Electrical Double Layer Theory Research Articles

A Century of Research Leading to Understanding the Scientific Basis of Selective Mineral Flotation and Design of Flotation Collectors

The design and development of selective flotation collectors has been the key to the remarkable success of flotation in beneficiating complex, difficult-to-process ores. Sustained research efforts in the field over the past hundred years have led to delineating the scientific basis of selective mineral flotation in terms of the crystal chemistry and the surface and colloid chemistry of minerals including their solubility, and the aqueous solution chemistry of added reagents. It is now well-established that the electrical double layer theory (EDL) is the most powerful means of quantifying the relative strength of mineral-reagent interactions in the case of nonsulfide minerals. We illustrate the utility and the power of the EDL in delineating the science underlying selective mineral flotation with the help of a few examples taken from our own work, in particular on the selective flotation of rare-earth minerals (bastnaesite) from associated semisoluble minerals (barite and calcite) using alkyl hydroxamate collectors and the flotation separation of lithium-containing minerals (spodumene) from associated alumino-silicate minerals with oleate (fatty acids). Both of these mineral separation systems are of contemporary research interest and of immense value to the industry today. Recent advances in utilizing molecular modeling computations, particularly in the context of quantifying the effect of crystal chemistry and the relative distribution of adsorption sites available on mineral cleavage planes, are also reviewed.

A Comparative Study of Force Measurements in Solution Using Micron and Nano Size Probe

Atomic force microscopy (AFM) is a device that is used for not only high-resolution imaging but also used for measuring forces. It is possible to quantify the surface density change for both colloid and nano probe as well as silica surface. By changing the quantity of ions within a potassium chloride solution, it then becomes possible to evaluate the quantity of ions that attach themselves to AFM colloid probe, nano probe and silica samples. In this study, the force was measured between AFM probes and silica surface in different ionic concentrations. Two different types of AFM probe were used: a colloid probe with a radius of 500 nano-meters and a nano probe with a radius of 10 nano-meters. This study is focused on measuring how the force magnitude, especially electrical double layer force, varied between the two types of probes by changing ionic concentrations. For all test trials, the results agreed with the electrical double layer theory. Although the micron probe was almost an exact match for all ranges, the nano probe was closest within its short-range forces. This is attributed to the formula use when analyzing the electrical double layer force. Because the formula was originally calculated for the micron probe, the shape and size of the nano probe created too many variables for an exact match. Along with quantifying the forces, this experiment allowed for an observation of Van der Waals force making it possible to calculate the Hamaker constant. Conclusively, all results show that the obtained surface charge density increases as the ionic concentration increases. In addition, through the comparison of the results obtained from the nano-sized probe and the micron-sized probe, it was concluded that nano size probe mapped higher surface charge density above the silica surface than the micron-sized probe under the same conditions.

Role of divalent ions, temperature, and crude oil during water injection into dolomitic carbonate oil reservoirs

Although wettability alteration has been shown to be the main control mechanism of Low Salinity and Smart Water (LS-SmW) injection, our understanding of the phenomena resulting in wettability changes still remains incomplete. In this study, more attention is given to direct measurement of wettability through contact angle measurement at ambient and elevated temperatures (28 °C and 90 °C) during LS-SmW injection to identify trends in wettability alteration. Zeta potential measurement is utilized as an indirect technique for wettability assessment in rock/brine and oil/brine interfaces in order to validate the contact angle measurements. The results presented here bring a new understanding to the effect of temperature and different ions on the wettability state of dolomite particles during an enhanced oil recovery process. Our observations show that increasing temperature from 28 °C to 90 °C reduces the contact angle of oil droplets from 140 to 41 degrees when Seawater (SW) is injected. Besides, changing crude oil from crude-A (low asphaltene content) to crude-B (high asphaltene content) contributes to more negative surface charges at the oil/brine interface. The results suggest that the sulphate ion (SO42-) is the most effective ion for altering dolomite surface properties, leading to less oil wetness. Our study also shows that wettability alteration at ambient and elevated temperatures during LS-SmW injection can be explained by Electrical Double Layer (EDL) theory.

