hyperbolically patterned 3d graphene metamaterial with negative poisson's ratio and...

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© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 wileyonlinelibrary.com COMMUNICATION Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson’s Ratio and Superelasticity Qiangqiang Zhang, Xiang Xu,* Dong Lin, Wenli Chen, Guoping Xiong, Yikang Yu, Timothy S. Fisher, and Hui Li* Q. Zhang, Dr. X. Xu, Prof. W. Chen, Y. Yu, Prof. H. Li Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology) Harbin 150090, P. R. China E-mail: [email protected]; [email protected] Q. Zhang, Dr. X. Xu, Prof. W. Chen, Y. Yu, Prof. H. Li Center of Structural Health Monitoring and Control School of Civil Engineering Harbin Institute of Technology Harbin 150090, P. R. China Q. Zhang, Dr. G. Xiong, Prof. T. S. Fisher School of Mechanical Engineering Purdue University West Lafayette, IN 47907, USA Q. Zhang, Dr. G. Xiong, Prof. T. S. Fisher Birck Nanotechnology Center Purdue University West Lafayette, IN 47907, USA Dr. L. Dong Department of Industrial and Manufacturing Systems Engineering Kansas State University Manhattan, KS 66506, USA DOI: 10.1002/adma.201505409 objects with higher indentation resistance, such as body armors, shock absorbers, and packing materials. [23,26,28–30] Since the pioneering work of Lakes on the negative Poisson’s ratio of foam structures in 1987, [24] many natural objects or designed artificial systems such as bucklicrystals, [26] tailored 2D graphene, [23] CNT sheets, [31,32] 2D/3D metallic lattices, [33,34] ceramic sponges, [35] cork stoppers, [36] and dip-in direct-laser- writing 3D nanostructures [37] have demonstrated negative Pois- son’s ratios effects. Moreover, metamaterials with re-entrant structures exhibit higher negative Poisson’s ratio and much larger indentation resistance under longitudinal compression than those of conventional porous scaffolds [24,25] because these anomalous properties primarily depend on topological micro- structures rather than material compositions. [29] Some reported graphene monoliths have exhibited large compressibility and high loading-to-weight ratios (40 000) [21] as soft materials but poor tensile resistance due to intrinsic brittleness and weak antisliding stability of interface between graphene sheets. [1–3,5–9,12,15–20,22] Such graphene monoliths often present early fracture, low stiffness, and poor fatigue resistance as long as suffering a large tensile strain, which have greatly limited their applicability in engineering. [6] However, a negative Poisson’s ratio response causes transverse contraction during longitudinal compression, leading to triaxial compres- sion states and larger volume shrinkage, and even compres- sive strain in the whole bulks. Such metamaterials can exhibit superior mechanical properties (e.g., energy absorbing capacity, indentation/fracture resistance, ultimate strength, maximum elastic strain, and fatigue life). [24] To further benefit mechanical robustness and to overcome the challenge of poor tensile resist- ance of graphene monoliths, significant attention is warranted to develop a scalable graphene metamaterial (GM) with a re- entrant microstructure and negative Poisson’s ratio response. [38] In this article, we highlight the synthesis of GM with well- ordered hyperbolic pattern and hierarchical honeycomb-like scaffold of microstructure by a modified hydrothermal approach and subsequent oriented freeze-casting process. The designed local oriented ‘buckling’ responses of multilayer graphene cel- lular walls in the microstructure generate a tremendously large macroscopic negative Poisson’s ratio ( ν = 0.38) that is tun- able by adjusting the structural porosity ( λ) or effective bulk density ( ρ e ) of the GM (where ρ e defines as ρ e = ρ 0 /(1| ε 11 |) during compression, ρ 0 is the density of GM at free state). The impacts of freeze-casting orientation and macroscopic aspect ratio (height, L, to diameter, D: L/D) on the Poisson’s ratio are systematically elucidated. Moreover, the mechanisms of nega- tive Poisson’s ratio and compressive strain mapping of GM are investigated by in situ observations of microstructural evolution 3D macroscopic graphene monoliths such as microlattices, [1] hydrogels, [2] sponges, [3,4] petal arrays, [5] and aerogels [6–14] offer a promising combination of lightweight (<10 mg cm 3 ), [3,6–10,13,15] large specific surface area (200 m 2 g 1 ), [16] outstanding elec- trical conductivity (20 S cm 1 ) [6,8,15] and excellent thermal insulating capacity (15 mW m 1 K 1 ). [14] Such 3D graphene functional materials have demonstrated their widespread appli- cations in scientific and engineering fields, including stretch- able electronics, [6,8,12,15,17] energy storages, [5,16,18,19] magnetic actuated elastomers, [12] and electrochemical catalysis. [11,20] Most contemporary reports focus on mechanical compressi- bility, [1,3,6,7,10,11,21] electric conductivity, [9,12,15,17] and electrochem- ical performance, [5,16,18–20,22] but few on Poisson’s ratio, [3,23] which is becoming highly important due to its great impacts on strain distribution and mechanical robustness as materials undergo large deformation. [24] In elastic theory, Poisson’s ratio ( ν ij = ε ii /ε jj ) defines the neg- ative ratio of transverse strain ( ε ii ) to longitude applied strain ( ε jj ). [25,26] The relationships between Young’s modulus ( E), bulk modulus ( B), shear modulus ( G), and Poisson’s ratio ( ν) are expressed as = + = + 2 (1 ) 3(1 2) and 2(1 ) B G v v G E v , where ν ranges in 1 to 0.5 to ensure the positive values of B and G. [24,25,27] Materials with negative Poisson’s ratio contract in the transverse direction under longitudinal compression to form hyperboloid-shaped configurations, thus making them for better use of protective Adv. Mater. 2016, DOI: 10.1002/adma.201505409 www.advmat.de www.MaterialsViews.com

