created_at":"2024-10-09 16:40:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":648979,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eModel predictions for mechanical properties of chiral, armchair, and zigzag macroscale SCGs.\u003c/strong\u003e (a) Weibull strength scaling from the present sample size to A4-sized sheets, as well as projecting to the theoretical strength of 130 GPa. It is provided for both length scaling corresponding to the edge-confined defects, and area scaling, where the fatal defects are surface-distributed. (b) Estimation of critical edge damage lengths via QFM, considering either a sharp crack or a V-notch at the edge, and detailing the corresponding stress levels at which fracture occurs for each chirality. (c) The calibrated nonlinear stress-strain curves obtained from the damage evolution model, illustrating the nonlinear softening behavior of SCGs on an ultra-thin polymer substrate.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/ca83203b32b60f48a752bbd8.png"},{"id":66285468,"identity":"72bd0e74-1299-46a1-a7d3-c488038a0070","added_by":"auto","created_at":"2024-10-09 16:56:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9106799,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/3394e86c-b5a1-4120-9b63-59f83b247eb9.pdf"},{"id":66284831,"identity":"4b177c8a-4b69-44c8-8c67-9f810a1023ba","added_by":"auto","created_at":"2024-10-09 16:40:07","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":141376326,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Information File\u003c/p\u003e","description":"","filename":"FinalSupplementaryFile20241007.docx","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/8436d76820a24cc1c076ccb3.docx"},{"id":66284830,"identity":"7f7049a8-1715-4cbf-9f3e-385d20f3672f","added_by":"auto","created_at":"2024-10-09 16:40:05","extension":"mp4","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":52117595,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Video_Crack Propagation\u003c/p\u003e","description":"","filename":"SupplementaryVideoS1.mp4","url":"https://assets-eu.researchsquare.com/files/rs-5223363/v1/3aba01bcc509fa2794e18f2b.mp4"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eUnprecedented Strength in Centimeter-Scale Single-Crystal Monolayer Graphene\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThere are very few materials that exhibit particularly high strength at macroscale (centimeter and larger), whereas \u003cem\u003emany\u003c/em\u003e materials can exhibit \u0026lsquo;ideal strength\u0026rsquo; at microscale (microns and smaller)\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Ideal strength refers to the theoretical maximum stress a material can withstand without failure when it is free of any defects or imperfections. As one example, \u0026lsquo;ultrahigh strength\u0026rsquo; commercial carbon fibers have tensile strength of 7 GPa\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, but the \u0026lsquo;ideal\u0026rsquo; in-plane strength of defect free graphite, (and graphene and carbon nanotubes), is ~\u0026thinsp;120 GPa\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. It is important not to confuse strength with modulus, which measures the material's stiffness (or resistance) to deformation, rather than the maximum stress it can endure.\u003c/p\u003e \u003cp\u003eWe note that strength is a kinetic, not thermodynamic, parameter. The \u0026lsquo;ideal tensile strength\u0026rsquo; of graphene could be thus taken as a well calculated value of the stress-at failure (at 0K or around room temperature, no reactive species present in such a calculation). It comes as no surprise that exfoliated (or CVD grown) graphene samples can exhibit \u0026lsquo;ideal\u0026rsquo; strength values when tested at the micron length scale\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e: \u003cem\u003eat this length scale a reasonably high fraction of samples will have no defects.\u003c/em\u003e At larger length scale (millimeters, centimeters, and up) it is much more likely that graphene (\u003cem\u003eor any other material\u003c/em\u003e) will have defects, referred to as \u0026ldquo;flaws\u0026rdquo; by the solid mechanics community\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Such defects are \u0026lsquo;stress concentrators\u0026rsquo;, and the far field tensile stress on a sample can be much larger very close to flaws\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, thus failure of macroscale samples of almost all materials occurs at a much lower stress than the ideal strength\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. This is the influence of \u003cem\u003elength scale\u003c/em\u003e on the fracture strength of real materials\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo the best of our knowledge, only ultralong (few millimeter of gauge length) carbon nanotubes (CNT)\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e exhibit \u0026ldquo;macroscale\u0026rdquo; \u003cem\u003eideal tensile strength\u003c/em\u003e. A few types of glass fiber also show macroscale tensile strength close to their ideal limit\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. If graphene had high strength \u003cem\u003eat large length scales\u003c/em\u003e and was produced at large scale (such as A4-size sheets in great quantity) and moderately inexpensive, it would have a very wide range of applications where it finds \u003cem\u003eno use now\u003c/em\u003e. Nanoindentation on exfoliated graphene of \u003cem\u003emicron-scale\u003c/em\u003e size led to reported values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e ~ 1.0 TPa and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e of ~ 130 GPa\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Theoretical calculations based on density functional perturbation theory (DFPT) had predicted \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and ideal strength \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\)\u003c/span\u003e\u003c/span\u003e values as 1 \u0026plusmn; 0.1 TPa and 100\u0026ndash;130 GPa, respectively\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAdvances in chemical vapor deposition (CVD) of graphene\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e have enabled the production of large-scale, \u003cem\u003esingle-crystal\u003c/em\u003e monolayer graphene (SCG)\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. The mechanical properties of CVD graphene have been characterized by atomic force microscopy (AFM) nanoindentation\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, indentation in scanning electron microscopy (SEM)\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, and push-to-pull (PTP) tensile tests in SEM\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e: these studies were on \u003cem\u003emicroscale\u003c/em\u003e sized samples. While microscale CVD-grown graphene has demonstrated high \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e values, its tensile strength can be lower than ideal due to point defects, grain boundaries, and edge defects\u003csup\u003e\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. But many samples at the micron length scale are readily achieved that show ideal strength by, e.g., nanoindentation.