Graphene under uniaxial and hydrostatic deformation

Τεχνικό σεμινάριο, 14 Νοεμβρίου 2012

Η δονητική φασματοσκοπία

και οι μηχανικές μετρήσεις στη

νανοτεχνολογία

Δρ Ι. Παρθένιος Κύριος Ε. Λ. Ε., ITE/IEXMH

CNT


(a) (b) (c) (d)

From macro to nano

1μm 25 cm

0D 1D 2D 3D

Vandeparre H., et al. PRL, 106, 224301 (2011)

25 cm

1 μm

Human Skin House Curtains Bilayer

Graphene Human Cell on Si

(t ~ 0.7 nm)


Various forms of carbon-based nanomaterials

P. Ehrenfreund and B. H. Foing, Science 329, 1159 (2010)


Mechanical characterization of nanomaterials

Yu MF, Lourie O, Dyer MJ, Moloni K, Kelly TF, and Ruoff RS, Strength and breaking mechanism of multiwalled

carbon nanotubes under tensile load, Science, 287, 637-640 (2000).

Fracture strength: 11-63 GPa

Strain at break: ~12%

Young’s Modulus: 274 to 954 GPa

Force = kd ~ 400 – 1340 nN

Strain = δL/L

k (soft)

Hard

MWCNT


Mechanical characterization of nanomaterials

Graphene

Lee, et al., Science, 321, (2008), 385-388

AFM nanoindentation of graphene membrane

The elastic properties and intrinsic breaking

strength of ‘defect-free’ monolayer

Breaking strength ~ 42 N/m

Young’s modulus ~1.0 Tpa

Tensile Strength ~ 130 GPa

Max deflection δ ~ 100 nm


Force to break a covalent bond in graphene

It is assumed that the deformation

for bond breaking of the C-C bond

in graphene is ~ 0.142 nm

1Breaking strength deformation 42 0.142 6bondF Nm nm nN

1N

Stretching DNA*

Force ~ 65 pN

Need: Precise force measurement

*Gross, P. et al. Quantifying how DNA stretches, melts and changes twist under tension. Nature Physics 7, 731–736 (2011).

optical

tweezers


Tensile strength and stiffnes of materials – A comparison

~100 GPa

~1000 GPa


Raman spectroscopy in Nanomechanics


Energy conservation:

Momentum conservation: i f k k k

s i f

Raman scattering


Remote Raman System

Experimental set-ups

Jobin Yvon microscope/Spex Triplemate 0.6m

0.22 m

0.60 m

Renishaw inVia 2000 spectrometer system

I. II.

III.


Raman spectra of graphitic materials - 2D

Raman shift (cm-1)


Raman Spectrum of SWCNT – 1D


CF Structure Development and the corresponding

Raman spectra of carbon fibres -3D

High Modulus

Low Modulus

(Source: A. R. Bunsell, Fibre Reinforcements for Composite Materials, Amsterdam, The Netherlands: Elsevier Science Publishers B.V., 1988, p. 120.)

Carbon fibres

(microscale)


G-band of graphene under Strain in Tension & Compression


Axial Experiments in Graphene

(tension & compression combined with Raman

measurements)


Experimental Set-up for Application of Uniaxial Strain

16 16

2

31

2

t xx

L L

δ: deflection of the beam neutral axis L: span of the beam t : beam thickness

• SU8 photo resist epoxy-based polymer • PMMA beam substrate (2.9x12.0x70) mm3 • x = 10.4 mm and L = 70 mm

Materials & Geometry

Mechanical strain at the top of the beam

Simply-supported flake

Embedded flake

F1

or S1805 (785 nm)

(514.5 nm)

Operating limits:

• L>> 10δmax

• -1.5% < ε < 1.5%


F1

G-band under Strain in Tension & Compression


0.0%

1.0%

Mohiudin et al, PRB, 2009

Frank et al, ACS-Nano, 2010

/%cm 0.36/ 1 G

/%cm 5.17/ 1

G

G-band vs. Strain (no residual strain)


Raman 2D-peak splitting in single-layer graphene

19

Ram

an I

nte

nsi

ty (

a.u.)

2560 2600 2640 2680 2720

Raman shift (cm-1)

0.00%

0.41%

0.61%

0.90%

1.30%

Tension

λ=785 nm λ=514.5 nm

Measurements of the 2D band alone, for excitation

energies lower than 2.41 eV (514.5 nm), may lead

to errors with regards to the detailed determination

state of stress/strain in the specimen.

Frank et al., ACS-Nano, 5, 2321 (2011)


A simply-supported (“bare”) flake can be loaded!

20

2600

2620

2640

2660

2680

2700

Po

s(2

D)

(cm

-1)

-1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Strain (%)

-80

-60

-40

-20

0

20

40

60

80

ω

2D/ε

(cm

-1/%

)

Compression Tension

ω = 2674.4 +25.8|ε | –17.3ε2

ω = 2672.8 – 9.1ε – 27.8ε2

PMMA

Graphene flake

λexc=514.5nm

Tsoukleri et al. Small 2009, 5, 2397]


2D Band for embedded flake

2600

2620

2640

2660

2680

2700

Pos(

2D

) (c

m-1

)

-1.5 -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Strain (%)

-80

-60

-40

-20

0

20

40

60

80

ω

2D/ε

(cm

-1/%

)

Compression Tension

λexc=514.5nm

ω = 2681.1– 30.2|ε|– 13.7ε2

ω = 2680.6+59.1|ε|–55.1ε2

PMMA 495

SU8

PMMA

Tsoukleri et al. Small 2009, 5, 2397


Lee et al, Science (2008)

Theory

Tensile testsin graphene – Current status

*


Graphene: a powerful stress/ strain sensor

1 1~ 27.0 (cm % )

T

G

Frank, O. et al. Development of a universal stress sensor for graphene and carbon fibres. Nat Commun 2, 255 (2011).

