REVIEW ON CRUMPLED GRAPHENE: UNIQUE MECHANICAL PROPERTIES · ing full atomistic molecular dynamics was performed in [66]. The crumpling phenomenon can be viewed as a network of ridges,

69Review on crumpled graphene: unique mechanical properties

© 2014 Advanced Study Center Co% Ltd%

Rev. Adv. Mater. Sci. 39 (2014) 69-83

Corresponding author: K. Zhou, e-mail: [email protected]

REVIEW ON CRUMPLED GRAPHENE: UNIQUEMECHANICAL PROPERTIES

J. A. Baimova1, E. A. Korznikova1, S. V. Dmitriev1,2, B. Liu3 and K. Zhou3

1Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Khalturina 39,Ufa 450001, Russia

2Saint Petersburg State Polytechnical University, Polytechnicheskaya 29, St. Petersburg 195251, Russia3School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue,

Singapore 639798, Singapore

Received: September 19, 2014

Abstract. Bulk carbon nanomaterials based on graphene and other sp2 carbon nanopolymorphsare structures with a low density but high resistance to compression. These materials arepromising candidates for supercapacitors, electronics, energy storage devices, etc. due to theirunique properties such as extremely high specific surface area, high conductivity and stabilityagainst graphitization. In this review, after a brief overview of the structure of graphene and itsmechanical properties, recent developments in the fabrication and understanding of mechanicalproperties of three-dimensional graphene nanostructures are discussed.

1. INTRODUCTION

Graphene, a two-dimensional (2D) material with asingle-atomic thickness, is the building unit forgraphite (see Fig. 1) [1]. It has been studied theo-retically for a long time as a building block of gra-phitic materials [2,3]. Since the first successful iso-lation of graphene in 2004 [4], its remarkable physi-cal, mechanical, chemical, and optical propertieshave been the subject of intensive investigations toimplement them in many applications such asgraphene-based electronics [5,6], optics [7], pho-tovoltaics [7,8], spintronics [9], hydrogen storage[10,11], thermal [12] and composite materials [13],to name a few. Very recently, graphene andgraphene-based materials have also been utilizedas electrode materials in energy related devices onwhich promising results were demonstrated [14-18].

Significant progress has been made recently inthe fabrication and understanding of graphene-basednanostructures. Various graphene nanostructureshave been developed and incorporated as key com-

ponents in supercapacitors, lithium-ion batteries,solar cells, and fuel cells. The other important goalis the production of energy supporting devices whichhold the key role to sustain our energy demand wellinto the future.

The curvature imposed on a graphene sheet byexternal confinement or forces concentrates largelyon the ridges [19,20] and leads to considerablechanges in various properties of the material.Graphene is very easy to bend and many research-ers have discussed how to introduce ripples, foldsor wrinkles in graphene sheets in a controllable fash-ion and how to use such corrugations [21-31] (seeFig. 2). In fact, wrinkling is a very general physicalphenomenon demonstrated by thin sheets andmembranes [32-35]. Such one-or two-dimensional(2D) ripples can strongly affect the electronic prop-erties of graphene by inducing effective magneticfields and changing local potentials [24,25,29].Moreover, crumpled graphene flakes, which can becharacterized by various distribution of folds and

70 J. A. Baimova, E. A. Korznikova, S. V. Dmitriev, B. Liu and K. Zhou

ripples, are one of the main structural units for bulknanomaterials and should be carefully studied.

For a perfectly elastic sheet, the work done incrumpling is stored in the elastic energy of thesefocused deformations, which is partitioned in finitefractions of bending and stretching energies [19].For most familiar examples of crumpled sheets suchas plastic, paper, or metal foils, the strains at ridgesexceed the yield strain and the ridges become irre-versibly creased into folds. As this aspect is scien-tifically intriguing and crumpled materials can havepotential use for structural applications due to thegood combination between properties, density andan easy way to process, further understanding ofpotential of this field is one of the main goals in thefuture. The final issue is to better describe the crum-pling phenomenon and to establish the link betweenthe macroscale mechanical behavior and the devel-oped complicated internal mesostructure. It is alsorequired to investigate various initial configurationsof foils with different thickness and made of differentmaterials. Understanding the mechanics of an in-teracting set of folds is a formidable challenge, andit is crucial to obtain experimental insights into theirthree-dimensional (3D) arrangement.

