Role of critical interfacial shear modulus between polymer matrix and carbon nanotubes in the tensile modulus of polymer nanocomposites

The main purpose of this paper includes the definition of critical interfacial shear modulus (G(c)) between polymer matrix and carbon nanotubes (CNT) and the investigation of its roles in the effective interphase properties and tensile modulus of polymer nanocomposites. Halpin-Tsai model is developed to determine the roles of "G(c)", interfacial shear modulus (G(i)) and interphase properties in the tensile modulus of nanocomposites. The calculations of the developed model for the modulus of various samples are compared to the experimental results. Furthermore, the effects of all parameters on the tensile modulus of nanocomposites are explained to support the developed model. The original Halpin-Tsai model overestimates the tensile modulus of the samples, but the predictions of the developed model properly agree with the experimental data. The high "G(c)" and poor interphase modulus cannot reinforce the nanocomposites. Also, CNT radius (R) > 15 rim considerably weaken the modulus of nanocomposites, but the modulus grows about 500% at R = 5 nm and interphase thickness (t) = 25 nm demonstrating the most important roles of these parameters in the modulus of nanocomposites.