Copyright held by Center for
Applied Energy Research,
Rheology of Carbon Nanotube Suspensions
University of Kentucky (2003)
http://www.caer.uky.edu/ Annapurna Karicherla and Eric A Grulke
Department of Chemical and Materials Engineering
University of Kentucky
Designing systems for processing materials to products like thin films, fibers and extrudates requires knowledge of the rheological behavior of the material. The
viscosity of mwnt suspensions in polystyrene /toluene solution as the continuous phase has been measured at shear rates between 1- 22 s-1 . The time dependent
shear-thinning behavior is a first order decay. The Carreau model best describes the viscosity dependence of the system on shear rate, with coefficients varying with
volume fraction. The model can be extended to elongational flows that would be used for fiber spinning.
Table 1: Estimated values of zero shear
viscosity, the time constant, and the power
Applications for MWNT-Filled Polymers Results and Discussion n.
Thin films Continuous phase rheology
Sample l h0 n
Coatings Poly styrene in toluene
Fibers Viscosity of continuous phase varied from 70-700 cp with VGB86, 0.1wt% 848 10,000 0.752
Extrudates concentration change from 10 –25 wt% PS.
Viscosity of the continuous phase is constant in the shear rate range VGB86, 0.2wt% 199 11,500 0.707
Rheological models for suspensions studied.
VGB78, 0.1 wt% 187 191,000 0.473
Possible independent variables: Suspension rheology
the viscosity of the continuous phase
Time Dependent Behavior VGB78,0.2wt% 150 486,000 0.393
volume fraction of the mwnt First order time decay constant varied from 0.012 – 0.10 min-1
the aspect ratio As the shear rate increases the time taken to reach steady state viscosity decreases. VGB63,0.1wt% 150 292,000 0.298
Time-Dependent Behavior VGB 86
2000 VGB 86 VGB 63 0. 1 wt%
1 800 1 0r pm 10000
1 600 model
v is c o s it y c p
1 5r pm
η= viscosity 1 300 model
0.1 wt% mwnt
Cae= steady state (final) viscosity
1 1 00
1 000 model 1000
Cao=initial viscosity 800
100 0. 2wt% mwnt
500 75r pm
Carreau Model 100
1 10 model
1 00r pm 0.1 1 10
0 500 1 000 1 500 2000 2500 3000 3500 4000
st r a i n / s
η= η0 [1+(λγ)2](n-Ι)/2 t i me s
Fig 1 :Viscosity Vs time for VGB 86 in 20 wt% PS/toluene solution.
η0=zero shear viscosity Conclusions
γ= shear rate
Shear Thinning Behavior
The multiwall nanotube suspensions exhibit “ thixotropy”. This behavior has been
Figures show the shear thinning behavior of the suspensions and Table 1 contains
λ=time constant modeled using a first order decay equation.
the Carreau model coefficients.
n=constant Shear thinning is exhibited and the Carreau model best describes the suspension
The viscosity is sensitive to an increase in volume fraction of mwnts: increases
from 0.1 wt% to 0.2 wt% increase the system viscosity. behavior.
Equipment: VGB 86 has an aspect ratio of 1800 and VGB 63 has an aspect ratio of 1000, L/D The volume fraction and length of mwnt & the continuous phase viscosity effect
does not seem to affect the model.
Brookfield viscometer the viscosity of the suspension system.However the length dependence has been
We have investigated the possibility of a network formation which would have an observed to be very negligible in a shear flow.
effect on system viscosity and this theory is consistent with our experimental
Rotating cylinder in infinite bath. results. The “ Network effect” has a significant impact on the suspension viscosity.
No mechanical comminution of Network theory The multiwall nanotubes are very flexible and this has an effect on the viscosity of
fibers the suspension.
The number of multiwall nanotubes in 0.1 wt% has been estimated to be of the
Shear rate range used 0.1-22 s-1 order of 10 12. We think every single nanotube will sweep out a certain volume as The model used for the shear flow is can be modified for an elongational flow field.
it rotates in the shear field. Due to their large number this volume is much larger The aspect ratio dependence is much greater in such a flow field than in a shear flow.
than the volume of the suspension as a whole(nearly 10 4 times greater) and
therefore they tend to form networks. This network formation is a major factor
that causes system viscosity to change.
Effective volume swept by a single
Nanotube. This work was funded by the National Science
Length of mwnt Foundation, Division of Materials Research under
grant no. DMR-9809686