Fig. 1. Direct image of a single-layer graphenemembrane (atoms appear white). Reprinted withpermission from [1].

Fig. 2. 2D ripples in strained graphene nanoribbon with clamped edges.

When subjected to deforming forces, thin sheetsof stiff materials tend to crumple, forming distinctivepatterns characterized by network of sharp folds andcone singularities. These patterns form due to theinteraction between low bending resistance and highin-plane stiffness. As buckling occurs, ridges formstructures that concentrate curvature at singularitiesand narrow folds. It is a challenge to experimentallyprobe the interior geometry of a 3D crumpled ob-ject. Ref. [36] studied, by laser profilometry, the sta-tistics of folds and vertices of a uniform crumpledsheet. However, unfolding the sheet leads to a lossof spatial information about the interactions of thefolds and of its final crumpled configurations.Graphene structure, consisting of six grapheneflakes with interlayer distance two times larger thanthat of graphite, folded by compressive forces act-ing along the sheets was studied in [37] (Fig. 3).This work showed that large in-plane strain ofgraphene sheets results in formation of folds withsharp edges and high energy. The same simulationwas carried out for the six times larger interlayerdistance between graphene sheets. It was shownthat in this case the sharp folds could not be ob-served under the same loading conditions. This canbe explained by the van der Waals forces actingbetween graphene flakes in the bulk graphene struc-ture with smaller distance between the sheets lead-ing to the strong folding. Graphene offers a uniqueplatform to explore crumpling due to the existenceof defects and self-adhesion properties.

Many attempts have been done nowadays in thegoing from crumpled and folded sheet of grapheneto various bulk carbon nanostructures both by ex-periment and simulation. The synthesis of new 3Dsp2–bonded carbon forms, such as fu__erites (Fig%4), entangled carbon nanotubes (Fig. 5), crumpledgraphene (Fig. 6), graphene foams, carbon nanotube(CNT)-based thin films and other hybrid carbonnanostructures can be based on the unique proper-ties of this carbon polymorphs [38-45].


Fig. 3. Structure and potential energy distribution in graphene sheets under in-plane compressive forces.Compressive strain increases from (a) to (c). In (c) formation of sharp folds with high energy localization iscomplete. Reprinted with permission from [37].

Fig. 4. Comparison of density evolutions of the com-pressed C

60 crystal starting from the face-centered-

cubic (fcc) (black curve) and that from a tetrago-nally polymerized phase (red curve). Insets showthe initial and intermediate configurations (at pres-sures 0 and 35 GPa, respectively) for the fcc (toprow) and tetragonal (bottom row) phases. Reprintedwith permission from [101].

Fig. 5. Top (a and 60° (b views of a typica_ vertica_single-wall-CNT sample observed by scanning elec-tron microscopy (SEM). Reprinted with permissionfrom [97].

The above-mentioned graphene-based materialsdemonstrate high thermal conductivity [46], field-emission [47], stimulus-responsive behavior [48],superhydrophobicity [40,49] and supercapacitance[50,51], which opens fascinating perspectives fortheir applications. Such materials, if prepared in afacile and cost-effective way [49], shall have signifi-cant implications for both academic and industrycommunities [52,53]. It is noted that another wayto produce new carbon materials is grain boundaryengineering [54].

This review intends to summarize the very re-cent status and progress in the studies of graphene-based nanostructures addressing their mechanicalproperties. The brief overview of production meth-

ods for various structures will be presented as wellas experimental and numerical results on their prop-erties. It will be suggested that these novel 3D car-bon nanostructures are very promising candidatesfor numerous applications.


2. 3D STRUCTURES. EXPERIMENTAND THEORY

The search for new forms of matter produced at thenanoscale with required properties constitutes oneof the fundamental challenges of nanotechnology.The possibility of existence of highly connected, fullycovalent sp2-bonded 3D carbon forms such asschwarzites [46,55,56], polybenzenes [57] and hol-low graphites [58] recently has been demonstratedtheoretically. Nowadays, there is clear evidence thatrandom carbon structures, taking the aspect of

Fig. 6. Representations of crumpled graphene: (a) SEM image of graphene sheets implemented inultracapacitor (scale bar indicating 10 m), reprinted with permission from [51]; (b) full atomistic schematicof crumpled graphene, reprinted with permission from [66].

