Dynamic Consequences of the Fractal Network of Nanotube - Poly(ethylene oxide) Nanocomposites*

In this work, SWNTs are successfully dispersed in a PEO matrix with the aid of an anionic surfactant. A geometric percolation at $\sim $ 0.1 vol {\%} of SWNTs ($\phi _{c})$ is observed and indicates a good state of dispersion of tubes with an effective aspect ratio of $\sim $ 650. At compositions ($\phi )$ well above the percolation threshold, the melt state rheological properties of the nanocomposites are dominated by the self-similar fractal network of the nanotubes (verified by scattering measurements) and demonstrate `time-temperature-concentration' superposition. The scaling of the network elastic strength, G $\left( {\propto \left( {\phi -\phi _c } \right)^{3.4}} \right)$, and critical strain for the onset of shear-thinning, $\gamma _{c} \quad \left( {\propto \left( {\phi -\phi _c } \right)^{-1.9}} \right)$, reveal a bond-bending mechanism to bear stress as expected from the strong short-range interactions between nanotubes. The onset of non-linearity and the damping behavior of the network show concentration invariance when represented against the local strain experienced by the network elements, with the onset occurring at a local strain value of 0.1.