Diamond & Related Materials 111 (2021) 108225

Available online 15 December 20200925-9635/© 2020 Elsevier B.V. All rights reserved.

Quasi-static compression properties of graphene aerogel

Lulu Niu a, Jing Xie a,*, Pengwan Chen a,*, Guangyong Li b, Xuetong Zhang b

a State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China b Suzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences, Suzhou, China

A R T I C L E I N F O

Keywords: Graphene aerogel Axial compression Microstructure evolution Negative structural Poisson’s ratio Toughness

A B S T R A C T

Graphene aerogel (GA) is a promising candidate for energy absorption purposes because of its very low density, high specific surface area and porous structure. GA samples, prepared by the Sol-Gel method, were tested under quasi-static compression, and characterized via surface area analyzer, as well as scanning electron microscopy and transmission electron microscopy. The results show that 98% (and above) porous GA samples, whose elastic modulus is 2.9 MPa, can support at least 35,000 times its weight. Scaling analysis shows that the mechanical properties of GA are superior to those of conventional polymeric open-cell foams. The GA samples exhibit a negative structural Poisson’s ratio under the uniaxial compression test, which is most likely due to the bread-like microstructural evolution. Due to the mesopores of the GA sample as well as the negative structural Poisson’s ratio, the GA has considerable toughness.

1. Introduction

Graphene is a one-atom-thick layer of carbon atoms (approximately 0.4 nm) arranged in a hexagonal lattice [1]. As a two-dimensional (2D) nanomaterial, it has been the focus of intense interest since its discovery in 2004 due to its remarkable carrier mobility (10,000 cm2∙V− 1∙s− 1), superior thermal conductivity (5000 W∙m− 1∙K− 1) [2] and excellent mechanical strength (130 GPa) [3]. A current challenging problem is about how to overcome the π-π stacking interactions between graphene sheets and convert the 2D graphene sheet to a bulk graphene material in order to fully exploit the properties of graphene. Certain methodologies have been devised to prepare three-dimensional (3D) structure gra-phenes such as aerogels [4], hydrogels [5] and cellular monoliths [6]. Among these structures, the aerogel shows a great promise because it can be lighter than air and has thus attracted much attention in recent years [7].

Aerogels were first synthesized from silica gels by replacing the liquid component with a gas [8]. Nowadays, the aerogels are prepared from molecular precursors (generally graphene oxides) by sol-gel methods and followed by either freeze or supercritical drying to replace the solvents with air [9]. Aerogels exhibit high porosity (>90%), low density (<3 kg∙m− 3), low thermal, low refractive index and low dielectric constant, which can be are applied in a variety of fields [10], such as energy storage/conversion [11], catalysis [12], environmental remediation [13], sensing devices [14], supercapacitor electrode [15],

electromagnetic interference shielding [16]. Aerogels are generally considered as elastic and brittle materials.

Several researchers reported that they have synthesized mechanical strong aerogels [17–19], whose elastic modulus (up to 180 MPa) is higher than that of the common silica aerogels (2.25 MPa with a density of 0.1 g∙cm− 3), but a few orders of magnitude lower compared to dense glasses (68 GPa) or other engineering materials (192 GPa for AISI4000 steel). However, thanks to the high concentration of nano-scale pores, aerogels can be used to capture the high-speed particles. NASA used silica aerogel to capture particles from comet Wild 2 in 2004 [20]. Laboratory hypervelocity impact experiments conducted by Japanese scientists have verified that at impact velocities below 6 km/s the pro-jectiles of aluminum oxide, olivine, or soda lime glass with diameters ranging from 10 to 400 μm were captured without fragmentation by the silica aerogel collector of 0.03 g∙cm− 3 [21]. Moreover, researchers re-ported a negative Poisson’s ratio in the graphene-based materials [22–24]. Materials with negative Poisson’s ratio possess enhanced shear resistance, indentation resistance and fracture toughness, which all point to a number of promising applications, particularly in aerospace, biomedicine, defense and intelligent systems [25].

Molecular Dynamics (MD) simulations have shown that the double vacancy defect can be considered as one of the mechanisms causing the negative Poison’s ratio of graphene [26,27]. The Schwartzite model for sp2-carbon phases was used to explain the near-zero Poisson ratio of sponge graphene [22]. Scanning electron in situ observations revealed

* Corresponding authors. E-mail addresses: jxie@bit.edu.cn (J. Xie), pwchen@bit.edu.cn (P. Chen).

