Abstract
The fraction (f) and modulus (E N ) of networked nanoparticles in Takayanagi model for tensile modulus of polymer/carbon nanotube (CNT) nanocomposites (PCNT) were not exactly explained in previous reports. In this paper, some proper equations are suggested to define these parameters to enable the Takayanagi model for prediction of tensile modulus by aspect ratio (α), Young’s modulus (E d ) and percolation threshold of nanoparticles together with the volume fraction, density (n), and modulus of network. The predictions of Takayanagi model are compared with the experimental results of several samples, and the outputs of the developed equations and model are justified. A direct relation is observed between “α” and the volume fraction of percolated network. Also, the modulus of nanocomposite can improve by 1000% at f = 0.25 and E N = 4000 GPa, while the relative modulus (E R ) (ratio of nanocomposite modulus to matrix modulus) of 1.8 is observed at f < 0.075 and E N < 1500 GPa. Additionally, the highest E R = 11 is obtained by E d = 2000 GPa and n = 5, but the least E R = 2 is calculated at E d < 700 GPa and n < 3. So, these parameters effectively govern the modulus of PCNT.
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