ELASTIC PROPERTIES OF NANOTUBES

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ELASTIC PROPERTIES OF NANOTUBES

• Nanotube learning seminar series
• SZFKI

B.Sas, T. Williams 12 September 2005
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HOW TO LEARN ABOUT ELASTICITY OF CNT
Approaches 1. Experimental i) Macroscopic
mechanical measurements ii) Microscopic
spectroscopic measurements 2. Modelling i)
Continuum elasticity ii) Phonon dispersion and
anharmonicity 3. Comparison with ab initio
calculation
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GPa
szz
30 -
E350GPa
dL/L
0 -
0
10
4

• Tensile Loading of Ropes of SWNTs (Yu et al
  PRL 2000)

E1000GPa
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2-D ELASTICITY
dR
Uniaxial force
F0
2R
Ff
LdL
L
dWpdWel
2pR
fdL?sxxuxxdS 2 pRLsxx dL/L
sxxf/2pR
Euxx sxx uyy dR/R -sP uxx
sP(K-µ)/(Kµ) E4K µ/(K µ)
E3-DE2-D /wall thickness
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(2-D Elasticity)
BENDING MODEL
F0
Ff
2R
d
L
compression
E3-D?E2-D/wall thickness
dilatation
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d nm
4 -
2 -
F nN
E3-D1000GPa E2-D300Nm-1
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COMPARISON WITH STEEL
STEEL 100 0.1 0.1 100 8 10
CNT 1000 10 100 50 0.6 5000
Young mod E3-D Strain limit stress limit filling
factor density stress limit cable
GPa GPa g cm-2 Kg force mm-2
Hung by F500µm CNT thread
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Micro-Mechanical Manipulations

• Rotational actuators based on carbon nanotubes
  (Nature, 2003.) Electrostatic motor.

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RAMAN EFFECT FOR BEGINNERS I
?0
?0
?0-?ph
a,?ph
dipole emission cos?0t , cos(?0?Pn)t
excitation Eincos?0t
?0
24000cm-1
25000cm-1
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Graphene phonons
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RAMAN FOR BEGINNERS II
CLASSICAL
QUANTUM
m,e
u
x
?m?2el
h?el
Eincos?0t
g
Dipole
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RAMAN III
APPLIED STRESS
ustatic?0 ? intensity change by d?el ?
reveals by d?Pn ? lifts phonon
mode degeneracies by symmetry reduction
Ustatic0
ustatic?0
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Eg
A2u
Sanchez-Portal et al.
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Hydrostatic pressure Capped ends
2-D ELASTICITY
dR
2R
L
L-dL
P0
Pp
dWpdWel
pR2pdL?sxxuxxdS 2 pRLsxx dL/L
2pRLpdR?syyuyydS2 pRL syydR/R
sxxpR/2
syypR
uyy/uxx2 if sP0
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2-D ELASTICITY
Hydrostatic pressure Pp Capped ends
sxxpR/2 syy0 uxxpR/2E uyy-sPpR/2E

sxx0 syypR uxx-sPpR/E uyypR/E

sxxpR/2 syypR uxx(1-2sP)pR/2E
uyy(2-sP)pR/2E
uyy/uxx (2-sP)/(1-2sP)
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