Contents lists available at ScienceDirect

Diamond & Related Materials

journal homepage: www.elsevier.com/locate/diamond

https://doi.org/10.1016/j.diamond.2020.108225 Received 22 October 2020; Received in revised form 2 December 2020; Accepted 10 December 2020

Diamond & Related Materials 111 (2021) 108225

2

an oriented “buckling” evolution of cellular walls of graphene aerogel under axial compression [23], macroscopically resulting in a negative Poisson’s ratio. Wen et al. [24] reported a microstructural hierarchy of graphene films that renders remarkable negative Poisson’s ratios ranging from − 0.25 to − 0.55. They proposed two controlling mecha-nisms for the negative Poisson’s ratios: first is the different microstruc-tural origins due to the different chemical modification methods, such as wrinkles, delamination of closed-packed laminates, ordered and disor-dered stacks; and the other one is by modulating the wavy textures of the inter-connected network of close-packed laminates in the graphene films. Different mechanisms are summarized in Table 1. However, the mechanism(s) that control the Poisson’s ratio of graphene aerogel is still an open question.

In this paper, the relationship between density and mechanical properties of uniaxially compressed GA samples is reported. Combining microstructural, physical and mechanical characterization results, as well as the toughness features, the compression properties of GA samples are analyzed. The scaling laws of mechanical properties of samples, the relationship between the negative Poisson’s ratio and the microstructure evolution, and the toughness are discussed before the conclusion. The present work intends to explore GA’s potential application in the field of energy absorption as a lightweight material.

2. Experiments

2.1. Preparation of graphene aerogels

GA samples were prepared by the Sol-Gel method following the procedure shown in Fig. 1. The graphene precursors (purchased from GaoXiTech, Hangzhou, China) are a graphene oxide (GO) solution, which has a lateral size of 20 nm on average. The GO solution was mixed with ascorbic acid (VC), keeping the mass ratio of GO to VC to 1:5. The mixed solution in a homogeneous dispersion was cast into sample molds

to form the graphene hydrogels through a hot water bath process. Subsequently, the graphene hydrogels were immersed in an ethanol solution via a solvent exchange, and then supercritical CO2 drying was applied to obtain GAs.

2.2. Characterizations

The apparent density (ρa) of GA samples was calculated from the mass (electronic scale, BSM-120.4) and volume of cylindrical samples, and the true density (ρt) was measured using the gas pycnometer (Micromeritics, AccuPyc II 1340). The relative density (ρr) is defined as the ratio of the apparent density to the true density, thus the porosity P of GA samples was calculated by ignoring the air inside the aerogels:

P(%) =

(

1 −ρa

ρt

)

× 100% = (1 − ρr)× 100% (1)

The pore structure of samples was investigated by a surface area analyzer (Micrometrics, ASAP 2460), the specific surface area and pore size distribution were calculated utilizing the Brunauer-Emmett-Teller (BET) method and Nonlocal Density Functional Theory (NLDFT), respectively. The microstructure of the samples was observed by scan-ning electron microscope (SEM, Quanta 400 FEG) and transmission electron microscope (TEM, Tecnai G2 F30). Quasi-static compression testing was performed on a universal material testing machine (Instron 3365) at room temperature with a constant compression speed of 3 mm∙min− 1. The elastic modulus was calculated as the slope of the initial linear portion of the stress-strain curve recorded during compression testing. The Poisson’s ratio is defined as the negative ratio of the transverse strain εxx to the longitudinal strain εyy in the loading direction under uniaxial compression, i.e. ν = − εxx/εyy. For a compression test, the transverse strain is considered positive for a lateral deformation, while the longitudinal strain is considered negative. Unlike the metal materials, it is not easy to define the initial and final deformation of the

Table 1 The mechanisms of negative Poisson’s ratio of graphene-based materials.

Materials Synthesis Poisson’s ratio Mechanism Ref.

Graphene MD simulation In-plane negative and defect density- dependent

Double vacancy defect [26,27]

Spongy graphene A modified solvothermal reaction of GO sheets in alcohol and a subsequent thermal annealing

Near-zero The Schwartzite model for sp2-carbon phases [22]

Graphene metamaterial

A modified hydrothermal approach followed with an oriented freeze-casting process

− 0.38 The oriented “buckling” of cellular walls and compressive strain of the whole region

[23]

Graphene films Vacuum-assisted filtration and evaporation- induced self-assembly methods

− 0.25 to − 0.55 Wrinkles, delamination of close-packed laminates, ordered and disordered stacks; modulating the wavy textures of the inter-connected networks of close-packed laminates

[24]

Fig. 1. The preparation of graphene aerogels. (Sc is in short of supercritical).