Fig. 7. (a) Illustration of a simple and green process of synthesizing porous 3D graphene-based materials.(b) Low-magnification and (c) high-resolution SEM images of products, which exhibit sponge-like morphol-ogy and porous structure. (d) Low-magnification and (e) high-resolution transmission electron microscopy(TEM) images of products, which also show a dense 3D pore structure with highly curved or wrinkledsurface. Reprinted with permission from [49].

highly porous, fully 3D sp2 graphite-like carbon, areformed under special controllable conditions [59]. Itwas shown that high pressure and high tempera-ture treatment can be successfully used for pro-duction of solid C

60 fullerites with astonishing me-

chanical properties [60,61]. In Ref. [49], a simpleapproach to produce 3D graphene-based porousmaterials with ultra-high specific surface area andexcellent bulk conductivity was presented. As canbe seen from structure analysis, thesenanomaterials mainly consist of defected/wrinkled


Fig. 8. Picture of a crumpled paper cross-section,in which the white lines represent two orthogonaldirections used to extract the number of folded lay-ers N. Reprinted with permission from [65].

single-layer graphene flakes in the dimensional sizeof a few nanometers, with at least some covalentbonds between them (Fig. 7). Carbon atoms withsp2 hybridization dominate, while carbon atoms inother hybridization states, such as sp3 or sp, havesmall fractions [49]. All the considered 3D struc-tures can be divided into different groups, e.g.,crumpled graphene, bulk CNT structures, fullerite,each with its own intriguing properties.

Crumpling occurs when a thin deformable sheetis crushed under an external load or grows within aconfining geometry. For crumpled graphene, boththe covalent sp2-bonds and the weak van der Waalsbonds contribute to its structure formation and prop-erties. All such materials can be classified basedon the type of chemical bonds formed in them andon the number of the nearest neighbors with whicheach atom forms covalent bonds [62,63]. Crumplinga sheet of paper (see Fig. 8) is a challenging pro-cess to simulate as it produces geometry with bothsharp creases and smooth areas [64,65]. The stablecrumpled graphene sheets of different lengths, us-ing full atomistic molecular dynamics was performedin [66]. The crumpling phenomenon can be viewedas a network of ridges, where formation is a modeof condensation of energy into a small subset of theavailable volume. Fractal dimension D=2%36±0%12presented here is higher than the theoretical valuefor an ideal elastic sheet with bending rigidity(D=2.3), which indicates that the self-adhesion ofmonolayer graphene facilitates a denser packingarrangement.

Crumpling a thin sheet of material into a smallvolume requires energy for creating a network ofdeformations such as vertices and ridges. By thelarge-scale computer simulations, the crumpling ofthin sheets by external forces was studied [67]. Thiswork showed the role of self-avoidance for the crum-pling process. Scaling properties of a single elasticvertex or ridge and sheet crumpling were analyzedtheoretically in [68], where a numerical model thatcan be purely elastic or elasto-plastic was intro-duced.

The direct measurements of the configurationsof a fully elastic sheet evolving during the dynamicprocess of crumpling under isotropic confinementwas presented in [69] with the aim to study dynamicevolution of 3D spatial configurations of crumplingsheets. The formation of a network of ridges andvertices into which the energy is localized was ob-served. It was shown that the evolution of thiscrumpled structure involves movements of ridges andvertices.

Programmable chemical functionalization bydoping a pristine graphene sheet in a certain pat-tern with hydrogen atoms to precisely control itsfolding morphology and produce the nanocages wasdeveloped in [77]. Molecular dynamics simulationwas performed to create a cubic graphene nanocageby warping the top graphene layer downward andthe bottom graphene layer upward to mimic the drugdelivery vehicle, which opens up a new avenue tocontrol the 3D architecture of folded graphene.

The other type of bulk carbon nanostructures isdensely compacted CNT bulk materials which canbe used in thermoelectric devices [71-73]. This iswhy production of solid structures that are composedentirely of CNTs [74] is of high importance. Somephysical properties of bulk samples are neededwhen we extend future applications of CNTs to alarger scale such as microelectromechanical sys-tems. Nevertheless, the solidified property of pureCNTs is poor, and the bulk CNT materials compactedby the conventional sintering method usually ex-hibit loose microstructure and inferior mechanicaland physical properties [75, 76]. The output of CNTsis restricted by previous nanotube growth methodssuch as arc discharge [76]. Hence, CNTs are onlyused as a reinforced second phase added into ma-trix materials, e.g., ceramics [77]. Catalytic chemi-cal vapor deposition (CVD) leads to large yields ofCNTs at a low cost of production compared withother synthesis methods such as the carbon arcdischarge [77] or laser vaporization methods [78].Therefore, the preparation of bulk CNT materials hasbecome feasible now. Furthermore, the cylindrical


