Dynamic consequences of the fractal network of nanotube-poly(ethylene oxide) nanocomposites

Dispersions of single walled carbon nanotubes (SWNTs), with an effective aspect ratio of $\sim 650$, in poly(ethylene oxide) (PEO) form fractal superstructures above their geometrical percolation and display rheological properties that follow time-temperature-composition-strain superpositioning. The concentration dependences of the elastic modulus of the network and the onset-strain for shear thinning are consistent with the short-range nature of the interactions that dominate these dispersions. The strain dependence of the damping behavior for the nanocomposites shows concentration invariance when represented against the local strain experienced by the network element, with the onset occurring at a local strain value of 0.1, similar to other nanocomposite systems dominated by weak interactions.

Figure 1

(a) Comparison of the measured linear stress-relaxation modulus $\left[G\left(t\right)\right]$ (solid line) and those calculated using Eq. (1) and linear dynamic measurements (symbols). For the nanocomposites with $p⩾0.3$ (with $p$ is vol% SWNT), a solid like behavior is observed. (b) Frequency dependence of the phase angle $\left(\tan \delta \right)$ from linear dynamic oscillatory measurements. For $p⩾0.3$, a composition invariant behavior is observed at low frequencies.

Figure 2

(a) Time-temperature-composition superposed mastercurves for different linear dynamic rheological properties. (b) Modulus scaling factors used to obtain the composition superposition as a function of $p$. Consistent with the data in Fig. 1, the shift factors for the oscillatory and stress relaxation measurements are identical. (c) Wave vector $\left(q\right)$ dependence of the ultra small angle neutron scattering intensities $I\left(q\right)$ for two nanocomposites. The data were obtained on BT5 instrument at NIST and reduced using standard methods [32]. The fits of the data to a power-law, smeared for experimental resolution and wavelength spread, are shown.

Figure 3

(a) Representative stress relaxation behavior $(p=0.7)$ as a function of the applied (bulk) strain amplitude. For low-amplitude strain, linear behavior is observed followed by a time-strain superposable zone. At higher strain amplitude, time-strain superposability is violated. (b) The composition dependence of the critical strain for the onset of shear thinning is shown; the scaling behavior is consistent with the short range interactions dominating these nanocomposites.

Figure 4

(a) Damping function $h\left(\gamma \right)$ required for time-strain superposition is plotted against a reduced strain $({\gamma }_{\text{bulk}}∕{\gamma }_{\text{critical}})$. (b) The local strain [Eq. (2)] dependence of $h\left(\gamma \right)$. The onset of the shear thinning is observed at ${\gamma }_{\text{local}}\sim 0.1$ and is similar to other nanocomposite systems with short-range interactions.