Calculation of the dielectric increment and characteristic time of the LFDD in colloidal suspensions of spheroidal particles

The alpha-dispersion amplitude of suspensions of colloidal particles is usu ally calculated from the low-frequency asymptotic of the frequency-dependen t solution of the electrodiffusion equations. Since these equations written in spheroidal coordinates do not separate, no theoretical results exist fo r the low-frequency dielectric properties of suspensions of spheroidal part icles. in order to sidestep this problem, we used another method which rela tes the dielectric properties to the energy stored in the system (Grosse, C ., Ferroelectrics 86, 171 (1988)) which, at low frequencies, mainly corresp onds to the Gibbs free energy associated to the field-induced electrolyte c oncentration changes outside the double layer (Grosse, C, and Shilov, V, N. , J. Colloid Interface Sci. 193, 178 (1997)). This method permits us to cal culate the static permittivity by solving a purely static problem, which ma kes it possible to calculate analytically the alpha-dispersion amplitude of suspensions of spheroidal particles since the electrodiffusion equations d o separate in the static case. We also calculate the characteristic time of the cu-dispersion from the dispersion amplitude and the static and high-fr equency values of the dipolar coefficient, The analytical results obtained are presented and discussed for both prolate and oblate geometries, and for parallel, perpendicular, and random orientations of the particles with res pect to the applied field. (C) 1999 Academic Press.