Ion Size Effects Research Articles

Ion-size effect on electrokinetic energy conversion in nanofluidic channels

ABSTRACTThe present study utilizes a modified Poisson–Boltzmann (MPB) equation to take into account ion-size (steric) effect and then performs a series of simulations to investigate the ionic transport phenomenon within two nanofluidic devices, namely a nanoslit and a nanotube. The results show that at all electrolyte concentrations, the streaming conductance increases when the ion-size effect is taken into account, particularly under conditions of high surface charge density. The net charge density is amplified by the ion-size effect for both nanogeometries as well. The enhancement in the streaming conductance is particularly pronounced in the nanotube since the net charge density has higher value by the geometry effect of the nanotube. The maximum ratio of net charge density () is 1.55 near the surface of nanotube. In addition, it is shown that for both configurations, the contribution of electroosmotic flow to the electrical conductance increases when the finite ion size is taken into account.

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes.

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.

Evidence for Lattice Strain and Non-ideal Behavior in the (La1−xEux)PO4 Solid Solution from X-ray Diffraction and Vibrational Spectroscopy

The monazite-type solid solution of LaPO$_4$ and EuPO$_4$ has been studied by X-ray diffraction, infrared (IR) and Raman spectroscopic techniques. A substantial excess molar volume has been derived from the X-ray data, and the Raman and IR spectra show band broadening typical for mixing of cations of different size on the cation sublattice. The IR spectra were interpreted by the autocorrelation method and the excess autocorrelation parameter $\Delta{corr}^{ex}$ shows clear deviation from ideal solution behaviour, similar to the observed broadening of the Raman bands. The results can be interpreted in terms of local lattice strains resulting from the ion size effects of substitution of La$^{3+}$ by Eu$^{3+}$, and correlate very well with calorimetric measurements of the excess enthalpy that was previously measured.

Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: Ion size effects

We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck model for ionic flows through membrane channels with fixed boundary ion concentrations and electric potentials. We consider two ion species, one positively charged and one negatively charged, and assume zero permanent charge. Bikerman's local hard-sphere potential is included in the model to account for ion size effects on the ionic flow. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Our analysis is based on the geometric singular perturbation theory but, most importantly, on specific structures of this concrete model. The existence of solutions to the boundary value problem for small ion sizes is established and, treating the ion sizes as small parameters, we also derive approximations of individual fluxes and I-V (current-voltage) relations, from which qualitative properties of ionic flows related to ion sizes are studied. A detailed characterization of complicated interactions among multiple and physically crucial parameters for ionic flows, such as boundary concentrations and potentials, diffusion coefficients and ion sizes, is provided.

Effect of orientational ordering of water dipoles on stratification of counterions of different size in multicomponent electrolyte solution near charged surface - a mean field approach

We theoretically studied electric double layer by using the mean-field approach including the non-uniform size effect and the orientational ordering of water dipoles in electrolyte solution. Performing the minimization of the free energy, the resulting ion and water distribution functions are determined numerically in the process of solving the Poisson's equation. The effect of non-uniform ionic size and orientational ordering of water dipoles on stratification of counterions of different size in multicomponent electrolyte solution near the charged surface are presented and discussed. Spatial dependence of relative permittivity and differential capacitance of electric double layer are also calculated for binary electrolyte solution and then compared with the predictions of the previous models. Effect of bulk concentration of counterions and ion size effects on surface charge density, excess portion of counterions, relative permittivity and differential capacitance are studied for multicomponent electrolyte solution in detail.

Aqueous Ion Intercalation in Hydrous Oxides

Transition metal oxides are often the materials of choice for energy storage and conversion applications due to their numerous oxidation states, mixed electronic/ionic conductivity, and structural variability. Here, we describe the electrochemical behavior of hydrous hexavalent tungsten and molybdenum oxides (WO3 and MoO3, respectively) as model material systems for investigating aqueous intercalation mechanisms. These oxides offer the benefits of multi-valent transition metal redox, diversity of crystal structure, hydrated polymorphs, and a variety of synthesis techniques that yield bulk powders, nanomaterials, and nanosheets. The mechanism of ion intercalation is dependent upon two different regions of the material: the internal structure, or the solid-state environment that controls the ion diffusion and favorable storage sites, and the external surface, or the nature of the electrochemical interface which controls the charge-transfer step of the intercalation reaction as well as stability. We characterize the behavior of these oxides in a variety of aqueous electrolytes in order to understand the effect of electrolyte ion size, charge, and hydration on the intercalation mechanism. We find that the presence of structural water and the nature of the intercalating ion both result in significant effects on the aqueous intercalation mechanism in tungsten and molybdenum oxides.