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

3

porous materials due to the inhomogeneous deformation. The transverse strain in the present work, therefore, is defined as the ratio of change in the width of the sample’s middle surface to its original width, and it is denoted as εxx*. Thus the Poisson’s ratio becomes ν* = − εxx*/εyy. In order to distinguish from the common Poisson’s ratio, it is called structural Poisson’s ratio hereafter, which is also because the negative Poisson’s ratio observed in the present work is due to the microstruc-tural evolution.

The energy that is invested to deform a material until its failure is regarded as its toughness. The toughness characteristics of GA samples are analyzed through the deformation work Wab absorbed per unit volume (i.e. strain energy density) and energy absorption efficiency Eab, which are respectively defined as follows [28]:

Wab(εi) =

∫ εi

0σ(ε)dε (2)

Eab(εi) =

∫ εi0 σ(ε)dε

σi(3)

where ε is the strain, σ(ε) is the stress function of the strain ε, εi is the strain at any point before the failure (final densification), σi is the stress at ε = εi. The deformation strain energy and the energy absorption ef-ficiency are plotted as a function of the strain, respectively.

3. Results

3.1. Structure and morphologies

The properties of the tested GA samples are summarized in Table. 2. As shown in Fig. 2a, the GA sample is extremely light that can be balanced on a tree leaf! The average apparent density ρa of GA samples is 35.25 mg∙cm− 3, while the true density ρt is 337.87 mg∙cm− 3 in the present work, thus the relative density ρr is 1.06%. The porosity of the GA sample calculated by using Eq. (1) is 98.94%. One GA sample of 28.5 mg can support a weight of 1 kg (>35,000 times heavier than its weight,

Fig. 2b), indicating an excellent static load-bearing capacity. The pore structure of GA samples is shown in Fig. 3, where the black

and red curves are the adsorption and desorption branches of nitrogen isotherms, respectively. The isotherms (Fig. 3a) have a typical type IV hysteresis loop, meaning the GA samples contain mesopores [29]. The specific surface area of GA is 530.87 m2∙g− 1. Comparing with the MoS2 aerogel (18 m2∙g− 1) [30], graphene-CNT aerogels (315 m2∙g− 1) [13], silica aerogels (450 m2∙g− 1) [31] and the 3D polypyrrole-graphene foam (463 m2∙g− 1) [32], GA has a larger specific surface area. As shown in Fig. 3b, the main characteristic macropore (>50 nm) size is 68.5 nm, and the most abundant mesopores (2–50 nm) is 37 nm.

The microstructure of GA samples obtained through SEM and TEM are shown in Figs. 4 and 5, respectively. Before compression (Fig. 4a–c), GA presents a nano-porous 3D network containing partial overlapping graphene sheets with a large number of randomly distributed pores. After compression (Fig. 4d–f), the graphene sheets are densified and have an obvious layered fold structure. The surface area analysis system (Micrometrics ASAP 2460) characterize the pore size ranges from 0.35 to 500 nm, but with SEM, the pores that larger than 500 nm are observed (Fig. 4c), thus the graphene aerogel is a typical hierarchy-porous structure. Fig. 5a–c shows that the smooth graphene sheets overlap each other. The random distribution of graphene sheets causes a variety of potential overlapping methods, such as edge-edge, edge-face, face- face and so on. After compression (Fig. 5d–f), most of the graphene sheets are squeezed into each other to form a folded structure. The simulation results of [33] reveal that there are mainly four typical microstructure evolutions of graphene sheets overlapping methods under external force, including the departure of two contact sheets, the transformation from edge-surface contacting configuration to the surface-surface one, the variation of contacting areas between two surface-surface contacting sheets, and the change of contacting partners. Mingling with a different pattern of microstructure evolution, the deformation energy of GA is dissipated.

)b()a(

Fig. 2. (a) An optical image showing a GA sample standing on a leaf, and (b) a GA sample of 28.5 mg can support a 1 kg weight, which is over than 35,000 times its weight.

Table 2 The properties of GA samples.

Apparent density (mg∙cm− 3)

True density (mg∙cm− 3) Relative density (%) Porosity (%) Specific surface area (m2∙g− 1) Pore sizea (nm) Stress at 73% strain (MPa)

35.25 3337.87 1.06 98.94 530.87 37 0.84

a Note: This is the most abundant mesoporous size.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

4

3.2. Compression behavior

Fig. 6 shows the experimental results of the uniaxial compression test of GA. According to the slope of the stress-strain curve, the strain value of 6.5% and 57% are defined as the split points that dividing the stress- strain curve into three stages, which are (i) elastic stage, (ii) plastic stage, and (iii) densification stage. Note that such stages are character-istic of the compressive response of foams [34], except perhaps for the plastic stage characterized by significant strain hardening, absent in most foams. Likewise, unlike other foams, one can notice a continuous transition from plastic to densification.

