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. For example: the characteristic frequency of the high-frequency dispersion decreases when the DC potential increases and/or the electrode spacing decreases in the closed cell case, while it remains essentially insensitive on these changes for open cells. Finally, approximate analytic expressions for the dependences of the main parameters of both dispersion processes are also presented.

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. In all cases the steric interactions improve upon the predictions of the standard model since the surface potential, the electrophoretic mobility, and the conductivity and permittivity increments increase. However, the corrections introduced by the Bikerman equation are generally small: less than 10% as compared to the standard model. On the contrary, the Carnahan-Starling equation leads to corrections to the surface potential versus surface charge and the electrophoretic mobility values that easily surpass 10% and can attain values as high as 50%. Corrections to the conductivity and permittivity increments are smaller but still non negligible.

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. surface charge dependence in the case of colloidal particles suspended in aqueous electrolyte solutions. On the contrary, for electrode-electrolyte systems, both the Bikerman and the Carnahan-Starling models might be able to explain this dependence.

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. As a result the surface potential value strongly increases as compared to the usual modified Poisson-Boltzmann theory that only includes steric interactions among ions. This effect is particularly important in the case of mixtures of univalent and divalent counterions, being significant even for relatively low surface charge values.

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).

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. Hsu, Y.C. Kuo, J. Membrane Sci. 108 (1995) 107). Approximate analytical expressions for the counterion concentration and the electric potential in the membrane are also presented, together with criteria that determine their ranges of validity. The limiting case of a distribution of fixed charges in the membrane that reduces to a surface charge is also analyzed. It is shown that the solution for this case, considering a vanishingly small radius of the core, reduces to a superposition of solutions corresponding to a charged impermeable particle suspended in an electrolyte solution and to a cavity filled with a charged electrolyte solution.

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. Electric potential and ion concentration profiles, as well as the total potential drop in the cavity, are calculated for different system parameter values. These results are discussed and compared to the corresponding results obtained for suspended particles. Important differences arise, except for very thin double layers. For instance, the usual definition of the Debye length can no longer be used, since the electrolyte solution is nonneutral in the whole volume of the cavity. Furthermore, the charge density at the center of the cavity cannot be assigned any arbitrary value, since the charge density and the ion densities are no longer independent quantities.

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. The evolution of the electric potential on the core as a function of the electrolyte concentration is also analyzed.