Deforming Single and Multilayer Graphenes in Tension and Compression

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1 Deforming Single and Multilayer Graphenes in Tension and Compression Costas Galio*s*, Georgia Tsoukleri, Konstan*nos Papagelis, John Parthenios Otakar Frank Kostya Novoselov FORTH/ICE- HT & Univ. Patras, Greece J. Heyrovský Czech Republic University of Manchester, UK

2 FORTH/ ICE-HT Rio, Patras FORTH/ICE-HT

BIOMEDICAL RESEARCH Ioannina Institute of

STRUCTURE & LASER Institute of MOLECULAR

3 Foundation of Research & Technology (FORTH) v ICE- HT: Physico- mechanical (Patras) v IESL: Devices (Heraklion) v IACM: Modeling (Heraklion) Institute of BIOMEDICAL RESEARCH Ioannina Institute of CHEMICAL ENGINEERING AND HIGH TEMPERATURE CHEMICAL PROCESSES Patras Institute of MEDITERRANEAN STUDIES Rethymno Heraklion Institute of APPLIED AND COMPUTATIONAL MATHEMATICS Institute of ELECTRONIC STRUCTURE & LASER Institute of MOLECULAR BIOLOGY & BIOTECHNOLGY Institute of COMPUTER SCIENCES FORTH/ICE-HT

4 Background Mechanical behaviour of graphene: High s*ffness, high strength, high duc*lity (toughness)

5 Current Status/ Aims v A great deal of modeling work (ab ini@o & other) has been accomplished (NB. large diversity of values). Progress towards verifica@on: v Rela*ve liule experimental work (mainly bending) for freely- suspended flakes v Axial deforma*on in tension (up to 1.5%) and compression (up to failure) has been accomplished on flexed beams in combina*on with simultaneous Raman measurements

6 Bending Experiments

7 Plate vs Membrane Analysis How should we treat graphene? v Membranes exhibit zero bending s*ffness (NB. graphene exhibits a finite value of κ). They can only sustain tensile loads; their inability to sustain compressive loads leads to wrinkling. v Plates have finite thicknesses that normally give rise to internal stress/ strain distribu*on during bending. The deflec*on of the mid- plane is small compared to thickness.

Graphene as a membrane: past bending experiments (2007) Lee et al, (2008) v For large deforma*ons there are no closed form solu*ons that allow us to convert to stress- strain curves and to extract

8 Graphene as a membrane: past bending experiments (2007) Lee et al, (2008) v For large deforma*ons there are no closed form solu*ons that allow us to convert to stress- strain curves and to extract Young s moduli, E, values and the UTS. ab ini*o v An axial stress- strain curve was derived assuming clamped freestanding elas*c thin circular membrane under point load of no bending s*ffness, a thickness of nm and a stress- strain rela*onship of the form σ =Eε +Dε 2 (D es*mated through σ max =- E 2 /4D) Lee et al, Science, 2008

Cantilever Mechanics Galilei, Galileo (1564-1642) Discorsi Axial e dimostrazioni Loading

9 Cantilever Mechanics Galilei, Galileo ( ) Discorsi Axial e dimostrazioni Loading (tension & compression matematiche, combined intorno with Raman à due measurements) nuoue scienze.

Experimental set-up for application of uniaxial strain Simply-supported

5 nm) Materials & Geometry SU8 photo resist epoxy-based polymer PMMA beam

4 mm and L = 70 mm Mechanical strain at the top of the beam ε 3tδ = 1 2L

10 Experimental set-up for application of uniaxial strain Simply-supported flake F1 Embedded flake or S1805 (785 nm (514.5 nm) Materials & Geometry SU8 photo resist epoxy-based polymer PMMA beam substrate (2.9x12.0x70) mm 3 x = 10.4 mm and L = 70 mm Mechanical strain at the top of the beam ε 3tδ = 1 2L ( x) 2 x L δ: deflection of the beam neutral axis L: span of the beam t : beam thickness Operating limits: L>> 10δ max -1.5% < ε < 1.5% 10

11 Raman Spectra of embedded layer graphene inside PMMA 100 nm 200 nm t Graphene flake PMMA 495 SU8 Graphene + PMMA Intensity (arb. units) PMMA b PMMA Raman Shift (cm -1 )

