Average gap distance between adjacent conductive fillers in polyimide matrix calculated using impedance extrapolated to zero frequency in terms of a thermal fluctuation-induced tunneling effect

Abstract

Temperature dependence of conductivity of polymer composites was analyzed using the DC component (frequency → 0 Hz) of AC conductivity in terms of thermal fluctuation-induced tunneling through thin barriers to evaluate the average gap distance (D) between adjacent vapor-grown carbon fibers (VGCFs) in a polyimide (PI) matrix. This approach was confirmed to be reasonable in comparison with direct calculation of the D value via the DC measurement. The direct DC measurement provides the average conductivity of the system, whereas the DC component (frequency → 0 Hz) of AC conductivity provides two or three types of phase lag mechanisms, the interface between the composites and electrode, the contact region between adjacent VGCFs and the impedance of VGCFs themselves. The best fit between experimental and theoretical frequency dependence of impedance was realized by the equivalent circuit models, which were classified into several phase lags. The D values calculated by the phase lag due to electron charge on adjacent VGCF surfaces were 1.20 and 1.00 nm for the composites with 3.11 and 6.28 VGCF vol% contents, respectively. The D values are independent of temperature from 25 up to 160 °C, which indicates high thermal resistivity of PI. Equivalent circuit with two units for the 3.11 vol% PI/VGCF composite and three units for the 6.28 vol% PI/VGCF composite was proposed to study the complicated relaxation behavior. The first unit was: interface between bulk and electrode; the second unit was: interface between adjacent VGCFs inserting PI; the third unit was: carrier movement within VGCFs.