Superflexibility of graphene oxidePhilippe Poulina, Rouhollah Jalilib, Wilfrid Neria, Frédéric Nalleta, Thibaut Divouxa, Annie Colina,Seyed Hamed Aboutalebic, Gordon Wallaceb, and Cécile Zakria,1

aCentre de Recherche Paul Pascal – CNRS, University of Bordeaux, 33600 Pessac, France; bAustralian Research Council Centre of Excellence for ElectromaterialsScience, Intelligent Polymer Research Institute, Australian Institute of Innovative Materials Facility, Innovation Campus, University of Wollongong, Wollongong,NSW 2522, Australia; and cCondensed Matter National Laboratory, Institute for Research in Fundamental Sciences, 19395-5531, Tehran, Iran

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved July 26, 2016 (received for review March 30, 2016)

Graphene oxide (GO), the main precursor of graphene-basedmaterials made by solution processing, is known to be very stiff.Indeed, it has a Young’s modulus comparable to steel, on the orderof 300 GPa. Despite its very high stiffness, we show here that GO issuperflexible. We quantitatively measure the GO bending rigidityby characterizing the flattening of thermal undulations in responseto shear forces in solution. Characterizations are performed by thecombination of synchrotron X-ray diffraction at small angles and insitu rheology (rheo-SAXS) experiments using the high X-ray flux of asynchrotron source. The bending modulus is found to be 1 kT, whichis about two orders of magnitude lower than the bending rigidityof neat graphene. This superflexibility compares with the fluidityof self-assembled liquid bilayers. This behavior is discussed byconsidering the mechanisms at play in bending and stretching de-formations of atomic monolayers. The superflexibility of GO is aunique feature to develop bendable electronics after reduction,films, coatings, and fibers. This unique combination of propertiesof GO allows for flexibility in processing and fabrication coupledwith a robustness in the fabricated structure.

graphene oxide | bending rigidity | rheo-SAXS

Bending of a thin plate simultaneously involves contractionand stretching of matter relative to a neutral plane (1, 2).

Because both contraction and stretching are at play, tensile rigiditydictates the ability of a thin platelet to be bent. Actually theresistance against flexion of a thin platelet is quantified by the so-called bending rigidity, which is given in classical continuummechanics by the following equation: κ=Eh3=ð12ð1− ν2ÞÞ whereE is the Young’s modulus of the material, h its thickness, and vits Poisson ratio (1, 2). At first sight, comparable to thin platelets,graphene and derived monolayers such as graphene oxide (GO),obtained by oxidation of neat graphene (3), are expected to berelatively flexible so that they can be implemented in flexibleelectronics (prior reduction) and easily deformable coatings,films, and fibers. If graphene (4–7) or GO (7–13) were actuallybehaving as thin platelets, they would display high bending ri-gidity. Indeed, measured and calculated values of the Young’smodulus of GO and reduced GO typically range from 200 to600 GPa, above that of steel, whereas the modulus of neat gra-phene is about 1,000 GPa (4–13). We note that a thickness has tobe defined to deduce the above values of Young’s moduli (14).Even if this definition is not straightforward for atomic mono-layers, it is often considered to be about 0.34 nm for neat graphene(4, 6), the interlayer spacing in graphite, and about 0.7–0.8 nmfor GO (9, 10, 12, 13). As indicated above, according to thin-platetheory the bending rigidity of atomic monolayers should alsodepend on their thickness and Young’s modulus. However,atomic monolayers are neither stretched nor compressed whenbent. The continuum mechanics picture is not applicable downto an atomic monolayer which can intrinsically be viewed as anindividual neutral plane. Nevertheless, the bending rigidity canbe determined experimentally or theoretically without necessarilydefining a well-given thickness. Indeed, the bending rigiditycorresponds to the ratio of the bending moment to the curvatureof the platelet, regardless of its thickness (14). It can also bedetermined in experiments and simulations from analysis of out-

