Ionic Volume Fraction Research Articles

Finite ion size effects on electrophoresis of a dielectric surfactant-laden droplet in a non-dilute electrolyte

The ion steric repulsion and ion-solvent interactions, due to the finite size of ions, are analyzed for electrophoresis of a droplet in a non-dilute electrolyte in which the ionic volume fraction is O(0.01). In this study, the viscosity of the suspension medium is considered to be dependent on the local ionic volume fraction. The electrochemical potential of the finite-sized ions is modified to take into account the steric interactions. The impact of the Marangoni stress due to the non-uniform distribution of the non-ionized surfactant is taken into account. Governing equations are solved under a weak applied field consideration. At a lower range of surface charge density, the mobility is found to increase with the droplet viscosity, in which the Marangoni stress is found to enhance the mobility. The counterion saturation created by the ion steric interaction attenuates the screening of the surface charge and hence, enhances the mobility. However, the enhanced viscosity of the medium for the non-dilute electrolyte reduces the mobility and this reduction is higher in a monovalent electrolyte as compared to a multivalent electrolyte. The standard model shows a singularity in mobility when the surface potential is varied. However, the dependence of mobility on surface potential in the modified model is found to exhibit a smooth variation.

Numerical model supplemented by thin-layer analysis for diffusiophoresis of a particle incorporating finite ion size effects

The impact of finite-sized ions on the diffusiophoresis of a charged colloid subjected to a concentration gradient of electrolyte solution consisting monovalent or multivalent ionic species, is studied. In diffusiophoresis, the ion concentration is of O(1M). In this non-dilute electrolyte solutions, the ion–ion steric interaction is important. We have adopted the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model to account for the ion steric interactions and the Batchelor–Green expression for the relative viscosity of suspension. We have solved the standard model numerically considering ions as point charge (PNP-model), the modified Nernst–Planck equations incorporating the ion steric interaction with constant viscosity (MNP-model), and modification of the MNP-model by incorporating the viscosity variation with the ionic volume fraction (MNPV-model). Semi-analytical expressions for mobility based on a linear perturbation technique under a thinner Debye length is presented for PNP- and MNP-models. In the MNP-model, counterion saturation in the Debye layer due to the ion steric interaction enhances the surface potential by attenuating the shielding effect, diminishes the surface conduction, and magnifies the induced electric field. These in combination create a larger mobility at a thinner Debye length compared with the PNP-model. This increment in mobility attenuates when the MNPV-model is considered. The MNPV-model is more appropriate to analyze the finite ion size effects, and it is found to yield the mobility values more close to the experimental data compared with the MNP- and PNP-model. The semi-analytical expressions for mobility based on the PNP- and MNP-models agree with the corresponding exact numerical solutions when the surface potential is in the order of thermal potential. However, a large discrepancy between the simplified expression and the exact numerical results is found for a concentrated electrolyte in which the induced electric field is large.

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- 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- 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 mobilityvalue.

Local inversion of the mean electrostatic potential, maximum charge reversal, and capacitive compactness of concentrated 1:1 salts: The crucial role of the ionic excluded volume and ion correlations

• A local inversion of the electrostatic potential in one and three ionic radii from the macroions’s surface is observed. • If the zeta potential is in the above region, an inversion of the macroion’s mobility could be driven by 1:1 electrolytes. • The capacitive compactness around a macroion immersed in very concentrated indiferent 1:1 salts is studied. Recent restricted primitive model Monte Carlo simulations (Takamichi Terao, Mol. Phys. 119 , e1831634, 2020) have suggested the possibility of observing the phenomenon of charge inversion in highly concentrated monovalent salts, in which ionic specific adsorption is absent. By using the non-linear Poisson-Boltzmann equation supplemented by a hard-spheres contribution, integral equations theory, and Monte Carlo simulations, the associated mean electrostatic potential, maximum charge reversal and capacitive compactness are studied here. The main finding of this study is the observation of a local inversion of the mean electrostatic potential in a region bounded by one and three ionic radii measured from the macroions’s surface. If the zeta potential is located in this region, the above result suggests the possibility of observing an inversion of the macroion’s electrophoretic mobility, driven by 1:1 aqueous electrolytes in the absence of ionic specific adsorption . On the other hand, the maximum charge reversal and the capacitive compactness increases and decreases montonically, respectively, as a function of the ionic volume fraction when the salt concentration and/or the ionic size of the aqueous electrolytes increase.

The non-dominance of counterions in charge-asymmetric electrolytes: non-monotonic precedence of electrostatic screening and local inversion of the electric field by multivalent coions.

The asymptotic convergence of the thermodynamic and structural properties of unequally-sized charge-symmetric ions in strong electric fields was postulated more than thirty years ago by Valleau and Torrie as the dominance of counterions via the non-linear Poisson-Boltzmann theory [Valleau and Torrie, J. Chem. Phys., 1982, 76, 4623]. According to this mean field prescription, the properties of the electrical double layer near a highly charged electrode immersed in a size-asymmetric binary electrolyte converge to those of a size-symmetric electrolyte if the properties of counterions are the same in both instances. On the other hand, some of the present authors have shown that, in fact, counterions do not dominate the electrical properties of a spherical macroion in the presence of unequally-sized ions, symmetric in valence, if ion correlations and ionic excluded volume effects are taken into account consistently. These ingredients are neglected in the classical Poisson-Boltzmann picture. In the present work, we show the occurrence of the non-dominance of counterions in the opposite scenario, that is, when ions are equally-sized but asymmetric in valence. This is performed in the presence of highly charged colloidal surfaces of spherical and planar geometries for different ionic volume fractions. In addition to the phenomenon of non-dominance of counterions, our simulations and theoretical data also exhibit a non-monotonic order or precedence in the mean electrostatic potential, or electrostatic screening, at the Helmholtz plane of a charged colloid. This interesting behaviour is analyzed as a function of the coion's valence, the ionic volume fraction, and the charge and size of the colloidal particle. All these phenomena are explained in terms of the decay of the electric field near the colloidal surface, and by the appearance of a local inversion of both the electric field and the integrated surface charge density of the colloidal particle in the presence of monovalent counterions and multivalent coions.

