Evaluation and Development of Expanded Equations Based on Takayanagi Model for Tensile Modulus of Polymer Nanocomposites Assuming the Formation of Percolating Networks

In this study, the tensile modulus of polymer nanocomposites is analyzed by the development of expanded Takayanagi models considering the fractions of networked and dispersed nanoparticles above the percolation threshold. The tensile moduli of networked and dispersed phases are calculated by suitable models. This study focuses on “polymer-carbon nanotubes” nanocomposites, but the developed model can be applied for samples reinforcing with long fillers such as clay and graphene. The expanded Takayanagi model suggests two different forms which are evaluated by the experimental results of “polymer-carbon nanotubes” nanocomposites. Only one form shows the best results compared to the experimental data, whereas another form underestimates the modulus. The developed model (correct form) shows that the fraction of filler network meaningfully changes the reinforcement of nanocomposites. The network level and other correlated parameters with the percolation threshold can be calculated by comparing the experimental data with the developed model. The logical outputs confirm the correct development of Takayanagi model assuming the network and dispersion of nanoparticles in polymer nanocomposites.