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© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1wileyonlinelibrary.com

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Hyperbolically Patterned 3D Graphene Metamaterial with Negative Poisson’s Ratio and Superelasticity

Qiangqiang Zhang , Xiang Xu ,* Dong Lin , Wenli Chen , Guoping Xiong , Yikang Yu , Timothy S. Fisher , and Hui Li*

Q. Zhang, Dr. X. Xu, Prof. W. Chen, Y. Yu, Prof. H. Li Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education (Harbin Institute of Technology) Harbin 150090 , P. R. China E-mail: [email protected]; [email protected] Q. Zhang, Dr. X. Xu, Prof. W. Chen, Y. Yu, Prof. H. Li Center of Structural Health Monitoring and Control School of Civil Engineering Harbin Institute of Technology Harbin 150090 , P. R. China Q. Zhang, Dr. G. Xiong, Prof. T. S. Fisher School of Mechanical Engineering Purdue University West Lafayette , IN 47907 , USA Q. Zhang, Dr. G. Xiong, Prof. T. S. Fisher Birck Nanotechnology Center Purdue University West Lafayette , IN 47907 , USA Dr. L. Dong Department of Industrial and Manufacturing Systems Engineering Kansas State University Manhattan , KS 66506 , USA

DOI: 10.1002/adma.201505409

objects with higher indentation resistance, such as body armors, shock absorbers, and packing materials. [ 23,26,28–30 ] Since the pioneering work of Lakes on the negative Poisson’s ratio of foam structures in 1987, [ 24 ] many natural objects or designed artifi cial systems such as bucklicrystals, [ 26 ] tailored 2D graphene, [ 23 ] CNT sheets, [ 31,32 ] 2D/3D metallic lattices, [ 33,34 ] ceramic sponges, [ 35 ] cork stoppers, [ 36 ] and dip-in direct-laser-writing 3D nanostructures [ 37 ] have demonstrated negative Pois-son’s ratios effects. Moreover, metamaterials with re-entrant structures exhibit higher negative Poisson’s ratio and much larger indentation resistance under longitudinal compression than those of conventional porous scaffolds [ 24,25 ] because these anomalous properties primarily depend on topological micro-structures rather than material compositions. [ 29 ]

Some reported graphene monoliths have exhibited large compressibility and high loading-to-weight ratios (≈40 000) [ 21 ] as soft materials but poor tensile resistance due to intrinsic brittleness and weak antisliding stability of interface between graphene sheets. [ 1–3,5–9,12,15–20,22 ] Such graphene monoliths often present early fracture, low stiffness, and poor fatigue resistance as long as suffering a large tensile strain, which have greatly limited their applicability in engineering. [ 6 ] However, a negative Poisson’s ratio response causes transverse contraction during longitudinal compression, leading to triaxial compres-sion states and larger volume shrinkage, and even compres-sive strain in the whole bulks. Such metamaterials can exhibit superior mechanical properties (e.g., energy absorbing capacity, indentation/fracture resistance, ultimate strength, maximum elastic strain, and fatigue life). [ 24 ] To further benefi t mechanical robustness and to overcome the challenge of poor tensile resist-ance of graphene monoliths, signifi cant attention is warranted to develop a scalable graphene metamaterial (GM) with a re-entrant microstructure and negative Poisson’s ratio response. [ 38 ]

In this article, we highlight the synthesis of GM with well-ordered hyperbolic pattern and hierarchical honeycomb-like scaffold of microstructure by a modifi ed hydrothermal approach and subsequent oriented freeze-casting process. The designed local oriented ‘buckling’ responses of multilayer graphene cel-lular walls in the microstructure generate a tremendously large macroscopic negative Poisson’s ratio ( ν = −0.38) that is tun-able by adjusting the structural porosity ( λ ) or effective bulk density ( ρ e ) of the GM (where ρ e defi nes as ρ e = ρ 0 /(1−| ε 11 |) during compression, ρ 0 is the density of GM at free state). The impacts of freeze-casting orientation and macroscopic aspect ratio (height, L, to diameter, D : L/D ) on the Poisson’s ratio are systematically elucidated. Moreover, the mechanisms of nega-tive Poisson’s ratio and compressive strain mapping of GM are investigated by in situ observations of microstructural evolution