\u003c/p\u003e \u003cp\u003eThe tensile loading response of centimeter-scale single-layer graphene using dynamic mechanical analyzer (DMA) in conjunction with a camphor-assisted transfer process\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, yielded \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e values up to 737 GPa. Recently, SCG was fabricated using the CVD method, which has a large area (centimeter scale) defect-free, adlayer-free graphene\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Transferring large-scale graphene remains challenging, as defects can be introduced in atomically thin monolayer graphene during the multistep transfer process\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. However, we can transfer centimeter scale graphene/polymer films on target substrate, especially on silicon wafer\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e or liquid surface. The \u0026ldquo;float on water\u0026rdquo; (FOW) tensile test techniques have been used to measure tensile loading response of millimeter-scale ultrathin polymer films\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. We have tested this method on single- SCG as we describe further below- and it has worked very well for macroscale SCG supported by thin polymer film.\u003c/p\u003e \u003cp\u003eWe report tensile loading of 1 cm long, 2 mm wide, SCG with graphene adhered to a 200 nm thick polycarbonate (PC) layer, and analysis of stress-strain curves to obtain the Young\u0026rsquo;s modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e), and stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e) and strain at failure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{f}\\)\u003c/span\u003e\u003c/span\u003e). We discovered that crack initiation and subsequent propagation within graphene is controlled by the graphene crystal orientation, armchair (ac) or zigzag (zz). Through modeling we anticipate the mechanical response of stacked graphene-polymer layers with a model system that mitigates the impact of edge defects. We elucidate the fracture mechanics of macroscale SCG, and the exceptionally high tensile strength values observed open avenues for its wide application in automobile and transportation (trains, planes) sectors, large scale optoelectronic devices, straintronics, etc.\u003c/p\u003e"},{"header":"Results and Discussions","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eTensile Test Measurements in FOW System\u003c/h2\u003e \u003cp\u003eWe conducted uniaxial tensile measurements on SCG films utilizing the FOW system. The primary objective of our study was to investigate the mechanical response in macroscale SCG films. We used a thin layer of Poly(bisphenol-A-carbonate) (PC) as the support material for our SCG films because the inherent ultrathin nature (~\u0026thinsp;0.34 nm) and brittleness of SCG have, to date, made it challenging to prepare a freestanding macroscale sample suitable for tensile measurement. This choice was made due to three key factors: First, PC exhibit high optical transparency, a crucial property for the FOW system\u0026rsquo;s accurate measurement capabilities. Second, the PC possesses considerable mechanical strength, ensuring minimal interference with the SCG film\u0026rsquo;s intrinsic behavior during the tensile testing process\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Third, PC\u0026rsquo;s higher tensile failure strain than SCG ensures full support until its failure point. This allows us to isolate the effects of the SCG film\u0026rsquo;s properties on its mechanical response.\u003c/p\u003e \u003cp\u003eSCG was synthesized on Cu(111) foils using thermal CVD. Raman spectroscopy of as-grown SCG on Cu (111) showed an \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{2D}/{I}_{G}\\)\u003c/span\u003e\u003c/span\u003e ratio of 2.56 and a 2D full width at half maximum (FWHM) of 35.16 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (Fig. S12)\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. SCG on the SCG-PC films was verified using Raman spectroscopy (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). In the Raman spectra of SCG-PC, the intense G (~\u0026thinsp;1584.9 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and 2D (~\u0026thinsp;2667.1 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) peaks with negligible D peak confirm the high quality of this single crystal graphene. We observed a blueshift in G (~\u0026thinsp;3.3 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and 2D (~\u0026thinsp;15.1 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) band after removal of PC film, which is attributed due to the removal of strain generated at the interface between the PC and SCG. PC/chloroform solutions were spin-coated onto the as-grown SCG/Cu(111) samples, with thickness variation controlled by adjusting the spin speed. AFM was used to determine film thickness (Fig. S13 and S14). PC and SCG-PC samples were designated based on their PC film thickness, as detailed in Tables S2-S3. A \u0026ldquo;dogbone\u0026rsquo; cutter (model no. SDMP-1000 and JISK 6251-7) was then used to cut out dog bone specimens (with gauge length 10 mm, width 2 mm, see Fig. S15), from which the Cu(111) was etched away, as described in Fig. S16. Thus, the dog bone 200 nm SCG-PC samples were floated on water and attached to the FOW system components that apply tensile loading with van der Waals type adhesion clamping.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe tensile tests were done on samples floating on the water surface at room temperature under constant displacement rates of 0.002 mm/s, equivalent to a strain rate of 0.0002 (mm/mm)/s (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea-b). The mechanical properties of similar 200-nm thick PC films (with no graphene) were characterized independently using the FOW system. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed shows the stress-strain curves for 200 nm PC and SCG-PC films. Complete stress-strain curves are presented in Fig. S17c and S18c.