Abstract
The past 2 decades have witnessed the explosion of research on two-dimensional (2D) materials, where notable efforts have been made in the synthesis and design of a wide spectrum of applications. To understand their mechanical properties and responses triggered by deformation, the prerequisites for reliable applications under realistic service conditions, novel experimental methods have to be developed due to the limitations of traditional bulk mechanical testing for atomically-thin structures. Besides, the nearly-ideal 2D crystalline structures of many 2D materials endow them the great capability of deformation, showing promising potentials in “strain engineering” and “interface engineering” applications. This review summaries several representative approaches in experimental nanomechanics and corresponding progresses in the characterization of structural and mechanical properties of 2D materials, with the aim to provide insights into the instrumental design for nanomechanical tests. In addition, examples of strain-tuned material behaviors and changes in their performance are also discussed to demonstrate the significance of the nanomechanical approach for functional device design and applications.
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References
Akinwande D et al (2017) A review on mechanics and mechanical properties of 2D materials: graphene and beyond. ExtremeMech Lett 13:42–77
Alden JS et al (2013) Strain solitons and topological defects in bilayer graphene. Proc Natl Acad Sci 110:11256–11260
Amorim B et al (2016) Novel effects of strains in graphene and other two dimensional materials. Phys Rep 617:1–54
Androulidakis C et al (2018) Strained hexagonal boron nitride: phonon shift and Grüneisen parameter. Phys Rev B 97:241414
Ares P et al (2020) Piezoelectricity in monolayer hexagonal boron nitride. Adv Mater 32:1905504
Azcatl A et al (2016) Covalent nitrogen doping and compressive strain in MoS2 by remote N2 plasma exposure. Nano Lett 16:5437–5443
Azizi A et al (2014) Dislocation motion and grain boundary migration in two-dimensional tungsten disulphide. Nat Commun 5:1–7
Begley MR, Mackin TJ (2004) Spherical indentation of freestanding circular thin films in the membrane regime. J Mech Phys Solids 52:2005–2023
Berman D et al (2018) Approaches for achieving superlubricity in two-dimensional materials. ACS Nano 12:2122–2137
Bertolazzi S et al (2011) Stretching and breaking of ultrathin MoS2. ACS Nano 5:9703–9709
Bhatia NM, Nachbar W (1968) Finite indentation of an elastic membrane by a spherical indenter. Int J Non-Linear Mech 3:307–324
Bhowmick S et al (2019) Advanced microelectromechanical systems-based nanomechanical testing: beyond stress and strain measurements. MRS Bull 44:487–493
Branny A et al (2017) Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor. Nat Commun 8:1–7
Brennan CJ et al (2015) Interface adhesion between 2D materials and elastomers measured by buckle delaminations. Adv Mater Interfaces 2:1500176
Bunch JS et al (2008) Impermeable atomic membranes from graphene sheets. Nano Lett 8:2458–2462
Cadelano E et al (2009) Nonlinear elasticity of monolayer graphene. Phys Rev Lett 102:235502
Cao G, Gao H (2019) Mechanical properties characterization of two-dimensional materials via nanoindentation experiments. Prog Mater Sci 103:558–595
Cao C et al (2015) Strengthening in graphene oxide nanosheets: bridging the gap between interplanar and intraplanar fracture. Nano Lett 15:6528–6534
Cao C et al (2016) In situ TEM tensile testing of carbon-linked graphene oxide nanosheets using a MEMS device. Nanotechnology 27:28LT01
Cao Y et al (2018) Unconventional superconductivity in magic-angle graphene superlattices. Nature 556:43
Cao K et al (2020) Elastic straining of free-standing monolayer graphene. Nat Commun 11:284
Castellanos-Gomez A et al (2012a) Elastic properties of freely suspended MoS2 nanosheets. Adv Mater 24:772–775
Castellanos-Gomez A et al (2012b) Mechanical properties of freely suspended atomically thin dielectric layers of mica. Nano Res 5:550–557
Castellanos-Gomez A et al (2013) Local strain engineering in atomically thin MoS2. Nano Lett 13:5361–5366
