Viscoelasticity of Single Wall Carbon Nanotube Suspensions

We investigate the viscoelastic properties of an associating rigid rod network: aqueous suspensions of surfactant stabilized single wall carbon nanotubes (SWNTs). The SWNT suspensions exhibit a rigidity percolation transition with an onset of solidlike elasticity at a volume fraction of 0.0026; the percolation exponent is $2.3\ifmmode\pm\else\textpm\fi{}0.1$. At large strain, the solidlike samples show volume fraction dependent yielding. We develop a simple model to understand these rheological responses and show that the shear dependent stresses can be scaled onto a single master curve to obtain an internanotube interaction energy per bond $\ensuremath{\approx}40{k}_{B}T$. Our experimental observations suggest SWNTs in suspension form interconnected networks with bonds that freely rotate and resist stretching. Suspension elasticity originates from bonds between SWNTs rather than from the stiffness or stretching of individual SWNTs.