\u003c/p\u003e \u003cp\u003eMonochromatic imaging showed wrinkles in bare PC films even at 0% strain (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee) due to their intrinsic flexibility\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, while SCG-PC films were smooth (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef), indicating uniform contact with the water surface facilitated by the SCG\u0026rsquo;s flatness. At 5% strain, both films displayed horizontal lines perpendicular to the displacement direction within the gauge area, indicating stress concentration zone(s) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee-f, detailed analysis in Fig. S19 and Fig. S20). The higher density of such lines in the SCG-PC film suggests greater stress than the bare PC film due to SCG\u0026rsquo;s higher strength, leading to earlier failure (~\u0026thinsp;7.69%) compared to bare PC (\u0026gt;\u0026thinsp;20%) films. Mechanical properties of PC and SCG-PC films are summarized in Tables S4-S5. The SCG-PC films exhibited roughly 1.5 times higher \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e compared to bare PC films. By using these values, we extracted \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e values for SCG using the rule of mixtures according to the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{E}_{SCG-PC}={E}_{PC}\\frac{{t}_{PC}}{{t}_{PC}+{t}_{SCG}}+{E}_{G}\\frac{{t}_{SCG}}{{t}_{PC}+{t}_{SCG}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{SCG}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{PC}\\)\u003c/span\u003e\u003c/span\u003e are the Young's modulus values for SCG and PC, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{SCG}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{PC}\\)\u003c/span\u003e\u003c/span\u003e are the thicknesses of graphene and PC, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg compares the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e, strain at maximum stress, and failure strain of SCG, SCG-PC, and PC films (a total of 25 combinations as summarized in Table S6). The highest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\:\\)\u003c/span\u003e\u003c/span\u003evalue for SCG was 970.5 GPa (Table S6), approaching microscale monolayer graphene\u0026rsquo;s modulus measured by a push-to-pull (PTP) micromechanical device\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. In our initial investigations, the edge orientation (zigzag or armchair) of SCG was not controlled during the preparation of dog bone samples, resulting in chiral SCG edges. The maximum tensile strength we observed was 30.48 GPa (Table S6), representing a nearly tenfold increase compared to the yield strength of previously reported macroscale graphene\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. However, this value remains lower than the theoretical tensile strength of graphene. This is likely due to edge defects in SCG introduced during mechanical cutting, as observed by SEM (Fig. S21) and TEM (Fig. S22a-b) analyses. TEM imaging shows the presence of nanometer-sized defects or cracks along the SCG edge. The average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e across 25 combinations (of five chiral SCG-PC and 5 bare PC samples) were 748.9\u0026thinsp;\u0026plusmn;\u0026thinsp;121.9 GPa and 23.56\u0026thinsp;\u0026plusmn;\u0026thinsp;3.42 GPa, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg). The ideal strength of monolayer graphene, approximately 130 GPa, has been observed at an applied strain reported as 25%\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. In our study here, the failure of chiral SCG occurred at an average strain of 4.53%, which corresponds to an estimated strength of 41.2 GPa at this strain (with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E=\\)\u003c/span\u003e\u003c/span\u003e 1 TPa and the third order modulus, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:D=\\)\u003c/span\u003e\u003c/span\u003e 2 TPa)\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. While the average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e is comparable to previous macroscale results obtained using a DMA system on free-standing graphene/polymer films\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, increased strength and failure strain is observed showing our approach (FOW measurement system and SCG) yields significantly higher values. While the DMA test\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, reported a yield strain of 0.6% and the corresponding strength of 3.33 GPa, our chiral SCG samples carry substantially higher stress of 5.58 GPa at a strain of 0.6%. This improvement can be attributed to the absence of grain boundaries and adlayers in our single-crystal SCG, and utilizing an optimal polymeric substrate with a 200 nm thickness compared to 100 nm\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e (see the supplementary section 4 on role of polymer thickness). Note that defining the strength of a centimeter-scale SCG solely by its yield stress underestimates its capacity. Although microcrack initiation can cause a deviation from linearity, our chiral SCGs smoothly continued to bear loads at stress levels up to 23.56 GPa, demonstrating their full failure strength\u0026mdash;7.08x greater than the previously reported yield stress. This highlights the well-known concept of \u003cem\u003edamage tolerance\u003c/em\u003e, where macroscale SCG, like many materials, can redistribute stress after the initiation of damage, thereby delaying total failure\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e,\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe crack initiation and propagation were visualized such as shown in supplementary Video S1. This video correlates the mechanical response with the formation and growth of a notch on the SCG-PC film. We observed that the strain at maximum stress of a SCG-PC sample denotes the failure strain of the SCG. The measured failure strain of macroscale SCG (~\u0026thinsp;4.53%) was comparable to microscale measurements by the push-to-pull method (~\u0026thinsp;5.8%)\u003csup\u003e20\u003c/sup\u003e. Lower SCG failure strain compared to the theoretical limits (that are reported to be approximately 13\u0026ndash;19% along the armchair and 20\u0026ndash;26% along the zigzag direction)\u003csup\u003e\u003cspan additionalcitationids=\"CR34\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e likely originated due to the existence of critical edge defects as discussed (through QFM analysis) in the model prediction section later. The similarity between the SCG failure strain and the strain at maximum stress of bare PC (Table S4-S5) suggests that the failure strain of SCG is influenced by the strain at the point of maximum stress in the PC layer. Mechanical property variation of SCG with PC thicknesses (with different \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e) are discussed in supplementary section 4.