Model Of Electrical Double Layer Research Articles

State of charge estimation for lithium-ion battery using an electrochemical model based on electrical double layer effect

This paper focuses on an efficient fundamental approach of the electrochemical model of lithium-ion batteries (LIBs), especially considering the effect of Electrical Double Layer (EDL) potential on the over-potential of batteries. Firstly, the electrode solid phase and electrolyte liquid phase in LIBs are modelled by electrochemical theory, especially emphasizing the influence of EDL structure. Three-parameter parabola method is effectively employed to simplify the model. Furthermore, a parameter identification method based on genetic algorithm is proposed according to the structure characteristics of EDL model. The accuracy of model is verified by comparing the output voltage of the EDL model under 0.1∼2C charging/discharging, 1C pulse discharging and New European Driving Cycle (NEDC) condition with the experimental terminal voltage. Finally, the battery SOC estimation method is developed by using the extended Kalman filter (EKF) algorithm based on EDL model and is verified by the 1C pulse discharge and the NEDC condition experiments. The results show that the proposed algorithm can accurately estimate the SOC value of LIBs. In addition, the algorithm has a strong correction effect on the initial SOC error and convergence.

Off-centre charge model of the planar electric double layer for asymmetric 2:1/1:2 valencies

ABSTRACTGrand canonical Monte Carlo simulation results are reported for the structure and capacitance of a planar electric double layer containing off-centre charged rigid sphere cations and centrally charged rigid sphere anions. The ion species are assigned asymmetric valencies, +2:−1 and +1:−2, respectively, and set in a continuum dielectric medium (solvent) characterised by a single relative permittivity. An off-centre charged ion is obtained by displacing the ionic charge from the centre of the sphere towards its surface, and the physical double layer model is completed by placing the ionic system next to a uniformly charged, non-penetrable, non-polarizable planar electrode. Structural results such as electrode-ion singlet distribution functions, ionic charge density and orientation profiles are complemented by differential capacitance results at electrolyte concentrations of 0.2 mol/dm3 and 1 mol/dm3, respectively, and for various displacements of the cationic charge centre. The effect of asymmetry due to off-centre cations and valency asymmetry on the double layer properties is maximum for divalent counterions and when the cation charge is closest to the hard sphere surface.

Study of the Surface Charge of a Porous Clay Heterostructure (PCH) and Its Adsorption Capacity of Alkaline Metals

A Porous Clay Heterostructure (PCH) was prepared by chemical modification of a natural clay, by intercalation of a cationic surfactant. Its surface charge properties as well as its adsorption capacity for alkali metals were studied using a potentiometric titration method. The PCH developed a pH-dependent charge (sH), probably due to the presence of amphoteric silanol groups (SiO2) coming from the pillars of silica interlayered during the pillared process. The PCH presented a region of zero charge in the range of pH of 4.0 to 7.7. The sH acquired by the PCH was adjusted with good correlation to the electric double layer model of Gouy-Chapman (r2 = 0.9925). The surface charge conferred the PCH ion exchange capacity for the studied metals (Li, Na, K, Rb and Cs) at high pH values (10 < pH), in comparable quantities (3.5 to 6 meq/g) to some Dowex resins. The results of this study suggest that PCH could have applications in the recovery of toxic metals from waste waters.

Atomic Force Spectroscopy on Ionic Liquids

Ionic liquids have become of significant relevance in chemistry, as they can serve as environmentally-friendly solvents, electrolytes, and lubricants with bespoke properties. In particular for electrochemical applications, an understanding of the interface structure between the ionic liquid and an electrified interface is needed to model and optimize the reactions taking place on the solid surface. As with ionic liquids, the interplay between electrostatic forces and steric effects leads to an intrinsic heterogeneity, as the structure of the ionic liquid above an electrified interface cannot be described by the classical electrical double layer model. Instead, a layered solvation layer is present with a structure that depends on the material combination of the ionic liquid and substrate. In order to experimentally monitor this structure, atomic force spectroscopy (AFS) has become the method of choice. By measuring the force acting on a sharp microfabricated tip while approaching the surface in an ionic liquid, it has become possible to map the solvation layers with sub-nanometer resolution. In this review, we provide an overview of the AFS studies on ionic liquids published in recent years that illustrate how the interface is formed and how it can be modified by applying electrical potential or by adding impurities and solvents.