Exploring the Distribution of Zn2+ in Inner and Outer Helmholtz Planes of the Electrical Double Layer of Soil based on Wien Effect

Core Ideas Wien effect measurements assess adsorbed cations distribution over the Helmholtz planes of the electrical double layer. Assessing cation distributions in the electrical double layer improves bioavailability predictions for plant nutrients and pollutant metals. Most of the zinc adsorption takes place in the inner Helmholtz plane layer and occurs via chemical interactions. The classical electrical double layer (EDL) theory explains the interaction between ions and charged soil colloidal particles, playing an importance role in the bioavailability and toxicity of ions in soils, which are of agricultural and environmental concern. A new approach based on extrapolating measurements of suspension Wien effect is suggested to determine the adsorbed ions distribution in the different compartments of the EDL. The new approach was applied to assess Zn2+ distribution in the EDL of Zn‐saturated soil colloids. The results showed that more than 84% of Zn2+ was adsorbed via chemical interactions and located in the inner Helmholtz plane layer. The remaining Zn2+ fraction was electrically adsorbed and distributed in the outer Helmholtz plane layer (0.3 to 2.1%) and in the Gouy–Chapman diffuse layer (7.4 to 15.0%). Independently, the results of linear combination fitting of extended x‐ray absorption fine structure (EXAFS) spectra indicated that the contents of outer‐sphere Zn in one paddy soil and the boggy soil were consistent with the proportions of Zn2+ electrostatically interacting with the soil colloids based on the extrapolation of the suspension Wien effect method, while the contents of outer‐sphere Zn in a second paddy soil, the yellow cinnamon soil, and the yellow brown soil was overestimated by the EXAFS method. The approach proposed in this paper to assess specific and electrostatic adsorption deepens our understanding of metal sorption processes in soils and reinforces the adequacy of the Grahame–Stern–Gouy–Chapman model of the EDL to describe the ion distribution in the solid‐water interface.

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.

Micro-electrode system designed to determine H+ concentration distribution at particle-water interface

The current understanding of the particle-water interface relies primarily on the use of electric double layer theory (EDL theory), in which the concentration distribution of ions with distance can be evaluated. However, although EDL theory provides a theoretical and mathematical basis, obtaining direct experimental results is also necessary. In this study, an instrument system set with a designed H+ selective micro-electrode was developed for in situ determination at the particle-water interface, and a preliminary investigation of the H+ concentration distribution at the particle-water interface was enabled using data collection at 1 nm/step. The experimental results agree with EDL theory and provide direct evidence to support its general assumptions. The compressible effect of the electric double layer with an increase in ionic strength is verified, and the defined length of the diffusion layer in this investigation is shown to have an approximately inverse proportion to the square root of ionic strength. The rise in H+ concentration near the particle surface is also determined during interactions between trace Fe3+ and particles. Results indicate that the method reported here can be applied to conduct dynamic in situ observations; based on its excellent performance, this innovative instrument system has great potential for interface mechanism research in the water environment.

A Novel Electrochemical Approach to Study the Interaction of Blinding Agents with Preg-Robbers in Carbonaceous Gold Systems

