Mechanical properties of graphene

Transcription

1 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 Chemical Processes (ICE-HT), Professor of Materials Science at the University of Patras and member of the Board of Directors of the Foundation of Research and Technology-Hellas FORTH. Editor-in-Chief of two international journals in the field of composites, nanostructures polymers and nanocomposites. Current research Interests: Graphene and Carbon Nanotubes, Composites, Polymers,and Non-Destructive Testing of Materials.

2 Mechanical Properties of Graphene Costas Galiotis Foundation for Research and Technology (FORTH) Institute of Chemical Engineering and High Temperature Chemical Processes, Patras, (ICE-HT) Greece & Department of Materials Science, University of Patras, Patras, Greece

3 Thessaloniki Ioannina Larissa Patras Athens Rethymno Heraklion

4 Thessaloniki Patras ICE-HT: : Physico-mechanical IESL: : Devices IACM: : Modelling Heraklion

5 FORTH/ ICE-HT Rio, Patras

6 Aims/ background Graphene s predicted mechanical behaviour: High stiffness, high strength, high ductility (toughness) Progress towards verification: A great deal of modeling work (ab initio & other) confirms the above. Relative little experimental work (mainly bending) for freely-suspended flakes Axial deformation in tension (up to 1.5%) and compression (up to failure) has been accomplished on flexed beams in combination with simultaneous Raman measurements

7 Bending Experiments

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

9 The question of graphene thickness [AFM vs. Raman : Graphene height over substrate] Gupta et al, Nano Lett., 2006, 6 (12),

10 Graphene as a membrane: bending experiments (1/2) For large deformations there are no closed form solutions that allow us to convert to stress-strain curves and to extract Young s moduli, E, values and the UTS. In Lee et al s paper a value of E=340 N/m is derived from fitting an approximate function F=f(δ) to the experimental data. For a clamped freestanding elastic thin circular membrane under point load, when the bending stiffness is negligible the maximum stress is given by: F : applied force, R: indenter tip radius Lee et al, Science, 2008

11 Graphene as a membrane: bending experiments (2/2) An axial tensile stress-strain curve is derived assuming h= nm and: σ =Eε +Dε 2 σ and ε: the uniaxial stress & strain, respectively D : third-order elastic constant (estimated through σ max =-E 2 /4D) (2007) Lee et al, (2008) ab initio

12 Theoretical methods to predict mechanical parameters Ab initio calculations Molecular Dynamics (Empirical potentials) Tight binding molecular dynamics Structural mechanics (FE method) Large diversity of values for the thickness and elastic properties of graphene depending on the simulation method and type of loading

13 Open questions: fracture processes Carbynes??? Ni et al. Physica B 2010 Gao and Hao, Physica E 2009

14 Axial Loading (tension & compression combined with Raman measurements)

15 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% 14

16 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 )

17 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]

18 2700 Simply-supported ( bare ) flake λ exc =514.5nm 80 Pos(2D) (cm -1 ) ω = ε 17.3ε 2 PMMA Graphene flake Compression ω = ε 27.8ε 2 Tension Strain (%) ù 2D/ å (cm -1 /%) Tsoukleri et al. Small 2009, 5, 2397] 17

19 Fully embedded flake 2700 λ exc =514.5nm 80 Pos(2D) (cm -1 ) ω = ε 55.1ε 2 PMMA PMMA 495 SU8 Compression ω = ε 13.7ε 2 Tension Strain (%) ù 2D / å (cm -1 /%) Tsoukleri et al. Small 2009, 5, 2397]

20 G mode vs. strain The eigenvectors of G + and G - modes are perpendicular to each other with G - polarized along the strain axis The degeneracy is lifted under uniaxial strain and the E 2g splits into distinct components. Mohiudin et al, PRB, 2009 Frank et al, ACS-Nano, 2010

21 Measurements at no residual strain- predictions in air 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 /%

22 Compression (Measurements & Analysis)

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

24 Graphene as a thin plate: critical buckling strain (1/2) The critical 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 κ w 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

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

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

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

29 Moving across the length scales (the development of a universal stress sensor)

30 Graphite Carbon fibres are turbostratic : no regular stacking order Interplanar distance significantly larger than that in graphite Guigon & Oberlin, FST, 20, (1984)

31 Evolution of structure in CF

32 BOEING 787 Dreamliner 80% CFC by volume and contains ~35 tons of carbon composite (23 tons of carbon fibre) Fuel consumption will be reduced by 20% than the comparable midsize 767 or Airbus A330 Toray industries (Japan) that signed a 16-year in 2006 with Boeing worth US $6 billion Demand for PAN (polyacrylonitrile)-based carbon fibre is growing 15 percent a year, driven now by the 787 At the end of 2003, Toray had capacity to produce 7,300 metric tons of carbon fiber products. By 2010, capacity has reached 13,900 metric tons

33 Europe s response: AIRBUS A350

34 TORAY Carbon Fibres

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36 Carbon fibres vs. graphene (1/2) [tensile strength vs. modulus]

37 Carbon fibres vs. graphene (2/2) [strain-to-failure vs. modulus]

38 Carbon fibre: G peak strain sensitivity (1/2) 1580 G line HMS 0.0 fibres % 1.0% Pos(G) (cm -1 ) last fibre fracture Strain (%) Raman shift (cm -1 )

39 HM carbon fibre: G peak strain sensitivity (2/2) compression experimental data polynomial fit Wavenumber Shift (cm -1 ) tension Strain (%)

40 Flexible Raman Systems for Mechanical Measurements analyser λ/2 MTS To Portable spectrometer Confocal pinhole DPSS 532 nm (Internal laser source)

41 Strain distribution along a short fibre at +0.3% Strain (%) tension: 0.3% compression: -0.3% Norm. position along the fibre (-) Goutianos et al, Composites-Part A, 35/4, (2004) Goutianos, Int. J. Solids & Structures, 40/21, (2003)

42 Strain (%) Detection of failure processes tension: 0.8% compression: -0.8% Norm. position along the fibre (-) Goutianos et al, Composites-Part A, 35/4, (2004) Goutianos, Int. J. Solids & Structures, 40/21, (2003)

43 Master plot of ω ε vs. E for graphene and CF G G + line average θ in =0 θ out =0 (our experiments) G - line Frank et al, Nature Comms, 2011

44 Carbon fibres (microscale) Stress/ strain sensors Graphene (nanoscale) Graphene: The ultimate molecular strain/ stress sensor G σ T = ω0 (cm MPa ) Bennet (1976) Frank et al, Nature Comms, DOI , 2011

45 Applications Stress and/or strain sensors (non-destructive) Reinforcing agents (particularly for thin films) Nano-mechanical resonators

46 Conclusions Graphene: the stiffest, strongest and toughest material ever made (experiments on purely axial loading yet to be performed) The fundamental studies on graphene pave the way for understanding and improving other graphitic materials such as carbon fibres. A universal value for the rate of waveno shift per stress can be established for graphene: the invisible stress/ strain sensor.

47 Acknowledgements/ Collaborations Asst. Prof. K. Papagelis, Dr J. Parthenios, Dr D. Tassis, Ms. G. Tsoukleri (FORTH/ICE-HT, Univ. Patras, Greece) Dr O. Frank (J. Heyrovský Institute, Czech Republic) Dr. A. Ferrari (Univ. Cambridge, UK) Prof. A. Geim, Prof. K. Novoselov (Univ. Manchester, UK)