Impedance-Frequency Response of Closed Electrolytic Cells.

The electric AC response of electrolytic cells with DC bias is analyzed solving numerically the Poisson-Nernst-Planck equations and avoiding the commonly used infinite solution approximation. The results show the presence of an additional low-frequency dispersion process associated with the finite spacing of the electrodes. Moreover, we find that the condition of fixed ionic content inside the electrolytic cell has a strong bearing on both the steady-state and the frequency response.

A program for the fitting of up to three Havriliak-Negami dispersions to dielectric data.

A new version of the DielParamFit program [J. Colloid Interface Sci. 419 (2014) 102-106] for the fitting of a superposition of dispersion terms to measured dielectric data is presented.

Numerical Solution of the Electrokinetic Equations for Multi-ionic Electrolytes Including Different Ionic Size Related Effects.

One of the main assumptions of the standard electrokinetic model is that ions behave as point-like entities. In a previous work (López-García, et al., 2015) we removed this assumption and analyzed the influence of finite ionic size on the dielectric and electrokinetic properties of colloidal suspensions using both the Bikerman and the Carnahan⁻Starling equations for the steric interactions.

Influence of steric interactions on the dielectric and electrokinetic properties in colloidal suspensions.

One of the main assumptions of the standard electrokinetic model is that ions behave as point like entities. In this work we remove this assumption and analyze the main consequences of finite ionic size on the dielectric and electrokinetic properties of colloidal suspensions. We represent the steric interactions by means of the Bikerman and the Carnahan-Starling equations and solve numerically the standard linearized electrokinetic equations in the stationary and the frequency domains, for surface charge density and electrolyte solution concentration values typically encountered in colloidal suspensions.

Influence of the finite size and effective permittivity of ions on the equilibrium double layer around colloidal particles in aqueous electrolyte solution.

The equilibrium properties of the electrical double layer surrounding a charged spherical colloidal particle immersed in an aqueous electrolyte solution are examined taking into account the finite ion size. This study includes the representation of the steric interactions among ions using both the Bikerman and the Carnahan-Starling models, an account of all the effects related to the representation of hydrated ions as dielectric spheres (dependence of the electrolyte solution permittivity, on the local ion concentration, and appearance of the Born and the dielectrophoretic forces acting on the ions), and solution of the problem for both high and low surface charge values. We find that the Carnahan-Starling model together with effective ion permittivity related effects appears to be able to provide an interpretation to the electrokinetic potential vs.

A program for the fitting of Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami dispersions to dielectric data.

The description and interpretation of dielectric spectroscopy data usually require the use of analytical functions, which include unknown parameters that must be determined iteratively by means of a fitting procedure. This is not a trivial task and much effort has been spent to find the best way to accomplish it. While the theoretical approach based on the Levenberg-Marquardt algorithm is well known, no freely available program specifically adapted to the dielectric spectroscopy problem exists to the best of our knowledge.

Influence of the dielectrophoretic force in mixed electrical double layers.

The equilibrium properties of a charged plane immersed in an aqueous electrolyte solution are examined using a generalized Poisson-Boltzmann equation that takes into account the finite ion size by modeling the solution as a suspension of polarizable insulating spheres in water. This formalism is applied to a general solution composed of two or more counterion species with different valences, sizes, and effective permittivity values. It is shown that, due to the dependence of the dielectrophoretic force on the ion size and effective permittivity value, the concentration of the smaller counterion strongly increases while that of the larger one decreases in the immediate vicinity of the charged surface.

Extension of a classic low frequency dielectric dispersion theory of colloidal suspensions to include different counterion and co-ion valences, a broad frequency range, and the stagnant layer conductivity.

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.

Equilibrium properties of charged spherical colloidal particles suspended in aqueous electrolytes: finite ion size and effective ion permittivity effects.

