The actual dielectric response function for a colloidal suspension of spherical particles

In this paper, we present a theoretical analysis of the dielectric response of a dense suspension of spherical colloidal particles based on a self-consistent cell model. Particular attention is paid to (a) the relationship between the dielectric response and the conductivity response and (b) the connection between the real and imaginary parts of these responses based on the Kramers-Kronig relations. We have thus clarified the analysis of Carrique et al. (Carrique, F.; Criado, C.; Delgado, A. V. J. Colloid Interface Sci. 1993, 156, 117). We have shown that both the conduction and displacement current components are complex quantities with both real and imaginary parts being frequency dependent. The dielectric response exhibits characteristics of two relaxation phenomena: the Maxwell-Wagner and the alpha-relaxations, with the imaginary part being the more sensitive instrument. The inverse Fourier transform of the simulated dielectric response is compared with a phenomenological, two-exponential response function with good agreement obtained. The two fitted decay times also compare well with times extracted from the explicit simulations.