Ion Size Effects Research Articles

Modeling Surface Charge Regulation of Colloidal Particles in Aqueous Solutions.

Colloidal particles are mostly charged in an aqueous solution because of the protonation or deprotonation of ionizable groups on the surface. The surface charge density reflects a complex interplay of ion distributions within the electric double layer and the surface reaction equilibrium. In this work, we present a coarse-grained model to describe the charge regulation of various colloidal systems by an explicit consideration of the inhomogeneous ion distributions and surface reactions. With the primitive model for aqueous solutions and equilibrium constants for surface reactions as the inputs, the theoretical model is able to make quantitative predictions of the surface-charge densities and zeta potentials for diverse colloidal particles over a wide range of pH and ionic conditions. By accounting for the ionic size effects and electrostatic correlations, our model is applicable to systems with multivalent ions that exhibit charge inversion and provides a faithful description of the interfacial properties without evoking the empirical Stern capacitance or specific ion adsorptions.

Influence of iron and nitrogen ion beam exposure on the gas sensing properties of CuO nanowires

A precise surface decoration technique, ion implantation, was examined for tuning the p-type gas sensing properties of CuO nanowires. To understand the effects of ion size, ion beam energy and ion beam fluence, heavy Fe and light N ions were implanted with two different ion beam energies (60, 100 keV) and fluences (1 × 1013, 2.5 × 1016 ions/cm2). The morphological changes after ion bombardments have been tracked by a scanning electron microscope (SEM), revealing massive destruction of the nanowires on Fe ion-implanted samples with high energy and fluence values. Transmission electron microscopy (TEM) provided a closer look on single ion-implanted nanowires, highlighting the different size and mass effects of Fe and N ions. The reduction of CuO peaks intensities registered in GI-XRD profiles and the shifts of Cu 2p peaks in X-ray photoemission spectra (XPS) suggest that the monoclinic crystal structure of the CuO nanowires was transformed to amorphous Cu2O and Cu(OH)2 after ion implantations. All ion-implanted sensors improved their sensing abilities compared to pristine CuO nanowires towards various concentrations of target gases (hydrogen, ethanol, and acetone) at 400 °C in dry air flows. In the presence of humid air, sensors showed different characteristics related to outcomes of surface-ion beam interactions.

Effects of finite ion size on transport of neutral solute across porous wall of a nanotube

Effect of finite ion size on the transport of a neutral solute across the porous wall of a nanotube is presented in this study. Modified Poisson–Boltzmann equation without the Debye–Huckel approximation is used to determine the potential distribution within the tube. Power law fluid is selected for the study, as its rheology resembles closely to the real-life physiological fluids. The flow within the tube is actuated by the combined effects of pressure and electroosmotic forces. Steady-state solute balance equation is solved by the similarity technique in order to track the solute transport across the tube. The effects of ionic radius, ionic concentration, and flow behavioral index on the length-averaged Sherwood number, permeate flux, and permeate concentration are analyzed. This study will be extremely helpful in predicting the transport characteristics of a neutral solute in real physiological systems and also to fine-tune the performance of microfluidic devices having porous wall.

Finite ion size effect on the stability ratio of colloidal dispersions

An algorithm is presented for calculating the stability ratio of a dispersion of spherical colloidal particles on the basis of the Derjaguin–Landau–Verwey–Overbeek theory. The finite ion size effect is taken into account by using the approximate form of ionic activity coefficients given by Carnahan and Starling. A simple approximate analytic expression for the stability ratio without involving numerical integration is also derived.