Preg-robbing usually refers to the adsorption of a gold cyanide complex, i.e. Au(CN)2 −, on the components of a gold ore including carbonaceous materials and other minerals during the gold leaching process (1-3). The adsorption of gold ions on carbonaceous materials is one of the most common phenomenon responsible for gold losses from the cyanide leaching process (1, 4). Depending on the carbon content of the ores, gold losses may reach 90 % of leachable gold due to preg-robbing during cyanidation (5). Chemical blinding agents have previously been investigated to passivate the surface of carbonaceous preg-robbers in the ores, thus reducing the extent of preg-robbing and allowing an increase in gold recovery (1, 3, 6, 7). However, the mechanism by which such agents suppress the ion-adsorption capability of the carbonaceous materials as well as their interactions with other components of the ore, including pyrite, and more importantly, gold, are yet to be fundamentally investigated. The latter process could severely affect final gold recovery if the surface of the gold becomes passivated. This study investigates the effect of various blinding agents on the main components of a gold-containing concentrate: carbon, gold and pyrite. A novel electrochemical approach is employed, i.e. double-layer capacitance measurements combined with electro-oxidation/reduction peaks obtained from cyclic voltammetry tests. Our group is the first to employ the electric double-layer theory to study the preg-robbing capacity of carbonaceous ores with total carbonaceous matter (TCM) contents as low as 0.3 % by weight. Figure 1 shows a comparison between the blinding activity, and durability, of various surfactants and chemical reagents, at different concentrations, on the surface of activated carbon particles over a 24-hour contact period. The capacitance is an indication of how well the chemical reagents have been adsorbed on the activated carbon particles with the lowest capacitance values showing the best surface adsorption. The study reveals that kerosene, Lecithin and Polymax 30 are among the best blinding agents for the activated carbon surfaces in terms of adsorption and durability. Further cyclic voltammetry studies on gold surfaces in alkaline cyanide solutions (with the added blinding agents) have shown that kerosene is the least detrimental to the gold cyanide leaching process, i.e. the electrochemical oxidation reaction for the formation of AuCN complex. Figure 1. A comparative study for the effect of various chemical reagents, i.e. Aristonate H and L, Lecithin, Sodium dodecyl sulfate (SDS), kerosene and Polymax 30, on the ion adsorption capability of the activated carbon particles over 24 hours.

Watervoltaic materials and energy conversion device based on carbon nanomaterials

Harvesting renewable energy and realizing its transformation into electricity is one of the effective ways to solve energy crisis and environmental problems. Hydroenergy has been considered as a promising energy with enormous development potential and application value because of its great advantages of large reserves, wide distribution, and environmentally friendly. Nowadays, the development and utilization of hydropower resources mainly rely on dams, generators and other steel facilities to convert mechanical energy to electricity, with inherent defects of inefficiency and damage to the ecological environment. Therefore, developing new types of watervoltaic materials and devices with diverse application environments, high energy conversion efficiency and low power generation costs is an effective improvement and complement to current water energy utilization condition. Carbon nanotube flow sensor reported by Shankar Ghosh in 2003 first proved the property of carbon nanotube that it can generate electricity in floating water, promoting the research of carbon nanomaterials for power generation in fluids. In the following years, several kind of carbon nanomaterials with different dimensions including carbon nanotube, graphene, et al. were successively confirmed that they have similar character to convert hydroenergy to electricity. Various theories including phonon dragging were proposed to explain this phenomenon as well as the form of electric double layer (EDL) and electrokinetic theory fit it reasonably both in charge transfer and electrical output. Related devices were also designed and assembled to convert energy in liquid water, such as ion water drops, saline solution, et al., to electricity, increasing electrical output from initial a few millivolts to a few volts with a small number of devices in series, which is enough to drive small loads. Subsequently, carbon nanomaterials/polymer conducting composite film was designed to harvest energy from real raindrops and seawater waves, making a great progress of watervoltaic materials and devices in practical application. In addition to converting energy in liquid water, devices based on carbon nanomaterials with different dimensions including quantum dots, nano-carbon film and graphene oxide can harvest energy in water vapor and water evaporation, making it possible to collect and convert energy in gaseous water in nature. Unique structures of holes, elemental concentration gradient, et al. were considered to make contributions to capture water molecule and transfer charges, resulting of the electrical output between electrodes. The combination of nano-carbon electrode and all inorganic perovskite solar cells realizes simultaneous collection of water vapor energy and solar energy, making great significance for implementing multi-energy integration of devices. Since carbon nanomaterials were confirmed to be able to convert extensive water energy in natural into electrical energy, different materials and devices were designed and manufactured to increase the electrical output, improve stability and reduce power generation costs. However, there are also challenges including unclear working mechanism, high environmentally demanding and difficulty to integrate devices on a large scale need to be overcomed in the future. Despite this, watervoltaic materials and energy conversion devices have become promising green energy capture technologies due to their high conversion efficiency, wide application environment, and simple device structure. Improving usability is one of the directions of watervoltaic devices development.