1 1(2 )~ 6.0 (cm GPa )

T

D

Knowing the wavenumber shift we can resolve the inverse problem i.e. to

obtain the values of axial σ and/or ε in graphene-based materials through the

above relations.

Phonon stress (σ) or strain (ε) sensitivities:

, 1TPaE E

1 1 1(2 )~ 60.0 cm (cm % )

T

D

1 1~ 2.7 (cm GPa )

T

G

[Lee et al, Science (2008)] For small(??) strains


Mechanical characterization of single layer graphene

AFM nanoindentation C. Lee, et al., Science 321, 385 (2008)

PDMS

Bending of the substrate (PDMS) & Raman Ti strip

M. Huang, et al., Proc. Nat. Acad. Sci. 106, 7304 (2009)

4-point bending of the substrate (PMMA) & Raman

T. M. G. Mohiuddin, et al., Phys. Rev. B 79, 205433 (2009)

1

G

1

G

1

2D

ω ε 12.5 cm %

ω ε 5.6 cm %

ω ε 21.0 cm %

Bulge test & Raman

(Biaxial deformation)

Controlled creation of periodic ripples in suspended graphene sheets using thermally generated strains

W. Bao, et al., Nat Nano 4, 562 (2009)

Imaging of a vibrating graphene beam using

SPM Graphene resonator with local buckling

Garcia-Sanchez, et al., Nano Lett., 8, 1399 (2008)

E = 2.4 TPa!!!

E =1.0 TPa, Fracture strength = 130 GPa

J.-U. Lee, et al., Nano Lett. 12, 4444 (2012)

Graphene under pressure & Raman

J. Nicolle, et al., Nano Lett. 11, 3564 (2011)


Axial Experiments in CNT yarns

(tension combined with Raman measurements)


Draw-Twist process for CNT yarn production

Spinning machine

MWNT forest

Si substrate

Spindle

Motor

Ribbon

Twisted Yarn

CNT forest

CNT yarn

M. Zhang, et al.“Multifunctional Carbon Nanotube Yarns by

Downsizing an Ancient Tecnology”, Science, 36, p. 1358, 2004


Yarn model geometry (Ideal helical structure)

Yarn segment concentric packing of l layers

layer helix angles (h is the height along the yarn axis

of one turn of twist)

R

(R is the radius of the outer layer of the yarn and rk is the radius of layer k )

rk

2arctan

s

Ra

h

Outer layer helix angle

Inner layer k helix angle tan

arctan k s

s

r aa

R


Twist (turns/m) of yarns

2arctan

s

Ra

h

tan1s

a

h D

11~ 14786 m

h

where αs = 26o and D = 10.5 μm were measured by SEM pictures

sa


CNT yarn mechanical performance

0 1 2 3 4 5 6 7

0

200

400

600

800

1000

0.002 min-1

0.01 min-1

0.02 min-1

0.05 min-1

0.1 min-1

strain rate: 0.002 min-1

0.010 min-1

0.020 min-1

0.050 min-1

0.100 min-1

Str

ess

/ M

Pa

Strain / %

CNT yarn (θ = 260 , D = 10.5 μm)

CNT yarns behave like a viscoelastic Material

Strain-to-failure increases with strain rate

CNT yarn strength is 620 MPa and is independent from strain rate

(friction forces are independent from the rate of the relative

movement between CNT bundles)

Shell Sliding Experiment in MWCNT

Qian D. eta al. Appl Mech Rev vol 55, no 6, November 2002 Yu, M.-F., et al., . J. Phys. Chem. B 104, 8764–8767 (2000).


CNT yarn fracture surface

(i) (ii)

A bundle of MWCNTs located at the yarn centre is clearly unveiled (ii)

showing that the bundle is subjected to higher strains when an external

tensile load is applied to the yarn. This is consistent with ideal helix yarn

models where when an ideal helical structure is under an external tensile

load, the fiber strains are largest along the yarn axis and smallest in

the outermost layer.

grab-like pike-like


Stress transfer in CNT yarns – Raman Spectroscopy

1200 1300 1400 1500 1600 1700 1800

Raman shift (cm-1)

2400 2500 2600 2700 2800 2900

Raman shift (cm-1)

D G2D

CNT yarn surface indicative spectrum

2D FWHM 2D peak position

2D peak position and FWHM as a function of uniaxial tensile strain

2D peak position decreases slightly

(~4cm-1) with strain

2D FWHM decreases showing a min

value which reflects the decreasing

of helix angle and consequently

the spread of strain values

These results indicate that the fiber

strains are largest along the yarn axis

and smallest in the outermost layer.


Breaking the diffraction limit with TERS

(Tip Enhanced Raman Spectrocopy)

AFM + Raman microscopy

Graphene

G 2D

P. Dorozhkin et al, Microscopy Today, doi:10.1017/S1551929510000982 (2010)

The AFM nano-antenna can locally enhance the electromagnetic field

intensity near the tip apex and become a localized “nano-source of light.”

Stadler, J., et al., Nano Lett. 10, 4514–4520 (2010).


Thank you very much for your kind attention !

Graphene under uniaxial and hydrostatic deformation

Documents

Transcript of Graphene under uniaxial and hydrostatic deformation