Analysis of the electrolyte characteristics on the performance of electric double layer capacitor

The characteristics of electrolyte have great impacts on the performance of electrical double layer capacitor (EDLC), in which the three electrolytes of binary fully ionized electrolyte, binary weak electrolyte and multi-species electrolyte are chosen in the current investigation. The generalized modified Poisson-Nernst-Planck (GMPNP) equations are employed to analyze the effects of ion valency and size as well as the valency and size difference between two ions on the ion concentration distribution and thickness of electric double layer (EDL) in electrolyte as well as the cell potential and specific energy in EDLC. More cell potential and specific energy occur in the capacitors with either lower ion valencies and valency sum of anion and cation, and the ion size and its difference between the anion and cation serve as the key factors in binary fully ionized electrolyte. The concentration distributions of ions in the diffuse layer and ionization reaction rate are closely related to the ionization degree in binary weak electrolyte. The ion size and valency difference among anions as well as the highest valency of anion in the multi-species electrolyte influence the performances of EDLC greatly.

Transport Properties in Nanochannels: Ionic Size-, Permittivity-, and Viscosity-Related Effects

The transport properties in nanochannels are examined using a modified electrokinetic model (MEM) that takes into account the finite ion size by modeling the hydrated ions as charged dielectric spheres so that the electrolyte solution becomes a nonhomogeneous fluid characterized by permittivity and viscosity values that are both functions of the local ionic concentrations. We show that the simultaneous consideration of ionic size, permittivity, and viscosity effects always improve on the predictions of the standard electrokinetic model for point-like ions (SEM), with corrections that are significant in the nanofluidic system’s parameter range. The results reported herein are expected to provide a deeper understanding of the ion transport and fluid flow in nanofluidic devices.

Origin and tuning of room-temperature multiferroicity in Fe-doped BaTiO3

Simultaneous co-existence of room-temperature(T) ferromagnetism and ferroelectricity in Fe doped BaTiO$_3$ (BTO) is intriguing, as such Fe doping into tetragonal BTO, a room-T ferroelectric (FE), results in the stabilization of its hexagonal polymorph which is FE only below $\sim$80K. Here, we investigate its origin and show that Fe-doped BTO has a mixed-phase room-temperature multiferroicity, where the ferromagnetism comes from the majority hexagonal phase and a minority tetragonal phase gives rise to the observed weak ferroelectricity. In order to achieve majority tetragonal phase (responsible for room-T ferroelectricity) in Fe-doped BTO, we investigate the role of different parameters which primarily control the PE hexagonal phase stability over the FE tetragonal one and identify three major factors namely, the effect of ionic size, Jahn-Teller (J-T) distortions and oxygen vacancies (OVs), to be primarily responsible. The effect of ionic size which can be qualitatively represented using the Goldschmidt's tolerance (GT) factor seems to be the major dictating factor for the hexagonal phase stability. The understanding of these factors not only enables us to control them but also, achieve suitable co-doped BTO compound with enhanced room-T multiferroic properties.

K2Fe3(SO4)3(OH)2(H2O)2: A new high-performance hydroxysulfate cathode material for alkali metal ion batteries

With advantages of safety benefits, high stability and tunable redox potentials, polyanionic electrode materials, especially sulfates draw lots of interests. Exploring general cathodes for alkali ion (Li, Na and K) battery is of great importance to understand the effect of ion size on materials’ electrochemical performance. Here, we report on a new K2Fe3(SO4)3(OH)2(H2O)2 sulfate as a promising cathode material for rechargeable alkali-ion batteries. Regardless of employing Li ions or large radius Na ions and K ions, the material manifests comparable capacities (~100 mA h•g−1) along with excellent rate behaviors (70 mA h•g−1 at 10C) and long lifetimes (~100% after 100 cycles at 1C). In addition, K2Fe3(SO4)3(OH)2(H2O)2 cathode delivers different electrochemical performances with three alkali ions, which is beneficial to understand the fundamental aspects of the reaction mechanisms. This work not only enriches the crystal chemistry of sulfate family, but also proposes a new design strategy to other K-based polyanionic compounds as cathode materials for Li ions and Na ions batteries.

