Thermal volume expansion in polymeric PTC composites: a theoretical approach

Polymeric PTC (positive temperature coefficient) composites have been prepared by incorporating carbon black into polyethylene matrices. The dependence of conductivity upon filler loading level obeys a mixtures rule, which was determined by fitting the experimental data into the general effective medium (GEM) equation. A phenomenological model is proposed which is based on the GEM equation and the dilution effect of filler volume fraction due to thermal volume expansion. By using this model, the contribution of the thermal expansion of the matrix to the jump-like PTC switch transition of the composite is quantitatively estimated, and a mechanical explanation is given. The thermal-expansion-dependent percolation curves can also be predicted. Comparisons between predicted and measured PTC effects reveal that thermal expansion is one of the leading factors responsible for the thermal switch effect. Other factors influencing the composite resistivity are discussed.