of-plane thermal fluctuations (15, 16) without definition of thegraphene thickness. The bending rigidity of atomic monolayersinvolves mechanisms which differ from that involved in tensiledeformations or bending of bi- and multilayered systems. Inparticular, bending of graphene monolayers is dominated bychanges of atomic bond and dihedral angles involving multibodyinteractions beyond two-body interactions of nearest-atom neigh-bors (14, 17, 18). Considering this unique character, determinationof the bending rigidity of atomic monolayers has been the topic ofnumerous theoretical and computational studies (14, 15, 17–25). Itis expected that the bending rigidity of graphene should be on theorder of 1–2 eV corresponding to 40–80 kT, where kT is thethermal energy at room temperature. A few experimental mea-surements of bending rigidity of multilayer systems could beachieved, but measurements for atomic monolayers remain par-ticularly challenging because of their difficult manipulation. Thebending rigidity of monolayers has been indirectly deduced fromthe phonon spectrum of graphite (26). Even if graphene sheets areinteracting in graphite, the obtained value, about 1.2 eV, is oftenconsidered as an acceptable estimate. Measurements on individualatomic monolayers were achieved by studying buckling instabilitiesof clamped, and therefore constrained, monolayers (27). Thereported value is about 7 eV, corresponding to 280 kT at roomtemperature. More recent estimates deduced from thermal fluc-tuations of cantilevers rise up to extremely large values of nearly105 kT (16). Measurements for GO, the main precursor of gra-phene-based materials made by solution processing, could not yetbe achieved to our knowledge. GO is obtained by oxidation ofneat graphene (3) in which the hexagonal lattice of sp2 carbonatoms is partially disrupted. As for graphene, tension and com-pression of GO involve changes of the length of C–C bonds,

Significance

Bending of a thin plate simultaneously involves contraction andstretching of matter relative to a neutral plane, and tensile ri-gidity dictates the ability of a thin platelet to be bent. If grapheneor graphene oxide (GO) were actually behaving as thin platelets,they would display high bending rigidity. Bending measurementsfor atomic monolayers remain particularly challenging because oftheir difficult manipulation. We quantitatively measure the GObending rigidity by characterizing the flattening of thermal un-dulations in response to shear forces in solution. The bendingmodulus is found to be 1 kT, which is about two orders ofmagnitude lower than the bending rigidity of neat graphene.Amazingly, the high stiffness of GO is associated with an un-expected low bending modulus.

Author contributions: P.P., R.J., G.W., and C.Z. designed research; P.P., R.J., W.N., F.N.,A.C., S.H.A., G.W., and C.Z. performed research; R.J. contributed new reagents/analytictools; P.P., W.N., F.N., T.D., A.C., and C.Z. analyzed data; R.J. and S.H.A. synthesizedsamples; and P.P. and C.Z. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: zakri@crpp-bordeaux.cnrs.fr.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1605121113/-/DCSupplemental.

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explaining thereby the high stiffness of GO, not so different fromthat of neat graphene. Throughout the present article, “stiffness”means the in-plane tensile/compression modulus. However, GOshows a hexagonal lattice of sp2 carbon atoms (3) that is partiallydisrupted and that may lead to unexpected mechanical propertiesregarding bending deformations.To answer this question, we use an approach that allows the

