Electrical Double Layer Theory Research Articles

Theory of the Electrochemical Impedance of Mesostructured Electrodes Embedded with Heterogeneous Micropores

We develop a phenomenological theory of electric double layer (EDL) dynamics at complex bimodal electrode morphology, viz. arbitrary shaped mesostructures with embedded heterogeneous micropores. The dynamics of the diffuse layer at mesoscale is described through the Debye-Falkenhagen (DF) model of EDL relaxation and dynamics at micropores is described by employing the de Levie’s transmission line (TL) model. The influence of mesostructure on the diffuse layer dynamics is incorporated elegantly, employing a Green’s function (obtained through multiple scattering formalism) expressing the local admittance of arbitrary shaped mesostructure in surface mean and Gaussian curvatures of electrode. The model also incorporates the finiteness of the molecular Stern layer through correction in surface curvatures and generalizes the EDL response for arbitrary shaped mesostructured electrodes. The contribution of morphological parameters, namely, micropore depth, mesostructure size, bimodal (micro- and meso-) structure ...

Electrosorption of monovalent alkaline metal ions onto highly ordered mesoporous titanium dioxide nanotube electrodes

Molecular modeling of electrical double layer (EDL) structure and electrosorption of ions in pores predicts the on-set of competitive entropic and energetic effects, such as electrosorption capacity mainly determined by size exclusion effects rather than applied electrical potential. Classical EDL Theory does not predict these effects. Although size-exclusion effects have been used to explain discrepancies between experimental observations and Classical EDL Theory, direct experimental validation of molecular modeling predictions have yet to be achieved. The main objective of the present work was to devise and test a model system that can be used to experimentally measure size-exclusion effects for future validation of molecular simulations. This work is a first attempt to bridge the gap between molecular modeling predictions of EDL structure and experimentally-measured macroscopic properties of the EDL.Highly-uniform, titanium dioxide nanotubes with three pore sizes (36.8, 41.4 and 44.9nm) were used as model electrodes to study the interactive effects of pore diameter, applied potential and ion size on the electrosorption of three monovalent alkaline-metal cations (Li+, Na+, Cs+).The proportionality of EDL electrical capacitance and ion-electrosorption capacity to surface area and applied potential predicted by Classical EDL Theory did not hold for all combinations of pore sizes and applied potentials examined in this work, and electrosorption capacity clearly depended on pore diameter rather than specific surface area, and on hydrated-ion radius. The measured electrosorption capacity trend in most cases corresponded to Cs+>Na+>Li+. This trend follows the hydrated radius size. Size exclusion effects on EDL capacitance and electrosorption capacity triggered by hydrated ion-size and pore diameter observed in this work were in qualitative agreement with molecular modeling predictions.

Mean-Field Theory of Electrical Double Layer In Ionic Liquids with Account of Short-Range Correlations

We develop the theory of the electrical double layer in ionic liquids as proposed earlier by Kornyshev (2007). In the free energy function we keep the so called ‘short-range correlation terms’ which were omitted there. With some simplifying assumptions, we arrive at a modified expression for differential capacitance, which makes differential capacitance curves less sharply depending on electrode potential and having smaller values at extrema than in the previous theory. This brings the results closer to typical experimental observations, and makes it appealing to use this formalism for treatment of experimental data. Implications on Debye length and the extent of ion paring in ionic liquids are then briefly discussed.

Molecular Insights into the Complex Relationship between Capacitance and Pore Morphology in Nanoporous Carbon-based Supercapacitors.

