A theoretical model for dielectric medium with a linear distribution of conductivity and dielectric constant was proposed. In order to simulate the dielectric relaxation behavior of the porous layer of a composite membrane, the theoretical expressions describing the quantitative relationship among electrical or structural properties of the inner medium and the capacitance and conductance obtained by dielectric measurements were derived. With a lot of simulations, we described and explained the laws that the dielectric spectrum of the porous layer changes with the change in distribution of dielectric constant or in thickness. Furthermore, the dielectric relaxation behavior of the layered composite membrane and the system composed of the membrane and solutions was also simulated. By comparing the dielectric spectra of the three systems: porous layer, composite membrane and solution/composite membrane/solution, the dependence of the dielectric spectra on the properties of each layer was revealed. The results suggest that the model proposed in this study for the porous layer with linearly distributed conductivity and dielectric constant can be expected to apply to other heterogeneous systems as well as membrane systems.

Key words: concentration polarization, dielectric spectroscopy, composite membrane, dielectric constant gradient