Effects of ion size, ion valence and pH of electrolyte solutions on EOF velocity in single nanochannels

Electroosmotic flow (EOF) in nanochannels as small as 85 nm and in small microchannels is systematically investigated by using the current-slope method. The effects of ion size, ion valence and pH of electrolyte solutions on the velocity of electroosmotic flow are experimentally studied. The results show that the large size of hydrated ions leads to higher EOF velocity in large nanochannels and microchannels, and, however, lower EOF velocity in small nanochannels with an overlapped electric double layer (EDL). Furthermore, the EOF velocity is proportional to the pH of the electrolyte solution and contrariwise proportional to the valence of counter-ions. It is also observed that the EOF velocity depends on the channel size in nanochannels, even without overlapped EDL. Several models of electric double layer (EDL) are proposed to explain the experimental results and provide an improved understanding of the effects of ion size, ion valence and pH of electrolyte solutions on the EOF velocity in nanochannels in terms of EDL structure.

Does capillary evaporation limit the accessibility of nonaqueous electrolytes to the ultrasmall pores of carbon electrodes?

Porous carbons have been widely utilized as electrode materials for capacitive energy storage. Whereas the importance of pore size and geometry on the device performance has been well recognized, little guidance is available for identification of carbon materials with ideal porous structures. In this work, we study the phase behavior of ionic fluids in slit pores using the classical density functional theory. Within the framework of the restricted primitive model for nonaqueous electrolytes, we demonstrate that the accessibility of micropores depends not only on the ionic diameters (or desolvation) but also on their wetting behavior intrinsically related to the vapor-liquid or liquid-liquid phase separation of the bulk ionic systems. Narrowing the pore size from several tens of nanometers to subnanometers may lead to a drastic reduction in the capacitance due to capillary evaporation. The wettability of micropores deteriorates as the pore size is reduced but can be noticeably improved by raising the surface electrical potential. The theoretical results provide fresh insights into the properties of confined ionic systems beyond electric double layer models commonly employed for rational design/selection of electrolytes and electrode materials.

Leaching mechanism of ion-adsorption rare earth by mono valence cation electrolytes and the corresponding environmental impact

Ion-adsorption rare earth (IARE) is a very important resource which is adsorbed on clay mineral surface and can be leached by appropriate electrolyte solutions. A comprehensive understanding of the leaching mechanism is crucial for achieving high extraction efficiency with low cost and less environmental impact. In this paper, a series of inorganic electrolytes with different concentrations were employed to leach the IARE, and the relationship between leaching efficiency (LE) of IARE and zeta potential of the leached clay mineral particles (CMPs) was investigated. A linear relationship between the LE of IARE and zeta potential of CMPs is observed for every electrolyte. However, the slope (S) of the linear relationship greatly depends on the type of the cations and follows a sequence of S(NH4+)＞S(K+)＞S(Na+). In addition, in the case of ammonium or potassium ions, the slope is almost the same for both SO42− and Cl−. But for sodium ions, a significant difference of slope is observed with the order of S(SO42−)＞S(Cl−). These facts suggest that the cations play a dominating role in affecting the leaching of IARE, while the anions also contribute to the LE of IARE. Based on the electric double layer model and hydration theory, a leaching mechanism is proposed to illustrate the dependence of zeta potential on the LE of IARE and the residual ion concentration in rinsing solutions which is considered to be the main factor influencing the environment of mine district. This work may provides a promising route for enhancing the LE and estimating the environmental impact of remaining electrolytes in mine tailing.

Treatment of Ion-Size Asymmetry in Lattice-Gas Models for Electrical Double Layer

A discreet consideration of the ubiquitous ion-size asymmetry is essential for an accurate description of the electrical double layer. The diversity of approaches in the literature to treat this ef...

