Post on 16-Apr-2018
Mechanics of carbon nanotubes
and their polymer composites
Chenyu WeiDepartment of Mechanical Engineering, Stanford University
NASA Ames Research Center
Collaboration With KJ Cho (Stanford University, CA)
and Deepak Srivastava (NASA Ames Research center, CA)
https://ntrs.nasa.gov/search.jsp?R=20020079422 2018-06-04T02:03:46+00:00Z
Carbon Nanotube: Structures
Atomic structure."
Quasi one dimensional; C-C bond length 1.43 A;
Radius- Nanometer; Length- gm (current upper range); Index (n,m)
Application of Carbon Nanotubes
Nanofibers: Strong mechanical properties
Nano devices: Wide variety of electronic properties and
mechanical-electronic couplings
Nano sensors: Physical and Chemical adsorption of gas
molecules, ions
IISimu,ationMethodsII(1) Molecular Dynamics: Newton's Equation
Force Field for Carbon nanotubes:
TersoffBrenner potential, fitted to carbon and hydrocarbon
systems, 3-body type, bond broken and formation
(2) Tight Binding method
(3) Ab initio method (Density Functional theory)
Elastic Properties of Carbon Nanotubes
Small strain: uniform deformations, elastic behavior
continuum theory applicable
Large strain: local deformations, defects, dislocations
Tension, Compression, bending, and (Torsion):
Yield Strain of CNT
Tension ]
Simulation: 30% yield strain from fast strain rate (1/ps) molecular
dynamics simulations (B.I. Yakobson et.al. Comput. Mater. Sci. 1997 )
Experiments: 6% maximum strain in SWCNT ropes; 12% maximum
strain in MWCNTs (D.A. Walter et al, Appl. Phys. Lett. 1999; M.F. Yu et al,
Phys. Rev. Lett. and Science 2000)
ompression
Simulation:
T-0K, Tersoff-Brenner potential: Super-elastic up to 20%
T=0K, Tight Binding: diamond like defects, collapsed at 12%
Experiment:Collapsing of CNT within polymer matrix under compression stress
(TEM study)
150GPA
Yielding under Tensile Stress
_° .
i11.5% tensile strained
CNT (10,0), T = 1600K
9% tensile strained
CNT (5,5), T=2400K
* D. Srivastava, C. Wei, and K. Cho, Appl. Mech. Review (2002)
Tensile strain applied to a 60/_ long (10,0) CNT
I , 0.25 -
0.25°IU I Ops
0.8 0.25%:20ps
o 0,25%!40ps
I- 0.6 T-800K ,:Z ./0
0.4. //T=1600K .,"
® ./
J0.2 T=2400K ' -,
o-_ if/0 0.05 0.1
T=300K/
0.2
• ____Ir___,__O T:3OOK
T=800Kr-"_ 0.15 •-- --_Ojjl-- "-I--_-i-_l'--ll
.-_ j_II--"I T:1600K
-_ o, .._'_"_-_>- •
QI_'_"" O T=2400K
- 0.05
0.15 0.2 0.25 0 -o ' '10 10-s 10 -4 10 -_
Tensile strain ! Strain rate (lips)
strongly dependent on strain rate and Temperature- Yielding:
10 -2
- Linear dependent on temperature of the slope of yield strain vs. strainrate : Activated Process
Yield Strain under Tension
E¢ k T Nda'y = t B In( )
VK VK n site_ 0
_. : Strain rate; £o " Constant related with vibrational frequency
K : Force constant; V: Activation volume; Ev: Activation energy
N : Number of process involving in yielding; nsite : Site available
Length effect:kBT ln(nsite/n 0A£y = site )VK
Temperature effect:( a:,N )T 1 __ ( G:2N )T 2
n site _ 0 n site _ 0
Yielding at Realistic Conditions
- Parameters obtainedfromfitting of MD simulations' data
F_ - 3.6eV;
°do _ 8x10-3
N
V-2.88A
-1ps
Experimental feasible conditions
length _ 1gm; strain rate _ 1%/hour; y 300K
'> Yield strain: 9 1%,f
Maximum tensile strains from experiments:
5-6 % for SWCNT ropes; 12% for MWCNTs
* D.A. Walter, et. al., Appl. Phys. Lett. V74, 3803 (1999)
M.-F. Yu et.al. Phys. Rev. Lett., V84, 5552 (2000); M.-F. Yu et. al., Science, V287, 637 (2000)
Yielding of MWCNT
c"
co
._
1 0 -31
0.25
0.15
10 -21 10-" 10 -1
1 i !
1' t t1/year 1%/hour
T=300K
(2)
(3)
For _ = l%/hour, and I=300K
gy (MWCNT)>(SWCNT): 3-4%;
Activation volume on MWCNT is
smaller (60%-70% of that on
SWCNT);
Crossover point of strain rate
exponentially dependent on T,
important for high temperaturesituations.
