Predicting the effective depth of a defective interphase in carbon nanofiber polymer system to estimate the percolation onset and electrical conductivity

Despite a perfect interphase, a defective interphase hinders the effective transfer of conductivity from carbon nanofibers (CNFs) to the surrounding medium, thereby diminishing the overall conductivity of the nanocomposites. Hence, understanding the role of a defective interphase is critical for analyzing and optimizing the percolation onset and electrical conductivity of samples. This paper introduces the effective depth of a defective interphase in polymer-CNF composites (PCNFs), defined by L c , which represents the minimum length of a CNF required to fully transfer its intrinsic conductivity to the polymer matrix. Furthermore, parameters such as effective CNF content, percolation threshold, and network concentration are described by the effective interphase depth and L c . A comprehensive model for PCNF conductivity is also developed based on these effective parameters and tunneling dimensions. The stimuli of factors on the effective interphase depth, percolation inception, and PCNF conductivity are analyzed and graphically presented. Additionally, experimental data on percolation threshold and PCNF conductivity are employed to validate the proposed equations. The findings highlight that longer CNFs, shorter L c , thinner CNFs, and higher interphase conductivity result in a more extensive effective interphase, a lower percolation threshold, and enhanced PCNF conductivity. Moreover, reduced waviness, larger contact diameters, greater contact numbers, and shorter tunneling distances contribute significantly to improved conductivity in this system. These data are valuable to obtain a lower percolation onset and higher conductivity to improve the performance of PCNFs.