Confinement effects and mechanistic aspects for montmorillonite nanopores

Owing to the ubiquity, critical importance and special properties, confined microenvironments have recently triggered overwhelming interest. In this work, all-atom molecular dynamics simulations have been conducted to address the confinement effects and ion-specific effects for electrolyte solutions within montmorillonite nanopores, where the pore widths vary with a wide range. The adsorption number, structure, dynamics and stability of inner- and outer-sphere metal ions are affected by the change of pore widths (confinement effects), while the extents are significantly dependent on the type of adsorbed species. The type of adsorbed species is, however, not altered by the magnitude of confinement effects, and confinement effects are similar for different electrolyte concentrations. Ion-specific effects are pronounced for all magnitudes of confinement effects (from non- to strong confined conditions), and Hofmeister sequences of outer-sphere species are closely associated with the magnitude of confinement effects while those of inner-sphere species remain consistent. In addition, mechanistic aspects of confinement have been posed using the electrical double layer theories, and the results can be generalized to other confined systems that are ubiquitous in biology, chemistry, geology and nanotechnology.

Electric double layer electrostatics of lipid-bilayer-encapsulated nanoparticles: Toward a better understanding of protocell electrostatics.

Lipid-bilayer-encapsulated nanoparticles (LBLENPs) or NP-supported LBL systems, such as protocells (which are lipid bilayer encapsulated mesoporous silica nanoparticles or MSNPs) have received extensive attention for applications like targeted drug and gene deliveries, multimodal diagnostics, characterization of membrane-geometry sensitive molecules, etc. Very often electrostatic-mediated interactions have been hypothesized to play key roles in the functioning of these LBLENPs. Despite that, very little has been done to theoretically quantify the fundamental electric double layer (EDL) electrostatics of such LBLENPs. In this study, we develop an EDL theory to describe the electrostatics of such LBLENPs. We show that the electrostatics is a manifestation of the charged/dielectric nature of the NP, LBL structure and charging, and the ionic environment in which the LBLENPs are present. We also establish that for certain conditions of charging of the NP one witnesses a most remarkable charge inversion like electrostatics within the LBL membrane or the NP itself. We anticipate that our findings will provide an extremely useful platform for better understanding the fabrication and functioning of such LBLENPs and discuss examples where our theory can be useful.

Electrical Double-Layer Modeling of Different Al-Content on the Performance of AlGaN/GaN HEMTs

The continuous tuning of the sheet electron density in GaN based transistors by Al content in the AlGaN layer is of great technological significance. A new physical model of the sheet electron density is proposed based on the electric double-layer theory. By comparing the sheet electron density and the threshold voltage predicted by the proposed model with those experimental data reported in the literature, a linear dependent relation can be found. Thus, the formation of electric double-layer at the AlGaN/GaN interface could be a physical origin of the sheet electron density. The proposed model predicates that the electric field distribution in the AlGaN layer is inhomogeneous, which agrees well with recently experimental results and still remains to be unraveled. These findings will benefit to better understand the physical mechanism of GaN based transistors and a possibility to improve its performance.

Characterization of Platinum Electrode Surfaces by Electrochemical Surface Forces Measurement

The surface forces between platinum, Pt, electrodes and those between the Pt electrode and mica in aqueous HClO4 were measured at various potentials (E) applied to the electrodes using an electrochemical surface forces apparatus (EC-SFA). This apparatus uses the twin-path surface forces apparatus, recently developed for opaque samples. The influence of the proton adsorption on the surface interactions was studied. The Pt electrodes were prepared by the template-stripping procedure using glass templates. The electrode surfaces were smooth (RMS roughness: 0.26 nm for a 5 μm × 5 μm area) and polycrystalline based on the atomic force microscopy and cyclic voltammetry results, respectively. When the applied potential E was decreased from 0.5 to 0.2 V (vs Ag/AgCl), the electric double layer (EDL) repulsion between the Pt electrodes decreased. The absolute values of the surface potentials, |ψ0|, calculated using the EDL theory were 58 and 43 mV at E = 0.5 and 0.2 V, respectively. The EDL force at E = 0.2 V was t...

