Electrical Double Layer Theory Research Articles

Exploring the impact of pore size distribution on the performance of carbon electrodes for capacitive deionization

Capacitive deionization (CDI) removes charged ions from aqueous solutions through entrapment in the electric double layer (EDL) when the porous electrodes are polarized. In this study, three types of activated carbon cloth (ACC) with different pore-size distributions were used to study the effect of pore characteristics on electrosorption during CDI. Removal of seven different monovalent ions was examined for each ACC in batch reactors under 5 different combinations of applied potential and ionic strength. Results show underlying sorption mechanisms in the meso- and micro-pores were different. Electrosorption in the mesopores is influenced by partially-distorted EDL caused by EDL overlapping. Sorption capacity increased with increasing applied potential or ionic strength as overlapping effects were reduced. In contrast, EDL in the microporous regions could be highly distorted resulting in enhanced sorption capacity, which cannot be adequately described using the classic EDL theories. Electrosorption density (i.e., sorption capacity normalized by pore volume) decreased as the mesoporosity-to-microporosity ratio increased. These results are in agreement with those obtained using mathematical modeling by other recent CDI studies. Charge efficiency values were between 20% and 40% and appear to be substantially influenced by Faradaic reactions and ion desorption from the electrode surfaces. These findings suggest that pore-size distribution of electrode materials, especially the meso/microporosity ratio, should be optimized for the removal of targeted ions by CDI and well characterized to conduct more precise CDI modeling.

Integrated sorption and diffusion model for bentonite. Part 2: porewater chemistry, sorption and diffusion modeling in compacted systems

It is important to understand the coupled processes of sorption and diffusion of radionuclides (RNs) in compacted bentonite, and to develop mechanistic models that can aid in the prediction of the long-term performance of geological disposal systems of radioactive waste. The integrated sorption and diffusion (ISD) model was developed based on the consistent combination of clay–water interaction, sorption and diffusion models. The diffusion model based on the electrical double layer theory describing relative ionic concentrations and viscoelectric effects at the negatively charged clay surface was coupled with porewater chemistry and sorption models. This ISD model was successfully tested for various actinides with a complex chemistry (Np(V), Am(III), U(VI) under conditions where variably charged carbonate complexes are formed) considered in Part 1, by using published diffusion and sorption data (Da, De, Kd) as a function of partial montmorillonite density. Quantitative agreements were observed by considering uncertainty in porewater chemistry and dominant aqueous species. It can therefore be concluded that the ISD model developed here is able to adequately explain the sorption and diffusion behavior of various RNs with a complex chemistry in compacted bentonites. The performed modeling indicates that uncertainties are mainly related to porewater chemistry and RN speciation and that these parameters need to be carefully evaluated.

Diffusion and sorption of Cs+, Na+, I− and HTO in compacted sodium montmorillonite as a function of porewater salinity: Integrated sorption and diffusion model

Montmorillonite clay is an important component of barrier materials such as bentonites and argillaceous rocks for the safe geological disposal of radioactive waste. The diffusion and sorption behaviors of cationic Cs+ and Na+, anionic I− and neutral tritiated water (HTO) tracers in compacted montmorillonite were investigated as a function of porewater salinity by experimental and modeling approaches. The effective diffusivities of these tracers were measured by the through-diffusion method coupled with multiple curve analysis including depth profiles, and typical salinity-dependent cation excess and anion exclusion effects were shown. The distribution coefficients for Cs+ and Na+ obtained by through-diffusion tests were sensitive to salinity because of competitive ion exchange and were in good agreement with those obtained by batch sorption tests. However, trends in the apparent diffusivities of Cs+ and Na+ were mostly independent of salinity.A diffusion model based on a simplified pore structure and electrical double layer theory, describing the change of ionic concentration and viscoelectric effects caused by the electrostatic interaction with negatively charged clay surfaces, could quantitatively account for the cation excess and anion exclusion behaviors and their salinity dependence. The trends in the distribution coefficients predicted by the ion exchange sorption model show good agreement with the measured values as a function of salinity. Salinity-independent apparent diffusivities could be interpreted as results of the coupled effects of the drastic dependence of diffusion and sorption on salinity. The difference in the diffusion and sorption behaviors between Cs+ and Na+ can be explained by the difference in the sorption mechanism (inner- and outer-sphere) and their representation in the diffusion model (cation excess diffusion). This integrated sorption and diffusion model was further demonstrated as being applicable to the diffusion data of these monovalent cations and anions in compacted bentonites over a wide range of compaction.

