Ion size effects on the dielectric and electrokinetic properties in aqueous colloidal suspensions

Electrohydrodynamics of diffuse porous colloids

The present article deals with the electrohydrodynamic motion of diffuse porous particles governed by an applied DC electric field. The spatial distribution of monomers as well as the charge distribution across the particle are considered to follow sigmoidal distribution involving decay length. Such a parameter measures the degree of inhomogeneity of the monomer distribution across the particle. The diffuse porous particles resemble several colloidal entities which are often seen in the environment as well as in biological and pharmaceutical industries. Considering the impact of bulk pH and ion steric effects, we modelled the electrohydrodynamics of such porous particulates based on the modified Boltzmann distribution for the spatial distribution of electrolyte ions and the Poisson equation for electric potential as well as the conservation of mass and momentum principles. We adopt regular perturbation analysis with weak field assumption and the perturbed equations are solved numerically to calculate the electrophoretic mobility and neutralization fraction of the particle charge during its motion as well as fluid collection efficiency. We further deduced the closed form relation between the drag force experienced by the charged porous particle and the fluid collection efficiency. In addition to the numerical results, we further derived the closed form analytical results for all the intrinsic parameters indicated above derived within the Debye-Hückel electrostatic framework and homogeneous distribution of monomers within the particle for which the decay length vanishes. The deduced mathematical results as indicated above will be useful to analyze several electrostatic and hydrodynamic features of a wide class of porous particulate and environmental entities.

Numerical study supplemented with simplified model on electrophoresis of a hydrophobic colloid incorporating finite ion size effects and ion-solvent interactions

We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non- z : z $z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non- z : z $z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Electrophoresis of Liquid-Layer Coated Particles: Impact of Ion Partitioning and Ion Steric Effects

The biomimetic core-shell nanoparticles coated with membranes of various biological cells have attracted significant research interest, because of their extensive applications in targeted drug delivery systems. The cell membrane consists of a lipid bilayer, which can be regarded as a two-dimensional oriented viscous liquid with low dielectric permittivity, compared to a bulk aqueous medium. Such a liquid layer comprised of cell membrane may bear additional mobile charges, because of the presence of free lipid molecules or charged surfactant molecules, which further results in nonzero charge along the surface of the peripheral layer. In this article, we present an analytical theory for electrophoresis of such cell membrane coated functionalized nanoparticles in the extent of electrolyte solution, considering the combined effects of finite ion size and of ion partitioning. Going beyond the Debye-Huckel approximations, we propose an analytical theory for Donnan potential and electrophoretic mobility. The derived expressions are applicable for moderate to highly charged undertaken core-shell particles when the thickness of the peripheral liquid layer greatly exceeds the electric double layer thickness. The impact of pertinent parameters on the electrophoretic response of such a particle is further discussed.

Impact of ion-steric and ion-partitioning effects on electrophoresis of soft particles

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

Influence of ion size effects on the electrokinetics of aqueous salt-free colloids in alternating electric fields

Electrokinetics is the science of the physical phenomena appearing at the solid-liquid interface of dispersed particles subjected to external fields. Techniques based on electrokinetic phenomena constitute an important set of tools for the electrical characterization of colloids because of their sensitivity to the properties of particle-solution interfaces. Their rigorous description may require inclusion of the effects of finite size of chemical species in the theoretical models, and, particularly in the case of salt-free (no external salt added) aqueous colloids, also consideration of water dissociation and possible carbon dioxide contamination in the aqueous solution. A new ac electrokinetic model is presented for concentrated salt-free spherical colloids for arbitrary characteristics of the particles and aqueous solution, including finite-size effects of chemical species by appropriate modifications of the chemical reaction equations to include such non-ideal aspects. The numerical solution of the electrokinetic equations in an alternating electric field has also been carried out by using a realistic non-equilibrium scenario accounting for association-dissociation processes in the chemical reactions. The results demonstrate the importance of including finite-size effects in the electrokinetic response of the colloid, mainly at high frequencies of the electric field, and for highly charged colloids. Findings of previous models for pointlike ions or for ideal salt-free colloids including finite ion size effects are recovered with the present model, for the appropriate limiting conditions.

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. It was shown that these interactions improved upon the standard model predictions so that the surface potential, electrophoretic mobility, and the conductivity and permittivity increment values were increased. In the present study, we extend our preceding works to systems made of three or more ionic species with different ionic sizes. Under these conditions, the Bikerman and Carnahan⁻Starling expressions cease to be valid since they were deduced for single-size spheres. Fortunately, the Carnahan⁻Starling expression has been extended to mixtures of spheres of unequal size, namely the "Boublik⁻Mansoori⁻Carnahan⁻Starling⁻Leland" (BMCSL) equation of state, making it possible to analyze the most general case. It is shown that the BMCSL expression leads to results that differ qualitatively and quantitatively from the standard electrokinetic model.

Analytical Interfacial Layer Model for the Capacitance and Electrokinetics of Charged Aqueous Interfaces

We construct an analytical model to account for the influence of the subnanometer-wide interfacial layer on the differential capacitance and the electro-osmotic mobility of solid-electrolyte interfaces. The interfacial layer is incorporated into the Poisson-Boltzmann and Stokes equations using a box model for the dielectric properties, the viscosity, and the ionic potential of mean force. We calculate the differential capacitance and the electro-osmotic mobility as a function of the surface charge density and the salt concentration, both with and without steric interactions between the ions. We compare the results from our theoretical model with experimental data on a variety of systems (graphite and metallic silver for capacitance and titanium oxide and silver iodide for electro-osmotic data). The differential capacitance of silver as a function of salinity and surface charge density is well reproduced by our theory, using either the width of the interfacial layer or the ionic potential of mean force as the only fitting parameter. The differential capacitance of graphite, however, needs an additional carbon capacitance to explain the experimental data. Our theory yields a power-law dependence of the electro-osmotic mobility on the surface charge density for high surface charges, reproducing the experimental data using both the interfacial parameters extracted from molecular dynamics simulations and fitted interfacial parameters. Finally, we examine different types of hydrodynamic boundary conditions for the power-law behavior of the electro-osmotic mobility, showing that a finite-viscosity layer explains the experimental data better than the usual hydrodynamic slip boundary condition. Our analytical model thus allows us to extract the properties of the subnanometer-wide interfacial layer by fitting to macroscopic experimental data.

Differential capacitance of the diffuse double layer at electrode-electrolyte interfaces considering ions as dielectric spheres: Part I. Binary electrolyte solutions

A full theoretical account of the differential capacitance of the diffuse part of the electric double layer at electrode-electrolyte solution interfaces is presented. It builds upon the standard electrokinetic model adding all the additional effects related to the finite ionic size. This includes steric interactions among ions by means of either the Bikerman or Carnahan-Starling expressions and all the permittivity related effects that arise when ions are represented as dielectric spheres. These include the solution permittivity dependence on the local ionic concentration, calculated by means of the Maxwell mixture formula, and two additional forces acting on the ions, namely the Born and the dielectrophoretic forces that depend on the permittivity and the electric field gradients, respectively. The obtained results show that the diffuse double layer behavior is sufficient to qualitatively account for the observed differential capacitance dependence on the electrode voltage. Moreover, when combined with an inner layer capacitance and using the Carnahan-Starling expression, a remarkably good quantitative agreement is achieved.