12 Raman spectra of 2D-peak from embedded graphene flakes and bulk graphite 2D 1 2D 2 PMMA PMMA 495 SU8 2D Tsoukleri et al. Small 2009, 5, 2397]

13 2700 Simply-supported ( bare ) flake λ exc =514.5nm 80 P o s ( 2 D ) ( c m - 1 ) ω = ε 17.3ε 2 PMMA Graphene flake C o m p re s s i o n ω = ε 27.8ε 2 T e n s i o n S tra i n ( % ) ù 2 D / å (c m - 1 /% ) Tsoukleri et al. Small 2009, 5, 2397] 13

14 Fully embedded flake 2700 λ exc =514.5nm 80 P o s ( 2 D ) ( c m - 1 ) ω = ε 55.1ε 2 PMMA PMMA 495 SU8 C o m p re s s i o n ω = ε 13.7ε 2 T e n s i o n S tra i n ( % ) ù 2 D / å (c m - 1 /% ) Tsoukleri et al. Small 2009, 5, 2397]

15 G peak vs. strain (no residual strain) 0.0% 1.0% Mohiudin et al, PRB, 2009 Frank et al, ACS- Nano, 2010 / ε = 36.0 cm ω G 1 /% ω G + / ε = 17.5 cm 1 /%

16 Loading a graphene bilayer 2D21 2D22 785nm (1.581 e V ) 2D12 2D11 633nm (1.961 e V ) 2500 D3d R a m a n Inte ns ity (a.u.) 830nm (1.495 e V ) R a m a n s hift ( c m )

Graphene bilayer under uniaxial tension G peak 1587 cm-1 1592 cm-1 Eg Eu [Yan et al.

17 Graphene bilayer under uniaxial tension G peak 1587 cm cm-1 Eg Eu [Yan et al. PRB 77, (2009)] ωg+ (2L) / ε = ± 4.9 cm- 1 / % ωg (2L) / ε = ± 5.4 cm- 1 / % Frank et al, to be submi[ed, 2011

18 Graphene bilayer under uniaxial tension 2D peak 2D11 2D12 2D21 2D22

19 (2007) Lee et al, (2008) ab ini*o Tensile (axial) measurements current status

20 Compression (Measurements & Analysis)

21 Compression of embedded graphene flakes - 2D band F2 F1 F3

Graphene as a thin plate: critical buckling strain (1/2) The cri3cal strain, ε c, for the buckling of a rectangular thin plate under uniaxial compression is given by the classical Euler formula: ε c

22 Graphene as a thin plate: critical buckling strain (1/2) The cri3cal strain, ε c, for the buckling of a rectangular thin plate under uniaxial compression is given by the classical Euler formula: ε c π k w κ C 2 = 2 l: length (dimension parallel to strain) w: width m: number of half- waves to appear at the critical load κ: flexural rigidity, 3.18 GPa nm 3 =20 ev 1 C: tension rigidity, 340 GPa nm 1 k = mw l + 2 l mw k For a layer of atomic thickness in air, ε c 10-9 (1 nanostrain) l/w

23 Graphene as a thin plate: critical buckling strain (2/2) k w 2 = a ε + c b slope a = 0.03 µ m -2 Euler regime applies for k> 0.05 μm - 2 For freely suspended flake in air: For embedded flake: 3 κ = 3.18 GPa n m ~ 20 ev ε κ embedded c embedded k κ = 2 w = embedded C π GPa nm ~ 70 MeV,

24 Shear failure or slippage

25 Bending Stiffness, κ, for h=0.335 nm Specimen κ (ev) κ (Joules) Free- standing ~20 1 ~3*10-18 Embedded ~7 * 10 7 (70 MeV) 2 ~1*10-11 (10 pj) Simply- supported ~2 * 10 7 (20 MeV) 2 ~3*10-12 (3 pj) 3 1 Lee et al, Science, Frank et al, ACS Nano, Unpublished Data

Estimation of compression strength SLG Flake F1 εc (%)1 σc (GPa)2 l (μm) w (μm) k k / w2 (μm- 2) - 1.25 12.5 6 56 89.12 0.028 F2-0.64 6.4 11 50 22.71 0.011 F3-0.53 5.3 56 25 4.02 0.006 F4-0.61 6.

