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.