Excluded Volume Effect on the Extensional Rheology of Carbon Nanotubes: A Mesoscopic Theory

We present a mesoscopic theory of the extensional rheology of liquid crystalline carbon nanotubes (CNTs). We implement the mesoscopic Leslie-Ericksen theory, considering the repulsive excluded volume potential acting in the direction opposite to the Frank elastic potential. Given the volume fraction, diameter, and length of the CNTs, our model predicts the extensional viscosity. The liquid crystalline phase of the CNTs exhibited extensional thinning behavior. In our theory, the rotational relaxation time is proportional to the reciprocal excluded volume, particularly for long CNTs with waviness. Our model also predicts the minimum draw ratio, below which the nanotube orientation cannot reach the target orientation. The existence of a minimum draw ratio is due to the large excluded volume potential of the long CNTs.