bending rigidity of free and weakly interacting individualized GOmonolayers to be measured. This approach consists of analyzingthe flattening of thermal undulations of GO sheets in response tominute forces of a shear flow. Considering their atomic thick-ness, GO monolayers are indeed expected to fluctuate in theabsence of any mechanical constraints. This behavior has beenreported for highly flexible and liquid systems formed by sur-factant or phospholipid membranes (28–30). Because of theirliquid nature, surfactant bilayers display an extremely lowbending modulus of only a few kT (31, 32). This low value makestheir thermal undulations of large amplitude, and sensitive to thestress resulting from a liquid flow. Similar to liquid mem-branes, GO is known to form lyotropic liquid crystal phases inboth aqueous (33–36) and organic solvents (37), even at lowconcentration due to a very large aspect ratio (38). GO liquidcrystals are oblate nematic with long-range orientational orderand pronounced spatial correlations along the nematic director,which is why they are often considered as pseudolamellar systems(39). Using the combination of synchrotron X-ray diffraction atsmall angles and in situ rheology (rheo-SAXS), we unravel severalfeatures of the behavior of GO suspensions under flow. Manysuspensions of 2D rigid platelets (40–42), clays in particular, exhibita strong shear-thinning behavior. In rigid systems, this shear-thin-ning behavior is generally correlated to shear-induced alignment ofthe particles. Here, we find that in contrast to other known plateletsystems (40–42), shear of GO suspensions is associated with anincrease of the fraction of aligned particles rather than an en-hancement of their orientational order. In addition, coexistence ofmaterials aligned in different directions is observed, and the relativefractions of these differently aligned species vary with the shear rate.More critically, the spacing between GO layers is found to decreasewith increasing shear. This behavior confirms that GO layers exhibitthermal undulations of large amplitude at rest or under weak shear.The GO layers are sufficiently large and flexible so that their un-dulations can be literally ironed out by the shear. This mechanism,which is reminiscent of the suppression of undulations in highlyswollen surfactant lamellar phases (28–30), allows us to measure thebending modulus of GO monolayers. Following models first de-veloped for lamellar phases, the bending rigidity is found to be 1 kT.Furthermore, we observe that the present undulations remain suf-ficiently small so that the layers, even at rest, can be viewed as 2Dextended objects rather than crumpled particles (43, 44). The foundbending rigidity of GO monolayers compares therefore with thebending rigidity of liquid membranes. Whereas liquid membranesexhibit low in-plane elasticity (45), GO ranks among the stiffestknown materials. This unique behavior is discussed by consideringthe different mechanisms at play in stretched and bent monolayers.

Results and DiscussionTwo types of GO materials, homemade GO (HGO) and com-mercial GO (CGO), have been used in the present study. Detailsof their preparation are given in Materials and Methods. Com-plete results for HGO are presented throughout the paper andadditional data for CGO are provided in Supporting Information.GO materials are polydisperse in size and shape. HGO sheetsdisplay lateral sizes as large as 10 μm, as shown by the scanningelectron micrograph in Fig. S1A, with a mean value of 4.3 μm(Fig. S1C). Qualitatively, both HGO and CGO suspensionsdisplay a solid-like behavior at rest while they flow above largeenough stresses. Such a behavior is quantitatively confirmed byflow curves pictured in Fig. S2A and determined through shear

startup experiments at different shear rates. For each value ofthe applied shear rate, the stress is observed to reach a constantvalue after a transient period of about 500–1,000 s. The HGOsample behaves as a yield stress fluid, the constitutive equationof which is well described by a Herschel–Bulkley model (46) witha yield stress of about σc = 24 Pa. CGO sample similarly behavesas a yield stress fluid with a yield stress σc = 72 Pa (Fig. S2B).The high flux of X-ray synchrotron radiation is well suited to

reveal the structure of the aforementioned solutions under shear.As depicted in Fig. 1, two measurement configurations are used:the radial one for which the incident beam passes through thecenter of the Couette cell along the radial direction, perpendicu-larly to the direction of the flow, and the tangential one for whichthe incident beam passes tangentially through the center of thecell gap and parallel to the direction of the flow. GO dispersionshave been reported to form liquid-crystalline phases with apseudolamellar organization (34, 39). Similar behavior is observedin some materials made of stiff platelets. Such systems align undershear with the particles oriented parallel to the cell walls, whichwould correspond to orientation 1 in Fig. 1 [sometimes this ori-entation is referred to as the “c” orientation (41)]. As seen further,the situation is more intricate for GO solutions. Two-dimensionalscattering steady-state patterns of an HGO dispersion flowingunder a constant shear stress of 66 Pa are shown in Fig. 2 A and B.Strongly anisotropic diffraction patterns are obtained in both

radial and tangential configurations. The anisotropy of the tan-gential pattern shows that orientation 1 is largely predominantamong the three main possible ones. Indeed, the flakes, even atrest, tend to spontaneously align parallel to the walls of the Couettecell. Such an alignment minimizes the excluded volume of theflakes and can be viewed as an entropic alignment of the particles.It is observed in lyotropic liquid crystals made of disk-like micellesat equilibrium (47, 48).In radial configuration, orientation 1 is not visible and no

anisotropy would be observed if all of the flakes were showing

Fig. 1. Scheme of the Couette cell depicting tangential (T) and radial (R) con-figurations of irradiation. The X-ray beam is represented by the arrows in bothgeometries. GO flakes are sketched by flat platelets and the three possible orien-tations of these flakes are illustrated (labeled 1, 2, and 3). Orientation 1: GO flakesare parallel to the flow direction and to the Couette cell walls. Orientation 2: GOflakes are parallel to the flow direction but perpendicular to the cell walls. Ori-entation 3: GO flakes are perpendicular to the flow direction and to the cell walls.