26 Estimation of compression strength SLG Flake F1 εc (%)1 σc (GPa)2 l (μm) w (μm) k k / w2 (μm- 2) F F F ε determined from the c 2 Assuming a modulus of nd order polynomials as maxima 1 TPa and a linear relationship Typical compression strength of carbon ﬁbres (microscale): 2-3 GPa

27 Stress transfer phenomena in polymer/ graphene composites

28 Graphene: A powerful stress/ strain sensor Phonon stress or strain sensi*vi*es: G peak G σ T G ε T ~ 2.7 (cm GPa ~ 2700 cm ) 2D peak (2 D) σ ( 2 D) ε T T 1 1 ~ 6.0 (cm GPa ) ~ 6000 cm 1 Knowing the wavenumber shiq we can resolve the inverse problem i.e. to obtain the values of axial σ and/or ε in graphene composites through the above rela*ons. Frank et al, Nature Comms,2:255, DOI , 2011

29 Strain maps of graphene flakes embedded into polymers 0.74% 0.0% released 10µm 10µm 2LG 2LG 1LG 1LG

30 Textbook stuff: Mechanisms of Stress Transfer in Composites σ f z x τ distance x x

31 Elastic transfer in polymer composites (1/2) (shear-lag analysis) Kevlar / epoxy Anagnostopoulos et al, Acta Materialia, 53, 2005

32 Elastic transfer in polymer composites (2/2) (shear-lag analysis) Same high- modulus carbon fibre but different oxida*ve treatment Melani*s & Galio*s, Proc. of Royal Soc.- A, , (1993)

sinh( βx) 2 H where wg T tln t and β 1 t G T Ef ln t mt, mt, = =

33 Shear lag analysis of graphene flakes embedded into polymers 2 d σ f H σ 2 dx wt E f f = ε βl σ f( x) = Ef ε 1 cosh( βx) + tanh( ) sinh( βx) 2 H where wg T tln t and β 1 t G T Ef ln t mt, mt, = = dσ dx f τ = t [ x ] σ f()~ x σ f, 1 exp( β ) τ ~ and te E e β f, fβ x

34 Shear lag analysis of a 1LG/ 2LG graphene flake in PMMA 10 µm L1 2LG 1LG L3 L1 L2 β_1lg β_2lg ISS_1LG ISS_2LG (µm -1 ) (µm -1 ) (MPa) (MPa) L1 0,43 0,43 L2 0,88 0,92 L2 0,63 0,54 1,43 2,60 L3 0,61 0,75 1,48 3,71 L3

35 Axial & Interfacial shear stress distributions

36 Conclusions v Experiments on purely axial loading of graphene in tension have not been performed as yet. v If no residual strain is present the phonon vs. strain rela*nonship in tension is linear at least up to ~1.5%. v In compression, the observed phonon relaxa*on is indica*ve of failure ini*a*on. The obtained values of cri*cal strain to failure for monolayer graphene agree well with Euler buckling analysis. v The stress transfer from a polymer matrix to graphenes (1LG &2LG) seems to proceed along macroscopic principles (shear- lag). v Pris*ne graphenes exhibit poor interfacial strength in PMMA matrices. AUen*on should be exercised when measurements are made near the flake edges.

37 Acknowledgements/ Collaborations v Dr. D. Tassis (Univ. Patras) v Dr. A. Ferrari (Univ. Cambridge, UK) v Prof. A. Geim (Univ. Manchester, UK) Financial support: v Marie- Curie TOK v GRAPHENE CENTRE (FORTH)

38 Graphene bilayer under uniaxial tension 2D band λ= 785 nm λ= 633 nm ω 2D ω 2D / ε ω 2D ω 2D / ε [cm - 1 ] [cm - 1 /%] [cm - 1 ] [cm - 1 /%] 2D ± ± ± ±7.3 2D ± ± ± ±8.4 2D ± ± ± ±4.4 2D ± ± ± ±5.4

Mechanical properties of graphene

Costas GALIOTIS Mechanical properties of graphene BSc in Chemistry University of Athens PhD in Materials Science- University of London, Director of the Institute of Chemical Engineering and High Temperature