tubular structure may be damaged during conven-tional powder sintering because a long soaking timeat elevated temperatures is needed to densify themicrostructures of the CNT compact. It was recentlyreported that CNTs were embedded into a ceramicmatrix and this composite was synthesized by thespark plasma sintering method [77,79]. The pris-tine tubular structure of the nanotube remained un-changed after the spark plasma sintering process-ing. The method of preparation of pure CNT bulkmaterials by spark plasma sintering was proposedin [72], where the thermal conductivity of the result-ant materials was evaluated and analyzed to ex-plore the physical elements associated with indi-vidual CNTs.

The other reported class of carbon bulknanopolymorphs is fullerite structures. It is wellknown that fullerites at ambient conditions adopt a

Fig. 9. Bulk nanomaterial consisting of (a,b) bended graphene flakes, (c,d) short carbon nanotubes, and(e,f) C

240 fullerenes. Reprinted with permission from [83].

close-packed face centered cubic lattice [80,81]. Inthis structure, there are no links between the C

60

molecules. When high pressure is applied, oftenaccompanied by annealing, strong covalent bondsare formed between neighbouring molecules and thematerial forms polymers with well-defined ordering.Polymers C

60 could thus find various technological

applications, for example, hard and super-hard ma-terials [82].

The materials fabricated using the approach de-veloped in [49] can naturally include not onlycrumpled graphene flakes but also some portionsof other basic carbon nanopolymorphs such asfullerenes and CNTs. The structure and propertiesof materials that consist of different building unitswere studied in [83-85] (see Fig. 9). It was shownthat the type of structure can significantly affect prop-erties of 3D nanopolymorphs. Furthermore, the


Fig. 10. (a) Single unit of crumpled graphene structure and (b) crumpled graphene.

Fig. 11. Schematic of nanoindentation of suspendedgraphene membrane. Reprinted with permissionfrom [86].

structure consisting of graphene flakes is very closeto the crumpled graphene. From the other point ofview, it is better to produce more inhomogeneousstructure to simulate crumpled graphene, consist-ing of small pieces of different sizes and shapes(see Fig. 10) or from mixed building units [84].

3. MECHANICAL PROPERTIES OF 2DAND 3D GRAPHENE

The covalent bonds between nearest-neighbor car-bon atoms in graphene are formed by sp2-hybridisedorbitals. These strong bonds give graphene its ex-traordinary mechanical strength, making it possibleto have stable free-standing graphene sheets, be-ing only one atomic layer thick. The mechanicalproperties of 2D graphene under strain have beeninvestigated extensively using both experimental andsimulation methods [86-98]. It was shown that car-bon-based nanostructures such as CNTs andnanofibers can fail near their ideal strengths due toexceedingly small dimensions [87].

The first systematic experimental analysis ofelastic properties and strengthening behavior ofgraphene was done in [86]. In this work, a graphenemembrane was mechanically deposited onto a sub-strate with arrays of circular wells and loaded by tipof atomic force microscope (Fig. 11). It was experi-mentally found that the graphene showed both non-linear elastic behavior and brittle fracture. The

graphene was characterized by the Young’s modu-lus of E=1 TPa and the third-order elastic stiffnessof D=-2 TPa. Brittle fracture of graphene occurredat a critical stress equal to its intrinsic strength of130 GPa. This value is the highest ever measuredfor real materials.

The above-mentioned experimental data on theYoung’s modu_us and the intrinsic strength exhib-ited by pristine graphene are consistent with furthercomputer simulations done by other researchers.Stability range and mechanical properties were in-vestigated for both pristine graphene (Fig. 12) andgraphene with Stone-Walles defect (Fig. 13) [93-96]. Fig. 12 shows that graphene can stay stableuntil ~40% tension along the zigzag direction, ~30%


tension along the armchair direction and ~40% ofshear. For example, quantum mechanics and quan-tum molecular dynamics calculations gave the fol-lowing limiting values for uniaxial loading along thezigzag (armchair) direction:

xx=0.38 and

xx =168

Fig. 12. Stability region of flat pristine graphene inthe space of in-plane strain components

xx,

yy, and

xy

. The values of shear strain xy

are given for eachstability area projected on the (

xxand

yy) plane.