Diffusion Modeling in Compacted Bentonite Based on Modified Gouy-Chapman Model

ABSTRACTThe integrated sorption and diffusion (ISD) model has been developed to quantify radionuclide transport in compacted bentonite. The current ISD model, based on averaged pore aperture and the Gouy-Chapman electric double layer (EDL) theory can quantitatively account for diffusion of monovalent cations and anions under a wide range of conditions (e.g., salinity, bentonite density). To improve the applicability of the current ISD model for multivalent ions and complex species, the excluded volume effect and the dielectric saturation effect were incorporated into the current model, and the modified Poisson-Boltzmann equations were numerically solved. These modified models had little effect on the calculation of effective diffusivity of Sr2+/Cs+/I−. On the other hand, the model, modified considering the effective electric charge of hydrated ions, calculated using the Gibbs free energy of hydration, agreed well with the diffusion data including those of Sr2+.

Observation of significant steric, valence and polarization effects and their interplay: a modified theory for electric double layers

Presented electric double layer theory achieves comparable results with experiments by including steric, polarization and valence effects and is applicable to all ions contrasting the classical theory only to hydrogen ions, which thus capably describes the selective adsorption on charged surfaces and is expected to clarify specific ion effects.

A review of molecular modelling of electric double layer capacitors

Electric double-layer capacitors are a family of electrochemical energy storage devices that offer a number of advantages, such as high power density and long cyclability. In recent years, research and development of electric double-layer capacitor technology has been growing rapidly, in response to the increasing demand for energy storage devices from emerging industries, such as hybrid and electric vehicles, renewable energy, and smart grid management. The past few years have witnessed a number of significant research breakthroughs in terms of novel electrodes, new electrolytes, and fabrication of devices, thanks to the discovery of innovative materials (e.g. graphene, carbide-derived carbon, and templated carbon) and the availability of advanced experimental and computational tools. However, some experimental observations could not be clearly understood and interpreted due to limitations of traditional theories, some of which were developed more than one hundred years ago. This has led to significant research efforts in computational simulation and modelling, aimed at developing new theories, or improving the existing ones to help interpret experimental results. This review article provides a summary of research progress in molecular modelling of the physical phenomena taking place in electric double-layer capacitors. An introduction to electric double-layer capacitors and their applications, alongside a brief description of electric double layer theories, is presented first. Second, molecular modelling of ion behaviours of various electrolytes interacting with electrodes under different conditions is reviewed. Finally, key conclusions and outlooks are given. Simulations on comparing electric double-layer structure at planar and porous electrode surfaces under equilibrium conditions have revealed significant structural differences between the two electrode types, and porous electrodes have been shown to store charge more efficiently. Accurate electrolyte and electrode models which account for polarisation effects are critical for future simulations which will consider more complex electrode geometries, particularly for the study of dynamics of electrolyte transport, where the exclusion of electrode polarisation leads to significant artefacts.

Generalization of the Gouy-Chapman-Stern model of an electric double layer for a morphologically complex electrode: Deterministic and stochastic morphologies

We generalize the linearized Gouy-Chapman-Stern theory of an electric double layer for morphologically complex and disordered electrodes. An equation for capacitance is obtained using a linear Gouy-Chapman or Debye-Hückel equation for the potential near the complex-geometry electrode-electrolyte interface. The effect of the surface morphology of an electrode on an electric double layer is obtained using multiple scattering formalism in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length to the local principal radii of curvatures of the surface. We also include a contribution of a compact layer, which is significant in the overall prediction of capacitance. Our general results are analyzed in detail for two special morphologies of electrodes, i.e., a nanoporous membrane and a forest of nanopillars. Variations of local shapes and global size variations due to residual randomness in morphology are accounted for as curvature fluctuations over a reference shape element. In particular, the theory shows that the presence of geometrical fluctuations in porous systems causes an enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. This theory is further extended to include contributions to capacitance from adsorption of ions and electrode material due to electronic screening. Our predictions are in reasonable agreement with recent experimental measurements on supercapacitive microporous and mesoporous systems.

