Shear-induced conductor-insulator transition in melt-mixed polypropylene-carbon nanotube dispersions

The blending of carbon nanotubes (CNTs) into polymer matrices leads to intrinsically nonequilibrium materials whose properties can depend strongly on flow history. We have constructed a rheodielectric spectrometer that allows for the simultaneous in situ measurement of both the electrical conductivity $\sigma \left(\omega \right)$ and dielectric constant $\epsilon \left(\omega \right)$ as a function of frequency $\omega$, as well as basic rheological properties (viscosity, normal stresses), as part of an effort to better characterize how flow alters the properties of these complex fluids. Measurements of $\sigma$ indicate a conductor-insulator transition in melt-mixed dispersions of multiwall CNTs in polypropylene over a narrow range of CNT concentrations that is reasonably described by the generalized effective medium theory. A conductor-insulator transition in $\sigma$ can also be induced by shearing the fluid at a fixed CNT concentration $\varphi$ near, but above, the zero shear CNT conductivity percolation threshold ${\varphi }_c$. We find that the shear-induced conductor-insulator transition has its origin in the shear-rate dependence of ${\varphi }_c$, which conforms well to a model introduced to describe this effect. Surprisingly, $\sigma$ of these nonequilibrium materials fully recovers at these elevated temperatures upon cessation of flow. We also find that the frequency dependence of $\sigma \left(\omega \right)$ follows a “universal” scaling relation observed for many other disordered materials.

Figure 1

Confocal optical image of CNT-PP melt at CNT concentration $x_m=0.01$.

Figure 2

Test fixture. The surface of the shearing disk consists of alternating nonconductive (polyimide) and conductive (aluminum) electrode rings (r1, r2, and r3) to improve accuracy of the shear-rate measurement.

Figure 3

(a) Real part ${\sigma }^{\prime }$ and (b) imaginary part ${\sigma }^{″}$ of complex conductivity as a function of frequency for $x_m=0.005$ CNT in PP measured at the following shear rates: (1) ${10}^{-3}{\mathrm{s}}^{-1}$, (2) $0.2{\mathrm{s}}^{-1}$, (3) $0.6{\mathrm{s}}^{-1}$, (4) $1.0{\mathrm{s}}^{-1}$, (5) $1.6{\mathrm{s}}^{-1}$, (6) $3.0{\mathrm{s}}^{-1}$, and (7) $6.3{\mathrm{s}}^{-1}$. (8) Conductivity of an air gap when the sample was removed.

Figure 4

(a) Real part ${\sigma }^{\prime }$ and (b) imaginary part ${\sigma }^{″}$ of complex conductivity as a function of frequency for $x_m=0.025$ CNT in PP measured at the following shear rates: (1) ${10}^{-3}{\mathrm{s}}^{-1}$, (2) $0.2{\mathrm{s}}^{-1}$, (3) $0.6{\mathrm{s}}^{-1}$, (4) $1.0{\mathrm{s}}^{-1}$, (5) $1.6{\mathrm{s}}^{-1}$, (6) $3.0{\mathrm{s}}^{-1}$, and (7) $6.3{\mathrm{s}}^{-1}$.

Figure 5

Conductivity recovery in time upon the cessation of shear from $\dot{\gamma }=6.3{\mathrm{s}}^{-1}$.

Figure 6

Conductivity ${\sigma }_0$ as a function of shear rate.

Figure 7

Conductivity as a function of CNT concentration. The lines represent the GEM percolation model and are plotted for guiding the eyes at the following shear rates: (1) ${10}^{-3}{\mathrm{s}}^{-1}$, (2) $0.2{\mathrm{s}}^{-1}$, (3) $0.6{\mathrm{s}}^{-1}$, (4) $1.0{\mathrm{s}}^{-1}$, (5) $1.6{\mathrm{s}}^{-1}$, (6) $3.0{\mathrm{s}}^{-1}$, and (7) $6.3{\mathrm{s}}^{-1}$.

Figure 8

Critical percolation concentration $\left({\varphi }_c\right)$ as a function of shear rate where symbols represent the calculated ${\varphi }_c$ data, while the solid line is a fit to Eq. (3).

Figure 9

Imaginary part of the dielectric permittivity for $x_m=0.025$ as a function of frequency at the following shear rates: (1) ${10}^{-3}{\mathrm{s}}^{-1}$, (2) $0.2{\mathrm{s}}^{-1}$, (3) $0.6{\mathrm{s}}^{-1}$, (4) $1.0{\mathrm{s}}^{-1}$, (5) $1.6{\mathrm{s}}^{-1}$, (6) $3.0{\mathrm{s}}^{-1}$, and (7) $6.3{\mathrm{s}}^{-1}$.

Figure 10

Scaled conductivity $({\sigma }^{\prime }∕{\sigma }_0)$ vs scaled frequency $(\omega ∕{\omega }_s)$ for $x_m=0.01$ (open symbols) and $x_m=0.025$ (closed symbols) at different shear rates: ${10}^{-3}{\mathrm{s}}^{-1}$ (squares), $0.2{\mathrm{s}}^{-1}$ (circles), $0.6{\mathrm{s}}^{-1}$ (triangles—up), $1.0{\mathrm{s}}^{-1}$ (triangles—down), $1.6{\mathrm{s}}^{-1}$ (diamonds), $3.0{\mathrm{s}}^{-1}$ (tilt triangles), and $6.3{\mathrm{s}}^{-1}$ (stars).