Lattice Defects Induce Multiferroic Responses in Ce, La‐Substituted BaFe0.01Ti0.99O3 Nanostructures

Single‐phase multiferroic Ba(Fe0.67Ce0.33)0.01Ti0.99O3 (BFTO:Ce) and Ba(Fe0.67La0.33)0.01Ti0.99O3 (BFTO:La) nanostructures were synthesized by a hydrothermal method (180°C/48 h). Rietveld refinement of X‐ray diffraction could confirm crystalline phase and lattice deformation by Ce, La into BFTO. The Ce and La doping induce nanoaggregation‐type BFTO nanostructural product due to their ionic size effect and chemical behavior with OH− ions. Raman active modes show tetragonal phase and defects due to vacancies in the BFTO lattice. Photoluminescence spectrum involves multiple visible emissions due to defects/vacancies. The observed ferroelectric polarization is enhanced due to shape/size effect of nanoparticles, lattice distortion, and filling of d orbital in the perovskite BaTiO3. The room‐temperature magnetic behavior is described due to antiferromagnetic interactions that strengthen by Ce and La doping. The zero‐field cooling and field cooling magnetic measurement at 500 Oe indicates antiferromagnetic to ferromagnetic transition. Dynamic magnetoelectric coupling was investigated, and maximum longitudinal magnetoelectric coefficient is 62.65 and 49.79 mV/cmOe, respectively, measured for BFTO:Ce and BFTO:La. The magnetocapacitance measurements induce negative values that described in terms of magnetoresistance and magnetic phase transition effects. The influence of oxygen vacancy on multiferroicity is evaluated by valance states of O ions.

A theoretical consideration of ion size effects on the electric double layer and voltammetry of nanometer-sized disk electrodes.

Considering that an electric-double-layer (EDL) structure may significantly impact on the mass transport and charge transfer kinetics at the interfaces of nanometer-sized electrodes, while EDL structures could be altered by the finite sizes of electrolyte and redox ions, the possible effects of ion sizes on EDL structures and voltammetric responses of nanometer-sized disk (nanodisk) electrodes are investigated. Modified Boltzmann and Nernst-Planck (NP) equations, which include the influence of the finite ion volumes, are combined with the Poisson equation and modified Butler-Volmer equation to gain knowledge on how the finite sizes of ions and the nanometer sizes of electrodes may couple with each other to affect the structures and reactivities of a nanoscale electrochemical interface. Two typical ion radii, 0.38 nm and 0.68 nm, which could represent the sizes of the commonly used aqueous electrolyte ions (e.g., the solvated K+) and the organic electrolyte ions (e.g., the solvated TEA+) respectively, are considered. The finite size of ions can result in decreased screening of electrode charges, therefore magnifying EDL effects on the ion transport and the electron transfer at electrochemical interfaces. This finite size effect of ions becomes more pronounced for larger ions and at smaller electrodes as the electrode radii is larger than 10 nm. For electrodes with radii smaller than 10 nm, however, the ion size effect may be less pronounced with decreasing the electrode size. This can be explained in terms of the increased edge effect of disk electrodes at nanometer scales, which could relax the ion crowding at/near the outer Helmholtz plane. The conditions and situations under which the ion sizes may have a significant effect on the voltammetry of electrodes are discussed.

Trifluoromethyl benzyl alcohol as a “shift reagent” in ion mobility spectrometry: The effect of intramolecular bridges, ion size and shift reagent-ion binding energy in ion mobility

α-Trifluoromethyl benzyl alcohol (F) was introduced as a “shift reagent” in the buffer gas of an electrospray ionization ion mobility spectrometer coupled to a quadrupole mass spectrometer to explain the mobility shifts of selected compounds; ion mobilities depended on ion sizes and F-ion adducts binding energies calculated using Gaussian 09 at the X3LYP/6-311++G(d,p) level. The mobility shifts with the introduction of F in the buffer gas were: −13% (ethanolamine), −10.6% (serine), −8.6% (threonine), −7.3% (phenylalanine), −7.0% (tyrosine), −6.2 (tributylamine), −5.1% (valinol), −4.7% (methionine), −3.9% (tryptophan), −3.1% (tribenzylamine), −1.3% (2,6-di-tert-butyl pyridine, DTBP), −1.2% (2,4-lutidine, 2,4-dimethyl pyridine), and −0.1% (atenolol). These mobility shifts showed a decreasing trend with the increase in molecular weight from ethanolamine to tribenzylamine excluding some ions due to steric hindrance (2,4-lutidine, DTBP and tetraalkylammonium ions), formation of intramolecular bridges (atenolol and methionine) or low binding energy with F (valinol). Ethanolamine (61.1g/mol) showed the largest mobility shift (−13%) due to its low molecular weight and tribenzylamine showed the smallest one due to its large size. We found a similar trend in mobility shifts when methyl chloro propionate, trifluoromethyl benzyl alcohol, ethyl lactate, nitrobenzene or 2-butanol were used as SRs. We also found that penicillamine adducts with F were not seen in the mass or mobility spectra probably because of the formation of an intramolecular bridge in this compound; F produced the average lowest mobility shifts of all SRs tried before, even of smaller size (methyl chloro propionate, phenylethanol, ethyl lactate, nitrobenzene, and 2-butanol) because of the inductive effects exerted by the three fluorine atoms that decreased F proton affinity and hindered its adduction to analyte ions. In summary, intramolecular bridges, size, inductive effects, steric hindrance and adduct binding energy were used to explain mobility shifts when trifluoromethyl benzyl alcohol was used as a “shift reagent” in ion mobility spectrometry.