Chen J et al (2013) Nanomechanical properties of graphene on poly (ethylene terephthalate) substrate. Carbon 55:144–150
Conley HJ et al (2013) Bandgap engineering of strained monolayer and bilayer MoS2. Nano Lett 13:3626–3630
Cooper RC et al (2013) Nonlinear elastic behavior of two-dimensional molybdenum disulfide. Phys Rev B 87:035423
Cui T et al (2020) Fatigue of graphene. Nat Mater 19:405–411
Czichos H et al (2006) Springer handbook of materials measurement methods. Springer, Berlin
Dai S et al (2016a) Twisted bilayer graphene: Moiré with a twist. Nano Lett 16:5923–5927
Dai Z et al (2016b) Mechanical behavior and properties of hydrogen bonded graphene/polymer nano-interfaces. Compos Sci Technol 136:1–9
Dai Z et al (2019) Strain engineering of 2D materials: issues and opportunities at the interface. Adv Mater 31:1805417
Defo RK et al (2016) Strain dependence of band gaps and exciton energies in pure and mixed transition-metal dichalcogenides. Phys Rev B 94:155310
Desai SB et al (2014) Strain-induced indirect to direct bandgap transition in multilayer WSe2. Nano Lett 14:4592–4597
Duerloo KAN et al (2012) Intrinsic piezoelectricity in two-dimensional materials. J Phys Chem Lett 3:2871–2876
Duerloo K-AN et al (2014) Structural phase transitions in two-dimensional Mo- and W-dichalcogenide monolayers. Nat Commun 5:1–9
Edelberg D et al (2020) Tunable strain soliton networks confine electrons in van der Waals materials. Nat Phys 16:1097–1102
Espinosa HD (2008) In-situ electron microscopy testing of 1-D nanostructures, ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, Washington, pp 551–552
Falin A et al (2017) Mechanical properties of atomically thin boron nitride and the role of interlayer interactions. Nat Commun 8:15815
Fei R, Yang L (2014) Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett 14:2884–2889
Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6:183–191
Georgiou T et al (2013) Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics. Nat Nanotechnol 8:100–103
Gogotsi Y, Anasori B (2019) The rise of MXenes. ACS Nano 13:8491–8494
Gong L et al (2010) Interfacial stress transfer in a graphene monolayer nanocomposite. Adv Mater 22:2694–2697
Gupta A et al (2015) Recent development in 2D materials beyond graphene. Prog Mater Sci 73:44–126
Han X et al (2014) Strain and orientation modulated bandgaps and effective masses of phosphorene nanoribbons. Nano Lett 14:4607–4614
Han J et al (2015) Nanoindentation cannot accurately predict the tensile strength of graphene or other 2D materials. Nanoscale 7:15672–15679
Han Y et al (2020) Large elastic deformation and defect tolerance of hexagonal boron nitride monolayers. Cell Rept Phys Sci 1:100172
Haque MA et al (2010) MEMS for in situ testing: Handling, actuation, loading, and displacement measurements. MRS Bull 35:375–381
He K et al (2013) Experimental demonstration of continuous electronic structure tuning via strain in atomically thin MoS2. Nano Lett 13:2931–2936
Hencky H (1915) Uber den Spannungszustand in kreisrunden Platten mit verschwindender Biegungssteifigkeit. Z Math Phys 63:311–317
Hod O et al (2018) Structural superlubricity and ultralow friction across the length scales. Nature 563:485–492
Hou W et al (2019) Strain-based room-temperature non-volatile MoTe2 ferroelectric phase change transistor. Nat Nanotechnol 14:668–673
Hui YY et al (2013) Exceptional tunability of band energy in a compressively strained trilayer MoS2 sheet. ACS Nano 7:7126–7131
Island JO et al (2016) Precise and reversible band gap tuning in single-layer MoSe2 by uniaxial strain. Nanoscale 8:2589–2593
Jang B et al (2017) Uniaxial fracture test of freestanding pristine graphene using in situ tensile tester under scanning electron microscope. Extreme Mech Lett 14:10–15
Jiang T et al (2014) Interfacial sliding and buckling of monolayer graphene on a stretchable substrate. Adv Funct Mater 24:396–402
Jiang L et al (2016) Soliton-dependent plasmon reflection at bilayer graphene domain walls. Nat Mater 15:840–844
Jiang L et al (2018) Manipulation of domain-wall solitons in bi-and trilayer graphene. Nat Nanotechnol 13:204–208
Ju L et al (2015) Topological valley transport at bilayer graphene domain walls. Nature 520:650–655