Electrochemical double layer capacitors, or supercapacitors, are high-power energy storage devices that consist of large surface area electrodes (filled with electrolyte) to accommodate ion packing in accordance with classical electric double layer (EDL) theory. Nanoporous carbons (NPCs) have recently emerged as a class of electrode materials with the potential to dramatically improve the capacitance of these devices by leveraging ion confinement. However, the molecular mechanisms underlying such enhancements are a clear departure from EDL theory and remain an open question. In this paper, we present the concept of ion reorganization kinetics during charge/discharge cycles, especially within highly confining subnanometer pores, which necessarily dictates the capacitance. Our molecular dynamics voltammetric simulations of ionic liquid immersed in NPC electrodes (of varying pore size distributions) demonstrate that the most efficient ion migration, and thereby largest capacitance, is facilitated by nonuniformity of shape (e.g., from cylindrical to slitlike) along nanopore channels. On the basis of this understanding, we propose that a new structural descriptor, coined as the pore shape factor, can provide a new avenue for materials optimization. These findings also present a framework to understand and evaluate ion migration kinetics within charged nanoporous materials.

Counterion Effects on Electrolyte Interactions with Gold Nanoparticles

Electrolyte interactions with nanoparticles (NPs) at the solid/liquid interfaces are highly complicated as the charged species can be directly adsorbed onto the NP surfaces, confined in the diffusion layer immediately surrounding the NPs, and dispersed in bulk solutions. Existing studies on electrolyte interactions with NPs are based primarily on the electrical double layer theory that focuses mainly on electrolyte interactions with NPs with fixed pre-existing charges. Demonstrated herein is a comprehensive study of counterion effects during the electrolyte bindings to gold nanoparticles (AuNPs), including halide-induced AuNP aggregation and fusion, quantitative cation and anion coadsorption, selective cation and anion displacement on AuNPs, and surface-enhanced Raman spectroscopic features of the ionic species adsorbed onto AuNP surfaces. In contradiction to previous reports that electrolyte effects are anion-specific, we demonstrated that cations can play a dominant role in the halide-induced AuNP aggre...

Aqueous Partition Mechanism of Organophosphorus Extractants in Rare Earths Extraction

The aqueous partition mechanism of traditional extractants and ionic liquid for the extraction of rare earths (REs) is explored in this work. To investigate the aqueous partition of extractants, the aqueous solubility of di(2-ethylhexyl) phosphoric acid (P204), 2-ethylhexyl phosphoric acid mono-2-ethylhexyl ester (P507), di(2-ethylhexyl) phosphinic acid (P227), bis (2,4,4-trimethylpentyl) phosphinic acid (C272), and [trialkylmethylammonium][di(2-ethylhexyl)orthophosphinate] ([A336][P507]) was analyzed systemically. The results demonstrated that the solubility of extractants decreased with increase of aqueous acidity, RE loading, and electrolyte concentration. Especially, the solubility of P204, P507, P227, and C272 decreased with the increase of RE complex, indicating that aqueous partition of the extractants was accompanied by the RE coordination reaction. The electrical double layer theory and the Pitzer equation was used to explain the inhibition of electrolyte on the aqueous partition of extractants. ...

Silver nanostructures synthesis via optically induced electrochemical deposition.

We present a new digitally controlled, optically induced electrochemical deposition (OED) method for fabricating silver nanostructures. Projected light patterns were used to induce an electrochemical reaction in a specialized sandwich-like microfluidic device composed of one indium tin oxide (ITO) glass electrode and an optically sensitive-layer-covered ITO electrode. Silver polyhedral nanoparticles, triangular and hexagonal nanoplates, and nanobelts were controllably synthesized in specific positions at which projected light was illuminated. The silver nanobelts had rectangular cross-sections with an average width of 300 nm and an average thickness of 100 nm. By controlling the applied voltage, frequency, and time, different silver nanostructure morphologies were obtained. Based on the classic electric double-layer theory, a dynamic process of reduction and crystallization can be described in terms of three phases. Because it is template- and surfactant-free, the digitally controlled OED method facilitates the easy, low cost, efficient, and flexible synthesis of functional silver nanostructures, especially quasi-one-dimensional nanobelts.