Steric-effect-induced enhancement of electrokinetic energy conversion efficiency in curved nanochannels with rectangular sections at high zeta potentials

In this work, we investigate the electrokinetic energy conversion in curved rectangular nanochannels at high zeta potentials, intending to increase the efficiency of electrokinetic generation. As we demonstrate, the geometry effect can have an important role in the investigations of the conversion efficiency. In addition, we consider the influences of steric effect (the effect of finite ion size) on the energy conversion efficiency, which is significant and can’t be ignored, especially at high surface potentials. The finite difference method is used to obtain numerical solutions for the corresponding efficiency. Our results show that, within optimized parameters ranges, the conversion efficiency can be increased by up to 50 percent by considering the influences of the steric effect. Additionally, the conversion efficiency η shows a increasing trend with the curvature ratio δ and a reversed trend with the aspect ratio AR of the rectangular cross section. These results are useful for estimating and designing more effective electrokinetic energy conversion devices.

Effect of hydrocarbon molecular ion size for amorphous region formation analyzed by X-ray photoelectron spectroscopy

We investigate the amorphous formation behavior on hydrocarbon molecular ion implantation conditions such as hydrocarbon molecular ion size by X-ray photoelectron spectroscopy (XPS). The cross-sectional radius of the amorphous region was obtained from the peak intensity of the amorphous component in Si 2p spectra analyzed by XPS, and using columnar formula for a model. We confirmed that the cross-sectional radius of the amorphous region formed by hydrocarbon molecular ions differs greatly from that formed by monomer carbon ions, and increases by 0.078 nm as the number of carbon atoms composing the hydrocarbon molecular ion increases. The dependence of amorphous formation on the hydrocarbon molecular size is related to the C–C binding distance, and the ratio of increase in the amorphous cross-sectional radius corresponds to half of the C–C binding distance. Therefore, the collision behavior of hydrocarbon molecular ions during implantation predominantly influence the size of hydrocarbon molecular ions.

Molecular dynamics simulations of alkaline earth metal ions binding to DNA reveal ion size and hydration effects.

The identity of metal ions surrounding DNA is key to its biological function and materials applications. In this work, we compare atomistic molecular dynamics simulations of double strand DNA (dsDNA) with four alkaline earth metal ions (Mg2+, Ca2+, Sr2+, and Ba2+) to elucidate the physical interactions that govern DNA-ion binding. Simulations accurately model the ion-phosphate distance of Mg2+ and reproduce ion counting experiments for Ca2+, Sr2+, and Ba2+. Our analysis shows that alkaline earth metal ions prefer to bind at the phosphate backbone compared to the major groove and negligible binding occurs in the minor groove. Larger alkaline earth metal ions with variable first solvation shells (Ca2+, Sr2+, and Ba2+) show both direct and indirect binding, where indirect binding increases with ion size. Mg2+ does not fit this trend because the strength of its first solvation shell predicts indirect binding only. Ions bound to the phosphate backbone form fewer contacts per ion compared to the major groove. Within the major groove, metal ions preferentially bind to guanine-cystosine base pairs and form simultaneous contacts with the N7 and O6 atoms of guanine. Overall, we find that the interplay among ion size, DNA-ion interaction, and the size and flexibility of the first solvation shell are key to predicting how alkaline earth metal ions interact with DNA.

Temperature effects on the spatial distribution of electrolyte mixtures at the aqueous liquid-vapor interface.

The microscopic picture of ions at the aqueous liquid-vapor interface continues to be an important and active area of research. Both experiments and simulations have shown that certain ions, such as Br- and I-, prefer to adsorb at the interface, but there is not yet a consensus as to the relative importance of various ion-specific properties that influence surface solvation. In a previous study, we systematically explored the effect of ion size on determining whether or not a monovalent ion would adsorb at the surface, and found that, for electrolyte mixtures represented by non-polarizable models, the larger/smaller anions are enriched/depleted at the interface. Here, we extend that study to include temperature effects enabling a van't Hoff analysis of the enthalpic and entropic contributions. We perform configurational-bias Monte Carlo simulations in the Gibbs ensemble to investigate the partitioning of mixtures of differently sized ions at the aqueous liquid-vapor interface from 284.09 K to 347.22 K at a pressure of 1 atm. Ions are represented using our own previously developed models that vary only in size (i.e., the Lennard-Jones σ parameter changes, while all other parameters are held constant across ion types). System properties studied include surface tension, interfacial width, ion surface excess, number density profiles, z-dependent transfer free energy, enthalpy, entropy, and anion-cation coordination numbers.