Below 6.5% strain, stress and strain show a linear relationship, and the calculated elastic modulus E of GA sample is 2.9 MPa, thus the specific stiffness (E/ρ) is 82.27 kN∙m∙kg− 1, which is higher than that of common silica aerogel (3.89 kN∙m∙kg− 1) [35]. The compressive strength σc of the GA sample is measured to be 0.2 MPa by averaging the

stress between 0.1 and 0.3 strain [36]. With a continued increase of the strain, the pore wall undergoes plastic deformation resulting in a long yield platform, and the deformed shape didn’t recover after unloading, indicating irreversible (plastic) deformation. For strains exceeding 57%, the pore structure is densified and damaged completely, and the maximum stress reaches 0.84 MPa at a strain of 73%.

We normalize the results (ρ, E, σc) by mechanical properties of gra-phene [3] (ρs = 2300 mg∙cm− 3, Es = 1.02 TPa), with other experimental results of GA samples found in the literature [9,37–39], as summarized in Fig. 7. By plotting the data points as functions of sample density on double logarithmic graphs, the scaling laws of the mechanical properties of samples are determined as

EEs

=

(ρρs

)3.13±0.08

(4)

σc

Es=

(ρρs

)3.61±0.08

(5)

3.3. Negative structural Poisson’s ratio

As shown in Fig. 8, the cylindrical GA sample exhibits a shrinkage in the macroscopic configuration at both transverse directions systemati-cally under uniaxial compression. Because of the axisymmetric profile of the cylindrical sample, the deformation discussed below is addressed only for the x-y plane by related strains of εxx and εyy. The shrinkage becomes larger with an increase of εxx (assuming compression as posi-tive direction), indicating a negative structural Poisson’s ratio of GA sample.

To quantify the negative structural Poisson’s ratio behavior, ν* is characterized for the three above-mentioned regimes of the compressive deformation (Fig. 6), as a function of εyy as shown in Fig. 9. The struc-tural Poisson’s ratio ν* drops rapidly during the elastic deformation stage because of the buckling of cellular walls during compression. It maintains a roughly constant value − 0.2 with small fluctuations during the plastic stage and the densification stage, because the GA sample lost the further deformation ability in the transverse direction.

3.4. Toughness analysis

The deformation energy Wab shows an increasing trend (Fig. 10a). During the elastic stage, the graphene skeleton plays a major supporting role in the compression of GA, resulting in low deformation energy. The pore structure collapses and is destroyed by continuous compression loading, and deformation energy increases significantly faster. In the calculated energy absorption efficiency curve (Fig. 10b), energy ab-sorption efficiency Eab increases slowly from the elastic stage to the plastic stage and reaches a maximum value of 0.31 in the densification stage. The GA sample is compressed completely and loses its deforma-tion capacity, the sample consequently cannot dissipate energy any further, thus leading to a decreasing energy absorption efficiency Eab.

4. Discussion

The scaling displayed in Fig. 7 shows a well-defined trade-off be-tween density and strength, so that GA samples can have exceptionally high strength at relatively high density. Considering the exponent of the mechanical properties (Eqs. (4) and (5)) versus density, elastic modulus (3.13 ± 0.08) and compressive strength (3.61 ± 0.08), one can note that those are overall larger than those reported by Ashby and Gibson et al. [40,41] for conventional polymeric open-cell foams (2, 2 for elastic

)a(

)b(

0.0 0.2 0.4 0.6 0.8 1.00

200

400

600

800

1000

1200

Adsorption Desorption

Qua

ntity

Ads

orbe

d (c

m3 /g

STP

)

Relative Pressure (P/Po)

2.5 5 7.5 25 50 7510 1000.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14 macropore

37

mesopore

Por

e V

olum

e(c

m3 /g

)

Pore Width (nm)

68.5

Fig. 3. (a) Nitrogen adsorption and desorption isotherms (BET) and (b) pore diameter distribution curves of the graphene aerogel (NLDFT, the pore diameter of pores is determined in the range between 1.591 nm and 400.309 nm). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

5

Fig. 4. The SEM images of graphene aerogel. (a–c) Original free states. (d–f) The states after compression test.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