A new methodology for computing ionic profiles and disjoining pressure in swelling porous media

A new two-scale computational model is proposed to construct the constitutive law of the swelling pressure which appears in the modified form of the macroscopic effective stress principle for expansive clays saturated by an aqueous electrolyte solution containing multivalent ionic species. The microscopic non-local nanoscale model is constructed based on a coupled Poisson-Fredholm integral equation arising from the thermodynamics of inhomogeneous fluids in nanopores (Density Functional Theory), which governs the local electric double layer potential profile coupled with the ion-particle correlation function in an electrolytic solution of finite size ions. The local problem is discretized by invoking the eigenvalue expansion of the convolution kernel in conjunction with the Galerkin method for the Gauss-Poisson equation. The discretization of the Fredholm equation is accomplished by a collocation scheme employing eigenfunction basis. Numerical simulations of the local ionic profiles in rectangular cell geometries are obtained showing considerable discrepancies with those computed with Poisson-Boltzmann based models for point charges, particularly for divalent ions in calcium montmorillonite. The constitutive law for the disjoining pressure is reconstructed numerically by invoking the contact theorem within a post-processing approach. The resultant computational model is capable of capturing ranges of particle attraction characterized by negative values of the disjoining pressure overlooked by the classical electric double layer theory. Such results provide further insight in the role the swelling pressure plays in the modified macroscopic effective stress principle for expansive porous media.

On the theory of electric double layer with explicit account of a polarizable co-solvent

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory, showing that accounting for the excluded volume of co-solvent molecules and ions slightly changes the main result of our previous simplified theory. Namely, in the case of small co-solvent polarizability with its increase under the enough small surface potentials of electrode, the differential capacitance undergoes the significant growth. Oppositely, when the surface potential exceeds some threshold value (which is slightly smaller than the saturation potential), the increase in the co-solvent polarizability results in a differential capacitance decrease. However, when the co-solvent polarizability exceeds some threshold value, its increase generates a considerable enhancement of the differential capacitance in a wide range of surface potentials. We demonstrate that two qualitatively different behaviors of the differential capacitance are related to the depletion and adsorption of co-solvent molecules at the charged electrode. We show that an additive of the strongly polarizable co-solvent to an electrolyte solution can shift significantly the saturation potential in two qualitatively different manners. Namely, a small additive of strongly polarizable co-solvent results in a shift of saturation potential to higher surface potentials. On the contrary, a sufficiently large additive of co-solvent shifts the saturation potential to lower surface potentials. We obtain that an increase in the co-solvent polarizability makes the electrostatic potential profile longer-ranged. However, increase in the co-solvent concentration in the bulk leads to non-monotonic behavior of the electrostatic potential profile. An increase in the co-solvent concentration in the bulk at its sufficiently small values makes the electrostatic potential profile longer-ranged. Oppositely, when the co-solvent concentration in the bulk exceeds some threshold value, its further increase leads to decrease in electrostatic potential at all distances from the electrode.

Determination of correct zeta potential of polyether sulfone membranes using CLC and AGC: ionic environment effect

In this study, the correct and apparent zeta potential of polyether sulfone (PES) ultrafiltration membranes at different ionic environments were determined using streaming potential measurements. The apparent zeta potential was found by calculation with classic Helmholtz-Smoluchowski (HS) and Fairbrother-Mastin (FM) equations of results obtained from clamping cell (CLC) and adjustable gap cell (AGC). Correct zeta potential was determined by calculation with a modified HS equation of obtained results from AGC. Obtained apparent zeta potential results from CLC and AGC differ from each other, and the reproducibility of results was found to be higher for measurements of AGC. Except for low pH values, apparent zeta potential that was obtained from classic HS equation with AGC could be accepted as correct zeta potential. In CLC measurements, underestimated or overestimated zeta potential values were determined in comparison with the correct zeta potential. The effect of membrane surface conductance on zeta potential decreased with increasing KCl concentration. In CLC, the deviation was observed from electrical double layer theory when KCl concentration was 0.1 M, therefore streaming potential measurements did not produce correct results at higher salt concentration. 0.001M KCl concentration was the value at which surface conductance became crucial.