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eIdentification of Crack Initiation and Propagation in Macroscale SCG\u003c/h3\u003e\n\u003cp\u003eThe transparent PC substrate in SCG-PC films allows direct visualization of crack initiation and propagation within the SCG layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-f). At 2% applied strain, stress concentration zones (SCZ) become evident, primarily at the edges (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). The reason for observing the SCZs at ~\u0026thinsp;2% can be attributed due to the transition from linear to non-linear response in the polymer\u0026rsquo;s stress-strain curve (see Fig. S16c). With increasing strain, the SCZs intensity manifests as horizontal lines to the loading direction (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec-d). At 3% strain, a significant increase in the density of horizontal lines at SCZs shows the initiation of macrocrack propagation (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg-h). An observed crack appears in SCG at 3.5% strain, originating from an existing SCZ (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh). Simultaneously, new SCZs emerge at other edges on the top of the SCG-PC film (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ei), serving as potential sites for further crack initiation. This process continues, ultimately leading to complete failure of the SCG layer. Crack identification is facilitated by the distinct contrast between SCG (bright white lines) and the PC layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ei-k). A crack that initiates at one edge appears to trigger the formation of a complementary crack on the opposite edge. These cracks then propagate in opposite directions, culminating in complete SCG failure (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003el). Even after SCG failure, the PC layer with fragmented SCG on its surface continues to elongate under tensile stress, and the SCG-PC film (Fig. S20) exhibits a faster breakdown compared to the bare PC films (Fig. S19) due to its higher ultimate stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further analyze crack characteristics, tensile testing was interrupted at various strain points, and the SCG films were transferred to a Si/SiO\u003csub\u003e2\u003c/sub\u003e wafer for SEM analysis. Chloroform treatment removed the PC layer, exposing the SCG morphology. Fig. S23 compares the effect of tensile loading on SCG at the crack initiation point and the failure strain of SCG. Smaller microcracks parallel to the main macrocrack were observed at initiation, likely contributing to its propagation until complete SCG failure. Further analysis (Fig. S23c-d) revealed that the crack angles were multiples of approximately 30\u003csup\u003eo\u003c/sup\u003e, reflecting that the crack in SCG propagates along armchair or zigzag directions. Microcracks were parallel to each other and perpendicular to the elongation direction, while larger macrocracks tended to align with the armchair or zigzag edges of graphene (Fig. S23e-f). These observations suggest that crack propagation in SCG is influenced by both stress concentration points at opposing edges and the intrinsic defects of graphene.\u003c/p\u003e\n\u003ch3\u003eMechanical Properties of SCG along armchair (ac) and zigzag (zz) directions\u003c/h3\u003e\n\u003cp\u003eThe zigzag (zz) edge of SCG grown on Cu(111) preferentially aligns with the Cu\u0026thinsp;\u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;direction, while the armchair (ac) edge aligns with the Cu(112) direction (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea)\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. The Cu\u0026thinsp;\u0026lt;\u0026thinsp;112\u0026thinsp;\u0026gt;\u0026thinsp;direction can be optically identified from rolling marks on the Cu foil (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) as confirmed by electron backscatter diffraction (EBSD) data (Fig. S35). To determine the orientation of graphene edges relative to Cu rolling marks, hexagonal SCG islands were grown on Cu(111) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, Fig. S36). The angle between the edge of SCG islands and rolling marks was calculated from optical and SEM images as 90.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.27 \u003csup\u003eo\u003c/sup\u003e and 90.14\u0026thinsp;\u0026plusmn;\u0026thinsp;2.06 \u003csup\u003eo\u003c/sup\u003e, respectively (Fig. S36). Polarized Raman spectroscopy performed on marked (black dotted line) graphene edges on Cu(111) foil (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec) showed an increase in the G peak intensity with the angle between incident and scattered light (varied using the analyzer), which also confirmed that the edge perpendicular to the rolling marks corresponds to the zz edge of SCG\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). Polymer coated SCG/Cu(111) foils were aligned with the rolling marks and cut to prepare dogbone-shaped SCG-PC samples with zz (perpendicular) and ac (parallel) edges.\u003c/p\u003e \u003cp\u003eThe perpendicular orientation (~\u0026thinsp;89.24\u0026thinsp;\u0026plusmn;\u0026thinsp;0.82 \u003csup\u003eo\u003c/sup\u003e) denotes the dogbone sample with zz edge, while the parallel orientation (~\u0026thinsp;0.63\u0026thinsp;\u0026plusmn;\u0026thinsp;1.27 \u003csup\u003eo\u003c/sup\u003e) denotes the ac edge; see supplementary Fig. S37. Polarized Raman spectra at these perpendicular and parallel edges are shown in Fig. S38. We performed TEM imaging at the edge of SCG parallel to the rolling marks. The diffraction pattern (Fig. S21c) and high resolution TEM image (Fig. S21d) confirms the ac direction along the edge\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eStress-strain curves were obtained from tensile loading in the FOW system along the zigzag (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee) and armchair (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef) direction for these different dogbone samples. The average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e values for ac and zz SCG-PC samples were 3.53 GPa and 3.68 GPa, respectively, while the average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e values were 99.8 MPa and 110.7 MPa, respectively. We thus observed 1.12 times (99.8 to 110.7 MPa) enhanced strength for zz SCG-PC samples, and similar \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e values. The ac SCG-PC samples showed a higher average failure strain of 10.10% compared to 7.79% for zz SCG-PC samples. The mechanical response of zz and ac SCG-PC samples are summarized in supplementary Table S10. The mechanical properties (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e) of zz-SCG and ac-SCG were obtained by comparing the stress strain curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee-f (and supplementary Fig. S39) with those of bare PC films (200 nm thick). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e values for zz- and ac-SCG were 1.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04 TPa and 1.01\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10 TPa, respectively. The average strength for zz-SCG was 27.40\u0026thinsp;\u0026plusmn;\u0026thinsp;4.36 GPa, while that for ac-SCG was 20.21\u0026thinsp;\u0026plusmn;\u0026thinsp;3.22 GPa. Chiral SCG (with edge orientations not aligned to zz or ac) samples exhibited an average strength of 23.56\u0026thinsp;\u0026plusmn;\u0026thinsp;3.42 GPa (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg), falling between the average strength for zz- and ac-SCG.\u003c/p\u003e \u003cp\u003eThe mechanical properties (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e and failure strain) of ac, zz, and chiral SCG are compared in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg. These results align with previously reported theoretical findings from density functional theory (DFT) and molecular dynamics (MD) simulations.