3D macroscopic graphene monoliths such as microlattices, [ 1 ] hydrogels, [ 2 ] sponges, [ 3,4 ] petal arrays, [ 5 ] and aerogels [ 6–14 ] offer a promising combination of lightweight (<10 mg cm −3 ), [ 3,6–10,13,15 ] large specifi c surface area (≈200 m 2 g −1 ), [ 16 ] outstanding elec-trical conductivity (≈20 S cm −1 ) [ 6,8,15 ] and excellent thermal insulating capacity (≈15 mW m −1 K −1 ). [ 14 ] Such 3D graphene functional materials have demonstrated their widespread appli-cations in scientifi c and engineering fi elds, including stretch-able electronics, [ 6,8,12,15,17 ] energy storages, [ 5,16,18,19 ] magnetic actuated elastomers, [ 12 ] and electrochemical catalysis. [ 11,20 ] Most contemporary reports focus on mechanical compressi-bility, [ 1,3,6,7,10,11,21 ] electric conductivity, [ 9,12,15,17 ] and electrochem-ical performance, [ 5,16,18–20,22 ] but few on Poisson’s ratio, [ 3,23 ] which is becoming highly important due to its great impacts on strain distribution and mechanical robustness as materials undergo large deformation. [ 24 ]

In elastic theory, Poisson’s ratio ( ν ij = −ε ii /ε jj ) defi nes the neg-ative ratio of transverse strain ( ε ii ) to longitude applied strain ( ε jj ). [ 25,26 ] The relationships between Young’s modulus ( E ), bulk modulus ( B ), shear modulus ( G ), and Poisson’s ratio ( ν ) are

expressed as =+

−=

+2 (1 )

3(1 2 )and

2(1 )B

G v

vG

E

v, where ν ranges in −1 to

0.5 to ensure the positive values of B and G . [ 24,25,27 ] Materials with negative Poisson’s ratio contract in the transverse direction under longitudinal compression to form hyperboloid-shaped confi gurations, thus making them for better use of protective

Adv. Mater. 2016, DOI: 10.1002/adma.201505409

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ON via scanning electron microscope (SEM) during longitudinal

compression. In particular, due to the negative Poisson’s ratio response, well-interconnected scaffolds and strong π–π interac-tions among graphene sheets, the GM shows superelasticity, and excellent mechanical robustness with the highest reported reversible compressibility up to 99%.

A fabrication schematic of the present GM with negative Poisson’s ratio is illustrated in Figure S1 (Supporting Infor-mation). Large-area graphene oxide (LGO) as precursor was employed to build 3D GM scaffolds (Figure S2, Supporting Information). The isolated LGO sheet has an average area of ≈2000 µm 2 (Figure S2b, Supporting Information). Statistically, over 83.4% GO sheets present monolayer with thickness less than ≈1.2 nm, while the remained 16.6% has few-layer struc-tures with thickness ranged from 1.2 to 2.0 nm (Figure S2d, Supporting Information). Such geometric characteristics facili-tate self-assembly of GO sheets into multilayer graphene cel-lular walls by π–π interactions with larger stacking interfaces and fewer interjunctions. [ 6 ] Figure 1 a presents a lightweight GM ( L/D = 1.1) standing on willow catkins in air with an ultralow bulk density of ρ 0 = 8 mg cm −3 . [ 39 ] The GM exhibits hyperboli-cally patterned scaffolds in the SEM images in longitudinal and spoke-like networks in the transverse cross sections, in which the curvatures of hyperbolic patterns are characterized with angle ( θ = 45°) of asymptotic lines (see Figure 1 b,c). As further demonstrated in Figure 1 d,e, the cylindrical GM con-sists of orthogonally combined cone and hourglass-like compo-nents in 3D perspective, indicating a re-entrant micro structure characteristic. The hyperbolically patterned microstructure is attributed to the orientated growth and squeezing of ice crystals during freeze-casting as schematically illustrated in Figure S1b,c of the Supporting Information. [ 10 ] Briefl y, ice crys-tals are synchronously growing inward of GM bulk at the two directions (transverse and longitudinal) under −80 °C ultracold conditions. The as-formed frameworks of LGO in hydrogel are primarily squeezed among the ice crystal boundaries and reori-ented to align along the growth of ice crystals. Subsequently, the ice crystals at two directions intersect around diagonal boundary. After dramatic confrontations, they compromise to defl ect directions and grow inward body center of GM sample, respectively. Eventually, GM forms the anisotropic microstruc-tures in two directions as hyperbolic patterns in longitudinal and spoke-like network in transverse (Figure 1 b,c). Compara-tively, the other reported conventional graphene monoliths, fab-ricated by supercritical freezing in liquid nitrogen (N 2 ) or dry ice (solid CO 2 ), or random freeze-casting processes with tem-perature higher than −80 °C, present chaotic or unidirectional oriented microstructures due to noncontrolling or random growth of ice crystals (Figure S2e,f, Supporting Information).