Interplay between Covalent and Noncovalent Interactions in Electrocatalysis

Electrocatalysis has been advanced to a point that understanding how noncovalent interactions interplay with covalent interactions becomes essential to precision design of efficient electrocatalysts. However, a conceptual framework for facilitating such understandings is yet missing; existing theories of electrocatalysis usually neglect noncovalent interactions. To fill in this gap, this study presents a refined theory of electrocatalysis by adding a noncovalent term that is self-consistently derived from a mean-field electrical double-layer (EDL) model into the model Hamiltonian, in addition to the electronic interaction term described by the Anderson–Newns model and the solvent term inspired by the Marcus theory. Applying the Green function technique allows us to portray the potential energy surface, to pinpoint multiple states along the reaction pathway and further to determine the reaction free energy and activation energies. Multifaceted interplay between covalent and noncovalent interactions is reve...

Asymmetric Finite Size of Ions and Orientational Ordering of Water in Electric Double Layer Theory Within Lattice Model.

In the present review, a brief historical survey of the mean-field theoretical description of Electric Double Layer (EDL) is presented. Special attention is devoted to asymmetric finite size of ions and orientational ordering of water dipoles. A model of Wicke and Eigen, who were first to explicitly derive the ion distribution functions for finite size of ions, is discussed. Arguments are given in favour of changing the recently adopted name of the mean-field EDL model for finite size of ions from Bikerman model to Bikerman-Wicke-Eigen model. Theoretically predicted asymmetric and symmetric camel-like shape of the voltage dependence of the differential capacitance is also discussed.

Low-Temperature Surface Forces Apparatus to Determine the Interactions between Ice and Silica Surfaces.

We have developed a low-temperature surface forces apparatus (SFA) using a thermoelectric Peltier module inserted below the bottom surface of the lower sample holder, giving easy access to the samples and allowing quick temperature changes. In air, the temperature can be decreased to ca. -20 °C. To demonstrate the performance of the apparatus, we measured the interactions between ice and a silica surface at -11.5 ± 0.5 °C. An exponentially decaying repulsion of the decay length, 11.2 ± 1.0 nm, was observed, and attributed to the electric double layer (EDL) repulsion. The surface potential of the ice was calculated to be -35 mV by fitting the data to the EDL model.

Sensing applications of hydrovoltaic effect in low-dimensional carbon materials

A variety of phenomena observed in low-dimensional carbon materials, such as waving potential, moving droplet induced drawing potential, flow-induced voltage, water-evaporation-induced electricity, moisture-enabled electricity, have exhibited that low-dimensional carbon materials can generate electrical signals by interaction with dynamic water. This series of phenomena, which is termed as hydrovoltaic effect, has the potential of developing advanced technologies for water energy harvesting and enables the design of flexible sensing systems. This review focuses on the sensing ability of low-dimensional carbon materials to transform those physical/chemical parameters such as flow velocity, ion concentration, humidity, etc. into electrical signals through the hydrovoltaic effect. Generally speaking, as long as dynamic water (including water solutions, water vapor or water molecules) interacts with low-dimensional carbon materials and simultaneously produce a measurable electrical signal, the signal then can be utilized to monitor various information of the solid-liquid interface. In the first section, we describe the fundamental properties of water-solid interfaces, look back the history of widely used electrical double layer model and four classical electrokinetic effects: electro-osmosis, electrophoresis, streaming potential and sedimentation potential. Then we discuss the recently proposed water-carbon interaction mechanisms, including phonon dragging, electrical friction, pseudocapacitance and dynamic boundary at the liquid-gas interface. Among these mechanisms, the latter two, pseudocapacitance and dynamic boundary, can be considered as an expandedness of streaming potential model under confinement low-dimensional space. The second section reviews the phenomena of moving water induced voltage and its applications for dynamic water detecting. Diverse kinds of bulk water movement such as flowing, waving and drops sliding, can partially separate the positive ions from negative ions to produce an electrical potential difference along a nano-carbon sample under proper interface conditions. This electrical potential difference is usually proportional to the velocity and mass of the moving water near the solid-liquid interface and thus can be used as an indicator to measure these physical quantities. The third section introduces several examples of detecting ingredients and concentration of water solution using hydrovoltaic effect. For drawing potential of moving droplets on graphene, the induced voltage increases with increasing ion concentration over a low concentration range (10–7–10–2 mol/L). However, for the electrical potential produced by water evaporation on carbon black film, the output voltage decreases rapidly as the ion concentration increases. The next section presents the humidity sensing performance of different hydrovoltaic devices of low-dimensional carbon materials. Graphene and graphene oxide devices can be utilized as humidity and temperature sensors with convenient features such as flexibility and transparency. Single-walled carbon nanotubes can output a millivolt level of voltage in response to humidity variation at parts per million level. Finally, this review makes suggestions for developments in this field by highlighting the potential of hydrovoltaic sensors to be applied in the fields of physiological nanodevices, wearable electronics and self-powered intelligent systems.