Application of a Multi-Scale form of Terzaghi’s Effective Stress Principle for Unsaturated Expansive Clays to Simulate Hydro-Mechanical Behavior During Hydration

Our recently developed multi-scale form of Terzaghi’s effective stress principle for unsaturated swelling clays that was rigorously derived by periodic homogenization starting from micro- and nano-mechanical analyses is applied to numerically simulate one-dimensional swelling pressure tests of compacted bentonites during hydration. The total macroscopic stress captures the coupling between disjoining forces at the nanoscopic scale of clay platelets and capillary effects at the microscopic scale of clay aggregates over the entire water content range. The numerical results allow to draw conclusions on the water transfer mechanism between inter- and intra-aggregate pores during hydration and consequently on the evolution of the external swelling pressure resulting from the competition between capillary and disjoining forces. In addition, such application highlights the abilities and the limits of the electrical double-layer theory to compute the disjoining pressure in the nano-pores. For large platelet distances, in the range of osmotic swelling, the nature of the disjoining pressure is electro-chemical and can be computed from Poisson-Boltzmann theory. Conversely, at small distances, in the crystalline swelling, a solvation component has to be added to account for the molecular nature of the solvent. As a first improvement of the nano-scale description the solvent is treated as a hard sphere fluid using Density Functional Theory.

Potential dependent structure of an ionic liquid at ionic liquid/water interface probed by x-ray reflectivity measurements

Abstract The structure at air interface and water (W) interface of a hydrophobic ionic liquid (IL), trioctylmethylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate ([TOMA+][TFPB−]), has been studied using x-ray reflectometry. Multilayering of ions has been found at the IL/air interface, with the topmost ionic layer having lower density than the IL bulk. For the IL/W interface, x-ray reflectivity data depends on the phase-boundary potential across the IL/W interface. When the phase-boundary potential of W with respect to IL, ΔILWϕ, is + 0.20 V, TFPB− ions are accumulated at the topmost ionic layer on the IL side of the IL/W interface. On the other hand, when ΔILWϕ = - 0.27 V, the accumulation of TOMA+ ions occurs with bilayer thickness, which is probably due to local interaction between TOMA+ ions at the topmost layer and at the second layer through interdigitation of their alkyl chains. To quantitatively analyze the x-ray reflectivity data, we construct a model of the electrical double layer (EDL) at the IL/W interface, by combining the Gouy–Chapman–Stern model on the W side and the Oldham model on the IL side. The constructed model predicts that the EDL on the IL side is within the topmost layer for the phase-boundary potentials in the present study, suggesting that the TOMA+ bilayer found at the negative potential results from the local interaction beyond the framework of the present mean-field theory. Even at the positive potential the surface charge density predicted by the EDL theory is significantly smaller than that estimated from x-ray reflectivity data, which implies that densification of the topmost ionic layer leads us to overestimate the surface charge density.

Fabrication of Ni Microbumps With Small Feature Size on Au Using Electroless Ni Plating With Noncontact Induction

This paper reports a method of fabrication for small-feature-sized nickel (Ni) microbumps on gold (Au) using a newly developed technique called electroless Ni plating with noncontact induction (ENPNI). This technique, differing from conventional electroless Ni plating with contact induction (ENPCI), which directly connects an active metal with an inactive metal to induce Ni electrochemical reaction, is characterized by separation of the active metal and the target metal. The mechanism of ENPNI is interpreted by employing the electric-double layer theory, and some phenomena are explained by the proposed mechanism. Ni microbumps with a diameter of 3–6 $\mu \text{m}$ and a height of 3–4 $\mu \text{m}$ have been successfully fabricated using ENPNI. The resistance of the Ni microbumps is measured, and yield and uniformity are evaluated. By breaking the restriction of contact, ENPNI has the advantages of no need for pretreatment and contact induction, allowing fabrication of microbumps with small feature sizes for applications in which direct contact of an active induction metal is impossible.

