Dielectric response of concentrated colloidal suspensions

Abstract

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.

Dielectric relaxation behavior of colloidal suspensions of palladium nanoparticle chains dispersed in PVP/EG solution

“…Figure 7 gives us the volume fraction dependency of the dielectric increments of low and high frequency dielectric relaxations of Pd NP chain suspensions, where ␦ l = ͑ l − m ͒ / and ␦ h = ͑ m − h ͒ / . From this figure we can tell that both ␦ l and ␦ h are decreasing with increasing , which is consistent with the prediction of the theory of Carrique et al, 36 but the decreases distinctly trail off after is about 0.08. This result thus also indicates that the aggregation happens when the volume fraction is bigger than 0.08.…”

“…5, was surprising to us because it is not in line with the prediction of Eq. ͑11͒ and also deviates from the prediction of the dielectric theory of concentrated dispersion proposed by Carrique et al 36 The theory predicts that the characteristic time for the low frequency relaxation l decreases with the increasing volume fraction, because the diffusion length of the counterion around the particle will be reduced by the presence of the neighboring particles as the volume fraction increases. For the present case, however, the dispersed particles are chainlike and easy to distort, therefore the result shown in Fig.…”

“…This result thus also indicates that the aggregation happens when the volume fraction is bigger than 0.08. It is well known that relaxation amplitude, for example, ⌬ l ͑= l − m ͒, increases with increasing volume fraction, [35][36][37] but dielectric increment denotes the relaxation amplitude per unit volume and thereby is only decided by the induced dipole coefficient of a single particle. As the volume fraction increases, ion concentration in the bulk solution increases, then more counterions will reside in the stagnant layer of EDL and fewer counterions will be left in the diffuse layer.…”

Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions: The Role of Boundary Conditions

“…[1][2][3][4][5][6][7][8][9][10][11][12][13] The electrokinetic properties of these systems are key factors in processing techniques and quality control.…”

General electrokinetic model for concentrated suspensions in aqueous electrolyte solutions: Electrophoretic mobility and electrical conductivity in static electric fields

“…There exist classical or standard models that predict that response. To begin with, these models [24][25][26][27][28][29][30][31][32][33][34][35] do not take into account the realistic chemistry of the aqueous solutions or the role of the (added) counterions released by the particles. For dilute suspensions and common electrolyte concentrations in solution, the latter two aspects have been historically underestimated or simply neglected, because of their admitted minor role in comparison with that of the salt.…”