Effects of solvent-mediated nonelectrostatic ion-ion interactions on a streaming potential in microchannels and nanochannels

Here, we capture the consequences of solvent-mediated nonelectrostatic ion-ion interactions, coupled with the considerations of finite-sized effects of the ionic species, on electrokinetic transport in narrow fluidic confinements. We consider pressure-driven flow in microchannels and nanochannels in the presence of electrical double layer effects and analyze the establishment of a streaming potential as mediated by a Yukawa-like pair potential that integrates the ion specificity with the governing nonelectrostatic interactions. We bring out the influences of these interactions on electroviscous effects manifested due to the establishment of the streaming potential. Our considerations provide a plausible explanation for the gross overestimation of electrokinetic energy conversion efficiencies as predicted by classical electrical double layer theories that ignore nonelectrostatic interactions between the ionic species.

Debye–Falkenhagen dynamics of electric double layer in presence of electrode heterogeneities

A phenomenological theory of electric double layer (EDL) polarization of an electrode (in the absence and presence of electroactive species) is obtained using the Debye–Falkenhagen equation for the potential. The influence of surface heterogeneities on the compact layer causes the distribution in relaxation time, resulting in constant phase element (CPE) response. This contribution of the compact layer is included through the current balance boundary constraint at the outer Helmholtz plane. The results for the impedance and the capacitance are obtained in terms Debye screening length and dynamic polarization length which is dependent on the surface heterogeneity parameter. At frequencies less than the characteristic compact layer relaxation frequency, the EDL is controlled by the compact layer dynamics and shows CPE response. The intermediate frequencies show the emergence of pseudo-Gerischer and pseudo-Warburg like behavior for systems with lower concentration and lower diffusion coefficients of ions. EDL behaves like a resistor at larger frequencies. Theoretical results capture various observations in the experimental capacitance dispersion data.

A coupled mechanical and chemical damage model for concrete affected by alkali–silica reaction

To model the complex degradation phenomena occurring in concrete affected by alkali–silica reaction (ASR), we formulate a poro-mechanical model with two isotropic internal variables: the chemical and the mechanical damage. The chemical damage, related to the evolution of the reaction, is caused by the pressure generated by the expanding ASR gel on the solid concrete skeleton. The mechanical damage describes the strength and stiffness degradation induced by the external loads. As suggested by experimental results, degradation due to ASR is considered to be localized around reactive sites. The effect of the degree of saturation and of the temperature on the reaction development is also modeled. The chemical damage evolution is calibrated using the value of the gel pressure estimated by applying the electrical diffuse double-layer theory to experimental values of the surface charge density in ASR gel specimens reported in the literature. The chemo-damage model is first validated by simulating expansion tests on reactive specimens and beams; the coupled chemo-mechanical damage model is then employed to simulate compression and flexure tests results also taken from the literature.

電気二重層の計算化学

The theory of electrical double layer has 100 year history since Gouy and Chapman proposed. Since then the three-dimensional numerical solutions of Poisson-Boltzmann (PB) equation were widely applied for many systems such as chemically modified electrode or the electrode with micro-pore. However there are some shortcomings in PB theory for strongly electrified interface, ion-ion interaction in concentrated solution, and multivalent counter ions. In this article the canonical Monte Calro simulation with primitive model, which is simplest way to simulate the electrical double layer, is introduced.

Microscopic mechanism of periodical electroosmosis in reservoir rocks

Based on the electric double layer (EDL) theory and the momentum equation governing the electroosmosis flow, this paper presents an analytical solution to the periodical electroosmosis with a parallel straight capillary bundle model of reservoir rocks to reveal the microscopic mechanism of the electroosmotic flows in rocks. The theory shows that both the frequency dispersion characteristics of the macroscopic electroosmotic Darcy velocity in unsealed rocks and the electroosmotic pressure coefficient in sealed rocks depend on the porosity and electrochemical properties of reservoir rocks. The mathematical simulation indicates that the distribution of the periodical electroosmotic velocity is wavelike in the rock pore. The greater the porosity is, the greater electroosmotic the Darcy velocity and the smaller electroosmotic pressure coefficient are generated. The module values of the electroosmotic Darcy velocity and the electroosmotic pressure coefficient increase with the decreasing solution concentration or the increasing cation exchange capacity without affecting the phase of the electroosmotic Darcy velocity.

