On the elastic properties of curved carbon nanotubes/polymer nanocomposites: A modified rule of mixture

The elastic modulus of curved single-walled carbon nanotube/polymer nanocomposites is studied. The effects of shape, number, and amplitude of curves and nanotube/matrix interphase on the mechanical properties of nanocomposites are investigated. Solid and hollow cylinder models are employed to model the nanotubes. Single-walled carbon nanotubes are selected with one, two, and three curves. The elastic modulus of polymer matrix reinforced by curved single-walled carbon nanotubes is compared with those of straight nanotube/polymer nanocomposites. Comparing the results with the results of the molecular dynamics simulations, it is shown that the employed model can predict the mechanical properties of nanocomposites with the error lower than that of 2%. The nanotubes with higher number of curves lead to weaker reinforcement of the matrix. Besides, increasing the diameter of the nanotube leads to better reinforcement of the nanocomposites. It is observed that the rule of mixtures cannot predict the elastic modulus of curved single-walled carbon nanotube/polymer nanocomposites correctly. Therefore, the rule of mixtures is modified to accurately predict the elastic modulus of polymer matrix reinforced by curved single-walled carbon nanotubes.