CD-MUSIC-EDL Modeling of Pb2+ Adsorption on Birnessites: Role of Vacant and Edge Sites.

The surface complexation modeling of metal adsorption to birnessites is in its infancy compared to the charge-distribution multisite ion complexation (CD-MUSIC) models for iron/aluminum (hydr)oxides. Therefore, using X-ray diffraction with Rietveld refinement to obtain the reactive sites and their densities, a CD-MUSIC model combined with a Stern-Gouy-Chapman electrical double layer (EDL) model for the external surface and a Donnan model for the interlayer surface is developed for birnessites with different Mn average oxidation state (MnAOS). Proton affinity constants and the charge distributions of Pb surface complexes were calculated a priori. By fitting Pb adsorption data to the model the obtained equilibrium constants (log KPb) of Pb complexes were 6.9-10.9 for the double-corner-sharing and double-edge-sharing Pb2+ complexes on the edge sites and 2.2-6.5 for the triple-corner-sharing Pb2+ complex on the vacancies. The larger log KPb value was obtained for higher MnAOS. Speciation calculations showed that with increasing MnAOS from 3.67 to 3.92 the interlayer surface contribution to the total Pb2+ adsorption increased from 43.2% to 48.6%, and the vacancy contribution increased from 43.9% to 54.7%. The vacancy contribution from interlayer surface was predominant. The present CD-MUSIC-EDL model contributes to understand better the difference in metal adsorption mechanism between birnessite and iron/aluminum (hydr)oxides.

Electrical Double Layer Probed by Surface-Specific Vibrational Technique

In this issue of Chem, Paesani and co-workers present a computational analysis of sum-frequency generation (SFG) spectra of water to disentangle the interfacial χ(2) and bulk χ(3) contributions. SFG line shapes are in good agreement with experimental results. The analysis reveals the molecular response of interfacial water, which is usually masked by the bulk water spectra at the water-charged surfactant interface.

Water Structure and Dynamics at Hematite Electrodes

Electrocatalysis at a transition metal oxide (TMO) electrode in aqueous electrolyte is controlled in part by the behavior of interfacial water. Atomically precise measurements of TMO-electrolyte interfaces under electrocatalytic working conditions are therefore prerequisite for developing accurate models of interfacial reactions. We present the most detailed measurements to date of electrolyte ordering at the reactive hematite (α-Fe2O3) (1-102) (r-cut) surface at open circuit conditions and under applied cathodic bias in 5 mM Na2SO­4 solution. Interface structures are measured in situ by synchrotron X-ray crystal truncation rod (CTR) scattering using a novel electrochemical mini-cell. CTR results are interpreted in light of first-principles molecular dynamics simulations. We find that the equilibrium structure of the r-cut hematite-electrolyte interface is defined by frequent exchange of water molecules between terminal aquo ligands and solution, resulting in a steady-state partial coverage of undercoordinated surface iron sites. Under cathodic bias, the surface is excessively protonated, strengthening the near-surface hydrogen-bonding network. The steady-state coverage of terminal aquo ligands subsequently increases, armoring the hematite electrode against reductive dissolution. The ordering and separation of water layers depend on the cathodic bias magnitude. Taken together, these results reveal the fine details of the interface structure which underlie the electrical double layer models used to describe macroscopic electrochemical measurements. The methods developed through this work open a new frontier for the in situ characterization of TMO-electrolyte interfaces during electrocatalytic reactions.

