Dynamic dipole polarizability of a dielectric sphere in an electrolyte

Analysis of the Dielectric Permittivity of Suspensions by Means of the Logarithmic Derivative of Its Real Part

Measurement of the dielectric permittivity of colloidal suspensions in the kilohertz frequency range (the so-called low-frequency dielectric dispersion) is a promising tool for the electrokinetic characterization of colloids. However, this technique is less used than would be desirable because of the difficulties associated with the measurements, the most important of which is the electrode polarization (EP). Recently (M. Wübbenhorst and J. Van Turnhout, Dielectrics Newsl. November (2000)) a method was proposed that appears capable of separating the unwanted electrode effects from the double-layer relaxation that we are interested in. The method, based on the logarithmic derivative of raw epsilon'(omega) data (epsilon'(omega) is the real part of the permittivity of the suspension for a frequency omega of the applied AC field), is first checked against the well-known theory of the AC permittivity of colloidal suspensions developed by DeLacey and White (E. H. B. DeLacey and L. R. White, J. Chem. Soc. Faraday Trans. 277, 2007 (1981)). We show that the derivative epsilon''(D)(omega)=-(pi/2)(partial differential epsilon'/partial differential ln omega) gives an excellent representation of the true imaginary part of the permittivity, epsilon''(omega). The technique is then applied to experimental data of the dielectric constant of polystyrene and ethylcellulose suspensions. We found that epsilon''(D) displays two separated behaviors when plotted against log omega in the frequency range 100 Hz-1 MHz: a monotonous decrease (associated with EP) followed by an absorption peak (associated with the double-layer relaxation, or alpha-relaxation). Interestingly, they are separated enough to make it possible to easily find the characteristic frequency of the alpha-relaxation. Fitting a relaxation function to epsilon''(D)(omega) after eliminating the part due to EP, we could calculate the real part epsilon'(omega) and compare it to the DeLacey and White (DW) theoretical predictions. A significantly better agreement between DW calculations and experimental epsilon'(omega) data is obtained when the logarithmic derivative method is used, as compared to the classical electrode-separation techniques.

Effect of Size Polydispersity on the Dielectric Relaxation of Colloidal Suspensions: A Numerical Study in the Frequency and Time Domains

In this article, a systematic numerical study is described of the effect of the polydispersity of suspensions of spherical particles on their dielectric behavior, in both the frequency and time domains, starting from the model proposed by DeLacey and White (J. Chem. Soc., Faraday Trans. 2 77, 2007 (1981)) for monodisperse suspensions. The distribution function of relaxation times, characterizing the dielectric response of the systems, is also calculated. It is found that in both the frequency and time domains the predicted behavior does not differ in any essential way from the one obtained for a monodisperse suspension with particle radius close to the volume-averaged mean radius of the polydisperse system. Hence, no arguments related to polydispersity seem to be useful for explaining the discrepancies frequently found between measured and calculated dielectric increments in suspensions, namely, those concerning the magnitude of the dielectric constant of the suspension (its low-frequency value), the value of the characteristic or relaxation frequency, or the overall shape of the relaxation pattern. Copyright 1998 Academic Press.