Development of a SOFC Performance Model to Analyze the Powder to Power Performance of Electrode Microstructures

A computational model that evaluates the triple phase boundary length, normalized effective transport coefficients, and charge production within solid oxide fuel cell electrode microstructures is described. Local charge production, within the electrode, is predicted by coupling the species transport equations with an expression for the electrochemical reaction rate. A particle placement model, employing the drop-and-roll algorithm, is used to generate the electrodes studied in this work. Parametric studies with the computational model are then preformed to investigate the influence of the anode porosity and solid volume fraction on charge production. It was found that charge production is jointly influenced by the reaction site (triple phase boundary) density, and ionic transport within the electrode structures. High current densities are observed in electrodes with low porosities and ionic volume fractions greater than 50%, for equal sized particles.

Probing the Interfacial Structure of Aqueous Electrolytes with Femtosecond Second Harmonic Generation Spectroscopy

The existence of polarizable anions at the outermost layer of electrolyte solutions has received much recent attention from both theory and experiment, but remains controversial. Anions can be probed directly in the UV via their strong charge-transfer-to-solvent (CTTS) transitions. We have recently described experimental characterizations of enhanced concentrations of several anions at the air-water interface, using the surface-specific technique of second harmonic generation. Here we present a detailed description of the experimental design and methodology used in these experiments, as well as a proof of principle experiment with the known surfactant tetrabutylammonium iodide (TBAI), yielding surface enhancements in excellent agreement with surface tension measurements. Furthermore, we analyze the observed increase in the nonresonant contribution to the SHG response from the water background of alkali halide solutions. The observed change in the water structure of alkali halide (except iodide) solutions is linear in concentration and correlates with the fractional saturation concentration of the salt and with the ionic volume fraction. Finally, the surface adsorption of iodide at high bulk concentrations is analyzed, but it is not possible to differentiate between a Gibbs free energy of adsorption of zero (surface concentration proportional to the bulk) or -0.8 kcal/mol, as predicted by recent molecular dynamics simulations.

Intermediate range structure of mixed phosphate glasses by X-ray diffraction

The effect of substitution of K 2O for Na 2O, BaO for SrO, BaO for Na 2O and CaO for MgO in metaphosphate glasses has been studied. The experimental results of density, ρ, molar volume, V, ionic volume fraction, w, and glass transition temperature, T g, are presented. The observed departures from additivity are discussed with respect to Dietzel's model. X-ray scattering has been used to characterize the structural features on an intermediate scale of distances. In the mixed metaphosphate samples there are no heterogeneities of electron density with dimensions greater than about 1 nm that are associated with the mixed oxide effect. The non-linearities observed for V and w are not attributable to packing effects correlated with the magnitude of the difference between the field strengths of the two modifier cations as suggested by Dietzel. These departures from additivity were found to be correlated with the molar volume of oxygen. The formation of dissimilar pairs, Me 1–O NB–Me 2, suggested by Dietzel is confirmed in the metaphosphate samples. However, the deviations in T g are independent of the differences of the field strengths of the modifier cations. The intermediate range structure of the mixed metaphosphate samples were found to be determined by the differences in spatial arrangement of the twofold-linked PO 4-units and the MeO n -polyhedra in the participating binary systems.

On the intermediate range structure in phosphate glasses

AbstractThe first prominent peak observed at s1 in the total X‐ray structure factors, S(s), of metaphosphate glasses containing the metal ions Li, Na, K, Ag, Ba, Sr, Cd, Pb, and of barium phosphate glasses with BaO mol% concentrations ranging from 2.5 to 56.5 has been studied to extract information on the intermediate range structure. The period, 27π/s1, of the quasi‐periodic real‐space electron density fluctuations is shown to be correlated with the ionic volume fractions of the glasses.

The dependence of structural peculiarities in binary phosphate glasses on their network modifier content

X-ray diffraction measurements were performed on four (MeO)x(P2O5)(1 - x) glass series, with Me = Zn, Mg, Ca, Ba, and x ranging from about 0.05 to 0.6. The parameters for the MeO coordination sphere are determined. Abrupt changes in the ionic volume fraction are found for the glasses, with different Me ions, at certain compositions which correlate with the behaviour of the MeO coordination sphere. These phenomena can be explained in terms of a model based on the chemical characteristics of P2O5 and on the interplay between the number of non-bridging oxygen atoms per Me cation and changes in the type of the MeOm polyhedron.

A study by density measurements and indentation tests of a calcium silicophosphate bioactive glass with different MgO or SrO contents

Vickers and Knoop indentation techniques and density measurements have been employed to study the structure of two series of glasses in the system CaOROSiO 2P 2O 5CaF 2 (R = Sr, Ca, Mg) with: (a) constant alkaline earth oxide content, but using different cations (Ca, Ca + Sr, Ca + Mg), and (b) increasing alkaline earth concentration (Mg and/or Ca). Samples have been prepared by melting the raw materials at 1400°C, and pouring the liquid on a steel plate. From the experimental data, microhardness, H V, fracture toughness, K IC, and values for mean atomic volume, V A, and ionic volume fraction, V F, were obtained. The last parameter is proposed as a suitable one for the analysis of variations in cationic coordination numbers, n. The results show that Mg, Ca and Sr have similar values of n. The value of n is proposed to be six.