Reprinted with permission from [93].

Fig. 13. Stability region of flat graphene with Stone-Walles defect. Reprinted with permission from [94].

GPa (yy =0.19 and

yy =120 GPa) [97]. Density func-

tional perturbation theory was employed to calcu-late the dispersion curves of uniaxially loadedgraphene and the phonon instability was found at

xx=0.266,

xx =121 GPa for the zigzag direction and

yy

=0.194, yy

=110 GPa for the armchair direction[87]. In molecular dynamics study of graphenenanoribbons oriented along the armchair direction,the critical parameters

yy=0.3,

yy =175 GPa were

reported [98]. It is well known that defects can con-siderably affect the mechanical properties andstrength of materials [94,99-101].

Superior mechanical properties of single-layergraphene suggest that 3D sp2-bonded structures willexhibit interesting properties. Such materials canbe divided into two groups. One group consists offully sp2-bonded structures such as schwarzites[46,55,56], polybenzenes [57], and hollow graphites[58], while the other is represented by graphite,fullerites and tubulenes aggregated into 3D solidsby means of weak van der Waals bonds. Below thediscussion of mechanical properties of the materi-als belonging to the second group is presented.

In early experiments, very hard and stiff materi-als were synthesized (stable under ambient condi-


Fig. 14. Density as a function of pressure in thepresence of external shear

xy. Reprinted with per-

mission from [104].

tions) by compressing fullerite under high pressure[102]. Pioneering molecular dynamics simulationshave shown that subjecting fullerite to high pres-sure and high temperatures may give rise to a denseamorphous phase with predominant sp3 hybridiza-tion [103]. Hydrostatic pressure transforms fulleriteinto amorphous carbon (Fig. 14) [104]. At the firststage of this process (P<10 GPa), the polymeriza-tion mainly by 2+2 ring formation took place. Then,breaking of the C

60 cages started at P 40 GPa.

Finally, the collapse of the broken C60

cages via for-mation of chemical bonds across the cage hap-pened. It was shown that remarkably high hydro-static pressures (exceeding 60 GPa) are requiredfor a complete collapse, while in case ofnonhydrostatic (external) stresses, the shear de-formation of the unit cell leads to rapid breaking andcollapse of the C

60 cages. Application of shear sig-

nificantly lowers the pressure of the transformationto amorphous carbon and that is why deformationcan be successfully used for the properties control.

Moreover, various types of strain can significantlyaffect mechanical and physical properties of car-bon nanostructures. The effect of strain on physicalproperties of fullerenes C

240 was studied [105]. It

was shown that even small deformation of sphericalgeometry evokes a shift of the electronic spectra.Deformation of CNTs by surface van der Waals forceswas investigated [106]. The behavior of schwarziteunder hydrostatic pressure was studied by tight-binding molecular dynamics [107]. The structurehad a density as low as 1.05 g/cm3 at 300K and abulk modulus, evaluated by measuring the volumevariation upon application of an external hydrostaticpressure, as large as 70 GPa. The volume of C

60

fullerites, in both the face centered cubic and simplecubic phases, as a function of pressure up to 1 GPaover the temperature range from 150 to 335K wasmeasured [108]. According to the measurements,at zero pressure, the samples had the density 1.66g/cm3, and the room-temperature bulk modulus 6.8GPa for the fcc phase and 8%7–9%5 GPa for thesimple cubic phase. For both phases, the bulk modu-lus increased rapidly with the pressure. A consider-able difference in elasticity under pressure forfullerites C

60 and C

70 was demonstrated using an

u_trasonic technique in the temperature range 77–340K at pressure up to 2.5 GPa [109]. The non-Hookean stress-strain response of carbon fiber crys-tallites was investigated in relation to changes incrystallite orientation with respect to the tensilestress direction [110]. It was found that the ratio ofthe tensile stress of the fiber to that of the crystal-lites is close to the crystallite volume fraction ratherthan the ratio of the fiber density to the crystallitedensity.

It can be seen that all the materials are com-pression-resistant just like paper balls as compres-sive stress makes them stiffer and harder [83-85,111]. Crumpled sheets have large resistance tocompression and their elastic energy is focused intoa complex network of localized structures. At mod-erate compression, the force-compression relationsof crumpled sheets for both self-avoiding and phan-tom sheets are found to obey universal power-lawbehavior. However, self-avoiding sheets are muchstiffer than phantom sheets and, for a given com-pression, develop many more folds [67]. The samebehavior has been observed for crumpled graphene[67] which is very close to the structure consistingof the bended flakes.