6

Fig. 5. TEM images of the graphene aerogel (a–c) before and (d–f) after compression.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

7

modulus and compressive strength, respectively), as well as the simu-lated GA [36] (2.73 ± 0.09, 3.01 ± 0.01). The difference suggests that the mechanical properties of GA are far superior to those of conventional polymeric open-cell foams. Zhou et al. [42,43] reported a similar structure named crumpled graphene that also became stronger with applied strain through the Molecular Dynamics simulation. They developed a non-linear power-law constitution relationship for describing the mechanical behaviors of carbon nanopolymorph-based nanomaterials, revealing that the structural unit significantly in-fluences the loading scheme. Therefore, the controllable assembly of the GAs’ microstructure is very crucial for improving the mechanical properties of GAs.

It is well known that a negative Poisson’s ratio effect derives pri-marily from microstructures rather than material compositions [23]. The cylinder shape of the mold (Fig. 1) used for preparing the GA sample, combining the inevitable volume shrinkage of the hydrogel of graphene during the supercritical CO2 drying, induce the GA sample appears a bread-like structure (Fig. 4a), i.e. a quite dense outer layer embraces a loose inter-core. When the sample is compressed under uniaxial loading, the loose interior phase deforms more than the sur-rounding dense (stiffer) layer. This deformation mismatch produces a contraction inside the sample and drags the boundary layer of the sample inwards. This microstructure evolution leads to a macroscopi-cally negative structural Poisson’s ratio.

The pores could be considered as an integral part of flaws responsible for the failure (densification under compression) of porous materials. GA sample with a negative structural Poisson’s ratio resulting in low crack propagation and require more energy to damage the material, thus has a higher toughness than the conventional positive Poisson’s ratio material with the same density. Energy absorption efficiency Eab is a function of the relative density (ρr) of the sample and can be simply modeled as Eab = a × ρr

− b, where a and b are fitting coefficients [44]. A lighter GA sample (with lower ρr) can absorb the prescribed amount of energy with larger deformation because there is a low-value yielding plateau, and the GA comes up to densification. On the contrary, the heavier GA (with higher ρr) does absorb the same amount of energy with lower

deformation and high stresses. The ideal GA as an energy absorption material is that with an intermediate density, which is able to absorb a sufficient amount of energy without being too heavy. Finding an opti-mum density is a key issue when applying the GA material in the energy absorption field.

Single-layer graphene is approximately 0.4 nm, but after self- assembling, the cellular wall of graphene aerogel is about 10 nm thick (Fig. 5c). What is exactly the assembling mechanism? Which process parameter is the most dominant one? How to control the self-assembling process in order to obtain the desired microstructure? Those questions are very crucial to the future industrial applications of GA.

5. Conclusion

⋅ The prepared GA sample by using the sol-gel method exhibits a hierarchy-porous structure and has a relative density of 1.06% and a porosity of >98%.

Fig. 7. The normalized elastic modulus (a) and compressive strength (b) of GA samples as a function of its mass density. The solid curves are plotted according to scaling laws obtained in the study with slopes of 3.13 and 3.61 for Eqs. (4) and (5), respectively.

0 10 20 30 40 50 60 70 800.0

0.2

0.4

0.6

0.8

1.0 (M

Pa)

yy (%)

i.Elastic stage

ii.Plastic stage

iii.Densification stage

Fig. 6. Compression properties of the graphene aerogel.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

8

Fig. 8. Experimental snapshots of the sample during uniaxial compression with εyy of 0%, 4.8%, 31.9% and 65.0%, respectively. Note that instead of barrelling, the specimen contracts laterally.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

9

⋅ Through the surface area analysis, it was obtained that the size of the most abundant mesopores is 37 nm.

⋅ The elastic modulus of the GA sample is 2.9 MPa, and the maximum energy absorption efficiency is 0.31 due to its nano-porous structure.

⋅ Scaling the mechanical properties of GA indicates its superior per-formance with respect to conventional polymeric open-cell foams.

⋅ The GA samples possess a negative structural Poisson’s ratio under the uniaxial compression test, which is most likely due to the bread- like microstructure evolution.

⋅ Due to the mesopores of the GA sample as well as the negative structural Poisson’s ratio, the GA has considerable toughness.

CRediT authorship contribution statement

Lulu Niu: Writing - original draft, Methodology, Validation, Inves-tigation. Jing Xie: Project administration, Conceptualization, Writing - review & editing,. Funding acquisition. Pengwan Chen: Supervision, Conceptualization, Review, Resources. Guangyong Li: Investigation, Review. Xuetong Zhang: Conceptualization, Resources.