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this orientation. Thus, the clear anisotropic signal pattern observedin the radial configuration reveals that a fraction of the flakes isoriented along the configuration labeled “2” in Fig. 1 [sometimesreferred to as “a” orientation (41)]. Moreover, the scattered in-tegrated intensity in the radial configuration is 100× smaller thanthe intensity in tangential geometry. This difference means thatorientation 2 is present but not predominant compared with theorientation parallel to the cell walls. A detailed discussion about thedegree of orientations of the GO flakes is given in Radial Integra-tions and Discussion About the GO Flake Orientations and Fig. S3.More quantitative analysis is provided in Fig. 2 with the results

of azimuthal integrations of the scattered intensity for both radial(R) and tangential (T) configurations for flows under differentapplied shear stresses. Azimuthal integrations are performed eitherhorizontally (H) or vertically (V) using an aperture angle of 45°.TH, TV, and RV data provide structural information on GOmonolayers that are oriented parallel to the flow direction (orien-tation 1 and 2), whereas the RH integration provides informationabout any ordering perpendicular to the shear flow (orientation 3).The presence of at least one broad peak in each spectrum is

noteworthy. A second-order peak is even observed in the TH in-tegration at a wave vector twice the wave vector of the first-orderdiffraction peak. The present data are characteristic of a lamellarphase, as previously observed in graphene suspensions at rest (39,49) and in other inorganic platelet systems (50, 51). This is why thepresent phase can be considered as a pseudosmectic or pseudola-mellar phase in such concentrated regimes. Related more dilutematerials could display nematic ordering without strong positionalcorrelations (52). At large wave vectors, Iq2 is found to be constant,at least for configurations in which the scattered intensity is largeand not potentially erroneously modified by subtraction of thebackground intensity. This behavior indicates that the flakes can beviewed as 2D extended objects with a fractal dimension of 2 ratherthan as crumpled particles. This behavior is reminiscent of the be-havior of conventional surfactant lamellar (53). The effect ofthermal undulations is not seen because of their small characteristiclength scales. We note that Iq2 is not constant in the RH integration(Fig. 2E). However, the data have to be considered with cautionin this configuration because the scattered intensity is very lowand likely affected by subtraction of the background intensity.

A B

C D

E F

Fig. 2. (A and B) Two-dimensional X-ray patterns of an HGO suspension flowing under a shear stress of 66 Pa. The two patterns are obtained, respectively, intangential (A) and radial configuration (B). (C–F) X-ray spectra: scattered intensity I multiplied by the square of the wave vector q as a function of q. Theintensity I is obtained by integration of a series of 2D patterns recorded at different shear stresses. (C) Horizontal integrations of the tangential pattern (TH).(D) Vertical integrations of the tangential pattern (TV). (E) Horizontal integrations of the radial pattern (RH). (F) Vertical integrations of the radial pattern(RV). Horizontal and vertical integrations are performed within a sector of angular aperture of 45°. Dashed black lines emphasize the peak shifts. “Notches”appearing in the TV or RV curves are artifacts originating from the masked detector areas (green arrays in A and B).

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Nevertheless, this subtraction, regardless of the considered config-uration, does not affect the existence of peaks resulting from spatialcorrelations between the particles. Actually such peaks are clearlyvisible in all configurations. The maxima that Iq2 displays in all of theconfigurations reveal a characteristic average uniform spacing be-tween the aligned flakes. However, in contrast to mineral lamellarphases (40–42), here the wave vector of the peak is sensitive to theshear stress, as schematized by black dotted lines in the differentgraphs of Fig. 2. The peaks shift toward larger wave vectors withincreasing values of the shear stress. By contrast to the TH, TV, andRV configurations, the RH intensity decreases with the shear stress.This result can be intuitively understood by considering that