As shown in the quarter 1–2 cross section (1–2 plane), the microtubules of graphene cellular walls are radially arrayed from horizontal to longitudinal orientation (Figure 1 f,g,h,i). Each microtubule consists of capsule-like cells by approximate size of 50 × 160 µm 2 , in which the LGO sheets self-assemble into a “Y-shaped” facial-linking junction by strong π–π interac-tions with stacked interfacial area ≈625 µm 2 (Figure 1 i). In 2–3 cross section (2–3 plane), these spoke-like interlaced microtu-bules in radial direction are connected with capsule units by an average area size of 20 × 100 µm 2 (Figure 1 g,k,l,m). These

well-orderly linked scaffolds account for the outstanding macro-scopic mechanical robustness and self-supported structural sta-bility of GM. Transmission electron microscope (TEM) images demonstrate that the cellular walls in GM are well-orderly stacked with 40-layer graphene sheets by an interlayer spacing of 0.353 nm (Figure 1 n,o), leading to an ultralarge aspect ratio l/t of more than 12 000 ( l and t are the length and thickness of cellular wall, respectively). This is of fundamental impor-tance for GM achieving a macroscopic negative Poisson’s ratio and superelasticity through oriented local ‘buckling’ and the mechanical robustness of these cellular walls. [ 24–26 ] Figure 1 p demonstrates typical “wrinkled” TEM morphologies of cellular walls and hexagonal diffractive pattern of selected area electron diffraction (SAED) (inset of Figure 1 p); the multilayer graphene stacked structure of “Y-shaped” junction is verifi ed by high-res-olution TEM imaging (Figure 1 q).

The structural sp 2 hybridization, thermal stability, and chemical compositions of GM were further characterized by X-ray diffraction (XRD), Raman spectra, thermo-gravimetric analysis (TGA), and X-ray photoelectron spectroscopy (XPS) (Figure S3, Supporting Information). The results, including a sharp XRD peak at 26.2° (Figure S3a, Supporting Informa-tion), small Raman intensity ratio ( I D /I G = 0.9) (Figure S3b, Supporting Information), large atomic ratio of carbon to oxygen (C 1s /O 1s = 13.3) (Figure S3d–f, Supporting Information), jointly indicate well-ordered stacking of graphene sheets during self-assembly and high graphitization of GM after thermal annealing at 1000 °C. [ 6,7 ] In addition, the GM presents out-standing thermal stability with weight loss less than ≈1 wt% at temperatures ranging from 25 to 1000 °C in an inert atmos-phere (Figure S3c, Supporting Information). Related detailed analysis is provided in the Supporting Information (Figure S3).

As shown in Figure 2 a and Movie S1 of the Supporting Infor-mation, the cylindrical GM sample demonstrates hyperboloid-shaped shrinkage in the macroscopic confi guration and signifi -cant contraction in its microstructure at both transverse direc-tions systematically (2–2 and 3–3) under longitudinal applied compression in the 1–1 direction. Because of the axisymmetric profi le of cylindrical sample, the deformation discussed below is addressed only for the 1–2 plane by related strains of ε 11 and ε 22 . Notably, the curvature of hyperbolic patterns in the micro-structure becomes larger ( θ decreasing from 45° to 20°) with a decrease of ε 11 to −50% ( ε 22 = −14.5%), indicating signifi cant negative Poisson’s ratio and auxetic behavior of this 3D GM scaffold. [ 24–26 ] As shown in Figure S4 of the Supporting Infor-mation, ε 22 monotonically decreases to negative peak of −15%, with ε 11 reaching −45% and subsequently rising to 0 at ε 11 of −85%. Thus the GM presents large transverse contraction in a wide range of longitudinal deformation. Upon further defor-mation, ε 22 becomes positive and increases up to 16.3% at ε 11 = −99%, which verifi es the tunable evolution of anomalous auxetic behavior to conventional transverse expansion response (Figure S5, Supporting Information).

To quantify the auxetic behavior, ν is calculated as the engi-neering Poisson’s ratio by ν = − ε 22 / ε 11 . As shown in Figure 2 b, ν is characterized by the two subsequent regimes as a function of ε 11 : a wide range of negative Poisson’s ratios followed by a posi-tive response. The microscopic structural evolution during com-pression is quantitatively addressed by the change of porosity

Adv. Mater. 2016, DOI: 10.1002/adma.201505409

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( λ ) and effective bulk density ( ρ e ). Initially, ν decreases from near-zero to a peak magnitude of −0.38 with ε 11 decreasing from 0 ( λ = 99.65%, ρ 0 = 8 mg cm −3 ) to −40% ( λ = 59.65%, ρ e = 13.3 mg cm −3 ). Then, ν monotonically increases to become positive at a strain ε 11 of −85% ( λ = 14.65%, ρ e = 53.3 mg cm −3 ) and even up to 0.165 in the hugely compacted state with ε 11 of −99 % ( λ = 0.65%, ρ e = 800 mg cm −3 ). [ 40 ] During unloading pro-cess, ε 11 and ε 22 reversibly return to their original values with a slight hysteretic loop, which is attributed to the anisotropic retardation of van der Waals adhesion between compacted

graphene cellular walls in two directions (1–1 and 2–2). [ 33 ] The GM not only demonstrates negative Poisson’s ratio, but also serve as a functional metamaterial with tunable Poisson’s ratios from negative to positive values depending on adjustments of its structural porosity ( λ ) and effective bulk density ( ρ e ).