Declaration of competing interest

The authors declare that there is no potential conflict of interest.

Acknowledgments

The project is supported by the Research Fund Program for Young Scholars of Beijing Institute of Technology. We also acknowledge sup-port from the Youth Scholars project of the State Key Laboratory of Explosion Science and Technology (Grants # QNKT19-07). Special thanks are given to Prof. M. Vesenjak for their warm help on the ex-periments, and to Prof. D. Rittel for his kind help in discussing the manuscript.

References

[1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I. V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science (80-.) 306 (2004) 666–669, https://doi.org/10.1126/science.1102896.

[2] D. Saini, Synthesis and functionalization of graphene and application in electrochemical biosensing, Nanotechnol. Rev. (2016), https://doi.org/10.1515/ ntrev-2015-0059.

[3] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science (80-.) 321 (2008) 385–388, https://doi.org/10.1126/science.1157996.

[4] H. Hu, Z. Zhao, W. Wan, Y. Gogotsi, J. Qiu, Ultralight and highly compressible graphene aerogels, Adv. Mater. 25 (2013) 2219–2223, https://doi.org/10.1002/ adma.201204530.

[5] Y. Xu, K. Sheng, C. Li, G. Shi, Self-assembled graphene hydrogel via a one-step hydrothermal process, ACS Nano 4 (2010) 4324–4330, https://doi.org/10.1021/ nn101187z.

[6] L. Qiu, J.Z. Liu, S.L.Y. Chang, Y. Wu, D. Li, Biomimetic superelastic graphene-based cellular monoliths, Nat. Commun. (2012), https://doi.org/10.1038/ncomms2251.

[7] G. Gorgolis, C. Galiotis, Graphene aerogels: a review, 2D Mater. 4 (2017), https:// doi.org/10.1088/2053-1583/aa7883, 032001.

[8] S.S. KISTLER, Coherent expanded aerogels and jellies, Nature. 127 (1931) 741, https://doi.org/10.1038/127741a0.

[9] X. Zhang, Z. Sui, B. Xu, S. Yue, Y. Luo, W. Zhan, B. Liu, Mechanically strong and highly conductive graphene aerogel and its use as electrodes for electrochemical power sources, J. Mater. Chem. 21 (2011) 6494, https://doi.org/10.1039/ c1jm10239g.

[10] M.J. Oh, P.J. Yoo, Graphene-based 3D lightweight cellular structures: synthesis and applications, Korean J. Chem. Eng. 37 (2020) 189–208, https://doi.org/10.1007/ s11814-019-0437-1.

[11] R. Sun, H. Chen, Q. Li, Q. Song, X. Zhang, Spontaneous assembly of strong and conductive graphene/polypyrrole hybrid aerogels for energy storage, Nanoscale. 6 (2014) 12912–12920, https://doi.org/10.1039/C4NR03322A.

[12] L. Peng, Y. Zheng, J. Li, Y. Jin, C. Gao, Monolithic neat graphene oxide aerogel for efficient catalysis of S → O acetyl migration, ACS Catal. 5 (2015) 3387–3392, https://doi.org/10.1021/acscatal.5b00233.

[13] S. Kabiri, D.N.H. Tran, T. Altalhi, D. Losic, Outstanding adsorption performance of graphene–carbon nanotube aerogels for continuous oil removal, Carbon N. Y. 80 (2014) 523–533, https://doi.org/10.1016/J.CARBON.2014.08.092.

[14] X. Xu, H. Li, Q. Zhang, H. Hu, Z. Zhao, J. Li, J. Li, Y. Qiao, Y. Gogotsi, Self-sensing, ultralight, and conductive 3D graphene/iron oxide aerogel elastomer deformable

)a(

)b(

0 10 20 30 40 50 60 70 800.00

0.05

0.10

0.15

0.20

0.25

iii.Densification stage

ii.Plastic stage

Wab

(MJ/

m3 )

yy (%)

i.Elastic stage

0 10 20 30 40 50 60 70 800.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35 iii.Densification stage

ii.Plastic stage

Eab

yy (%)

0.31

i.Elastic stage

Fig. 10. (a) Compression deformation energy curve and (b) energy absorption efficiency curve of the graphene aerogel.

Fig. 9. The structural Poisson’s ratio of graphene aerogels as a function of applied longitudinal strain.

L. Niu et al.

Diamond & Related Materials 111 (2021) 108225

10

in a magnetic field, ACS Nano 9 (2015) 3969–3977, https://doi.org/10.1021/ nn507426u.