Jung GS et al (2018) Interlocking friction governs the mechanical fracture of bilayer MoS2. ACS Nano 12:3600–3608
Kim NY et al (2017) Evidence of local commensurate state with lattice match of graphene on hexagonal boron nitride. ACS Nano 11:7084–7090
Kitt AL et al (2013) How graphene slides: measurement and theory of strain-dependent frictional forces between graphene and SiO2. Nano Lett 13:2605–2610
Klimov NN et al (2012) Electromechanical properties of graphene drumheads. Science 336:1557–1561
Koenig SP et al (2011) Ultrastrong adhesion of graphene membranes. Nat Nanotechnol 6:543
Komaragiri U et al (2005) The mechanical response of freestanding circular elastic films under point and pressure loads. J Appl Mech 72:203–212
Lee C et al (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–388
Lee JU et al (2012) Estimation of Young’s modulus of graphene by Raman spectroscopy. Nano Lett 12:4444–4448
Lee GH et al (2013) High-strength chemical-vapor-deposited graphene and grain boundaries. Science 340:1073–1076
Levy N et al (2010) Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329:544–547
Li L et al (2014a) Black phosphorus field-effect transistors. Nat Nanotechnol 9:372–377
Li J et al (2014b) Elastic strain engineering for unprecedented materials properties. MRS Bull 39:108–114
Li Y et al (2014c) Modulation of the electronic properties of ultrathin black phosphorus by strain and electrical field. J Phys Chem C 118:23970–23976
Li H et al (2015) Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide. Nat Commun 6:7381
Lin YC et al (2011) Clean transfer of graphene for isolation and suspension. ACS Nano 5:2362–2368
Lin QY et al (2013) Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition. ACS Nano 7:1171–1177
Lindahl N et al (2012) Determination of the bending rigidity of graphene via electrostatic actuation of buckled membranes. Nano Lett 12:3526–3531
Liu Y et al (2012) Mechanical properties of graphene papers. J Mech Phys Solids 60:591–605
Liu K et al (2014) Elastic properties of chemical-vapor-deposited monolayer MoS2, WS2, and their bilayer heterostructures. Nano Lett 14:5097–5103
Lloyd D et al (2016) Band gap engineering with ultralarge biaxial strains in suspended monolayer MoS2. Nano Lett 16:5836–5841
Lloyd D et al (2017) Adhesion, stiffness, and instability in atomically thin MoS2 bubbles. Nano Lett 17:5329–5334
López Polín G et al (2015) Increasing the elastic modulus of graphene by controlled defect creation. Nat Phys 11:26–31
Ly TH et al (2017) Dynamical observations on the crack tip zone and stress corrosion of two-dimensional MoS2. Nat Commun 8:14116
Manasevit H et al (1982) Electron mobility enhancement in epitaxial multilayer Si-Si1-xGex alloy films on (100) Si. Appl Phys Lett 41:464–466
Manzeli S et al (2015) Piezoresistivity and strain-induced band gap tuning in atomically thin MoS2. Nano Lett 15:5330–5335
Mishchenko A et al (2014) Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures. Nat Nanotechnol 9:808–813
Mohiuddin T et al (2009) Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation. Phys Rev B 79:205433
Nayak PK et al (2017) Probing evolution of twist-angle-dependent interlayer excitons in MoSe2/WSe2 van der Waals heterostructures. ACS Nano 11:4041–4050
Nemes-Incze P et al (2017) Preparing local strain patterns in graphene by atomic force microscope based indentation. Sci Rep 7:3035
Ni ZH et al (2008) Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2:2301–2305
Ni GX et al (2014) Tuning optical conductivity of large-scale CVD graphene by strain engineering. Adv Mater 26:1081–1086
Niu T et al (2018) Indentation behavior of the stiffest membrane mounted on a very compliant substrate: Graphene on PDMS. Int J Solids Struct 132:1–8
Novoselov KS et al (2004) Electric field effect in atomically thin carbon films. Science 306:666–669
Novoselov KS et al (2005) Two-dimensional atomic crystals. Proc Natl Acad Sci 102:10451–10453
Novoselov K et al (2016a) 2D materials and van der Waals heterostructures. Science 353:9439
Novoselov KS et al (2016b) 2D materials and van der Waals heterostructures. Science 353:aac9439
Oh Y et al (2013) Micro/nano-mechanical test system employing tensile test holder with push-to-pull transformer, US Patents US8789425B2.