Enhanced breakdown strength of polymer composites by low filler loading and its mechanisms

Dielectric polymer materials with high energy density and low dielectric loss are highly desired for applications in advanced electronic devices and electric power systems. Here, we report on flexible dielectric composites using semiconductor nanoparticles as fillers and polyvinylidene fluoride (PVDF) as a matrix. The introduction of a small amount of ZnO filler results in significantly enhanced voltage breakdown strength and energy density in comparison with pure PVDF. Based on the multi-core model, combining the electric double layer theory and the interface contact theory, we investigate mechanisms and come out with that transportation of carriers under applied voltage is regulated by the charged interface, which delays the formation of the conduction path. Besides, the electric field imposed on the composites is alleviated by the internal micro-electric field.

Modelling of diffusion behavior of ions in low-density and high-density calcium silicate hydrate

To investigate the relationship between morphology and specific ion transport properties in low-density (LD) and high-density (HD) calcium-silicate-hydrate (C-S-H), a numerical method of directly achieving diffusivities is developed. Firstly, a multiscale structural model is proposed to reconstruct C-S-Hs in which self-similarity and quantitative physical properties are compared to experimental results. Subsequently, electrical double layer (EDL) theory is introduced into analysis of ion transport in pore solution. The quantitative analysis of various influence factors of EDL on ion diffusivities in pore solution is carried out and average diffusivity in pore solution is also obtained. Moreover, a numerical method for solving Fick’s first law equation is performed on the simulated C-S-H structures to obtain numerous diffusivities of common ions in C-S-H. Finally, the significant parameter for durability in reinforcement concrete, chloride diffusivity in hardened cement paste, is predicted using simulated diffusivities in C-S-Hs, based on a multiscale method. It is found that compared to the atomic force microscope image and surface area of C-S-H, this self-similar model can well reconstruct real C-S-H structures. In addition, the influence factors of EDL including overlapping diffuse layer, relative potential, cation/anion, valence, zeta potential and bulk solution have great effects on ion diffusivities, which demonstrates EDL effects cannot be ignored when investigating ion transport behavior in C-S-H. Furthermore, using an appropriate case of pore solution with diffusivities of 8.2×10−12m2/s in LD C-S-H and 2.0×10−13m2/s in HD C-S-H, estimated chloride diffusivities in cement pastes agree well with measured values, which can indirectly indicate this modelling work is reasonable.

Survey on Ion Sensitive Field Effect Transistor from the View Point of pH Sensitivity and Drift

Objectives: To study on the development of ISFET, encompassing the site binding concept, the electrical double layer theory and further investigation on the improvement of pH sensitivity and effect of drift on sensitivity. Methods/Analysis: In this study, analysis of pH sensitivity based on the usage of different membranes, structures and various techniques employed are discussed. In addition, it also enunciates about few techniques which aim to improve the pH sensitivity beyond Nernst limitation. Methods such as Rapid Thermal Nitridation (RTN), oxygen-plasma treatment, multilayer dielectrics stacking, radio frequency sputtering, electrostatic screening and Inner Metal Dielectric (IMD) overlying external gate, charge-accumulation technique and compensation techniques to suppress drift effect have been discussed. Findings: The Nernst limit for an ISFET is defined as 59 mV/pH. Various reported works suggest the use of techniques such as charge-accumulation, capacitive coupling and use of a second gate layer leading to sensitivity up to 2.25 V/pH. Secondary effect such as drift that can deteriorate the sensitivity can be suppressed using high k dielectric materials in sensing layer. External circuitry has also been reported that compensates this effect. With improved sensitivity and suppressed drift the ISFET based biosensors can generate stable output in both in-vivo and in-vitro measurements. Novelty/Improvement: Study on key issues surrounding the ISFET sensors such as sensitivity and drift has been carried out in consensus with the current reports and findings in various scientific journals. In the realm of sensor development this work can act as a stepping stone for researchers thriving to fabricate devices with higher sensitivity and better stability. Keywords: Drift, Electrical Double Layer, Ion Sensitive Field Effect Transistor, Sensor, Sensitivity, Site Binding

Reconciling DLVO and non-DLVO Forces and Their Implications for Ion Rejection by a Polyamide Membrane.