[15] P. Lv, X. Tang, R. Zheng, X. Ma, K. Yu, W. Wei, Graphene/polyaniline aerogel with superelasticity and high capacitance as highly compression-tolerant supercapacitor electrode, Nanoscale Res. Lett. 12 (2017) 630, https://doi.org/10.1186/s11671- 017-2395-z.

[16] C.-B. Li, Y.-J. Li, Q. Zhao, Y. Luo, G.-Y. Yang, Y. Hu, J.-J. Jiang, Electromagnetic interference shielding of graphene aerogel with layered microstructure fabricated via mechanical compression, ACS Appl. Mater. Interfaces 12 (2020) 30686–30694, https://doi.org/10.1021/acsami.0c05688.

[17] X. Liu, K. Pang, H. Yang, X. Guo, Intrinsically microstructured graphene aerogel exhibiting excellent mechanical performance and super-high adsorption capacity, Carbon N. Y. 161 (2020) 146–152, https://doi.org/10.1016/j.carbon.2020.01.065.

[18] H. Huang, P. Chen, X. Zhang, Y. Lu, W. Zhan, Edge-to-edge assembled graphene oxide aerogels with outstanding mechanical performance and superhigh chemical activity, Small. 9 (2013) 1397–1404, https://doi.org/10.1002/smll.201202965.

[19] N. Leventis, Three-dimensional core-shell superstructures: mechanically strong aerogels, Acc. Chem. Res. 40 (2007) 874–884, https://doi.org/10.1021/ ar600033s.

[20] S.M. Jones, Aerogel: space exploration applications, J. Sol-Gel Sci. Techn. 40 (2006) 351–357, https://doi.org/10.1007/s10971-006-7762-7.

[21] Y. Kitazawa, A. Fujiwara, T. Kadono, K. Imagawa, Y. Okada, K. Uematsu, Hypervelocity impact experiments on aerogel dust collector, J. Geophys. Res. E Planets. 104 (1999) 22035–22052, https://doi.org/10.1029/1998JE000554.

[22] Y. Wu, N. Yi, L. Huang, T. Zhang, S. Fang, H. Chang, N. Li, J. Oh, J.A. Lee, M. Kozlov, A.C. Chipara, H. Terrones, P. Xiao, G. Long, Y. Huang, F. Zhang, L. Zhang, X. Lepro, C. Haines, M.D. Lima, N.P. Lopez, L.P. Rajukumar, A.L. Elias, S. Feng, S.J. Kim, N.T. Narayanan, P.M. Ajayan, M. Terrones, A. Aliev, P. Chu, Z. Zhang, R.H. Baughman, Y. Chen, Three-dimensionally bonded spongy graphene material with super compressive elasticity and near-zero Poisson’s ratio, Nat. Commun. 6 (2015), https://doi.org/10.1038/ncomms7141, 6141.

[23] Q. Zhang, X. Xu, D. Lin, W. Chen, G. Xiong, Y. Yu, T.S. Fisher, H. Li, Hyperbolically patterned 3D graphene metamaterial with negative Poisson’s ratio and superelasticity, Adv. Mater. 28 (2016) 2229–2237, https://doi.org/10.1002/ adma.201505409.

[24] Y. Wen, E. Gao, Z. Hu, T. Xu, H. Lu, Z. Xu, C. Li, Chemically modified graphene films with tunable negative Poisson’s ratios, Nat. Commun. 10 (2019) 2446, https://doi.org/10.1038/s41467-019-10361-3.

[25] C. Huang, L. Chen, Negative Poisson’s ratio in modern functional materials, Adv. Mater. 28 (2016) 8079–8096, https://doi.org/10.1002/adma.201601363.

[26] J.N. Grima, S. Winczewski, L. Mizzi, M.C. Grech, R. Cauchi, R. Gatt, D. Attard, K. W. Wojciechowski, J. Rybicki, Tailoring graphene to achieve negative Poisson’s ratio properties, Adv. Mater. 27 (2015) 1455–1459, https://doi.org/10.1002/ adma.201404106.

[27] J.N. Grima, M.C. Grech, J.N. Grima-Cornish, R. Gatt, D. Attard, Giant auxetic behaviour in engineered graphene, Ann. Phys. 530 (2018) 1700330, https://doi. org/10.1002/andp.201700330.

[28] G. Belingardi, R. Montanini, M. Avalle, Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram, Int. J. Impact Eng. 25 (2001) 455–472.