Modeling and experimental investigation for electrolytic corrosion prevention in high frequency micro EDM using deionized water

The characteristics of the prevention of electrolytic corrosion during micro electrical discharge machining (EDM) using deionized water and high frequency bipolar pulse were investigated. Electrolytic corrosion during micro EDM using deionized water was analyzed using an equivalent electrical circuit based on the electrical double layer theory. Based on the analysis and experimental verification, a narrow positive pulse duration should be provided to the workpiece to prevent corrosion. A negative voltage with zero average applied voltage (Vavg, app) is also essential for this purpose. If Vavg, app is positive or negative, electrolytic corrosion occurs on the workpiece or tool, respectively. Micro holes and 3D structures without corrosion were successfully fabricated using a high frequency bipolar pulse with a pulse duration of 0.2 μs and a period of 1 μs, as well as Vavg, app = 0 V.

Experimental measurements of short-term adsorption of Acidithiobacillus ferrooxidans onto chalcopyrite

The influencing factors in adsorption such as adsorption time, pulp concentration, bacterial concentration, pH as well as ionic strength were investigated to explore the relationship among them and bacterial adsorption. The adsorption was a rapid process for bacterial adhesion to chalcopyrite. The extent of adsorption increased with increasing initial bacterial concentration and pulp concentration. The optimal pH for Acidithiobacillus ferrooxidans adsorption onto chalcopyrite surfaces was in the range of pH 1-3. The increase of ionic strength led to decrease in bacterial adsorption, which can be well explained by electric double layer theory. The adsorption behavior appeared to be controlled by both hydrophobic and electrostatic interactions at the interface of bacteria and mineral.

High frequency micro wire EDM for electrolytic corrosion prevention

Electrolytic corrosion occurs if water is used as a dielectric fluid during micro EDM process, ultimately resulting in serious inaccuracies on a machined part. In order to prevent electrolytic corrosion, a high frequency AC power source was developed for micro wire EDM processes. This study presents an analysis based on the electrical double layer theory. Based on this theory, the effects of electrolytic corrosion decrease as the AC power source frequency increases. As an anticorrosion power source, a 13.56 MHz AC power source was developed using class E power amplifier. This new power source produced discharge current pulses with a peak of 1.1 A and a duration of 20 ns. With the new power source, micro shafts were successfully machined by micro wire EDM using tap water without exhibiting electrolytic corrosion. In comparison to a conventional RC type power source, the high frequency AC power source with tap water ensured 7 times higher material removal rate while maintaining similar surface roughness (< 0.1 μm Ra).

Electrostatic Discharge of Aviation Oil and Damage Protection

The generation of static electricity of aviation oils is based on the theory of double electrical layer on the boundary layer formed by charged particles in the liquid.The theory of electric double layer is used to explain reasons for the static electricity of aviation oil and expound main factors affecting its generation including conductivity, impurities, water, pipeline material and wall roughness; propose in details measures on the prevention of static electricity of aviation oil, including adding anti-static additives, controlling the oil flow rate, fuel control mode, electrostatic grounding and bridging and installing the static moderator and static eliminator devices, etc.

Unifying Model for the Electrokinetic and Phase Behavior of Aqueous Suspensions Containing Short and Long Amphiphiles

