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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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)

!

©i

O©Rii

/,

r._I

o_

4-i

II

i4-

II

88

88

8'_-

oe_od

x!_)eLu3/e],_oduJo03

8T--

ooo

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