Rheology of Carbon Nanotube Suspensions

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					            Copyright held by Center for
            Applied Energy Research,
                                                      Rheology of Carbon Nanotube Suspensions
            University of Kentucky (2003)
                          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%
            η=Cae+(Cao-Cae)e –kt
                                                            1 900
                                                            1 800                                                                      1 0r pm                                                                                                                      10000
                                                            1 700
                                                            1 600                                                                      model


                                                                                                                                                                              v is c o s it y c p
                                                            1 500
                                                                                                                                       1 5r pm
                                                            1 400

            η= viscosity                                    1 300                                                                      model

                                                                                                                                                                                                                                                  0.1 wt% mwnt
                                                            1 200
                                                                                                                                       25r pm
            Cae= steady state (final) viscosity
                                                            1 1 00
                                                            1 000                                                                      model                                                        1000
            Cao=initial viscosity                             800
                                                                                                                                       50r pm
                                                                                                                                                                                                    100                                           0. 2wt% mwnt
                                                              500                                                                      75r pm

  Carreau Model                                                                                                                                                                                                                                                       100
                                                                                                                                                                                                           1                                 10   model
                                                              1 00
                                                                                                                                       1 00r pm                                                                                                                             0.1                  1                      10
                                                                 0                                                                     model
                                                                     0   500   1 000   1 500    2000    2500   3000     3500   4000
                                                                                                                                                                                                                        strain /s
                                                                                                                                                                                                                                                                                           st r a i n / s
            η= η0   [1+(λγ)2](n-Ι)/2                                                             t i me s
                                                                                                                                                                                                                                                                                                            calc viscosity

                                                         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

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