Cooperative elastic fluctuations provide tuning of the metal–insulator transition

Metal-to-insulator transitions1 driven by strong electronic correlations occur frequently in condensed matter systems, and are associated with remarkable collective phenomena in solids, including superconductivity and magnetism. Tuning and control of the transition holds the promise of low-power, ultrafast electronics2, but the relative roles of doping, chemistry, elastic strain and other applied fields have made systematic understanding of such transitions difficult. Here we show that existing data3-5 on the tuning of metal-to-insulator transitions in perovskite transition-metal oxides through ionic size effects provides evidence of large systematic effects on the phase transition owing to dynamical fluctuations of the elastic strain, which have usually been neglected6. We illustrate this using a simple yet quantitative statistical mechanical calculation in a model that incorporates cooperative lattice distortions coupled to the electronic degrees of freedom. We reproduce the observed dependence of the transition temperature on the cation radius in the well studied manganite7 and nickelate8 materials. Because elastic couplings are generally strong, we anticipate that these conclusions will generalize to all metal-to-insulator transitions that couple to a change in lattice symmetry.

The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients.

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables-e.g., the finite ion size-or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods.

Understanding Dynamics of Electrochemical Double Layers via a Modified Concentrated Solution Theory

Understanding the dynamics of an electrochemical double layer (EDL) is of fundamental importance to a wide array of electrochemical energy devices. We develop in this study a modified concentrated solution theory to simulate EDL dynamics in the concentrated regime, in which the driving force of ion transport in EDL is derived from a free energy functional that considers ion size effect, short-range correlations, and solvent polarization. The model features a mobility matrix with non-zero off-diagonal elements due to short-range correlations. Model results are compared with molecular dynamic simulations and surface force measurement for an EDL in ionic liquids. The model gives out insights into how the ion size, various short-range correlations, and the solvent polarization affect the charging dynamics. The model is instrumental to design, optimization and control of high-power electrochemical devices.

Features of Electrical Double Layers Formed Around Strongly Charged Nanoparticles Immersed in an Electrolyte Solution. The Effect of Ion Sizes

Using the modified Poisson–Boltzmann (PB) theory, which includes restrictions on the maximum attainable concentration of ionic species in a solution Cmax determined by their effective sizes, the distributions of electrostatic potential φ(r) and ion concentration near a spherical nanoparticle with radius a immersed in a 1 : 1 electrolyte solution have been studied under the conditions of constant surface charge density σs. For weakly charged particles, the φ(r) profiles are almost independent of Cmax and coincide with the profile obtained in terms of the classical PB model. Surface potential |φs| gradually increases with a rise in |σs|. Far from the particle, when the potential becomes lower than its thermal value $${{\varphi }_{{\text{T}}}} = \frac{{kT}}{e}$$ (k is the Boltzmann constant, T is the temperature, and e is the elementary charge), the potential decreases exponentially irrespective of the counterion sizes: $$\psi \left( r \right) = \frac{{\varphi \left( r \right)}}{{{{\varphi }_{{\text{T}}}}}} = {{\psi }_{{{\text{eff}}}}}\frac{a}{r}\exp \left( { - \kappa \left( {r - a} \right)} \right),$$ where r is the distance from the particle center and κ is the reciprocal Debye radius. According to the classical PB theory, the growth of the surface charge leads to the saturation of $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|~\left( { \to 4} \right),$$ with the value of $$\left| {{{\psi }_{{\text{s}}}}} \right|$$ obtained by solving the nonlinear PB equation being higher than $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|.$$ In the modified PB theory, which takes into account the size of electrolyte ions in the simplest form, this effect of saturation is absent. Now, $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|$$ depends on both the value of the surface charge and the sizes of counterions. Moreover, at a large size of counterions, $$\left| {{{\psi }_{{{\text{eff}}}}}} \right|$$ substantially exceeds the corresponding value obtained by solving the nonlinear modified PB equation. The difference between the electrical double layer properties obtained by solving the classical and modified PB equations directly follows from the fact that the modified theory predicts the appearance of a condensed layer at a particle surface, with the concentration of counterions in this layer being equal to Cmax. Therewith, the thickness of the layer grows with increasing |σs| (at a constant size of the ions) and the size of the ions (at constant σs).

