Development of an advanced Takayanagi equation for the electrical conductivity of carbon nanotube-reinforced polymer nanocomposites

Abstract

Currently available models for the conductivity of nanocomposites commonly disregard the roles of interphase and tunneling sections. Here, the interphase and tunneling parts are considered to yield an expanded Takayanagi equation to express a model for the electrical conductivity of carbon nanotubes (CNTs)-reinforced polymer nanocomposites (PCNTs). Invoking the interphase section, the operative filler loading and percolation onset are shown to control the volume fraction of networks. Application of the advanced model allows calculation of the conductivity over disparate ranges of various factors and estimation of the conductivity for real specimens. Experimental data for several examples show good matching with the predictions. Straighter CNTs, a dense interphase region, large nets, large tunneling diameter, low polymer tunneling resistivity, and short tunnels give rise to high conductivity. Conductivity is increased to 3.5 S/m at a CNT radius (R) of 5 nm and a CNT length of 20 μm, whereas an insulating sample is observed at R > 8 nm. A percolation onset (ϕp) below 0.0012 results in a conductivity of 0.13 S/m, but it decreases to 0.1 S/m at ϕp> 0.0044. A high CNT volume fraction of 0.02 raises the conductivity to 0.35 S/m, whereas a low CNT volume fraction of 0.005 lowers it to 0.05 S/m.