Ab initioperspective on the Mollwo-Ivey relation forFcenters in alkali halides

The authors revisited the Mollwo--Ivey relation of $F$ centers in alkali halide crystals, a prototypical color center, based on post-density-functional-theory and post-Hartree-Fock methods. In contrast to earlier interpretations, which stress the importance of the Madelung potential, they find ion-size effects to be the predominant mechanism. These determine the shape of the defect-electron wave function and are responsible for the fractional Mollwo--Ivey exponent of 1.8.

Steric effects on electrokinetic flow of non-linear biofluids

Abstract Some of electrokinetic-based biomicrofluidic devices work at zeta potentials that are sufficiently high for ionic size (steric) effects to show up. In the present effort, consideration is given to the steric effects on the hydrodynamics of electroosmotic flow in a rectangular microchannel. The distinction between this research and the previous ones is that we account for non-linear rheology of the fluids encountered in biomicrofluidic systems by means of the power-law viscosity model. The method of analysis consists of a finite-difference-based numerical procedure for a non-uniform distribution of grid points, which is applied to the dimensionless form of the governing equations including the modified Poisson-Boltzmann equation. Our findings show that, unlike the electroosmotic flow of Newtonian fluids, the inclusion of the ionic size may enhance the velocity of the power-law fluids. We demonstrate that this phenomenon is due to the reduction of the fluid effective viscosity which is another consequence of the steric effects, besides the already explored feature of lowering the electroosmotic body force. Consequently, the ultimate influence of the ionic finite volumes on the electroosmotic flow of the power-law fluids is determined by the relative importance of the above-mentioned phenomena. Generally, the reduction of the body force is dominant; nevertheless, the opposite is true for shear-thickening fluids of very high flow behavior index, resulting in higher fluid velocities in the presence of the steric effects.

Asymmetric size of ions and orientational ordering of water dipoles in electric double layer model - an analytical mean-field approach

Electric double layer is theoretically described within the mean-field approach by taking into account the orientational ordering of water dipoles and asymmetric size of cations and anions. Analytical expressions for the spatial distribution of ions and water dipoles are derived. The effect of asymmetric ionic size on accumulation of counterions and partial depletion of water molecules near the charged surface, on spatial dependence of relative permittivity and on differential capacitance of electric double layer are presented.

Quantitative characterization of non-classic polarization of cations on clay aggregate stability.

Soil particle interactions are strongly influenced by the concentration, valence and ion species and the pH of the bulk solution, which will also affect aggregate stability and particle transport. In this study, we investigated clay aggregate stability in the presence of different alkali ions (Li+, Na+, K+, and Cs+) at concentrations from10−5 to 10−1 mol L−1. Strong specific ion effects on clay aggregate stability were observed, and showed the order Cs+>K+>Na+>Li+. We found that it was not the effects of ion size, hydration, and dispersion forces in the cation–surface interactions but strong non-classic polarization of adsorbed cations that resulted in these specific effects. In this study, the non-classic dipole moments of each cation species resulting from the non-classic polarization were estimated. By comparing non-classic dipole moments with classic values, the observed dipole moments of adsorbed cations were up to 104 times larger than the classic values for the same cation. The observed non-classic dipole moments sharply increased with decreasing electrolyte concentration. We conclude that strong non-classic polarization could significantly suppress the thickness of the diffuse layer, thereby weakening the electric field near the clay surface and resulting in improved clay aggregate stability. Even though we only demonstrated specific ion effects on aggregate stability with several alkali ions, our results indicate that these effects could be universally important in soil aggregate stability.

Effects of finite ionic size and solvent polarization on the dynamics of electrolytes probed through harmonic disturbances

We address the implications of finite ionic size and solvent polarization on the response of the electric double layer (EDL) at two cation-selective electrodes in nonequilibrium conditions. The current between the electrodes is driven by a steady-state dc bias in conjunction with a probing high-frequency ac voltage. We report that the finite ionic size (steric) effect is prominent at high voltages near the electrodes where the ion densities are high, while the solvent polarization dramatically alters impedance characteristics for thick EDLs owing to the alteration of solvent permittivity in regions with a high electric field. Depending on the magnitude of the dc bias, our results show that the steric effects and solvent polarization lead to dramatic alterations in the net impedance for moderately thick electric double layers as compared to an extremely thin one. We also highlight that the solvent polarization suppresses the anomalous growth of dc current (anomalous rectification effect) for applied high-frequency ac voltages.