Load transfer on MWCNT
g
cl
1oo
5O
0
I ' I ' I ' I
/
/./
J /"Outer shell (20,0)
/ I"
" _ Intershell VDW-- -, 1- I ,
0 1 2 3 4 5
Tensile strain on outer shell (20,0) (%)
0
0
v
CC
om
C
C
o
3O
2O
10
-10
Y = 2400K
I I
i
Rate3: 0.25°/d20ps
/
J Rate1: 0.25°/USOps __
Rate4: O.25°/dlOps
5 10
Tensile strain on outer shell (20,0) (%)
CNT: Nano Fibers
CNT to reinforce composites
- High Strength & High flexibility & Toughness & light-
weight (Young's Modulus> 1TPa)
High aspect ratio L/D, can reach 1000
Critical length: Lc/D_Smax/2"_
- L c : length of CNT; D: diameter of the CNT;
-- (Ymax :tensile strength of CNT;
- _: interfacial shear stress
Large surface area, good for bonding, adhesion
Polymer-CNT Composite
Structural and thermal properties
Load transfer and mechanical properties
SEM images of epoxy-CNT composite
SEM images of CNT fibers ribbon
(processing in polyvinylacohol solution) &knotted CNT fibers
(L.S.Schadler et.al., Appl. Phys. Lett. V73 P3842, 1998) (B. Vigolo et.al., Science, V290 P1331, 2000)
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suo!leaedoad]
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V0E:0I=dN'spoqlomoi.m3olUOlAIgqpoxglo.i
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uo!mlntu!su!tuols,{s]
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orceFieldI]
Intramolecular potentials
Valence angle potential: ¢_(0) - 0.5k 0(cos 0 - cos 0o)2,
Torsion potential: _(a) / J. tool -_ - Co+ C_cos a + C2cos 2a + C3cos 3
Harmonic potential: 0.5 k b(1-1o) 2
Density Dependence on Temperature
Small system: L/D-2, Np=l 0
0.95
0.9O
O')v 0.85
.i
C 0.8Q)
D0.75
0.7
Tgglass
"--. rubber• ""O...
composite"_L liquid
poly
glass -._ a,
robber ",.,
Tg liquid
_oo 200 KiOO/ernperature (
Results
l-Glass transition temperature Tg
from 150K to 175K
-Thermal expansion coefficients:
PE PE-CNT
-4 -43.8 x 10 4.5 x 10_T<Tg
T>Tg 8.6 x 10 -4
I
I
J i -44°°(Experimental value: 1.0 x 10
-412.0x 10
increased
-1K ;T <Tg)
Diffusion Coefficients
Small system: L/D-2, Np-10
1.5 r
"_" Alor'o CNT direction
in CNTcomposite
(- '\, m
.__. Perpendicular •to CNT direction
in CNT composite •
o 0.5 -
a Aram. Alor_ X,Y,Z
.. _ in pure PEf i- •
0 L -I_ ..... "Q" ....... _ J !i
0 1O0 200 300 4001
Temperature (K) i
Diffusion coefficients of polymerwith CNTs embedded
Diffusion coefficient increased,
especially along CNT axis direction,
indicating enhancement of thermal
conductivity
•Experiments on ABS/CNT & RTV/
CNT show larger increase
(Rick Berrera's group at RICE)
(Ajayan's group at R.P.I. is investigating
these subjects in detail)
* C. Wei, D. Srivastava, and K. Cho (Nano Letters, in press)
Stress-Strain Curve & Load Transfer
Mechanical behavior of Composite:
Elastic rcgion and Yiclding
],2 i I _ i i l I I i I
CNT: L/D~2; unit of polyethylene=10 j/
composite_
0.6
_0A
[/ T=a0K
0 5 10 15 20 25 30 35 40 45 5
Tensile Strain (%)
Enhancement ofYoung's modulus: 30%
Load transfer: within 0.7%
Poisson Ratio effect:
CNT - 0.1-0.2, Polyethylene - 0.44
Compression pressure perpendicular to tube
axis contribute to improvement
Loading Sequence
Work hardening of
with strctching
composite
1.s .... /!T=50K
stress rate=l bar/1 ps 1
/
composite
i= !
0"5/# // /restretch Itf unstretch t CNT: L/D~2 1
V [0 t I ., I , J, _ 1 _ _1
0 10 20 30 40
t Tensile strain (%)
5J
TEM images of alignment of CNTs
in a polymer matrix by strctching
• Residue strain (L. Jin et.a|., Appl.Phys. Lett., V73 P1197, 1998)
1.5
.13
v
t/lt/l9
G)
t-0.5
I-
Young's Modulus
-Young's modulus of CNT composites 30% higher than polymer matrix
-Stretching trcatlncnts enhance Y by 50%
(L/D_2, Np = l 0)
I I i I
0
compositeA
Ik
/5 10 15 20 2
Tensile strain (%)
v
t./)
4--1
03
_.e.m
t-
04
0.3
0.2
01
0
I I
[1]: Polymer bulk; Y=1492MPa
[2]: Polymer bulk after streching
[3]: Composite: Y=1907MPa
; Y=1585MPa
[4]: Composite after strechi ng; Y=2308M Pa
0
b I pP
i .,s,-..._." _/ T=SOK
;_ stress rate=l bar/1 ps
, I i I i l
O.5 1 15 2,
Strain (%)
Conclusions
Yielding of carbon nanotubes strongly dependent on strain rate andtemperature: transition state theory
Polymer-CNT composite has larger thermo-expansion above Tg
- Phonon modes and Brownian motion leading to larger excludevolume of embedded CNT
- Diffusion of polymer matrix increased above Tg
Young's modulus of composite enhanced by 30% through VDWinteraction.
- Load transfer happening within 0.7%; stiffness of CNT bondincreases modulus of composite
- Loading sequence can improve the enhancement of modulus ofcomposite