It is well known that a negative Poisson’s ratio effect derives primarily from microstructures rather than material composi-tions, [ 24–26,29 ] while freeze-casting orientation and macroscopic aspect ratio L/D account for the formation of GM microstruc-tures. As shown in Figure 2 c, three freezing strategies were

Adv. Mater. 2016, DOI: 10.1002/adma.201505409

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Figure 1. Structural characterization of the GM. a) Cylindrical sample with ultralight weight (bulk density of 8 mg cm −3 ) standing on willow catkins. b,c) Optical images of cross section with a hyperbolic pattern in longitudinal and spoke-like network in transverse directions, respectively. d,e) Optical 3D perspective images of GM structured with cone and funnel-like components as re-entrant structures. f–i) SEM images of hierarchical 3D scaffolds in the quarter region of 1–2 cross section (1–2 plane) with different magnifi cations (500, 200, 50 and 10 µm, respectively). g,k,l,m) SEM images in 2–3 cross section (2–3 plane) with different magnifi cations (1 mm, 50 and 20 µm, respectively). n,o) TEM images of cellular wall cross sections with well-orderly stacked graphene sheets by an interlayer spacing of 0.353 nm. p) TEM image of multilayer graphene cellular walls. The inset shows typical SAED pattern. q) High-resolution TEM image of “Y-shaped” interjunction cross section in (i).

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conducted to investigate their impacts on microstructures of GM. The R-FD label indicates freezing only in the radial direc-tion; S-FD indicates noncontact oriented freezing in two direc-tions (this is the adapted approach for fabricating GM in this paper); and A-FD is frozen only in the axial direction. The other pending directions were thermally insulated by polystyrene baf-fl es (20–30 mW m −1 K −1 ). [ 14 ]

Due to the different orientations and squeezing mechanisms of ice crystals during the freezing process, these as-fabricated 3D graphene monoliths exhibit diverse microstructure patterns.

The S-FD GM shows an orthogonal-hyperbolic pattern with curvature of θ = 45° corresponding to L/D = 1.1, while the R-FD and A-FD samples present unidirectional aligned or chaotic net-works (Figure 2 c, and Figure S6, Supporting Information). The diverse microstructures lead to different responses in terms of Poisson’s ratio and mechanical deformation characteristics. As shown in Figure 2 d, Table S1 and Movie S1 of the Supporting Information, S-FD fabricated GM ( L/D = 1.1) reveals the largest ranged negative Poisson’s ratio from 0 to −0.38 with ε 11 decreasing from 0 to −85%. In contrast, both R-FD and A-FD

Adv. Mater. 2016, DOI: 10.1002/adma.201505409

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Figure 2. The negative Poisson’s ratio of the GM. a) Experimental snapshots and optical images of microscopic confi guration and cross-section view of sample during uniaxial compression in the 1–1 direction with ε 11 of 0%, −35%, and −50%, respectively. b) Evolution of Poisson’s ratio ν as a function of applied ε 11 in a loading-releasing cycle. c,d) The effects of freeze-casting strategies on Poisson’s ratio ν . e,f) The effects of L/D on Poisson’s ratio ν .

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samples produce typical transverse expansion and positive Poisson’s ratios during longitu-dinal compression at all times (Movies S2 and S3, Supporting Information). The reason that R-FD and A-FD produce positive Pois-son’s ratios is because of their unidirectional or chaotic microstructures (Figure S6, Sup-porting Information), the ‘buckling’ induced elastic-instability randomly happens out-of-plane without specifi c orientations, resulting in transverse expansion as well as those reported graphene monoliths (Tables S2 and S3, Supporting Information). [ 6 ]

