Effect of stagnant-layer conductivity on the electric permittivity of concentrated colloidal suspensions

Abstract

A long-lasting experience in the electrokinetics of suspensions has shown that the so-called standard model may be partly in error in explaining experimental data. In this model, the stagnant layer is considered nonconducting (Ksigmai=0), and only the diffuse layer contributes to the total surface conductivity (Ksigma=Ksigmad). In the present work, the authors analyze the consequences of assuming a nonzero stagnant layer conductivity on the permittivity of concentrated suspensions. Using a cell model to account for the particle-particle interactions, and a well established ion adsorption isotherm on the inner region of the double layer, the authors find the frequency-dependent electric permittivity of suspensions of spherical particles with volume fractions of solids up to above 40%. It is demonstrated that the addition of Ksigmai significantly increases the contributions of the double layer to the polarization of the suspension: the alpha or concentration polarization at low (kilohertz) frequencies, and the Maxwell-Wagner-O'Konski (associated with conductivity mismatch between particle and medium) one at intermediate (megahertz) frequencies. While checking for the possibility that the results obtained in conditions of Ksigmai not equal 0 could be reproduced assuming Ksigmai=0 and raising Ksigmad to reach identical total Ksigma, it is found that this is approximately possible in the calculation of the permittivity. Interestingly, this does not occur in the case of electrophoretic mobility, where the situations Ksigma=Ksigmad and Ksigma=Ksigmad+Ksigmai (for equal Ksigma) can be distinguished for all frequencies. This points to the importance of using more than one electrokinetic technique to properly evaluate not only the zeta potential but other transport properties of concentrated suspensions, particularly Ksigmai.