Aqueous suspensions containing oppositely charged colloidal particles and amphiphilic molecules can form fluid dispersions, foams, and percolating gel networks, depending on the initial concentration of amphiphiles. While models have been proposed to explain the electrokinetic and flotation behavior of particles in the presence of long amphiphilic molecules, the effect of amphiphiles with less than six carbons in the hydrocarbon tail on the electrokinetic, rheological, and foaming behavior of aqueous suspensions remains unclear. Unlike conventional long amphiphiles (≥10 carbons), short amphiphiles do not exhibit increased adsorption on the particle surface when the number of carbons in the molecule tail is increased. On the basis of classical electrical double layer theory and the formerly proposed hemimicelle concept, we put forward a new predictive model that reconciles the adsorption and electrokinetic behavior of colloidal particles in the presence of long and short amphiphiles. By introducing in the classical Gouy-Chapman theory an energy term associated with hydrophobic interactions between the amphiphile hydrocarbon tails, we show that amphiphilic electrolytes lead to a stronger compression of the diffuse part of the electrical double layer in comparison to hydrophilic electrolytes. Scaling relationships derived from this model provide a quantitative description of the rich phase behavior of the investigated suspensions, correctly accounting for the effect of the alkyl chain length of short and long amphiphiles on the electrokinetics of such colloidal systems. The proposed model contributes to our understanding of the stabilization mechanisms of particle-stabilized foams and emulsions and might provide new insights into the physicochemical processes involved in mineral flotation.

Experimental and Modeling Study on Diffusion of Selenium under Variable Bentonite Content and Porewater Salinity

Effective diffusion coefficients of selenium through bentonite/sand mixtures were obtained by the through-diffusion method under reducing conditions where selenium was dissolved as HSe− and Se4 2–. Experiments were carried out under variable bentonite content and porewater salinity. Bentonite contents in bentonite/sand mixtures varied from 20 to 70 wt%. The salinities of experimental solutions varied from 0.05 to 0.5 mol dm−3, simulating brackish groundwater and seawater. Effective diffusion coefficients were also obtained under anaerobic conditions where the dominant selenium species was determined to be SeO3 2–. The effective diffusion coefficients of selenium species decreased with increasing bentonite content and with decreasing salinity. This tendency is primarily due to anion exclusion that was caused by the negative surface charge of montmorillonite. A diffusion model for anionic species was developed based on the electric double layer theory and the pore diffusion model, to evaluate the diffusion behaviors of HSe−, Se4 2–, and SeO3 2– in bentonite porewater. In this model, pores in bentonite/sand mixtures are assumed to consist of two types of space; one is the space between mineral particles and the other is the space between layers of montmorillonite. The scope of application of this model is limited to less than or equal to 1,600 kg m−3 in dry density. The effective diffusion coefficients of selenium species predicted using this model showed good agreement with experimentally measured ones.

Structure of Hydrated Sodium Ions and Water Molecules Adsorbed on the Mica/Water Interface

Solid/liquid interfaces control many physical and chemical properties such as electrophoresis, friction, and dispersion of colloid particles. Atomic distribution at solid/liquid interfaces has a strong correlation with these properties, and understanding these structures is necessary to establish the fundamental physics and chemistry of the solid/liquid interfaces. In this study, we have investigated the structure of mica/aqueous NaCl solution interfaces using surface X-ray scattering measurements and molecular dynamics simulations. The sub-Å-scale atomic distribution of the mica/aqueous NaCl solution interface is revealed as a function of the distance normal to the interface. The density of the NaCl solution oscillates to be 12 Å apart from the surface observed by the surface X-ray scattering measurements. Molecular dynamics simulations indicate that the oscillation corresponds to hydrated Na+ ions, adsorbed water molecules, and water molecules surrounding the hydrated ions. The structure helps to understand the origin of repulsive force and tribological properties between mica surfaces immersed in the NaCl solution and to develop electric double-layer theory.

Effect of Electric Fields on the Ultrafast Vibrational Relaxation of Water at a Charged Solid–Liquid Interface as Probed by Vibrational Sum Frequency Generation

The effect of the surface electric field on the ultrafast vibrational dynamics of interfacial water is studied using IR pump-sum frequency generation (SFG) probe spectroscopy. At very low salt concentrations, a vibrational lifetime (T1) of ∼200 fs, similar to bulk H2O, is observed for the O–H stretch at the H2O/silica interface at pH 6, where the silica surface is negatively charged. However, T1 increases to ∼700 fs by increasing the NaCl concentration to 0.01 M. The observation of similar dynamics for a range of salt concentrations, associated with different extensions of the electric field, suggest that the surface electric field is screened faster than predicted by classical electrical double-layer theories and that the Debye length may not be the appropriate measure of the depth sampling of the SFG response. An interfacial excess of cations is hypothesized to explain the faster decay of the static electric field than predicted by the Gouy–Chapman theory.