flakes perpendicular to the flow experience large drag viscousforces and tend to be reoriented along the flow with increasingshear. Other features are less intuitive and arise from distinctivefeatures of GO materials. The average interlayer distance d be-tween the flakes is given by d = 2π/q*, where q* denotes the wavevector at which Iq2 is maximum. As a key result, d is found todecrease with increasing shear stress (Fig. 3). Changes of d arequite surprising because the GO concentration is unchanged andno water is expelled from the sample. The phenomenon is ob-served for both HGO and CGO (Fig. S4). A similar behavior hasbeen observed in highly swollen and flexible surfactant lamellarphases. It originates from a flattening under shear of thermalundulations (28, 54–56). In conventional lamellar phases, longwavelength bending fluctuations induce repulsive interactionsthat stabilize the membranes. Suppression of undulations isassociated with a decrease of the repulsive interactions betweenthe membranes which can lead to instabilities and even to thecollapse of the lamellar phase (30). The stability of GO sus-pensions is essentially due to electrostatic repulsions between theflakes. Therefore, the decrease of their separation cannot beexplained by a direct reduction of repulsive interactions. The pre-sent flattening reflects in fact an intrinsic elastic response of theflakes that sustains the shear applied to the suspension. This effectis schematized in Fig. 3. As indicated in ref. 30, the volume fractionφ for flat lamellae is given by φ= t=d, where t is the actual thicknessof the membranes and d the layer spacing. When the membranesfluctuate the volume fraction is now given by φ= hA=dit=Ap, whereA is the total surface area of the sheets, and Ap is the projectedarea orthogonal to the mean normal surface. In our experiments,the volume fraction is kept constant and changes of d are only dueto changes of Ap. The latter are governed by thermal fluctuationsand by their suppression under flow, regardless of the exact originof the repulsive interactions between the sheets. Following modelsdeveloped for thermal fluctuations of lamellar phases, it is possibleto predict the effect of shear on the flattening of undulations (29,30) and in particular the evolution of the relative variation of thelayer spacing:

Δdd0

=kT24πκ

ln�1+

R6   η2 _γ2

24π4κ2

�, [1]

where kT is the thermal energy, R the diameter of the flakes, ηthe viscosity of water, and κ the bending modulus of the flakes.Δd = d0 − d is the variation of layer spacing with respect to thereference taken at rest d0. Derivation of Eq. 1 is given in Determi-nation of the Bending Modulus from Shear-Induced Flattening ofUndulations and Fig. S5. We note that a related approach has beenused in numerical simulations to analyze thermal fluctuations ofgraphene sheets and deduce thereby its theoretical bending rigidity(15). This analysis is consistent with our experiments except thatthere is an effective tension arising from shear forces in the presentapproach. In the absence of tension, the amplitude of simulatedgraphene fluctuations remains below 1 Å at 330 K (15). Here, at aneven lower temperature of 298 K, the spacing between GO flakesvaries by almost 15 Å when the material is sheared. Unfortunately,

similar simulations for GO have not yet been performed to ourknowledge. Those would be particularly interesting for closer com-parisons with the present experiments. Undulation fluctuations arehere of giant amplitude and hint at a very low value of bendingrigidity of GO compared with neat graphene. Measurements at restcould actually not be performed in the Couette cell, which had tobe maintained under rotation for averaging purposes of the diffrac-tion intensity. We have taken for the reference a value of d veryclose to that measured for the smallest stress above the yield stressof the suspensions. For HGO the d measured for a stress of 66 Pais 17.95 nm and d0 is taken as 18 nm. For CGO the dmeasured fora stress of 77 Pa is 17.35 nm and d0 is taken as 17.4 nm. We shallemphasize that the rest of the discussion is not very sensitive tothe choice of d0. The presently considered values are in good agree-ment with interlayer spacing distances previously measured on sim-ilar systems at rest (39). Variations of d as a function of the shearstress provide therefore an unprecedented opportunity to measurethe bending modulus of GO layers. Such a measurement is of courseonly possible provided that Eq. 1 can fit the experimental data withonly two unknown independent parameters, which are the averagesize of the flakes R and their bending modulus κ. As shown in Fig.3B, we actually find an excellent agreement between the model andthe experimental data (see Fits of Experimental Data with DistinctValues of the Bending Rigidity, Fig. S6, and Table S1). The parametersdeduced from the fits are R = (5.5 ± 2.0) μm and κ = (1.0 ± 0.2) kTfor HGO, and R = (3.4 ± 0.3) μm and κ = (1.0 ± 0.2) kT for CGO.The fact that reasonable values are found for the average lateral