Oostinga JB et al (2008) Gate-induced insulating state in bilayer graphene devices. Nat Mater 7:151–157
Pak S et al (2017) Strain-mediated interlayer coupling effects on the excitonic behaviors in an epitaxially grown MoS2/WS2 van der Waals heterobilayer. Nano Lett 17:5634–5640
Palacios-Berraquero C et al (2017) Large-scale quantum-emitter arrays in atomically thin semiconductors. Nat Commun 8:1–6
Peng P et al (2015) Joining of silver nanomaterials at low temperatures: processes, properties, and applications. ACS Appl Mater Interfaces 7:12597–12618
Pereira VM, Neto AC (2009) Strain engineering of graphene’s electronic structure. Phys Rev Lett 103:046801
Pérez Garza HH et al (2014) Controlled, reversible, and nondestructive generation of uniaxial extreme strains (> 10%) in graphene. Nano Lett 14:4107–4113
Pierucci D et al (2017) Tunable doping in hydrogenated single layered molybdenum disulfide. ACS Nano 11:1755–1761
Plechinger G et al (2015) Control of biaxial strain in single-layer molybdenite using local thermal expansion of the substrate. 2D Mater 2:015006
Pruessner MW et al (2003) Mechanical property measurement of InP-based MEMS for optical communications. Sens Actuator A 105:190–200
Qi J et al (2012) Strain-engineering of band gaps in piezoelectric boron nitride nanoribbons. Nano Lett 12:1224–1228
Radisavljevic B et al (2011) Single-layer MoS2 transistors. Nat Nanotechnol 6:147
Reina A et al (2008) Transferring and identification of single-and few-layer graphene on arbitrary substrates. J Phys Chem C 112:17741–17744
Reserbat-Plantey A et al (2014) Strain superlattices and macroscale suspension of graphene induced by corrugated substrates. Nano Lett 14:5044–5051
Rice C et al (2013) Raman-scattering measurements and first-principles calculations of strain-induced phonon shifts in monolayer MoS2. Phys Rev B 87:081307
Rodin A et al (2014) Strain-induced gap modification in black phosphorus. Phys Rev Lett 112:176801
Rostami H et al (2018) Piezoelectricity and valley Chern number in inhomogeneous hexagonal 2D crystals, NPJ 2D. Mater Appl 2:15
Ruiz Vargas CS et al (2011) Softened elastic response and unzipping in chemical vapor deposition graphene membranes. Nano Lett 11:2259–2263
Schweizer P et al (2018) In situ manipulation and switching of dislocations in bilayer graphene. Sci Adv 4:eaat4712
Senturia SD (2007) Microsystem design. Springer Science and Business Media, Berlin
Shin BG et al (2016) Indirect bandgap puddles in monolayer MoS2 by substrate-induced local strain. Adv Mater 28:9378–9384
Song L et al (2010) Large scale growth and characterization of atomic hexagonal boron nitride layers. Nano Lett 10:3209–3215
Song Z et al (2015) Defect-detriment to graphene strength is concealed by local probe: the topological and geometrical effects. ACS Nano 9:401–408
Tao J et al (2015) Mechanical and electrical anisotropy of few-layer black phosphorus. ACS Nano 9:11362–11370
Tran K et al (2019) Evidence for moiré excitons in van der Waals heterostructures. Nature 567:71–75
Tsoukleri G et al (2009) Subjecting a graphene monolayer to tension and compression. Small 5:2397–2402
Vaezi A et al (2013) Topological edge states at a tilt boundary in gated multilayer graphene. Phys Rev X 3:021018
Wang QH et al (2012) Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotechnol 7:699–712
Wang Y et al (2013a) Raman spectroscopy study of lattice vibration and crystallographic orientation of monolayer MoS2 under uniaxial strain. Small 9:2857–2861
Wang P et al (2013b) Numerical analysis of circular graphene bubbles. J Appl Mech 80:040905
Wang Y et al (2015) Strain-induced direct-indirect bandgap transition and phonon modulation in monolayer WS2. Nano Res 8:2562–2572
Wang JY et al (2016a) Elastic properties of suspended black phosphorus nanosheets. Appl Phys Lett 108:013104
Wang F et al (2016b) Strain-induced phonon shifts in tungsten disulfide nanoplatelets and nanotubes. 2D Mater 4:015007
