Percolation Studies of Metal-insulator Composites at Microwave Frequencies

We present a systematic study of the effective dc conductivity ($\sigma _{eff} )$, complex permittivity ($\varepsilon _{eff} )$, and complex permeability ($\mu _{eff} )$ at microwave frequencies, of metal-insulator mixtures up to and beyond the critical volume fraction ($p_c )$ for conductive percolation. Samples made with varying concentrations of Teflon and micron-sized metallic inclusions of copper, silver, cobalt, and tungsten were subjected to separated microwave electric and magnetic fields of a 2.45 GHz, TM$_{010}$ resonant cavity. Using cavity perturbation techniques, the real and imaginary components of $\varepsilon _{eff} $ and $\mu _{eff} $ were thus measured at room temperature. We observe the expected strong dependence of $\sigma _{eff} $, $\varepsilon _{eff} $, and $\mu _{eff} $ on volume fraction near $p_c $ and analyze the results using McLachlan's Generalized Effective Medium (GEM) theory to extract $p_c $ and the percolation exponents $s$ and $t$.