Polarization of the Electrical Double Layer. Time Evolution after Application of an Electric Field.

Electrophoresis is one of the electrokinetic phenomena most widely investigated, both from a fundamental point of view and as a research tool in academia and industry. However, the dependence between electrophoretic mobility and zeta potential is, in a general case, far from simple, because of the many physical processes involved. In this work, we first describe qualitatively and (in some cases) quantitatively the time behavior of the dipole moment induced in the electrical double layer by an applied electric field. Further, a simple relationship is deduced between the dipole moment and the electrophoretic mobility. Through the analysis of the time dependence of the former, it is possible to resolve the different contributions to the stationary values of the mobility. Three characteristic relaxation times are distinguished in the time evolution of the dipole moment: tau(H) (the time needed for hydrodynamic flows to be established), tau(MW) (time for ionic electromigration to develop), and tau(VD) (after this time, diffusion flows are established in the system, and the double layer polarization is complete). This means that different mechanisms are operating on the double layer for different times after the application of the field, and that computing the mobility at such different times is equivalent to calculating the steady-state electrophoretic mobility under different approximations. A comparison is shown between estimated and computed mobility values as functions of time and of zeta potential, confirming the validity of the asymptotic calculations. Copyright 2000 Academic Press.

Influence of Fixed Charge Distribution on Ion Mobility: Small Deviations of Equilibrium Potential from Donnan Value.

The influence of the electrostatic interaction on the diffusion coefficients of ions is estimated in the approximation of the slightly varying equilibrium potential. Various assumptions have been considered for the fixed charge distribution, namely, the discrete charge distributed in the bulk, the surface charge, and the linear charge distributed around a macroion. Both the random and regular distributions of the fixed charge groups are being separately analyzed as applied to each assumption. Obtained dependencies show in some measure various types of the fixed charge heterogeneity contribute to the effect of the diffusion coefficient decrease. Copyright 1999 Academic Press.

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 usually calculated from the low-frequency asymptotic of the frequency-dependent solution of the electrodiffusion equations. Since these equations written in spheroidal coordinates do not separate, no theoretical results exist for the low-frequency dielectric properties of suspensions of spheroidal particles. In order to sidestep this problem, we used another method which relates the dielectric properties to the energy stored in the system (Grosse, C., Ferroelectrics 86, 171 (1988)) which, at low frequencies, mainly corresponds to the Gibbs free energy associated to the field-induced electrolyte concentration changes outside the double layer (Grosse, C. and Shilov, V. N., J. Colloid Interface Sci. 193, 178 (1997)). This method permits us to calculate the static permittivity by solving a purely static problem, which makes it possible to calculate analytically the alpha-dispersion amplitude of suspensions of spheroidal particles since the electrodiffusion equations do separate in the static case. We also calculate the characteristic time of the alpha-dispersion from the dispersion amplitude and the static and high-frequency 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 respect to the applied field. Copyright 1999 Academic Press.

Electrophoretic Mobility of Colloidal Particles in Weak Electrolyte Solutions.

The analytical theory of the thin double layer concentration polarization in suspensions of colloidal particles is generalized to the case of weak electrolyte solutions, i.e., when the dissociation-recombination equilibrium and rate constants have both finite values. It is shown that under the action of a static applied field, regions near the particle appear where there is departure from the dissociation-recombination equilibrium. The resulting ion and ion-pair sources have a strong bearing on their flows, leading to a change of the electrolyte concentration gradients around the particle. This phenomenon also modifies the value of the particle electrophoretic mobility, which is dependent on the concentration polarization. At constant ionic strength, the theoretical maximum of the electrophoretic mobility versus zeta potential curve can substantially surpass in weak electrolyte solutions the corresponding value attained in strong electrolytes. Copyright 1999 Academic Press.

Calculation of the Static Permittivity of Suspensions from the Stored Energy

It is shown that the static permittivity of suspensions of charged particles in electrolyte solution can be deduced from the field-induced change of the Gibbs free energy stored outside the double layer. This energy is related to the changes of the electrolyte concentration around the particle and is obtained solving a purely static problem. The method is first verified deducing well-known results corresponding to suspensions of spherical particles. It is then used to calculate the static permittivity of suspensions of spheroidal particles, leading to a new result that cannot be analytically obtained using the classical approach. Copyright 1997 Academic Press. Copyright 1997Academic Press

The ac and dc Conductivities of a Disperse System of the "Conductor-in-Conductor" Type

The relationship is derived, within the scope of irreversible thermodynamics, to predict the dc conductivity of a disperse system of the "conductor-in-conductor" type. The results enable one to describe the dc conductivity of the system with the help of the preliminary known expression for the ac conductivity as a function of the specific conductivities of the constituent phases. The derived relationship is used to study the systems with various types of morphology. It is discussed how the difference between the ac and dc conductivities depends on the system morphology and transport characteristics of both the connected and the disconnected constituent phases. Some ways of using the results are suggested.