The results of hydrostatic compression for threestructures, consisting of bended graphene flakes,short CNTs and fullerenes are shown in Fig. 15 [83].Note that the structure consisting of fullerenes rep-resents the fullerite and the structure consisting ofbended graphene flakes is very close to the crumpledgraphene. Pressure-strain and pressure-densitycurves for all the materials show very different be-havior for loading as well as for the unloading. Theinset in Fig. 15a demonstrates that fullerite showslinear relation between p and up to = 0.08, whilethe structures build from CNTs and graphene flakesshow nonlinear relation with p~2 even for small .Deformation of CNTs and graphene flakes is accom-panied by the formation of new sp2 bonds at theedges of structural units even at relatively smalldensities, resulting in gradual increase in the rigid-ity of these materials. From the slope of the pres-


sure–strain curve for fu__erite, the bu_k modu_us isestimated as B=0.35 GPa. The loading curves forall three materials do not show large difference inthe range of large densities. However, during un-loading process, the fullerite shows behavior verydifferent from two other bulk nanostructures in termsof the elasticity limit.

To understand the mechanical behavior of con-sidered nanostructures, the structural changes dur-ing deformation were analyzed [84,85]. The struc-tural transformations of the single unit (grapheneflake, CNT and fullerene) are shown in Fig. 16. It is

Fig. 15. Pressure as the function of (a) strain and (b) density for the material consisting of bended grapheneflakes (red thin line), CNTs (black solid line), and fullerenes (blue dashed line). The density range forgraphite ( = 2.09-2.23 g/cm3) is shown by grey dashed vertical lines and for diamond ( = 3.47-3.55 g/cm3)by green dotted vertica_ _ines% (c–e Pressure as the function of density for _oading (so_id _ines and un_oad-ing from different strain levels (dashed lines) for the structure consisting of graphene flakes, CNTs andfullerenes, respectively. The threshold density (the elasticity limit) is denoted by *. Reprinted with permis-sion from [83].

clearly seen that graphene flakes can be easilydeformed at any loading scheme, while the fullerenespreserve their spherical shape until quite high den-sities [85]. Calculations of the elastic properties ofCNTs confirmed that they are extremely rigid in theaxial directions and are most likely to distort per-pendicular to the axes. It can also be seen that thecollapse of the CNTs took place under all loadingconditions at the densities lower than for the break-ing and collapse of the fullerenes.

The effect of the loading scheme and tempera-ture on the mechanical properties of bulk carbon


Fig. 16. Transformation of building unit in 3D carbon polymorphs. Reprinted with permission from [85].

Fig. 17. Pressure (stress) as a function of density for the material consisting of bended graphene flakes(red triangles), CNTs (blue squares), fullerenes (black dots) and mixture of various buiding units (greenrhombuses) at T = 300K (a–c and T = 3000K (d–f % Three _oading schemes are tested: (a, d hydrostatic,(b, e) biaxial and (c, f) uniaxial compression. Reprinted with permission from [84].

nanostructures was studied [84]. A temperaturerange of 300–3000K for the three _oading schemeswas considered. Additionally, the structure build asa mixture of graphene flakes, CNTs and fullereneswas simulated. Fig. 17 shows the pressure (stress)as a function of density for the four materials con-sisting of graphene flakes, CNTs, fullerenes andmixture of different structural units. Two different

temperatures were taken as the examples for thehydrostatic, biaxial and uniaxial compressions. Itshows that there is almost no effect of temperatureunder hydrostatic compression, while temperatureslightly affects the strengthening behaviour underbiaxial and uniaxial compression. Surprisingly, thegreatest effect of temperature is observed for mixedstructure. The changes of the curve shape and even


the increase of final value of stress for uniaxial com-pression can be seen. The effect of loading schemesstrongly depends on the type of structural units. Itis observed that fullerite could be deformed moreeasily using hydrostatic compression than underuniaxial and biaxial compressions; mixed structureshows average mechanical properties compared tothe other nanostructures, which is determined bythe interactions of the structural units; while themechanical properties of crumpled graphene are onlyslightly affected by the loading scheme.The initia_ re_ative Young’s modu_us and yie_d

strength both are power law-like relations of the ini-tial foam relative density as it was proved for cellu-lar-like materials [112,113]. Relations E

0/E

s

(0/

s)n and

0/

s (

0/

s)m, where 0 and s refer to

the properties of the foam and its bulk material, re-spectively, and where the typical values of the power-law exponent n and m are summarized as the func-tion of the foam architecture, describing also defor-mation meso-mechanisms [114].

