The results of an extensive study of percolation in order to verify some theoretical predictions about percolation critical indices for changes in static and dynamic dielectric properties of a microemulsion as a function of temperature and frequency are presented in this paper. The dynamic behavior of the microemulsions was also studied in order to reveal the mechanisms that are responsible for dielectric polarization of the system. The measurements were made by means of the time domain dielectric spectroscopy method in the frequency range ${10}^5$–${10}^{10}$ Hz and at temperatures from 10 °C to 40 °C. It was shown in our study that critical indices for conductivity and dielectric permittivity have the values s≊1.2 below and t≊1.9 above the percolation threshold. The value for the critical index s is in agreement with a dynamic percolation picture. This confirms the idea that the mechanism responsible for the temperature dependence of conductivity and permittivity has the same origin. The numerical value of t indicates a percolation picture above the threshold; however, it does not provide information about the nature of percolation. The data treatment for the dynamic behavior of the microemulsions was carried out in the time domain in terms of dipole correlation functions. It was found that the correlation functions exhibit complex nonexponential relaxation behavior in the percolation region and must be deconvoluted into normal modes and represented as the sum of the simple exponential exp(-t/τ) and nonexponential terms exp[-(t/τ${)}^{\mathrm{\beta }}$].

The frequency scaling parameters m, p, and u, as well as the stretched parameters in the time window β, provide information about the microstructure and dynamics of the system. The analysis of their temperature dependence shows the existence of spatial, temporal, and energetic disorder associated with anomalous diffusion of charge carriers in the percolation clusters. On the basis of a detailed analysis of the time relaxation data spectrum, the molecular dynamic mechanism of dielectric polarization in the percolation region was suggested.

• Received 5 July 1994

DOI:https://doi.org/10.1103/PhysRevE.51.478