size of the flakes supports the validity of the present approach.Furthermore, the greater value of R found for HGO is also con-sistent with the origin of the samples. Indeed, particular care wastaken for the production of HGO to achieve large flakes. Suchcare was not taken to our knowledge for the preparation ofcommercial CGO, which is therefore expected to display a smalleraverage lateral size.The same value of κ found within error bars for both HGO

and CGO is natural because both materials are chemically sim-ilar, and further confirms the validity of the approach. Thebending modulus of about 1 kT is almost 2 orders of magnitude

A

B

Fig. 3. (A) Sketch of the shear-induced flattening of the GO flakes. (B) Nor-malized variation of the spacing between GO layers for HGO and CGOmaterialsas a function of shear rate (blue circles experiments for HGO, green squaresexperiments for CGO). The black lines show fits of the data using Eq. 1. (Inset)Evolution of the smectic distance d with the shear stress σ in the HGO sample(see Fig. S4 for CGO).

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lower than the value of neat graphene (14, 15, 17–27). Thisdifference is much greater than the differences of Young’smoduli of GO and neat graphene, which reflects that bendingand stretching do not involve the same mechanisms. Stretching isprimarily dominated by changes of the length of C–C bondsbetween neighboring atoms, whereas bending of an atomicmonolayer is dominated by changes of bond and dihedral angles(18). Therefore, bending involves multibody interactions beyondnearest-neighbors interactions. The small difference of Young’smoduli between GO flakes and neat graphene suggests that thedisruption of the carbon sp2 lattice when graphene is oxidizedhas a limited effect on mechanical properties as long as interactionsbetween nearest neighbors are considered. However, as reflectedby the large difference of bending rigidity, this disruption has muchmore dramatic consequences when multibody interactions areconsidered. The present results call for theoretical and compu-tational studies to more deeply understand the above phenom-ena. Actually, the ultralow bending rigidity of GO compares withthe bending rigidity of self-assembled liquid bilayers (31, 32) whichinvolve only physical interactions.Self-assembled liquid bilayers display an in-plane elastic

modulus of 10 MPa (45), whereas GO has a Young’s modulus ofseveral hundred gigapascal. Nevertheless, despite its quasi-liquidstate, GO, such as self-assembled bilayers, preserves a nonnegligiblerigidity sufficient to form liquid crystalline phases. This picture isfurther confirmed by the scattering patterns which indicate a fractaldimension of 2, in contrast with previous light-scattering exper-iments (43) but in agreement with electron micrographs of freeze-fractured materials (44).

ConclusionUsing the high flux of synchrotron radiation, we have shown thatthe main precursor of monolayer graphene in material process-ing exhibits unique structural features under flow. GO particlesdisplay a pronounced shear-induced alignment, which is not onlyvaluable for the fabrication of flow-aligned structures and de-vices (57–65) but also for analyzing the giant thermal fluctuationsrelated to the bending rigidity of GO particles. As observed insome self-assembled soft materials (66–68), rheo-SAXS studiesreveal that the flow-induced alignment of GO is more subtlethan intuitively expected. Depending on the flow velocity, dif-ferent fractions of materials align along different directions.More importantly, the spacing between the flakes decreases inresponse to viscous forces. The above phenomena may stronglyalter the structure and therefore the resultant properties ofmaterials made by liquid processing. They also allow for mea-surements of the bending rigidity of GO flakes, which is found tobe 1 kT, and comparable with the bending rigidity of liquid self-assembled bilayers. It is known that the aromatic system andchanges of dihedral angles play an important role in the bendingrigidity of graphenic materials. The superflexibility of GO showshow disruption of this system can dramatically reduce thebending rigidity. Such a superflexibility is expected to be a sig-nificant advantage for the development of functional and highlybendable coatings, films, and fibers based on GO flakes (38, 60,62, 69–75). The unique combination of in-plane stiffness andflexibility of GO allows for versatility in processing and fabrica-tion coupled with a robustness in the fabricated structure.

