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The determination of the low-frequency ͑typically 0-1 MHz͒ dielectric dispersion of colloidal suspensions may become an electrokinetic tool of wider use if the accuracy of experimental data can be improved and if trustable theories, available for a wide range of situations, are made available. In the present work, we focus on the latter aspect: Since the dielectric constant of the suspensions is in fact a collective property, its determination could be most useful in concentrated suspensions. This is our aim in this paper. Using the classical electrokinetic equations and a cell model accounting for particle-particle interactions, we present calculations of the dielectric spectra of concentrated ͑volume fractions up to 50%͒ suspensions of spheres. Most of our results cannot be thought of as any sort of extrapolation of those corresponding to dilute suspensions ͑the reverse is true͒, and in fact the notion of a dilute colloidal system is itself not free of uncertainties, as no ''critical volume fraction'' can be identified separating the dilute and concentrated ranges. According to the calculations described, increasing the particle concentration by a sufficient amount can lead to a decrease of the dielectric constant of the whole system that can be well below that of the dispersion medium, even for high zeta potentials,. The latter quantity affects ͑and this is also true if → 0͒ considerably both the dielectric constant r Ј and the relaxation frequency, f rel : When is increased, both the low-frequency value, r Ј͑0͒, of r Ј , and f rel increase at all particle concentrations. We also analyze the effect of the product a, where a is the particle radius and is the reciprocal Debye length: higher a values correspond to larger r Ј͑0͒ and lower f rel. Finally, the model is compared to previously reported experimental data: it is found that the qualitative agreement is excellent both concerning r Ј͑0͒ and f rel. Possible improvements of the theory, particularly the inclusion of a dynamic Stern layer, are suggested.

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In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the abovementioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.

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