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e We compared the previously reported theoretical and experimental results with our experimental values in supplementary Table S13. Failure strains of ~\u0026thinsp;3.69% and ~\u0026thinsp;6.01% for SCG were observed for the ac and zz direction, respectively. Observation of higher strength and failure strain along the zz direction compared to the ac direction can be attributed to the larger bond angle variation along the zz direction.\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eTheoretical Model Predictions\u003c/h3\u003e\n\u003cp\u003eWe now consider scaling from our current dimensions of 1 cm along the tensile loading axis with an area of 0.2 cm\u0026sup2;, to an A4-sized sheet. This results in scale ratios of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e = 29.7 for length and 3118.5 for the area. According to the Weibull scale law provided in the Section 1 of supplementary information, the strength of a reference sample, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003e (here our current samples), is related to the scaled strength, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e, (such as of an A4-sized sheet) by the power law, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:={\\sigma\\:}_{0}{\\left(R\\right)}^{-\\frac{1}{\\alpha\\:}}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e is the Weibull modulus, which characterizes the material's statistical strength distribution\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. To perform strength scaling, we fitted a Weibull distribution (Fig. S1) on the measured strengths of chiral, zz, and ac SCGs listed in Tables S6, S11, and S12. From this, the reference strengths of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003e were determined to be 25.00, 29.24, and 21.54 GPa for chiral, zz, and ac SCGs, respectively. The Weibull moduli \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e were 8.22, 7.35, and 7.46, corresponding to chiral, zz, and ac. When scaling by length, we assume the critical flaws are edge-confined, consistent with our experimental findings where failure initiates at the edge. For an A4-size SCG sample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e = 29.7, the predicted strengths for zz, chiral, and ac orientations are 18.43 GPa, 16.55 GPa, and 13.67 GPa, respectively. However, when scaling by area (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e = 3118.5), assuming surface-distributed flaws, the predicted strengths drop to 9.78 GPa, 9.39 GPa, and 7.32 GPa, indicating a significant reduction in strength due to the increased number of critical flaws; however as noted, the flaws were always identified at the edges, and not in the interior. To estimate the size corresponding to theoretical strength, we inversely scaled down by setting \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e = 130 GPa and solving for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e. For zz SCGs, the theoretical strength would correspond to a length of 0.174 \u0026micro;m and an area of 350 \u0026micro;m\u0026sup2;. Using the same approach, ac SCGs yield lengths of 0.015 \u0026micro;m and areas of 30.2 \u0026micro;m\u0026sup2;, while chiral samples result in 0.013 \u0026micro;m and 26 \u0026micro;m\u0026sup2;. These scaling estimates, from theoretical strength to A4-size sheets, are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea.\u003c/p\u003e \u003cp\u003eWe did a fracture mechanics analysis using QFM (quantized fracture mechanics), which extends linear elastic fracture mechanics by introducing a fracture quantum\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, as detailed in the Section 2 of supplementary information. This fracture quantum is calculated such that a crack length of zero exhibits an ideal strength of 130 GPa. Accordingly, we determine critical lengths of 6.23, 8.53, and 11.70 nm for a sharp crack at the edge of zz, chiral, and ac SCGs with the strength 27.40, 23.56, and 20.21 GPa, respectively. By substituting the sharp crack with a V-notch as the critical defect on the SCG edge\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e and assuming a notch angle of 30\u0026deg;, we find critical notch depths (perpendicular to the edge) of 13.43, 19.65, and 28.87 nm for zz, chiral, and ac SCGs, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb illustrates the variation of the critical edge defect against the SCG strength.\u003c/p\u003e \u003cp\u003eFinally, we used a damage evolution model to capture the softening behavior of SCG on an ultra-thin polymer substrate, as detailed in Section 3 of supplementary information. The calibrated nonlinear stress-strain curves, derived from the constitutive laws presented in Eqs. S30-S32, are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. We also applied this model to a stack created by folding a SCG-PC sample, allowing us to predict the stack's stress-strain response, as shown in Fig. S9. We find that the folded SCG-PC sample with 100 layers of SCG-PC stacking can sustain a stress of 125.15 MPa at 4.53% strain, which is 1.80 times higher than the PC sample and 1.19 times higher than the SCG-PC sample.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe found near-intrinsic tensile loading mechanical properties in centimeter-scale single crystal monolayer graphene (SCG) measured with a float on water testing system. We report average values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e = 1.11 TPa and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\)\u003c/span\u003e\u003c/span\u003e = 27.40 GPa along the zigzag edges of SCG, approaching the theoretical limits for graphene. Loading along the armchair edges yielded \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e = 1.01 TPa and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\)\u003c/span\u003e\u003c/span\u003e = 20.21 GPa while chiral SCG exhibits had \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e of 0.75 TPa and 23.56 GPa, respectively. Fitting a Weibull distribution on the experimental data set of the current sample size, i.e., 10 x 2 mm, we predict that if the fatal damage is initiated solely on the edges of a macroscale sample (as we observed in all samples), the strength of an A4-size SCG can range from 13.67 to 18.43 GPa depending on chirality with zigzag as the maximum, armchair the minimum, and chiral in between. Although edge defects and supporting layer slightly impact tensile strength, our findings confirm that optimizing the support layer thickness enhances stiffness. This study establishes the \u003cem\u003eremarkable mechanical resilience of large-scale single crystal monolayer graphene\u003c/em\u003e, demonstrating a failure strain of up to 6.01% for tensile loading along the zigzag edge. The developed methodology of macroscale graphene mechanics, characterized by uniform and well-controllable tensile loading, offers potential for studying the mechanical properties of other 2D materials and their heterostructures. This work could advance graphene-based straintronics, large-scale optoelectronic devices through strain engineering, and industrial applications, particularly in the transportation sector.