Materials and MethodsTwo different samples of GO solutions are used in this study. The first type ofsample, further referred to asHGO, ismade fromGOproducedby theAustralianNational Fabrication Facility (ANFF) following our previous report (34). Expandedgraphite (EG) is first prepared as a precursor of HGO and is mixed with 100 mLsulfuric acid and 5 g potassium permanganate KMnO4 per gram of EG. Themixture is stirred for 24 h before being cooled down in an ice bath. The ad-dition of 100 mL deionized water and subsequently of 50 mL H2O2 at 35 vol %leads to a light-brown solution. The HGO particles are then washed with asolution of hydrochloric acid at 3 vol %, purified by cross-flow dialysis, whichfixes the pH in between 4 and 5. Finally, a gentle shaking leads to the exfoli-ation of the HGO particles in water, with a final HGO concentration of 13mg/mLThe absence of any sonication in the above protocol allows us to producelarge GO sheets with lateral sizes as large as 10 μm, as shown by the scanningelectron micrograph in Fig. S1A, with a mean value of 4.3 μm (Fig. S1C). At last,the solution is concentrated by two successive centrifugations: a first one isperformed under 1,400 × g during 20 min to clean the solution from theremaining aggregates and few layer particles; second, the supernatant is centri-fuged again at 50,000 ×g during 45minwhich produces a suspension at 48mg/mL,as measured in the dry matter. The second type of sample is a CGO watersuspension provided by Graphenea, which contains 4 mg/mL of solid material,among which 95% consists of monolayers. CGO suspensions are further concen-trated following the same protocol for HGO materials. This produces a solutionconcentrated at 54 mg/mL. Assuming a density of 1.8 g/cc for GO materials, it isdeduced that HGO and CGO materials have GO volume fractions of 2.7% and3.0%, respectively. At such large volume fractions, the samples are well above theso-called Onsager isotropic–nematic transition critical volume fraction. This con-centration is theoretically given by φiso ∼ 4ðt=DÞ, where t is the particle thicknessand D the diameter of the flakes (76). For GO materials with e ∼ 0.7 nm and D ∼4 μm, one indeed would expect φiso to be on the order of only 0.1%.

In this article we have decided to focus on the data obtained with thehomemade materials. Data for commercial GO are reported in SupportingInformation. Similar behaviors are observed for both types of solutionsprepared with different sources of graphene, which confirms the robustnessof the present findings.

Rheological Setup. The experiments are performed at the synchrotron, in apolished polycarbonate Taylor–Couette shear cell (rotating inner cylinder ofradius 24 mm, gap e = 1 mm). Rheological data are recorded with a stress-controlled rheometer (Anton Paar Physica MCR 501). Experiments consist ofshear startup flows with shear rates ranging between 0.026 and 262 s−1.

SAXS Measurements. These experiments are performed on the small-anglescattering beamline I22 at Diamond Synchrotron (UK). The incident beam crossesa thin vacuum pipe up to the Couette cell where it goes through the sample. Thescattered beam enters another wide vacuum pipe in which is placed the 2Ddetector (Pilatus P3-2M). The typical size of the beam is 320 (H) × 80 (V) μm. Thesize of the beam being smaller than the gap of the shear cell, we adjust itsposition to get an impact in the center of the gap. The wavelength of the in-cident beam is fixed at 0.999 Å (or 12.4 keV) and the detector is positioned at9.7 m from the sample so that the accessible range for the wave vector q definedby q= (4π/λ)sinθ, where 2θ denotes the scattering angle, is 0.002 Å−1<q< 0.15 Å−1.The intensity I scattered by the materials is computed by subtracting the in-tensity scattered by the sample to that of pure water, using the software suiteDAWN provided at the synchrotron. The very high photons incident flux allowsthe determination of coupled structural and rheological behaviors.

ACKNOWLEDGMENTS. The authors thank James Doutch and the team ofthe I22 beamline for their professionalism and advice. The authors alsothank the Australian National Fabrication Facility and Dr. Sanjeev Gambhirfor the synthesis of GO dispersions. G.W. and R. J. gratefully acknowledgefunding from the Australian Research Council Centre of Excellence Scheme(Project CE 140100012). We acknowledge funding from the French NationalGrants ANR-10-LABX-0042-AMADEus and ANR-GAELIC ANR-15-CE09-0011.

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