Furthermore, to optimize the negative Poisson’s ratio of the S-FD GM, four dif-ferent aspect ratios ( L/D = 0.5, 0.75, 1.1, and 1.5, respectively) were employed to identify size effects on microstructure cur-vatures (Figure 2 e,f). Because of the dif-ferent growth distances of ice crystals at two directions before intersecting, the compro-mised hyperbolic boundary in microstruc-ture is hugely impacted by macroscopic geometric shapes (Figure S1b,c, Supporting Information and Figure 2 e). As a result, the hyperbolic pat-terns of microstructure show various curvatures ( θ = 21° to 55°) depending on L/D (ranged in 0.5 to 1.5). As shown in Figure 2 f, negative Poisson’s ratios signifi cantly depend on L/D or related curvature of the hyperbolic microstructure. With a large L/D ( L/D = 1.5) and smaller curvature ( θ = 55°), the GM only presents negative Poisson’s ratio with ε 11 greater than −25% ( ν = −0.11), and then loses stability with fractures observed in the macroscopic entity for ε 11 below of −35% (Movie S4, Supporting Information, and Figure 2 e). In com-parison, ν presents a negative value over larger extents with ε 11 ranging from 0 to −74%, −75%, and −85% for L/D of 0.5, 0.75, and 1.1, respectively (Figure 2 f). The GM with L/D = 1.1 and orthogonal curvature ( θ = 45°) produces a prior nega-tive Poisson’s ratio with the largest value of −0.38 compared with other two cases ( ν = −0.20 for L/D = 0.75, ν = −0.16 for L/D = 0.5) (Movies S1, S5, and S6, Table S1, Supporting Information). Such GM suggests a signifi cant size effect of geometric confi guration on negative Poisson’s ratio response.

The fundamental reasons for the GM’s signifi cant nega-tive Poisson’s ratio relate to its orthogonally arrayed hyper-bolic pattern in microstructure. Specifi cally, the related cel-lular walls are prone to yield oriented out-of-plane “buckling” events with nearby wall-to-wall contraction or densifi cation, as illustrated in Figure 3 by in situ observation via SEM, leading to macroscopic negative Poisson’s ratio. Using LGO as a pre-cursor to build 3D GM scaffolds, the stacked graphene cellular walls are designed with ultralarge aspect ratios ( t/l = 12 000) to make them easily bend out-of-plane under in-plane applied compression.

Mathematically, as demonstrated in Figure S7 of the Sup-porting Information, the cellular wall is simplifi ed with two edges fi xed element in a mechanical model for the honeycomb-like cellular structures. [ 41–43 ] The stress that triggers “buckling” is calculated by Equation ( 1)

σα α ( )=

+ −⎛⎝⎜

⎞⎠⎟

20

(1 ) 1cr

graphene

graphene2

3

sin cos

E

v

t

l

(1)

where σ cr is the yield stress for cellular wall occurring “buck-ling” event, α is the angle in Figure S7 of the Supporting Infor-mation as a structural parameter, ν graphene is Poisson’s ratio of multilayer graphene sheet and estimated as 0.165, [ 40,44,45 ] E graphene is the Young’s modulus of pristine graphene ( E graphene = 1.0 TPa), [ 40,45 ] t/l is the aspect ratio of the cellular wall ( t/l = 1/12 000).

The yield stress σ cr is calculated to be less than 0.2 kPa (cor-responding strain ε 11 larger than −1%), indicating the designed local “buckling” of cellular walls within the microstructure can be easily triggered under compressive load. This theoretical estimate agrees well with experimental results as shown in Figure 2 b and Movie S1 of the Supporting Information. The GM immediately exhibits a signifi cant auxetic behavior and negative Poisson’s ratio response when ε 11 is less than 0%. Particularly, in situ SEM characterization during compressing in the 1–1 direction demonstrates the defi nite orientation of “wrinkle” morphologies on cellular walls inward, refl ecting the detailed procedure of microstructure “buckling”-induced mac-roscopic negative Poisson’s ratio response (Figure 3 ).

To elucidate the oriented “buckling” process further, the microstructural evolution of a quarter region in 1–2 cross sec-tion was also characterized by SEM in situ observations during compression as shown in Figure S8 of the Supporting Informa-tion. Local displacements in microstructure were extracted by comparing SEM digital images at adjacent times using 2D dig-ital image correlation, [ 46 ] and the strain maps were estimated by the ratio of these relative displacements with respect to the length of tested sample ( L = 5 mm). As shown in Figure 4 and Movie S7 of the Supporting Information, three characteristic regions in longitudinal cross section (1–2 plane, the inset in Figure 4 a) are marked with three lines (A–B, C–D, and E–F) to

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Figure 3. In situ observations via SEM of oriented “buckling” evolution of cellular walls during compression in the 1–1 direction (longitudinal). a) Original free state. b–e) Compression with strains ε 11 of −10%, −35%, −50%, −65%, respectively. f) The released state after removing the applied compression.

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track microstructural evolution as quantifi ed by the azimuthal angle ( β ) referenced to the axis of symmetry (1–1 direction).