Ionic size, permittivity, and viscosity-related effects on the electrophoretic mobility: A modified electrokinetic model

The standard electrokinetic model (SEM) is modified by considering hydrated ions as charged dielectric spheres so that in the modified model (MEM) the electrolyte solution becomes a non-homogeneous fluid with permittivity and viscosity values that are both functions of the local ionic concentrations.

Screening length for finite-size ions in concentrated electrolytes.

The classical Debye-Hückel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge but can equivalently be derived from the charge-charge correlation function. By going beyond DH theory, we predict the effects of ion size on the charge-charge correlation function. A simple modification of the Coulomb interaction kernel to account for the excluded volume of neighboring ions yields a nonmonotonic dependence of the screening length (correlation length) on the ionic concentration, as well as damped charge oscillations for high concentrations.

Transition-Metal Distribution in Brownmillerite Ca2FeCoO5.

Ca2Fe2-xCoxO5 (0 ≤ x ≤ 1) with higher Co content, which crystallizes in a brownmillerite-type structure, is currently one of the best oxygen-evolution-reaction (OER) catalysts. Identifying the Fe/Co occupancies at the octahedral (Oh) and tetrahedral (Td) sites in the structure is the foundation for the understanding of the role of cobalt in each site and the exploration of further improvement in the OER activity. Here, we investigate the Fe/Co distribution in Ca2FeCoO5 by means of atomic-resolution energy dispersive X-ray spectroscopy in scanning transmission electron microscopy and dynamical image simulations combined with systematic density functional theory calculations. Our careful microscopic study reveals the absence of long-range Fe/Co order within the transition-metal (TM) layers, but cobalt is slightly enriched at the Td and Oh sites in the as-synthesized (1100 °C) and 800 °C annealed for a month samples, respectively. The observed Co site preferences are interpretable from the viewpoints of TM ionic size effect and ligand field effect, which are competitive around a crossover point at a certain temperature between 800 and 1100 °C. We also elucidate that the as-synthesized sample with Co enrichment at the Td site shows the better OER activity, and the optimum annealing temperature for more OER active Ca2FeCoO5 should be higher than the crossover temperature.

Differential capacitance of ionic liquid interface with graphene: The effects of correlation and finite size of ions

We use a mean field model for ionic liquids, which takes into account both the ion correlation and the finite ion size effects, in order to calculate the differential capacitance of the ionic liquid interface with single-layer graphene. Besides choosing ion packing fractions that give rise to the camel-shaped and bell-shaped capacitances of the diffuse layer in ionic liquids, we also explore small packing fractions in the regime of “dilute electrolytes”, as well as different packing fractions for different ion species in asymmetric ionic liquids. We find that the main effect of a graphene electrode arises due to a V-shaped minimum in its quantum capacitance at the point of zero charge (PZC), which is a manifestation of the Dirac cone structure of graphene's π electron bands. As a result, the total capacitance of a graphene–ionic liquid interface exhibits a camel-shaped dependence on the total applied potential, even for large ion packing fractions and finite ion correlation lengths. While the minimum at the PZC in the total capacitance is “inherited” from graphene's quantum capacitance, the two peaks that occur for applied potentials ∼±1 V are sensitive to the presence of the ion correlation and a Stern layer, which both tend to reduce the height and flatten the peaks in the camel-shaped total capacitance. Finally, we have found that the largest fraction of the applied potential goes to charging the graphene electrode.