Effects of metal ions with different valences on colloidal aggregation in low-concentration silica colloidal systems characterized by continuous online zeta potential analysis

In the removal of silicate and impurities in the acid treatment of high-alumina fly ash, the transition from silica sol to gel in the presence of metal cations has a major role in filtration and product quality. In this work, an online physical analysis method that can continuously measure zeta potential, pH, and viscosity is established for low-concentration colloidal systems. The change in zeta potential can be explained by Derjaguin.Landau.Verwey.Overbeek (DLVO) theory and model of electric double layer, which is verified by the morphology of colloids in different periods. The influences of metal cations with different valences and contents on the transition from silica sol to gel are investigated in detail. Results show that trivalent ions have a positive role in the delayed coagulation because of their hydrolysis and complexation in relatively low concentrations. By contrast, divalent and monovalent ions have a negative role in the transition from sol to gel because of the bridging effect. In terms of concentration, divalent ions have greater influence on the transition from sol to gel than monovalent ions. This established method is adaptable for the analysis of a low-concentration colloidal system and could be applied in the acid treatment of silicon-containing solid wastes. (C) 2015 Elsevier B.V. All rights reserved.

Effective adsorption of Cr(VI) on mesoporous Fe-functionalized Akadama clay: Optimization, selectivity, and mechanism

A Japanese volcanic soil, Akadama clay, was functionalized with metal salts (FeCl3, AlCl3, CaCl2, MgCl2, MnCl2) and tested for Cr(VI) removal from aqueous solution. FeCl3 was selected as the most efficient activation agent. To quantitatively investigate the independent or interactive contribution of influencing factors (solution pH, contact time, adsorbent dose, and initial concentration) to Cr(VI) adsorption onto Fe-functionalized AC (FFAC), factorial experimental design was applied. Results showed initial concentration contributed most to adsorption capacity of Cr(VI) (53.17%), followed by adsorbent dosage (45.15%), contact time (1.12%) and the interaction between adsorbent dosage and contact time (0.37%). The adsorption showed little dependence on solution pH from 2 to 8. Adsorption selectivity of Cr(VI) was evaluated through analyzing distribution coefficient, electrical double layer theory, as well as the valence and Pauling's ionic radii of co-existing anions (Cl−, SO42−, and PO43−). EDX and XPS analyses demonstrated the adsorption mechanism of Cr(VI) onto FFAC included electrostatic attraction, ligant exchange, and redox reaction. Improved treatment for tannery wastewater shows a potential application of FFAC as a cost-effective adsorbent for Cr(VI) removal.

Energy Consumption and Recovery in Capacitive Deionization Using Nanoporous Activated Carbon Electrodes

Capacitive deionization (CDI) is an emerging desalination technology which utilizes porous electrodes to remove ions in water by electrosorption. Similar to electric capacitors, energy is stored and released during charging and discharging cycles, respectively. In this study, a nanoporous activated carbon coupled flow-through CDI device was used to evaluate energy consumption and recovery under various operational conditions by charging and discharging the cell at a constant current, respectively. Results indicated that the charging/discharging current, salt concentration and water flow rate were major factors impacting electrosorption and energy consumption, by changing the structure of the electrical double layer (EDL) and how ion transport occurs between the interface and bulk solution. A porosity-based EDL theory was applied to explain the experimental observations. Between 30 and 45% of the energy consumed during charging could be recovered depending on operational conditions, although thermodynamically more than 98% of the total energy should be recoverable. Results indicated that overpotential and faradaic reactions induced irreversible energy are the major reasons for gaps in observed energy losses. Energy consumption for reducing the salinity of brackish water from 32.7 to 5.5 mM by our device could be as low as 0.85 kWh/m3 under most optimized conditions (dependent on materials used and cell configuration). The energy consumption can be dramatically reduced by employing more electron-conductive and Faradaic-resistant electrode materials.

Modification of the surface of activated carbon electrodes for capacitive mixing energy extraction from salinity differences

The “capacitive mixing” (CAPMIX) is one of the techniques aimed at the extraction of energy from the salinity difference between sea and rivers. It is based on the rise of the voltage between two electrodes, taking place when the salt concentration of the solution in which they are dipped is changed. We study the rise of the potential of activated carbon electrodes in NaCl solutions, as a function of their charging state. We evaluate the effect of the modification of the materials obtained by adsorption of charged molecules. We observe a displacement of the potential at which the potential rise vanishes, as predicted by the electric double layer theories. Moreover, we observe a saturation of the potential rise at high charging states, to a value that is nearly independent of the analyzed material. This saturation represents the most relevant element that determines the performances of the CAPMIX cell under study; we attribute it to a kinetic effect.

