A model for the tensile modulus of polymer nanocomposites assuming carbon nanotube networks and interphase zones

In this paper, we develop a conventional model for the tensile modulus of polymer/carbon nanotube (CNT) nanocomposites that assumes the stiffening and percolating effects of the interphase between polymer matrix and CNTs. The developed model expresses the modulus using the radius and length of the CNTs as well as the thickness, volume fraction, aspect ratio and modulus of the interphase. Similarly, the percolation volume fractions of the nanoparticles (ϕ_p) and interphase regions (ϕ_pi) are inversely linked to the aspect ratio as a ratio of length to diameter. The predictions generated from the developed model are compared with many experimental results, and the roles of the model’s parameters are studied. The calculations show good agreement with the experimental results in the samples that include the percolating network and interphase, while an overprediction is observed in the samples without them. The ideal effects of long and thin CNTs as well as thick and strong interphase on the reinforcing and percolating efficiencies of the interphase are described in detail. The modulus shows an improvement of less than 20% at ϕ_p> 0.0055 and ϕ_pi> 0.0025 , while the highest relative modulus of 2.4 is obtained with the minimal values of these parameters (ϕ_p= 0.002 and ϕ_pi= 0.001).