[29] M.A. Aegerter, N. Leventis, M.M. Koebel (Eds.), Aerogels Handbook, Springer New York, New York, NY, 2011, https://doi.org/10.1007/978-1-4419-7589-8.

[30] M.A. Worsley, S.J. Shin, M.D. Merrill, J. Lenhardt, A.J. Nelson, L.Y. Woo, A. E. Gash, T.F. Baumann, C.A. Orme, Ultralow density, monolithic WS 2, MoS 2, and MoS 2/graphene aerogels, ACS Nano 9 (2015) 4698–4705, https://doi.org/ 10.1021/acsnano.5b00087.

[31] K.E. Parmenter, F. Milstein, Mechanical strength of silica aerogels, J. Non-Cryst. Solids 223 (1998) 179–189, https://doi.org/10.1016/S0022-3093(97)00430-4.

[32] Y. Zhao, J. Liu, Y. Hu, H. Cheng, C. Hu, C. Jiang, L. Jiang, A. Cao, L. Qu, Highly compression-tolerant supercapacitor based on polypyrrole-mediated graphene foam electrodes, Adv. Mater. 25 (2013) 591–595, https://doi.org/10.1002/ adma.201203578.

[33] C. Wang, D. Pan, S. Chen, Energy dissipative mechanism of graphene foam materials, Carbon N. Y. 132 (2018) 641–650, https://doi.org/10.1016/j. carbon.2018.02.085.

[34] L.J. Gibson, M.F. Ashby, Cellular Solids, Cambridge University Press, Cambridge, 1997, https://doi.org/10.1017/CBO9781139878326.

[35] A.H. Alaoui, T. Woignier, G.W. Scherer, J. Phalippou, Comparison between flexural and uniaxial compression tests to measure the elastic modulus of silica aerogel, J. Non-Cryst. Solids 354 (2008) 4556–4561, https://doi.org/10.1016/j. jnoncrysol.2008.06.014.

[36] Z. Qin, G.S. Jung, M.J. Kang, M.J. Buehler, The mechanics and design of a lightweight three-dimensional graphene assembly, Sci. Adv. 3 (2017), e1601536, https://doi.org/10.1126/sciadv.1601536.

[37] H. Sun, Z. Xu, C. Gao, Multifunctional, ultra-flyweight, synergistically assembled carbon aerogels, Adv. Mater. 25 (2013) 2554–2560, https://doi.org/10.1002/ adma.201204576.

[38] Y. Tao, X. Xie, W. Lv, D.-M. Tang, D. Kong, Z. Huang, H. Nishihara, T. Ishii, B. Li, D. Golberg, F. Kang, T. Kyotani, Q.-H. Yang, Towards ultrahigh volumetric capacitance: graphene derived highly dense but porous carbons for supercapacitors, Sci. Rep. 3 (2013) 2975, https://doi.org/10.1038/srep02975.

[39] M.A. Worsley, S.O. Kucheyev, H.E. Mason, M.D. Merrill, B.P. Mayer, J. Lewicki, C. A. Valdez, M.E. Suss, M. Stadermann, P.J. Pauzauskie, J.H. Satcher, J. Biener, T. F. Baumann, Mechanically robust 3D graphene macroassembly with high surface area, Chem. Commun. (2012), https://doi.org/10.1039/c2cc33979j.

[40] L.J. Gibson, M.F. Ashby, G.S. Schajer, C.I. Robertson, The mechanics of two- dimensional cellular materials, Proc. R. Soc. London. A. Math. Phys. Sci. 382 (1982) 25–42, https://doi.org/10.1098/rspa.1982.0087.

[41] M.F. Ashby, The properties of foams and lattices, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. (2006), https://doi.org/10.1098/rsta.2005.1678.

[42] J.A. Baimova, B. Liu, S.V. Dmitriev, N. Srikanth, K. Zhou, Mechanical properties of bulk carbon nanostructures: effect of loading and temperature, Phys. Chem. Chem. Phys. 16 (2014) 19505–19513, https://doi.org/10.1039/c4cp01952k.

[43] J.A. Baimova, B. Liu, S.V. Dmitriev, K. Zhou, Mechanical properties and structures of bulk nanomaterials based on carbon nanopolymorphs, Phys. Status Solidi Rapid Res. Lett. 8 (2014) 336–340, https://doi.org/10.1002/pssr.201409063.

[44] S.F. Fischer, Energy absorption efficiency of open-cell pure aluminum foams, Mater. Lett. 184 (2016) 208–210, https://doi.org/10.1016/j.matlet.2016.08.061.

L. Niu et al.