Recognizing the significance of surface interactions for ion rejection and membrane fouling in nanofiltration, we revise the theories of DLVO (named after Derjaguin, Landau, Verwey, and Overbeek) and non-DLVO forces in the context of polyamide active layers. Using an atomic force microscope, surface forces between polyamide active layers and a micrometer-large and smooth silica colloid were measured in electrolyte solutions of representative monovalent and divalent ions. While the analysis of DLVO forces, accounting for surface roughness, provides how surface charge of the active layer changes with electrolyte concentration, scrutiny of non-DLVO hydration forces gives molecular insight into the composition of the membrane-solution interface. Importantly, we report an expansion of the diffuse layer at high ionic strength, consistent with the recent development of the electrical double layer theory, but in contrast to the widely accepted phenomenon of aggregation in the secondary minimum. Further, the enhanced repulsion acting on modified membranes via polyelectrolyte adsorption can be quantitatively predicted by DLVO and non-DLVO forces. This work serves to solve past misunderstandings about the interaction forces acting on nanofiltration membranes, and it provides guidance for future work on the relation between surface properties and rejection mechanisms and fouling.

Toward the Theory of an Electric Double Layer in a Plasma

The conditions for the appearance of a double layer are considered. A theoretical description of the latter is given. Based on experimental data on probe diagnostics of oxygen and helium plasmas, a self-consistent theory of the volume charge layer is being constructed. Analysis of the phenomenon of screening the probe potential by charged particles is carried out. The procedure used for correcting the particle temperature determined by the logarithmic operation method is presented. The problem of application of Langmuir probes, the 3/2 law, and of the theory of electric double layer in a plasma is discussed.

Classical density functional theory and Monte Carlo simulation study of electric double layer in the vicinity of a cylindrical electrode

We have performed extensive Monte-Carlo simulations and classical density functional theory (DFT) calculations of the electrical double layer (EDL) near a cylindrical electrode in a primitive model (PM) modified by incorporating interionic dispersion interactions. It is concluded that (i) in general, an unsophisticated use of the mean field (MF) approximation for the interionic dispersion interactions does not distinctly worsen the classical DFT performance, even if the salt ions considered are highly asymmetrical in size (3:1) and charge (5:1), the bulk molar concentration considered is high up to a total bulk ion packing fraction of 0.314, and the surface charge density of up to 0.5 C m−2. (ii) More specifically, considering the possible noises in the simulation, the local volume charge density profiles are the most accurately predicted by the classical DFT in all situations, and the co- and counter-ion singlet distributions are also rather accurately predicted; whereas the mean electrostatic potential profile is relatively less accurately predicted due to an integral amplification of minor inaccuracy of the singlet distributions. (iii) It is found that the layered structure of the co-ion distribution is abnormally possible only if the surface charge density is high enough (for example 0.5 C m−2); moreover, the co-ion valence abnormally influences the peak height of the first counter-ion layer, which decreases with the former. (iv) Even if both the simulation and DFT indicate an insignificant contribution of the interionic dispersion interaction to the above three ‘local’ quantities, it is clearly shown by the classical DFT that the interionic dispersion interaction does significantly influence a ‘global’ quantity like the cylinder surface-aqueous electrolyte interfacial tension, and this may imply the role of the interionic dispersion interaction in explaining the specific Hofmeister effects. We elucidate all of the above observations based on the arguments from the liquid state theory and at the molecular scale.

A one-dimensional model for water desalination by flow-through electrode capacitive deionization

Capacitive deionization (CDI) is a fast-emerging water desalination technology in which a small cell voltage of ~1V across porous carbon electrodes removes salt from feedwaters via electrosorption. In flow-through electrode (FTE) CDI cell architecture, feedwater is pumped through macropores or laser perforated channels in porous electrodes, enabling highly compact cells with parallel flow and electric field, as well as rapid salt removal. We here present a one-dimensional model describing water desalination by FTE CDI based on modified Donnan electric double layer theory, and employing simple cell boundary conditions derived via scaling arguments. We further provide a comparison of model results to data obtained from a custom-built FTE CDI cell. We show good model-to-equilibrium data fits with reasonable values for fitting parameters such as the Stern layer capacitance, micropore volume, and attraction energy. Further, the model well-describes dynamic effluent salt concentration and cell current obtained from the experimental cell. Thus, we demonstrate that from an engineering modeling perspective, an FTE CDI cell can be described with simpler one-dimensional models, unlike more typical flow-between electrodes architecture where 2D models are required.

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 ...