RESUMEN
A unified extension of the classic Shilov-Dukhin theory of the low frequency dielectric dispersion of colloidal dispersions is presented. Purely analytical expressions for the AC dielectric and electrokinetic response over a broad frequency range including different counterion and co-ion valences and the presence of the stagnant layer conductivity are deduced. The obtained results are generally in good to very good agreement with available numerical data, showing that they should be useful for the interpretation of a broad range of experimental results without having to rely on numerical calculations.
RESUMEN
A rigorous extension of the classic Dukhin-Shilov thin double layer polarization theory including the stagnant layer conductivity is presented. Precisely the same assumptions and approximations made in the original theory are maintained, and the same adsorption isotherms are used as in most of the existing numerical calculations. The obtained analytical results improve upon existing approximate extensions, mainly for low surface conductivities and high surface potentials and for high surface conductivities and low surface potentials. Moreover, they avoid the assumption that all the adsorbed ions in the stagnant layer must have a single sign. Finally, they present a very good agreement with numerical calculations specifically made using the same system parameters.
RESUMEN
The classic Shilov-Dukhin theory of the low frequency dielectric dispersion of colloidal suspensions in binary electrolyte solutions [ Shilov , V. N. ; Dukhin , S. S. , Colloid J. 1970 , 32 , 245. ; Dukhin , S. S. ; Shilov , V. N. Dielectric Phenomena and the Double Layer in Disperse Systems and Polyelectrolytes ; Wiley : New York , 1974 ] was developed for the frequency range corresponding to the concentration polarization phenomenon: up to a few megahertz. While a few extensions to a broad frequency range including the Maxwell-Wagner-O'Konski dispersion exist, they all consist of modifications of the final results of the theory rather than modifications of its hypothesis, extending their validity to high frequencies. In this work we avoid this artificial process by providing a high frequency extension fully from within the theory.
RESUMEN
The classic Shilov-Dukhin theory of the low frequency dielectric dispersion of colloidal suspensions in binary electrolyte solutions was developed for symmetric electrolytes: equal counterion and co-ion valences. A rigorous generalization of this theory to asymmetric electrolytes, such that the valence of counterions is double or half the valence of co-ions, is presented. This generalization is possible because analytical solutions of the intervening integrals exist for these two particular cases but do not exist in the general case of different counterion and co-ion valences, a result apparently overlooked or ignored in the past.
RESUMEN
The classic Dukhin-Shilov theory for the thin double layer polarization of colloidal suspensions in binary electrolyte solutions was developed for symmetric electrolytes: equal counterion and co-ion valences. A rigorous generalization of this theory to asymmetric electrolytes, such that the valence of counterions is double or half the valence of co-ions, is presented. This generalization is possible because analytical solutions of the intervening integrals exist for these two particular cases but do not exist in the general case of different counterion and co-ion valences, a result apparently overlooked or ignored in the past.
RESUMEN
It is shown that the fundamental expression for the complex permittivity epsilons* of a dilute suspension of monodispersed, spherical particles, epsilons*=epsilone*(1+3phid*), where epsilone* is the complex permittivity of the suspending medium and d* the dipolar coefficient, is strictly valid for any value of the volume fraction phi of particles in the suspension, provided that d* is interpreted as the ensemble average value of the dipolar coefficient of the particles and is defined in terms of the macroscopic electric field in the suspension.
Asunto(s)
Suspensiones/química , Conductividad Eléctrica , Tamaño de la Partícula , Electricidad Estática , Propiedades de SuperficieRESUMEN
Dielectric properties of four suspensions of spherical polystyrene particles were measured at 25 degrees C over a broad frequency range extending from 100 Hz to 10 MHz, using a HP 4192 A Impedance Analyzer. The instrument was coupled to a cell with parallel platinum black electrodes and variable spacing, and the quadrupole calibration method was used. The aqueous electrolyte solutions were prepared using equal concentrations of NaCl, KCl, NaAc, or KAc, so that the calculated Debye screening length and Zeta potential remained constant, while the conductivity changed. The polystyrene particles used (Interfacial Dynamics Corp., surfactant-free white sulfate latex) have a diameter of 1 micron and a surface charge density that is independent of the pH. The dielectric spectra were described using the Nettelblad-Niklasson expression combined with a Debye type high-frequency term and analyzed using the Shilov-Dukhin theory and numerical results. The theoretical prediction that the low-frequency dispersion parameters are determined by the co-ion diffusion coefficient was experimentally confirmed. This also allowed to justify an alternative definition of the characteristic time of the low-frequency dispersion. On the contrary, the prediction that the high-frequency dispersion parameters are determined by the diffusion coefficient of counterions could not be confirmed, possibly due to experimental problems. However, the zeta-potential values deduced from high-frequency data were compatible with values deduced from electrophoretic mobility measurements.
RESUMEN
The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant zeta potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.
RESUMEN
A correction of a recent work on the dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of dispersed particles (C. Grosse, S. Pedrosa, V.N. Shilov, J. Colloid Interface Sci. 251 (2002) 304) is presented. It is shown that the procedure used in that work to calculate the contribution of the particles to the conductivity of the suspension leads to a result that includes the variation of the conductivity of the dispersion medium. Revised analytical and numerical calculations are presented, which strongly reinforce the conclusions reached in the original work: The expression for the conductivity increment based on the value of the dipolar coefficient of the suspended particles (calculated taking into account their electrophoretic motion) appears to be valid over the whole range of particle sizes.
RESUMEN
A numerical calculation of the electrophoretic mobility of colloidal particles in weak electrolyte solution is presented. It is based on a previous work (C. Grosse, V.N. Shilov, J. Colloid Interface Sci. 211 (1999) 160-170), where the analytical theory of the thin double layer concentration polarization is generalized to the case of weak electrolytes, i.e., when the dissociation-recombination equilibrium and rate constants both have finite values. The analytical results are first completed by including terms corresponding to co-ions that were neglected in the original presentation. It is shown that these terms that have little bearing in the case of strong electrolytes, become quite important in the case when the electrolyte is weak. The problem is then solved using the network method, leading to numerical results for the electric potential and the concentrations of counterions, co-ions, and neutral ion pairs. Finally, the electrophoretic mobility is calculated both analytically and numerically. It is shown that the hypothesis of a weak electrolyte leads to changes of mobility with respect to the classical results that are even stronger than predicted analytically.
RESUMEN
The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.
Asunto(s)
Coloides/química , Modelos Químicos , ElectroquímicaRESUMEN
The analytical theory of the thin double-layer concentration polarization in dilute suspensions of colloidal particles, generalized by the authors to the case of weak electrolyte solutions [C. Grosse and V. N. Shilov, J. Colloid Interface Sci. 211, 160 (1999)], was used to determine the conductivity dispersion amplitude, the dielectric increment, and the characteristic time of the low-frequency dielectric dispersion (LFDD). It is shown that at constant ionic strength, the conductivity dispersion amplitude always diminishes for weak electrolytes. This is due to the increment in the zero-frequency dipolar coefficient, which occurs because the field-induced ion concentration change around the particle is lowered. On the contrary, while the dielectric increment and the characteristic time of the LFDD usually decrease, they can actually increase when the diffusion coefficient of co-ions is larger than that of counterions. The origin of this behavior is in the appearance of volume charge distributions outside the double layer, which do not vanish for weak electrolytes in the low-frequency limit. Copyright 2000 Academic Press.