Research on the critical conditions for clay particle release during saline aquifer freshening process

Water sensitivity phenomenon occurs during saline aquifer freshening process in seawater intrusion area, and clay particles released in the phenomenon can damage the infiltration capacity of the aquifer. In order to find out the factors and mechanisms for clay particle release, laboratory column infiltration experiments simulating saline aquifer freshening process were designed to measure the critical conditions (critical flow velocity, critical salt concentration and critical ionic strength) and force analysis for clay particle according to DLVO electric double layer theory was employed to illustrate the mechanisms for particle release. The research results showed that critical flow velocity for clay particle release is influenced by salt concentration of injecting solution. When salt concentration of injecting solution is very high, clay particles are not released, indicating that there does not exist a critical flow velocity in this situation. As salt concentration of injecting solution decreases, particles start to be released. The critical salt concentration for clay particle release is 0.052 mol L−1 in our work, which was determined by a constant-flux experiment for stepwise displacement of high concentration NaCl solution. The critical ionic strength for clay particle release decreases as Ca2+ molar content percentage of the mixed solution of NaCl and CaCl2 increases following the first-order exponential decay equation y = 0.0391e−0.266x + 0.0015.

Structure of water at charged interfaces: a molecular dynamics study.

The properties of water molecules located close to an interface deviate significantly from those observed in the homogeneous bulk liquid. The length scale over which this structural perturbation persists (the so-called interfacial depth) is the object of extensive investigations. The situation is particularly complicated in the presence of surface charges that can induce long-range orientational ordering of water molecules, which in turn dictate diverse processes, such as mineral dissolution, heterogeneous catalysis, and membrane chemistry. To characterize the fundamental properties of interfacial water, we performed molecular dynamics (MD) simulations on alkali chloride solutions in the presence of two types of idealized charged surfaces: one with the charge density localized at discrete sites and the other with a homogeneously distributed charge density. We find that, in addition to a diffuse region where water orientation shows no layering, the interface region consists of a "compact layer" of solvent next to the surface that is not described in classical electric double layer theories. The depth of the diffuse solvent layer is sensitive to the type of charge distributions on the surface and the ionic strength. Simulations of the aqueous interface of a realistic model of negatively charged amorphous silica show that the water orientation and the distribution of ions strongly depend on the identity of the cations (Na(+) vs Cs(+)) and are not well represented by a simplistic homogeneous charge distribution model. While the compact layer shows different solvent net orientation and depth for Na(+) vs Cs(+), the depth (~1 nm) of the diffuse layer of oriented waters is independent of the identity of the cation screening the charge. The details of interfacial water orientation revealed here go beyond the traditionally used double and triple layer models and provide a microscopic picture of the aqueous/mineral interface that complements recent surface specific experimental studies.

Critical interparticle distance for the remarkably enhanced dielectric constant of BaTiO3-Ag hybrids filled polyvinylidene fluoride composites

Discrete nano Ag-deposited BaTiO3 (BT-Ag) hybrids with varied Ag content were synthesized, and the hybrids filled polyvinylidene fluoride (PVDF) composites were prepared. The effect of Ag content on the dielectric properties of the composites were analyzed based on the diffused electrical double layer theory. Results showed that with a higher Ag content in BT-Ag hybrids, the dielectric constant of BT-Ag/PVDF composites increases fast with the filler loading, while the dielectric loss and conductivity showed a suppressed and moderate increase. The dielectric constant of BT-0.61Ag/PVDF (61 wt. % of Ag in BT-Ag hybrid) composites reached 613, with the dielectric loss of 0.29 at 1 kHz. It was deduced that remarkably enhanced dielectric constant appeared when the interparticle distance decreased to a critical value of about 20 nm.