Effects of Ti charge state, ion size and beam-induced compaction on the formation of Ag metal nanoparticles in fused silica

Metal nanoparticles formed by ion implantation in fused silica exhibit linear and nonlinear optical properties that can be altered by co-doping the silica substrate with transition-metal ions. For example, implantation of scandium in fused silica creates a directional optical dichroism due to the different spatial distribution of silver nanoparticles subsequently formed by Ag ion implantation. In this paper, we show that implantation of titanium ions alters the short- and intermediate-range order in the silica and thereby alters the diffusion and nucleation processes that lead to formation of silver nanoparticles. In particular, the dichroic response observed for Ag nanoparticles in Sc-implanted silica is, with one exception, in Ti-implanted silica. Compaction of the silica due to the ion implantation process appears to be similar for both Sc and Ti implantations, based on the observed shift of the 1,124 cm−1 transverse-optical phonon mode in the infrared reflectance spectrum. However, differences in chemical reactivity, bond lengths and electronic structure of Sc and Ti produce changes in electronic structure and strain that are sensitively reflected in the reflectance spectra of the Ag nanoparticles. These differences lead to modifications in the size, shape and spatial distributions of the silver nanoparticles and offer a powerful means of controlling their optical properties.

Effect of ionic size on solvate stability of glyme-based solvate ionic liquids.

A series of binary mixtures composed of glymes (triglyme, G3; tetraglyme, G4; pentaglyme, G5) and alkali-metal bis(trifluoromethanesulfonyl)amide salts (M[TFSA]; M = Li, Na, and K) were prepared, and the correlation between the composition and solvate stability was systematically investigated. Their phase diagrams and Raman spectra suggested complexation of the glymes with M[TFSA] in 1:1 and/or 2:1 molar ratio(s). From isothermal stability measurements, it was found that the formation of structurally stable complexes in the solid state did not necessarily ensure their thermal stability in the liquid state, especially in the case of 2:1 complexes, where uncoordinating or highly exchangeable glyme ligands existed in the molten complexes. The phase-state-dependent Raman spectra also supported the presence of free glymes in certain liquid complexes. The effect of the electric field induced by the alkali-metal cations on the oxidative stability of certain glyme complexes was examined by linear sweep voltammetry and quantum chemical calculations. Although the actual oxidative stability of complexes did not necessarily reflect the calculated HOMO energy levels of the glymes, the strong electric field induced by the smaller M(+) cations and proper coordination structures impart high stability to the glyme complexes. The results of thermogravimetry of complexes with different M(+) cations revealed that a balance of competitive interactions of the M(+) ions with the glymes and [TFSA](-) anions predominates the thermal stability.

An Electrochemical Investigation of Nano Cerium Oxide/Graphene as an Electrode Material for Supercapacitors

In this paper, the effect of cationic and anionic ion sizes on the charge storage capability of graphene nanosheets is investigated. The electrochemical properties of the produced electrode are studied using cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) techniques in 3M NaCl, NaOH, and KOH electrolytes. Scanning electron microscopy (SEM) is used to characterize the microstructure and nature of the prepared electrode. The SEM images and X-ray diffraction (XRD) patterns confirm the layered structure (12 nm thickness) of the used graphene with an interlayer distance of 3.36 A. The electrochemical results and the ratio of

Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates

A new theory quantifies the effect of finite ion size in osmotic pressure (Πosm) between two soft charged plates.

Effect of the Cation Size Disorder at the A-Site on the Structural Properties of SrAFeTiO<SUB>6</SUB> Double Perovskites (A = La, Pr or Nd)

In this paper, the cation size disorder effect of the A-site on the structural properties of the SrAFe- TiO6 (A = La, Pr or Nd) was investigated. The compounds were synthesized—as the best of our knowledge—for the first time by conventional and precursor method to get crystalline materials. The results obtained from the experimental measurements carried out on new double perovskite materials were presented. The data of X-ray diffraction (XRD), Fourier Transform Infra Red FTIR were measured at room temperature. From the X-ray diffraction, and by means of standard Rietiveld method, all the samples have the same structure (orthorhombic) with Pnma space group. The difference in the tolerance factor is clearly noticed and refers to the cation size disorder at the A-sites. The Fourier Transform Infra Red FTIR measurement has been done; the results of it confirm the double perovskite structure and the difference between the samples were noticed. The tolerance factors for the samples altered from SrLaFeTiO6 up to SrNdFeTiO6 and this difference return to ionic radius and cation size effect.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.