\u003c/p\u003e "},{"header":"Experimental Methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003cp\u003e \u003cstrong\u003eGrowth of Large-Area Single-Crystal Graphene\u003c/strong\u003e \u003cp\u003eTo grow single-crystal single-layer graphene (SCG), 35 mm \u0026times; 50 mm Cu(111) foils were loaded into a 40 mm diameter quartz tube with a uniform heating zone around 100 mm and placed at the center of the heating zone. First, the furnace was heated to 1060\u0026deg;C within 60 min in a 300 sccm Ar and 40 sccm H\u003csub\u003e2\u003c/sub\u003e atmosphere at 30 Torr pressure, followed by introducing 34 sccm 0.1 mol% CH\u003csub\u003e4\u003c/sub\u003e for 60 min while the temperature was held at 1060\u0026deg;C. The sample was then rapidly cooled to room temperature under the same gaseous conditions (300 sccm Ar, 40 sccm H\u003csub\u003e2\u003c/sub\u003e, and 34 sccm 0.1 mol% CH\u003csub\u003e4\u003c/sub\u003e). The as-prepared SCG on Cu(111) was characterized using Raman spectroscopy and SEM to confirm the uniformity and quality of graphene.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003ePreparation of Polycarbonate-Graphene Film (SCG-PC)\u003c/strong\u003e \u003cp\u003ePoly(bisphenol A carbonate) [PC] from Sigma-Aldrich (average Mw\u0026thinsp;~\u0026thinsp;45000) was dissolved in chloroform, and 0.5-5 wt% solutions were prepared. PC/chloroform solution was spin-coated at a speed of 3000 RPM on bare Cu(111) foil to prepare PC films and on Gr/Cu(111) foil to prepare SCG-PC films. The thicknesses of the PC and SCG-PC films were measured by AFM after transferring the sample onto Si/SiO\u003csub\u003e2\u003c/sub\u003e wafers.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eTensile Test Measurement Setup\u003c/em\u003e: The Float-on-Water (FOW) measurement setup was built by assembling two critical components: (i) a force sensor (model no. LTS-100GA from the Kyowa Electronic Instruments Co. Ltd.) and (ii) a displacement motor (model no. C863 from Physik Instrumente (PI)). The force exerted upon the samples due to displacement was recorded using a Kyowa sensor interface (Model No: PCD-430A). Monochromatic images of the thin films were captured using the Allied Vision camera (Model No: Manta G-146B).\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eMechanical Cutter\u003c/strong\u003e \u003cp\u003ePC-coated graphene films and bare PC films on Cu foil were transferred into the mechanical cutter (model no. SDMP-1000 and JISK 6251-7 from Dumbell Co. Ltd.) and cut into \"dumbbell\" or \"dogbone\" shapes (gauge length \u0026times; gauge width) conforming to the international ISO-34-1 standard. The optical image of the mechanical cutter and a schematic of the shape were presented in Fig. S8.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eArmchair and zigzag SCG-PC dogbone sample preparation\u003c/strong\u003e \u003cp\u003eRolling marks of as grown SCG-Cu(111) foil were identified using the optical microscope. The orientation of armchair (ac) and zigzag (zz) direction of SCG with respect to the rolling marks were recognized by polarized Raman spectroscopy. The variation in edge (ac or zz) orientation were further measured by optical and SEM images. PC coated graphene films were aligned with the mechanical cutter in parallel and perpendicular direction to the rolling marks of Cu(111) to obtain the ac or zz edge in the dogbone sample. The orientation of rolling marks was further measured from the optical images after preparation of dogbone samples.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTransferring SCG-PC Film onto Water Surface\u003c/strong\u003e \u003cp\u003eThe PC and SCG-PC films on Cu foil were floated on an aqueous etchant (0.5 M (NH\u003csub\u003e4\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e8\u003c/sub\u003e) to remove Cu(111). The floated films were then transferred to a water bath (repeated three times) to remove excess etchant and were further used for FOW measurements. As per requirements, the films were transferred onto Si/SiO\u003csub\u003e2\u003c/sub\u003e wafers for AFM and Raman spectroscopic characterizations. The floated SCG-PC films were transferred on the Qunatifoil Cu TEM grid (200 mesh) followed by removal of PC layer for TEM samples preparation.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eCharacterization\u003c/strong\u003e \u003cp\u003eA Bruker Dimension Icon atomic force microscope (AFM) was used to measure the surface morphology and thickness of the PC and SCG-PC films studied in this work. Raman spectroscopy was performed using a WiTec micro-Raman instrument with a 488 nm (for SCG on Cu(111)) and 532 nm (for SCG/SCG-PC on Si/SiO\u003csub\u003e2\u003c/sub\u003e) laser line. A Zeiss optical microscope (OM, AxioCamMRc5) was used to characterize the morphology of the specimens. A scanning electron microscope (SEM, Verios 460, FEI) was used to image the morphologies of the samples and the graphene structures. TEM imaging was done using an aberration corrected TEM (JEM-ARM300F) at an acceleration voltage of 80 kV.\u003c/p\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Institute for Basic Science (IBS-R019-D1). We thank J. H. Lee of the UNIST Center Research Facilities for the TEM imaging.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eR.S.R. supervised the project. R.S.R., W.K.S. and A.K. conceived the experiments. A.K. and M.H.K. did the SCG and Cu(111) growth experiments. A.K. characterized the SCG samples. W.K.S. designed, assembled and built the FOW tensile test measurement system. A.K. prepared the PC and SCG-PC dogbone samples and performed the tensile test measurement in the FOW system. S.K.J. and N.P. performed the theoretical calculations. M.W. helped in performing the initial graphene sample preparation and measurements. D.L. contributed through discussion about the growth of graphene and suggested the orientation of graphene on Cu(111) foil. S.H.L contributed through discussion in optimizing the choice of polymer and understanding polymer mechanics. A.K. and S.K.J. wrote a draft manuscript and R.S.R., W.K.S., N.P., S.K.J., and A.K. revised it. All co-authors commented on the manuscript before its submission.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang G et al (2023) Recent advances in the mechanics of 2D materials. Int J Extreme Manuf 5. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/2631-7990/accda2\u003c/span\u003e\u003cspan address=\"10.1088/2631-7990/accda2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eInc. TI (2014) \u003cem\u003eToray Develops High Tensile Strength and Modulus Carbon Fiber TORAYCA\u0026reg; T1100G and High-performance TORAYCA\u0026reg; Prepreg\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu F, Ming P, Li J (2007) Ab initiocalculation of ideal strength and phonon instability of graphene under tension. Phys Rev B 76. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.76.064120\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.76.064120\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai Y et al (2021) Mechanical Behavior of Single and Bundled Defect-Free Carbon Nanotubes. Acc Mater Res 2:998\u0026ndash;1009. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/accountsmr.1c00120\u003c/span\u003e\u003cspan address=\"10.1021/accountsmr.1c00120\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee C, Wei X, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385\u0026ndash;388. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.1157996\u003c/span\u003e\u003cspan address=\"10.1126/science.1157996\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGwan-Hyoung, Lee et al (2013) High-Strength Chemical-Vapor \u0026ndash; Deposited Graphene and Grain Boundaries. Science 340:1073\u0026ndash;1076. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.1235126\u003c/span\u003e\u003cspan address=\"10.1126/science.1235126\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKrajcinovic D (1996) Damage mechanics. Elsevier, Amsterdam, New York\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKachanov ML (2003) \u003cem\u003eHandbook of Elasticity Solutions\u003c/em\u003e. 1st. edn, (Dordrecht: Springer Netherlands : Imprint: Springer, 2003)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAnderson TL (2005) Fracture mechanics: fundamentals and applications, 3rd edn. Taylor ༆ Francis, Boca Raton, FL\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu T, Li J (2010) Ultra-strength materials. Prog Mater Sci 55:710\u0026ndash;757. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.pmatsci.2010.04.001\u003c/span\u003e\u003cspan address=\"10.1016/j.pmatsci.2010.04.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbernethy RB (1996) The New Weibull Handbook. R.B., Abernethy\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBai Y et al (2020) Super-durable ultralong carbon nanotubes. Science 369:1104\u0026ndash;1106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.aay5220\u003c/span\u003e\u003cspan address=\"10.1126/science.aay5220\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXuesong Li et al (2009) Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324:1312\u0026ndash;1314. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.1171245\u003c/span\u003e\u003cspan address=\"10.1126/science.1171245\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang Y, Zhang L, Zhou C (2012) Review of Chemical Vapor Deposition of Graphene and Related Applications. Acc Chem Res 46:2329\u0026ndash;2339. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ar300203n\u003c/span\u003e\u003cspan address=\"10.1021/ar300203n\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi X, Colombo WCL, Rodney S (2009) Ruof. Evolution of Graphene Growth on Ni and Cu by Carbon Isotope Labeling. Nano Lett 9:4268\u0026ndash;4272. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nl902515k\u003c/span\u003e\u003cspan address=\"10.1021/nl902515k\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang M et al (2021) Single-crystal, large-area, fold-free monolayer graphene. Nature 596:519\u0026ndash;524. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41586-021-03753-3\u003c/span\u003e\u003cspan address=\"10.1038/s41586-021-03753-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLuo D et al (2019) Adlayer-Free Large-Area Single Crystal Graphene Grown on a Cu(111) Foil. Adv Mater 31:e1903615. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/adma.201903615\u003c/span\u003e\u003cspan address=\"10.1002/adma.201903615\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu K et al (2014) Elastic properties of chemical-vapor-deposited monolayer MoS2, WS2, and their bilayer heterostructures. Nano Lett 14:5097\u0026ndash;5103. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nl501793a\u003c/span\u003e\u003cspan address=\"10.1021/nl501793a\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSuk JW, Mancevski V, Hao Y, Liechti KM, Ruoff RS (2015) Fracture of polycrystalline graphene membranes by in situ nanoindentation in a scanning electron microscope. Phys status solidi (RRL) \u0026ndash; Rapid Res Lett 9:564\u0026ndash;569. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/pssr.201510244\u003c/span\u003e\u003cspan address=\"10.1002/pssr.201510244\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCao K et al (2020) Elastic straining of free-standing monolayer graphene. Nat Commun 11:284. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41467-019-14130-0\u003c/span\u003e\u003cspan address=\"10.1038/s41467-019-14130-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang X, Beyer A (2021) Mechanics of free-standing inorganic and molecular 2D materials. Nanoscale 13:1443\u0026ndash;1484. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1039/d0nr07606f\u003c/span\u003e\u003cspan address=\"10.1039/d0nr07606f\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLopez-Polin G, Gomez-Navarro C, Gomez-Herrero J (2022) The effect of rippling on the mechanical properties of graphene. Nano Mater Sci 4:18\u0026ndash;26. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.nanoms.2021.05.005\u003c/span\u003e\u003cspan address=\"10.1016/j.nanoms.2021.05.005\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang B et al (2018) Camphor-Enabled Transfer and Mechanical Testing of Centimeter-Scale Ultrathin Films. Adv Mater 30:e1800888. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/adma.201800888\u003c/span\u003e\u003cspan address=\"10.1002/adma.201800888\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang C, Wang J, Barber AH (2017) Stress concentrations in nanoscale defective graphene. AIP Adv 7. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1063/1.4996387\u003c/span\u003e\u003cspan address=\"10.1063/1.4996387\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu F et al (2022) Achievements and Challenges of Graphene Chemical Vapor Deposition Growth. Adv Funct Mater 32. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/adfm.202203191\u003c/span\u003e\u003cspan address=\"10.1002/adfm.202203191\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang J et al (2017) Clean Transfer of Large Graphene Single Crystals for High-Intactness Suspended Membranes and Liquid Cells. Adv Mater 29. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/adma.201700639\u003c/span\u003e\u003cspan address=\"10.1002/adma.201700639\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang S, Galuska LA, Gu X (2021) Water-assisted mechanical testing of polymeric thin‐films. J Polym Sci 60:1108\u0026ndash;1129. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/pol.20210281\u003c/span\u003e\u003cspan address=\"10.1002/pol.20210281\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKim JH et al (2013) Tensile testing of ultra-thin films on water surface. Nat Commun 4:2520. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/ncomms3520\u003c/span\u003e\u003cspan address=\"10.1038/ncomms3520\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChoi WJ, Bay RK, Crosby AJ (2019) Tensile Properties of Ultrathin Bisphenol-A Polycarbonate Films. Macromolecules 52:7489\u0026ndash;7494. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/acs.macromol.9b00835\u003c/span\u003e\u003cspan address=\"10.1021/acs.macromol.9b00835\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMiyagawa A, Korkiatithaweechai S, Nobukawa S, Yamaguchi M (2013) Mechanical and Optical Properties of Polycarbonate Containing p-Terphenyl. Ind Eng Chem Res 52:5048\u0026ndash;5053. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/ie302035e\u003c/span\u003e\u003cspan address=\"10.1021/ie302035e\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eToor PM (1973) A review of some damage tolerance design approaches for aircraft structures. Eng Fract Mech 5:837\u0026ndash;880. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0013-7944(73)90054-4\u003c/span\u003e\u003cspan address=\"10.1016/0013-7944(73)90054-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRitchie RO (2011) The conflicts between strength and toughness. Nat Mater 10:817\u0026ndash;822. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/nmat3115\u003c/span\u003e\u003cspan address=\"10.1038/nmat3115\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCadelano E, Palla PL, Giordano S, Colombo L (2009) Nonlinear elasticity of monolayer graphene. Phys Rev Lett 102:235502. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevLett.102.235502\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.102.235502\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWei X, Fragneaud B, Marianetti CA, Kysar JW (2009) Nonlinear elastic behavior of graphene:Ab initiocalculations to continuum description. Phys Rev B 80. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.80.205407\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.80.205407\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWei Y, Yang R (2019) Nanomechanics of graphene. Natl Sci Rev 6:324\u0026ndash;348. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1093/nsr/nwy067\u003c/span\u003e\u003cspan address=\"10.1093/nsr/nwy067\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNie S, Wofford JM, Bartelt NC, Dubon OD, McCarty KF (2011) Origin of the mosaicity in graphene grown on Cu(111). Phys Rev B 84. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.84.155425\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.84.155425\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCong C, Ting Yu, Wang H (2010) Raman Study on the G Mode of Graphene for Determination of Edge Orientation. ACS Nano 4:3175\u0026ndash;3180. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nn100705n\u003c/span\u003e\u003cspan address=\"10.1021/nn100705n\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYu Q et al (2011) Control and characterization of individual grains and grain boundaries in graphene grown by chemical vapour deposition. Nat Mater 10:443\u0026ndash;449. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/nmat3010\u003c/span\u003e\u003cspan address=\"10.1038/nmat3010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao H (2009) Aluru. Size and Chirality Dependent Elastic Properties of Graphene Nanoribbons under Uniaxial Tension. Nano Lett 9:3012\u0026ndash;3015. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nl901448z\u003c/span\u003e\u003cspan address=\"10.1021/nl901448z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTraian Dumitrica M Hua, Yakobson BI (2006) Symmetry-, time-, and temperature-dependent strength of carbon nanotubes. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e 103, 6105\u0026ndash;6109 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1073/pnas.0600945103\u003c/span\u003e\u003cspan address=\"10.1073/pnas.0600945103\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePugno NM, Ruoff RS (2006) Nanoscale Weibull statistics. J Appl Phys 99:024301. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/https://doi.org/10.1063/1.2158491\u003c/span\u003e\u003cspan address=\"10.1063/1.2158491\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePugno NM, Ruoff RS (2004) Quantized fracture mechanics. Phil Mag 84:2829\u0026ndash;2845. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/14786430412331280382\u003c/span\u003e\u003cspan address=\"10.1080/14786430412331280382\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCarpinteri A, Pugno N (2005) Fracture instability and limit strength condition in structures with re-entrant corners. Eng Fract Mech 72:1254\u0026ndash;1267. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.engfracmech.2004.09.008\u003c/span\u003e\u003cspan address=\"10.1016/j.engfracmech.2004.09.008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea.","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Single Crystal Graphene, High Tensile Strength, Near-ideal Stiffness, Chiral Dependency, Damage Evolution","lastPublishedDoi":"10.21203/rs.3.rs-5223363/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5223363/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDespite extensive microscale studies, the macroscopic mechanical properties of monolayer graphene remain underexplored. Here, we report the Young’s modulus (E = 1.11 ± 0.04 TPa), tensile strength (σ = 27.40 ± 4.36 GPa), and failure strain (ε\u003csub\u003ef\u003c/sub\u003e = 6.01 ± 0.92 %) of centimeter-scale single-crystal monolayer graphene (SCG) ‘dog bone’ samples with edges aligned along the zigzag (zz) direction, supported by an ultra-thin polymer (polycarbonate) film. \u0026nbsp;For samples with edges along the armchair (ac) direction, we obtain E = 1.01 ± 0.10 TPa, σ = 20.21 ± 3.22 GPa, ε\u003csub\u003ef\u003c/sub\u003e = 3.69 ± 0.38 %, and for chiral samples whose edges were between zz and ac, we obtain E= 0.75 ± 0.12 TPa, σ = 23.56 ± 3.42 GPa, and ε\u003csub\u003ef\u003c/sub\u003e = 4.53 ± 0.40 %. The SCG is grown on single crystal Cu(111) foils by chemical vapor deposition (CVD). We used a home-built ‘float-on-water’ (FOW) tensile testing system for tensile loading measurements that also enabled in situ crack observation. The quantized fracture mechanics (QFM) analysis predicts an edge defect size from several to tens of nanometers based on chirality and notch angle. Through Weibull analysis and given that the fatal defects are confined on the edges of macroscale samples, we projected strength ranging from 13.67 to 18.43 GPa for an A4-size SCG according to their chirality. Our findings demonstrate exceptional mechanical performance of macroscale single crystal graphene (SCG) and pave the way for its widespread use in a very wide variety of applications. \u0026nbsp;\u003c/p\u003e","manuscriptTitle":"Unprecedented Strength in Centimeter-Scale Single-Crystal Monolayer Graphene","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-09 16:39:59","doi":"10.21203/rs.3.rs-5223363/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1d63a914-9304-438c-93ce-44af4c0172b9","owner":[],"postedDate":"October 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":38669389,"name":"Nanoscience"}],"tags":[],"updatedAt":"2024-10-09T16:39:59+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-09 16:39:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5223363","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5223363","identity":"rs-5223363","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}