Fractal Interpretation of Dielectric Response

In this paper we put forward a fractal interpretation of the dielectric properties of disordered materials. In materials having charge carriers of low mobility, the dielectric permittivity e(ω) = e1(ω) + ie2(ω) often displays an anomalous low frequency dispersion1 (ALFD), $$ {{\varepsilon }_{1}}(\omega )-{{\varepsilon }_{\infty }}\sim {{\varepsilon }_{2}}(\omega )\sim {{\omega }^{-p}},\omega {{\omega }_{c}} $$ (1) Here e∞ is the high frequency dielectric constant, ωc is a crossover frequency, and the exponents p and n can have values between zero and unity. Below we relate the values of these exponents to the fractal structure of the material and to fractal time processes. The theory is used to interpret experiments on Co-Al2O3 composites, pyrolyzed polyimide and iron oxide films.