The equilibrium properties of a charged spherical colloidal particle immersed in an aqueous electrolyte solution are examined using an extension of the Standard Electrokinetic Model that takes into account the finite ion size by modeling the aqueous electrolyte solution as a suspension of polarizable insulating spheres in water. We find that this model greatly amplifies the steric effects predicted by the usual modified Poisson-Boltzmann equation, which only imposes a restriction on the ability of ions to approach one another. This suggests that a solution of the presented model under nonequilibrium conditions could have important consequences in the interpretation of dielectric and electrokinetic data in colloidal suspensions.

Poisson-Boltzmann description of the electrical double layer including ion size effects.

The electrical double layer is examined using a generalized Poisson-Boltzmann equation that takes into account the finite ion size by modeling the aqueous electrolyte solution as a suspension of polarizable insulating spheres in water. We find that this model greatly amplifies the steric effects predicted by the usual modified Poisson-Boltzmann equation, which imposes only a restriction on the ability of ions to approach one another. This amplification should allow for an interpretation of the experimental results using reasonable effective ionic radii (close to their well-known hydrated values).

Extension of a classic thin double layer polarization theory of colloidal suspensions to include the stagnant layer conductivity.

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.

Extension of a classic theory of the low frequency dielectric dispersion of colloidal suspensions to the high frequency domain.

The classic Shilov-Dukhin theory of the low frequency dielectric dispersion of colloidal suspensions in binary electrolyte solutions [ Shilov , V. N. ; Dukhin , S.

Generalization of a classic theory of the low frequency dielectric dispersion of colloidal suspensions to electrolyte solutions with different ion valences.

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.

Generalization of a classic thin double layer polarization theory of colloidal suspensions to electrolyte solutions with different ion valences.

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.

Dependence of the dielectric properties of suspensions on the volume fraction of suspended particles.

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.

Numerical calculation of the dielectric and electrokinetic properties of vesicle suspensions.

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.

Dependence of the broad frequency dielectric spectra of colloidal polystyrene particle suspensions on the difference between the counterion and co-ion diffusion coefficients.

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.

On the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension.

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.

Numerical solution of the poisson-boltzmann equation for a spherical cavity.

The Poisson-Boltzmann equation is numerically solved for a spherical cavity filled with a charged electrolyte solution. The network method used makes it possible to solve the problem in the most general case: the electrolyte solution can have any number of ion types with valences having any value. Furthermore, no a priori assumption concerning electroneutrality at the center of the cavity is required.

Suspended particles surrounded by an inhomogeneously charged permeable membrane. Solution of the Poisson-Boltzmann equation by means of the network method.

The Poisson-Boltzmann equation is numerically solved for a suspended spherical particle surrounded by a permeable membrane that contains an inhomogeneous distribution of fixed charges. The calculations are carried out using the network simulation method, which makes it possible to solve the problem in the most general case, extending previous results (J.P.

Corrected results for the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension.

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.

Field-induced disturbance of the double layer electro-neutrality and non-linear electrophoresis.

The influence of applied electric field on the field-induced variation of the electrolyte concentration (concentration polarization) disturbs the electro-neutrality of the system, represented by a dispersed particle and its electric double layer in electrolyte solution. The manifestation of this electro-neutrality disturbance in the non-linear electrophoresis was considered in the framework of a procedure of successive approximations in powers of the applied field strength. Analytic expressions describing the component of the electrophoretic velocity proportional to the cubic power of the applied field strength (cubic electrophoresis) were obtained for arbitrary values of the surface conductivity (of Dukhin number).

Numerical calculation of the electrophoretic mobility of colloidal particles in weak electrolyte solutions.

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.

Numerical study of the equilibrium properties of suspended particles surrounded by a permeable membrane with adsorbed charges.

The network simulation method is used to calculate the electrostatic potential distribution for suspended spherical particles made of a charged core surrounded by a permeable membrane with adsorbed charges. The structure of the equilibrium diffuse double layers on both sides of the membrane-electrolyte solution interface is analyzed considering an anion adsorption process described by a Langmuir-type isotherm. It is shown that the thickness of the double layer in the membrane strongly depends on the adsorption constant, while it is almost independent of this constant in the electrolyte solution.

Conductivity, Permittivity, and Characteristic Time of Colloidal Suspensions in Weak Electrolyte Solutions.

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.