Shear Banding in EntangledCarbon Nanotube Networks

Erik K. HobbieNIST Polymers Division

Euromech

2007 –

Shear Banding in Entangled Systems

Generalized Definition of Shear BandingShear-induced separation into two or more macroscopic regions of different strain rate

γ0.

γ1.

= 0

γ2.

>>>

>>>

γ2.γ1

.

Sheared Carbon Nanotube Suspensions

z

x

y

γησ &=xyxv ˆyγ&= ,

Simple Shear Flow

Nanotubes

are in closed periodic Jeffery orbits

cL3

≤

1, cL2d < 1 (dilute)

cL3

>> 1, cL2d < 1 (semi-dilute)

cL3

>> 1, cL2d > 1 (concentrated)

Orbit period scales inversely with shear rate

Sheared Carbon Nanotube Suspensions

Width of image = 200 micrometers

Nanotubes Movie(nanotubes.avi)

Small-Angle Light Scattering from MWNT Suspensions

Good MWNT dispersion

SWNTs

and MWNTsare optically active, so ‘depolarized’

light scattering is needed …… polarization and absorption are bothanisotropic along and normal to the symmetry axis of the tube

E. K. Hobbie

et al, RSI 74, 1244 (2003)

3.5 μm-1

10 μm

h

vh

v

s

p

h

vh

v

s

p

xy

z

μm4 μ

1 μm-1

S = 0.23

Shear-Induced Orientation in Suspensions -Scaling of SALS in the Semi-dilute Regime

Scaling of depolarized light scattering data corroborates the

scaling observed in the dichroismand the birefringence, and a zeroth-order fitting scheme describes all of the data with only one adjustable parameter, a small back ground in a Gaussian ODF, p(θ). Fitting trends consistent with modest to minimal tube deformation.

D. Fry, et. al. Phys. Rev. Lett. 95, 0383304 (2005)

1 μm-1

S = 0.23

Orientation in Sheared Suspensions -Scaling of Birefringence and Dichroism

0.06 nm-15 μm

...)( ||21 +′−′≈′Δ ⊥ Sn

sn ααφ

...)( ||21 +′′−′′≈′′Δ ⊥ Sn

sn ααφ

)1cos3( 221 −= θS

(rotational Peclet

number)

(dilute )3

]8.0)/[ln(3L

dLTkDD B

o πη−

==

Dγ&

=Pe

(semi-dilute - Doi and Edwards)2−∝ φoDD

3/116.0Pe φ∝∝S

D. Fry, et. al. Phys. Rev. Lett. 95, 0383304 (2005)

0.17 wt. % MWNTnL3 ≈

54nL2d ≈

0.23

MWNTsd ≈

50 nmL ≈

10 μmdispersed in PIB

(Mn = 800)η = 10 Pa-s at 25 oC

Flow-Induced Aggregation - Banding in Weak Shear?

S. Lin-Gibson et al, Phys. Rev. Lett. 92, 048302 (2004)

Schmid & Klingenberg, Phys. Rev. Lett. 84, 290-293 (2000)

Generic pattern at early timeexaggerated by confinement effectsat late time …

ψ = area fraction

[width of FFT = 1.2 μm-1]

)0()()( ψψ rr =c

Shear-Induced Aggregation and Coarsening

S. Lin-Gibson et al, Phys. Rev. Lett. 92, 048302 (2004)

Many Other Systems …Clay gels under simple shear flow

Gel of 0.56 % XLGin water (25 oC)

Pignon, Magnin, & Piau, Phys. Rev. Lett. 79, 4689 (1997)

Macroscopic Voriticty Rolls (0.1 s-1 – sped up x10)

Width of image = 1 mm

Banding Movie

(vorticityrolls.avi)

A Simple Cartoon of a Flow Induced InstabilityA number of vastly different systemsexhibit the same shear-induced pattern because they each represent elastic droplets suspended in a viscous fluid

.

HA

S

Generic phase diagram for shear-inducedaggregation in semi-dilute non-Brownian

MWNT suspensions

z

yh

x

‘phase diagram’

.

Bird, Armstrong, & HassagerMontesi, Pena, & Pasquali

50 μm

Unusual Rheological Signal

Negative normal stressLarge intrinsic viscosityDecreasing φConfinement effectsVorticity

elongation

Re ≈10-5, Wi ≈

10

Growth Cycle

Flow orientationPositive normal stressMulti-step processRe ≈10-3, Wi < 1

Dissolution Cycle

N1 = σxx - σyy N = σxx - σzz[J. M. Dealy, J. Rheol. 39, 253 (1995)]

S. Lin-Gibson et al, Phys. Rev. Lett. 92, 048302 (2004)

430 μm

MWNTs

in 500 PIBCone-and-plate geometry

Controlled-Stress

Rheology of Semi-Dilute to Concentrated Suspensions

t (s)

Controlled-Strain

Controlled-Strain

Scaling of Linear Viscoelasticity with Concentration

αφκ ∝

E. K. Hobbie

and D. J. Fry, Phys. Rev. Lett. 97, 036101 (2006)

1.7=α

αφκ ∝

Network Yield Stress

Controlled Strain

E. K. Hobbie

and D. J. Fry, J. Chem. Phys. 126, 124907 (2007)

Relating Shear Modulus and Yield Stress to Network Morphology

E. K. Hobbie

and D. J. Fry, Phys. Rev. Lett. 97, 036101 (2006)E. K. Hobbie

and D. J. Fry, J. Chem. Phys. 126, 124907 (2007)

1.7=ααφκ ∝

5.3=ββφσ ∝0

)3()3(

f

b

dd

−+

=α)3(

2

fd−=β

45.2≈fd1≈bd

W.-H. Shih et al., Phys. Rev. A 42, 4772 (1990).

Processing Phase DiagramMorphology as a function of concentration, confinement, and strain ratefor MWNTs

in 500 PIB -

controlled strain measurements:

E. K. Hobbie

and D. J. Fry, Phys. Rev. Lett. 97, 036101 (2006)

Universal Phase Diagram – Critical Parameters

00 / RR ∝δφδ

1

2

/

)(cos−∝∝

=

γτγδδ

θ

&&S

PS

[ ]00 /)(exp/ SSSac −=σσ

xθ0

R0 ~φ -1/3

ε

θ

3/1

0

φε

∝∝R

SE. K. Hobbie

and D. J. Fry, Phys. Rev. Lett. 97, 036101 (2006)

D. Fry (NIST –

NRC now at JPL)H. Wang (NIST –

now at SUNY)

B. Langhorst

(SURF)S. Lin-Gibson (NIST), J. Pathak

(NIST, now at NRL)

H. Kim (Kyunghee

U)E. Grulke

(U Kentucky)

S. Hudson (NIST)

Thanks!!