Critical Behavior of the Complex Dielectric Constant near the Percolation Threshold of a Heterogeneous Material

The behavior of the effective bulk conductivity ${\sigma }_e$ and of the effective bulk dielectric constant ${\epsilon }_e$ of a heterogeneous mixture of a conducting phase and an insulating dielectric phase is analyzed in the vicinity of the percolation threshold. Exact considerations of a general nature lead to the conclusion that ${\epsilon }_e$ diverges as the conductivity threshold is approached from either side. The introduction of a homogeneity or scaling hypothesis leads to relations between the critical behavior of ${\sigma }_e$ and ${\epsilon }_e$.