Positive temperature coefficient effect of polymer-carbon filler composites under self-heating evaluated quantitatively in terms of potential barrier height and width associated with tunnel current

A new approach for positive temperature coefficient (PTC) effect of resistivity for polymer-filler composites by self-heating and external forced heating was proposed, based on SEM, ESR and positron annihilation in terms of tunnel effect of electrons through polymer matrix between neighboring short carbon fibers (CFs). The CF content as fillers in polymer matrix was fixed at the concentration slightly higher than the percolation threshold. The fitting between theoretical resistivity calculated by tunnel current density and experimental resistivity indicated that transport hindrance of electrons with elevating temperature was attributed to a drastic increase in potential barrier height resulted from free volume expansion in polymer matrix as well as air volume expansion between neighboring CFs. Different from the well-known concept, this effect was much more predominant than an increase in potential barrier width. The proposed quantitative analysis also satisfied time-dependence of resistivity at a fixed applied electric field and an increase in conductivity by γ-ray irradiation.