Along line A–B, cellular walls arrayed in the 1–1 direc-tion display “wrinkled” morphologies at ε 11 of −5% to −50% and then evolve to a hugely compacted state ( ε 11 = 80%) with β increasing to 65° (Figure 4 a–c), indicating oriented “buck-ling” out-of-plane and a contracting shift inward of the GM bulk. The C–D, as a compromisingly converged boundary after squeezing of ice crystals at diagonal intersection between 1–1 and 2–2 directions, shows an apparent counterclockwise rota-tion with β enlarged from 40° to 90° (Figure 4 a–c). Along line E–F, the horizontal aligned networks near the middle of the cylindrical sample present a large-scale translational motion in the 1–1 direction and contract inward with β almost reaching 90° (Figure 4 a–c). As a result, such oriented evolution of micro-structure results in a macroscopic transverse shrinkage and a negative Poisson’s ratio response. In addition, as shown in Figure 4 a–c and Movie S8, Supporting Information, the strain mapping demonstrates the uniform deformation and oriented contractions of microstructure in the 1–1 direction with the whole region undergoing compressive stress (the arrows point the direction of local displacement). Such deformation charac-teristics serve to strengthen structural robustness and enhance the GM’s mechanical properties (Young’s modulus, compres-sive strength, ultimate compressive strain, fracture/indentation resistance, and fatigue life). [ 11,24,25 ]

As shown in Figure 5 a and Figure S9 of the Supporting Information, the GM exhibits nonlinear superelastic behavior and ultralarge compressibility with a reversible strain up to 99% and corresponding stress over 0.71 MPa (Movies S1 and S9, Supporting Information). This result is the largest supere-lastic deformation and highest record of loading-to-weight ratio (≈ 880 000) reported to date among all prior 3D carbon mono-liths [ 1–3,5–12,15–22,39 ] (Table S3, Supporting Information). Notably, there are no obvious macroscopic fractures or microstructural

degenerations observed during large-scale “buckling” of cel-lular walls (Figure 3 ). Because the negative Poisson’s ratio induces higher volume shrinkage and compressive strain in the microstructure, larger elastic restoring forces of cellular walls can overcome the van der Waals adhesion between graphene sheets. Therefore, the excellent indentation resistance and loading capacity of graphene sheets can be exploited as much as possible under nontensile strain state.

To investigate the effects of negative Poisson’s ratio on fatigue resistance, the GM sample was dynamically compressed for 1000 loading–unloading loops at 0.5 Hz with strains up to 95% (Figure 5 b). The loading–unloading curves in air reveal slight degradation of maximum stress less than 10% with the GM maintaining its original superelasticity and structural robustness (Figure S10, Supporting Information), which is superior to previous maximum strains of ≈90% (Table S3, Sup-porting Information). [ 1–3,5–12,15–22,39 ] Moreover, the GM exhibits a reversible damping capability to absorb vibration energy with an associated energy density of 2.2 J g −1 , with most energy con-verted at strains above 60% when the graphene cellular walls are severely wrinkled or folded (Figure 3 , and Figure S10a, Supporting Information). Importantly, the energy density and ultimate stress of the GM are minimally affected by loading speed (Figure S10b, Supporting Information), which is impor-tant for use as a damping material for energy dissipation. The structural robustness and fatigue resistance of the GM is fur-ther demonstrated by the stability of electrical conductivity (≈1 S cm −1 ) within 100 cyclic compressive deformations at a strain of 95%. [ 3 ]

Normally, Young’s modulus of porous carbon monoliths depends on density as a power function ( E = A ρ e

n , where E is the Young’s modulus, ρ e is the effective bulk density, and A is a constant). [ 1–3,5–12,15–22,39 ] As demonstrated in Figure 5 c, the relationship between E and ρ e of the present GM is related as E ∝ ρ e 1.998 ± 0.046 . For comparison, the index n is 2.17 ± 0.27 for

Adv. Mater. 2016, DOI: 10.1002/adma.201505409

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Figure 4. Microstructure evolution and strain mapping of the GM’s auxetic behavior by in situ observation in SEM. a) Small deformation with ε 11 of −5%. Inset: a quarter region in the bottom-left corner of the transverse cross-section. b,c) Large-scale deformation with ε 11 of −50% and −80%, respectively.

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other 3D graphene monoliths (e.g., aerogels, sponges, cellular, lattices, and foams) and 3.3 ± 0.69 for carbon nanotubes (CNT) foams, respectively. [ 1–3,6–10,12 ] The smaller n in the present GM can be explained by the fact that graphene cellular walls with ultralarge aspect ratio ( t/l = 12 000) have a relatively low stiffness.

In addition, the GM also presents superelasticity with strain up to of 95% in organic solutions such as acetone (3.10 × 10 −4 Pa s) and silicon oil (6.0 × 10 −4 Pa s) (Figure 5 d, and Figure S9, Supporting Information), and 200 charge–discharge

cycles of silicon oil leads to the stress decayed of only 14% without apparent structural degeneration, implying a prom-ising application as a recyclable absorbing material for spilled organic solutions in environmental remediation (Figure 5 e, and Figure S11, Supporting Information).