Past and future on nanodielectrics

Flexible polymer-matrix nanodielectrics have recently been attracting more attention in the fields of frontier research internationally since the beginning of the 21st century. It would accelerate a technical reformation for the applications in new energies, bioscience and biomedical engineering, artificial intelligence, electronic skin, wearable electronic clothing, Internet of things, and electrical insulation. This review summarises the recent development and achievements of nanodielectrics, including space charge suppression, high energy density storage, partial discharge resistance, non-linear field grading properties, high thermal conductivity, and future applications in biomedical area. Special attention is given to two representative interface models that are the Lewis's diffusion electrical double-layer model and Tanaka's multi-core model. At last, some issues related to the technology of nanodielectrics have also been discussed.

A discussion on the leaching process of the ion-adsorption type rare earth ore with the electrical double layer model

The practice of in-situ leaching of the ion-adsorption type rare earth ore using (NH4)2SO4 had revealed serious ammonia-nitrogen pollution. Therefore, a discussion on the leaching process of the ion-adsorption type rare earth ore with the electrical double layer model was presented in this paper, so as to screen out the green and efficient leaching agent and the appropriate leaching measures to improve the rare earth leaching efficiency and reduce or even eliminate ammonia-nitrogen emissions. It was determined that the leaching process could be described as the formation of a new stable electric double layer (EDL). The potential φ(x) with the distance x from clay surface to bulk solution in the diffusion layer was obtained, it showed that the potential φ(x) would decrease with the increase of the cationic charge of leaching agent, the leaching temperature and the concentration of leaching agent, leading to a higher rare earth leaching efficiency. The theoretical analysis was verified by soak leaching experiments. The results showed that the law of rare earth leaching efficiency was in agreement with the theoretical analysis. And the rare earths partition in the leaching liquor under different conditions was substantially constant except cerium element. Therefore, the cation and anion of leaching agent should have a large electric density and be environmental friendly, of which magnesium sulfate could be preferred. Moreover, chemical substances, which could form a more stable coordination with rare earth ions, could be used as an assistant to promote the leaching equilibrium to move toward a favorable direction. This paper had provided a theoretical foundation and application basis for the leaching of rare earth from the ion-adsorption type rare earth ore, and show the direction on reducing or even eliminate ammonia-nitrogen emissions.

Potential‐Specific Structure at the Hematite–Electrolyte Interface

AbstractThe atomic‐scale structure of the interface between a transition metal oxide and aqueous electrolyte regulates the interfacial chemical reactions fundamental to (photo)electrochemical energy conversion and electrode degradation. Measurements that probe oxide–electrolyte interfaces in situ provide important details of ion and solvent arrangements, but atomically precise structural models do not exist for common oxide–electrolyte interfaces far from equilibrium. Using a novel cell, the structure of the hematite (α‐Fe2O3) ()–electrolyte interface is measured under controlled electrochemical bias using synchrotron crystal truncation rod X‐ray scattering. At increasingly cathodic potentials, charge‐compensating protonation of surface oxygen groups increases the coverage of specifically bound water while adjacent water layers displace outwardly and became disordered. Returning to open circuit potential leaves the surface in a persistent metastable state. Therefore, the flux of current and ions across the interface is regulated by multiple electrolyte layers whose specific structure and polarization change in response to the applied potential. The study reveals the complex environment underlying the simplified electrical double layer models used to interpret electrochemical measurements and emphasizes the importance of condition‐specific structural characterization for properly understanding catalytic processes at functional transition metal oxide–electrolyte interfaces.

Effect of bound chloride on extraction of water soluble chloride in cement-based materials exposed to a chloride salt solution

In this study, chloride ion concentration in the water extracted solution was measured. For comparison, it was also calculated based on the electrical double layer model under extraction equilibrium. The results indicated that the release of physically bound chloride can result in 1–7 times higher water extracted chloride ion concentration than free chloride ion concentration. With increase of fineness of powder, the chloride ion concentration in the water extracted solution increased. When powder fineness was higher than 1 µm, a very small amount of water could completely extract the water soluble chloride under extraction equilibrium. With increase of water/solid ratio and water temperature, release of chemically bound chloride led to a higher concentration of chloride ions in water extracted solution. The calculation is very helpful for discussing the effects of physically and chemically bound chlorides on extraction of water soluble chloride. Finally, suggestions for improvement of water extraction method were proposed by taking into account the experimental parameters influencing the release of bound chloride.

Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes.

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access-for the first time-to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models.