Wang G et al (2017) Measuring interlayer shear stress in bilayer graphene. Phys Rev Lett 119:036101
Wang G et al (2019) Bending of multilayer van der waals materials. Phys Rev Lett 123:116101
Watanabe K et al (2004) Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal. Nat Mater 3:404
Wei X, Kysar JW (2012) Experimental validation of multiscale modeling of indentation of suspended circular graphene membranes. Int J Solids Struct 49:3201–3209
Wei X et al (2009) Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description. Phys Rev B 80:205407
Wei N et al (2011) Strain engineering of thermal conductivity in graphene sheets and nanoribbons: a demonstration of magic flexibility. Nanotechnology 22:105705
Wei X et al (2015) Comparative fracture toughness of multilayer graphenes and boronitrenes. Nano Lett 15:689–694
Williams J (1997) Energy release rates for the peeling of flexible membranes and the analysis of blister tests. Int J Fract 87:265–288
Wu W et al (2014) Piezoelectricity of single-atomic-layer MoS2 for energy conversion and piezotronics. Nature 514:470–474
Xiong S, Cao G (2017) Continuum thin-shell model of the anisotropic two-dimensional materials: single-layer black phosphorus. Extreme Mech Lett 15:1–9
Xu Z, Zheng Q (2018) Micro-and nano-mechanics in China: a brief review of recent progress and perspectives. Sci China Phys Mech Astron 61:74601
Xu C et al (2015) An experimental investigation on the tangential interfacial properties of graphene: size effect. Mater Lett 161:755–758
Xu C et al (2019) Rate-dependent decohesion modes in graphene-sandwiched interfaces. Adv Mater Interfaces 6:1901217
Yang S et al (2015) Tuning the optical, magnetic, and electrical properties of ReSe2 by nanoscale strain engineering. Nano Lett 15:1660–1666
Yang Y et al (2017a) Brittle fracture of 2D MoSe2. Adv Mater 29:1604201
Yang R et al (2017b) Tuning optical signatures of single-and few-layer MoS2 by blown-bubble bulge straining up to fracture. Nano Lett 17:4568–4575
Zandiatashbar A et al (2014) Effect of defects on the intrinsic strength and stiffness of graphene. Nat Commun 5:3186
Zhang H (2015) Ultrathin two-dimensional nanomaterials. ACS Nano 9:9451–9469
Zhang Y, Pan C (2012) Measurements of mechanical properties and number of layers of graphene from nano-indentation. Diam Relat Mater 24:1–5
Zhang JL, Shan GC (2019) Stacking control in graphene-based materials: A promising method for fascinating physical properties. Front Phys 14:23301
Zhang P et al (2014) Fracture toughness of graphene. Nat Commun 5:3782
Zhang R et al (2016a) Elastic properties of suspended multilayer WSe2. Appl Phys Lett 108:042104
Zhang H et al (2016b) Approaching the ideal elastic strain limit in silicon nanowires. Sci Adv 2:e1501382
Zhang Q et al (2016c) Strain relaxation of monolayer WS2 on plastic substrate. Adv Funct Mater 26:8707–8714
Zhao J et al (2015) Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping. Nat Commun 6:8935
Zhu Y, Chang TH (2015) A review of microelectromechanical systems for nanoscale mechanical characterization. J Micromech Microengr 25:093001
Zhu T, Li J (2010) Ultra-strength materials. Prog Mater Sci 55:710–757
Zhu C et al (2013) Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS2. Phys Rev B 88:121301
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The authors acknowledge the financial supports from Hong Kong Research Grant Council (RGC) under the GRF CityU11216515 and CityU11207416, City University of Hong Kong under SRG 7005070, and National Natural Science Foundation of China (NSFC) through Grants No. 11825203 and No. 11922215.
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Han, Y., Zhou, J., Wang, H. et al. Experimental nanomechanics of 2D materials for strain engineering. Appl Nanosci 11, 1075–1091 (2021). https://doi.org/10.1007/s13204-021-01702-0
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DOI: https://doi.org/10.1007/s13204-021-01702-0