Moreover, although there are slight changes in both of strength and Young’s modulus, the GM retains its original excellent compressibility and superelasticity even at ultralow (−190 °C in liquid nitrogen) and high temperatures (500 °C in

Figure 5. Superelasticity and mechanical robustness of the GM. a) Uniaxial compression with reversible strain up to 99%. Inset: incremental strain up to 20%, 50%, 65%, 80%, 90%, and 95%, respectively. b) 1000 cyclic compressions at strain of 95%. Inset: the related degenerations of curve and max-stress during cyclic compressions. c) Young’s modulus of GM as a function of effective bulk density compared with other 3D carbon monoliths. d) Comparison of GM compressed in air, acetone and silicone oil at strain up to 95%. e) 200 cyclic compressions in silicone oil with strain up to 95%. f) The temperature dependence of storage modulus, loss modulus and Tan delta by DMA measurements at 10 Hz between −100 and 400 °C.

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air, 1000 °C 1 h annealing in vacuum condition) with a strain of 95%, which is superior to that of other elastomers (Figure S10d, Supporting Information). For instance, rubber-like elastomers become brittle at −50 °C and degenerate at 300 °C in air. [ 3 ] The dynamic material analysis (DMA) was further conducted to demonstrate remarkable viscoelatic stability of the GM in a wide temperature range (−100 to 400 °C), both storage and loss modulus little dependence on temperature. Notably, the loss modulus and Tan delta, as parameters related to mate-rial damping effi ciency, are over one order magnitude higher than those of conventional graphene monoliths. [ 1–3,5–9,12,15–20,22 ] These results imply that the GM has outstanding energy dis-sipation ability due to larger volumetric strain and effective frictions between cellular walls, which makes it promising in applications of protective equipment such as body armor, shock energy absorbers, and packing materials. [ 20,24–27 ]

In conclusion, 3D graphene metamaterial, prepared by a modifi ed hydrothermal approach followed with an oriented freeze-casting process, exhibits a large negative Poisson’s ratio ( v = −0.38) and superelasticity (99% reversible compressibility), which is attributed to its unique hyperbolic pattern and hon-eycomb-like scaffolds in macrostructure. The Poisson’s ratio of GM is highly dependent on its macroscopic aspect ratio ( L/D ), structural porosity and freeze-casting strategies. The microstructural evolution and strain mapping of GM during compression is characterized by in situ SEM, the oriented “buckling” of cellular walls and compressive strain of whole region are combined to explain the fundamental mechanism of negative Poisson’s ratio response. Furthermore, due to nega-tive Poisson’s ratio and strong-connected scaffolds, GM shows outstanding mechanical robustness, superelaticity, high viscoe-lastic stability, and large damping ability. This 3D GM suggests promising applications such as soft actuators, sensors, shock energy dissipation, and environmental remediation.

Experimental Section GM Fabrication : LGO precursor, synthesized by a modifi ed Hummers’

method, [ 6,12,47,48 ] was used to build 3D GM scaffolds. GM was fabricated by a modifi ed hydrothermal approach and a followed oriented freeze-casting strategy. Briefl y, a mixture of LGO precursor (10 mL, 8 mg mL −1 ), ethylenediamine (EDA, C 2 H 4 (NH 2 ) 2 , 20 µL) and sodium borate solution (SBS, Na 2 B 4 O 7 ·10H 2 O, 1 mL, 5 wt%) was ultrasonically dispersed for 0.5 h, and then statically reacted for 6 h at 120 °C after transferred into a Tefl on-lined hydrothermal synthesis autoclave. The as-formed hydrogels was dialyzed in ethanol solution (C 2 H 6 O, 20 vol%) for 24 h to remove residual impurities (EDA, SBS) and some free water. Then, the dialyzed hydrogels was placed in an ultralow chamber (−80 °C) for 24 h without any contacted with thermal baffl es of expanded polystyrene (EPS, (C 8 H 8 ) n , 20–30 mW m −1 K −1 ) to make sure isotropic ice crystallization at both transverse and longitudinal directions. The 3D GM scaffold was obtained by subsequent drying process for 48 h. After followed thermal annealed at 1000 °C for 1 h under argon atmosphere (Ar, 200 sccm at a pressure of 14.5 psi), the reduced GM was fi nally obtained with ultralow bulk density (8 mg cm −3 ) and four different aspect ratio ( L/D = 1.5, 1.1, 0.75, and 0.5, respectively). The other control groups were frozen only in axial or in transverse direction with other directions protected by EPS thermal baffl es, respectively.

Other experimental details, including characterizations and mechanical/electrical properties tests, are provided in the Supporting Information.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements The authors gratefully acknowledge support from China National Key Technology R&D Program (Grant No. 2011BAK02B02), China Scholarship Council (CSC) 7000 Oversea Scholarship program (Grant No. 201406120186), the US Air Force Offi ce of Scientifi c Research under the MURI program on Nanofabrication of Tunable 3D Nanotube Architectures (Grant No. FA9550-12-1-0037), and the US National Science Foundation under its Scalable Nanomanufacturing program (Grant No. 1344654).

Received: November 3, 2015 Revised: December 4, 2015

Published online:

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