In our recent work [84], the parameters of theconstitutive relationships describing the deformationof bulk carbon nanostructures (including crumpledstructure were) found for various temperatures anddensities.

The pressure-density (stress-density) nonlinearcurves can be well fitted by the power law

P Lp A A A

0 0 0

, , , (1)

where p is the pressure, p is the averaged stress

under biaxial compression, L is the averaged stress

under uniaxial compression, A and are constants,and

0 and are the initial and current densities,

respectively. To achieve a better fit, the constants Aand were taken different for the two density ranges1< <1.5 g/cm3 and 1.5< <3 g/cm3. As an ex-

ample, the constitutive relation parameters for thecase of hydrostatic compression of three differentstructures are given in Table 1.

5. CONCLUSIONS

The experimental data and computer simulation re-sults presented in this review show that 3D carbonnanostructures are of great interest nowadays be-cause they are promising candidates for numerousapplications. 3D assembly of 2D graphene materi-als can lead to a variety of porous and non-porousstructures with other unique properties. The pos-sible applications of graphene-based material includetransparent flexible electrodes, solar cells, graphene/polymer composites for mechanical parts, energystorage, sensors and actuators, organic electron-ics, and supercapacitors. In addition, 3D graphenealso provides a new material platform for lithium ionbatteries, catalysis, water purification, biomedicaldevices, etc.

The design of bulk nanostructures proposed inthe literature potentially allows the production of awide variety of new carbon allotropes with outstand-ing properties. The attempts made to create bulkcarbon structures with novel properties have beendone by experiment and computer simulations inrecent years.

A number of future research directions becomepossible, such as systematic investigations of theeffects of crumpling on the electrical and electro-chemical properties of graphene and on thestrengths and fracture mechanisms of graphene-based 3D structures. Also, the ridges and verticesin the crumpled graphene are highly deformed andmicroscopically patterned, which can potentially leadto other new properties and functions, such as pat-terned chemical reactions. Furthermore, by control-ling the microscopic patterns of graphene with a

Structural unit T (K) A<1.5 <1.5

A>1.5 >1.5

graphene flake 300 0.041 3.8 0.018 5.381500 0.066 3.73 0.034 4.853000 0.096 3.18 0.046 4.62

CNT 300 0.014 7.52 0.023 5.281500 0.024 6.6 0.035 4.963000 0.04 5.9 0.059 4.43

fullerene 300 0.023 7.0 0.057 4.51500 0.014 8.0 0.076 4.213000 0.027 6.94 0.078 4.3

Table 1. Constitutive relation parameters for hydrostatic compression for three structures with differentstructural units [84].


simple macroscopic tool, one can develop newgraphene-based systems with novel tunability andflexibility to make nanoscale mechanisms visibleat the macroscale.

Though studies in this area are in their infancy,several intriguing results and remarkable trends havebeen reported serving as a basis for further progress.The core issues such as the homogeneous distri-bution of individual graphene platelets, their orienta-tion, connectivity, and bonding with each other stillrequire additional studying. The other unresolvedissue is how to overcome the energy barrier of thefolding process to fold the graphene with the spe-cific morphology. Thermo-mechanical treatment in-cluding severe plastic deformation at elevated tem-peratures can be applied to activate structural re-construction in 3D graphene to change its proper-ties in a controllable fashion.

With further understanding of the role of graphenein electron transfer in bulk nanostructures, and re-ducing the cost of crumpled graphene preparation,carbon bulk nanomaterials could be promising inthe future design of various devices.

AKNOWLEGEMENTS

J.A.B. gratefully thanks financial support from thegrant of Russian Science Foundation 14-13-00982.E.A.K. thanks the Russian Foundation for BasicResearch, grant 14-02-97029 povolzhie_a. This workwas partly supported (for S.V.D.) by the RussianGovernment Program 5-100-2020. A part of the simu-lations reported here were carried out onsupercomputer of RAS Supercomputer Center.

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