Classical Electrical Double Layer Research Articles

Nanoscale Investigations of the Electric Double Layer in Protic Ionic Liquids

A hydrogen-based energy storage system will be the backbone of a future energy grid using renewable energies. Polymer electrolyte membrane fuel cells (PEMFCs) are a key element in this energy system as they convert chemical energy stored as hydrogen into electrical energy on demand. PEMFC systems, especially for automotive application, could be significantly improved by increasing the operation temperature above 100 °C. Protic ionic liquids are promising candidates as non-aqueous protic electrolytes for next-generation high-temperature polymer electrolyte membrane fuel cells. These fuel cells have a target operation temperature of 160 °C and allowing for a more efficient water and heat management compared to conventional Nafion®-based PEMFCs, which operate at temperatures below 80 °C [1].In order to ensure a reliable and efficient operation an electrolyte with a high electrochemical performance and stability has to be selected. For this purpose, protic ionic liquids have been proposed and first fuel cell tests have shown promising results [2]. Hence, we aim on understanding the properties of this class of novel electrolytes on an atomistic level, which would allow designing suitable material combinations and predicting their properties for an efficient fuel cell operation. As ionic liquids are molten salts, which are liquid below 100 °C, their electrochemical properties differ significantly from those of aqueous solutions. Instead of a classical electric double layer, which can be described by the models provided by Helmholtz, Gouy-Chapman and Stern, the interface structure formed between the electrolyte and a charged electrode is governed by the interplay between coulomb interaction and steric effects between the (large) molecular ions [3]. In order to understand the formation of this double layer on a metallic electrode, we employ atomic force microscopy and infrared spectroscopy in combination with molecular dynamics simulations. Our results show that in the interface region between the prototype protic ionic liquid diethylmethylammonium triflate ([Dema][TfO]) and a Pt electrode, a dense layered structure consisting of alternating anion and cation layers is present, that extends several nanometres into the bulk of the electrolyte [4]. The composition and structure changes with applied potential due to a preferential attraction of anions or cations depending on the electrode charge. When water is added to the ionic liquid, the layered structure becomes distorted and water molecules appear near the electrode. Since the presence of water will also influence the relevant electrochemical processes such as the oxygen reduction reaction (ORR), the analysis of the double layer structure on an atomistic scale is necessary in order to understand the subtle interactions between the molecules in the electrolyte and to propose design routes for novel more efficient ionic liquid-based electrolytes. Wippermann, K.; Suo, Y.; Korte, C. Oxygen Reduction Reaction Kinetics on Pt in Mixtures of Proton-Conducting Ionic Liquids and Water: The Influence of Cation Acidity. J. Phys. Chem. C 2021, 125, 4423–4435, doi:10.1021/acs.jpcc.0c11374.Skorikova, G.; Rauber, D.; Aili, D.; Martin, S.; Li, Q.; Henkensmeier, D.; Hempelmann, R. Protic Ionic Liquids Immobilized in Phosphoric Acid-Doped Polybenzimidazole Matrix Enable Polymer Electrolyte Fuel Cell Operation at 200 °C. Journal of Membrane Science 2020, 608, 118188, doi:10.1016/j.memsci.2020.118188.Rodenbücher, C.; Wippermann, K.; Korte, C. Atomic Force Spectroscopy on Ionic Liquids. Applied Sciences 2019, 9, 2207, doi:10.3390/app9112207.Rodenbücher, C.; Chen, Y.; Wippermann, K.; Kowalski, P.M.; Giesen, M.; Mayer, D.; Hausen, F.; Korte, C. The Structure of the Electric Double Layer of the Protic Ionic Liquid [Dema][TfO] Analyzed by Atomic Force Spectroscopy. International Journal of Molecular Sciences 2021, 22, 12653, doi:10.3390/ijms222312653. Figure 1

Direct Experimental Observations of Ion Distributions during Overcharging at the Muscovite-Water Interface by Adsorption of Rb+ and Halides (Cl- , Br- , I- ) at High Salinity.

Classical electric double layer (EDL) models have been widely used to describe ion distributions at charged solid-water interfaces in dilute electrolytes. However, the chemistry of EDLs remains poorly constrained at high ionic strength where ion-ion correlations control non-classical behavior such as overcharging, i. e., the accumulation of counter-ions in amounts exceeding the substrate's surface charge. Here, we provide direct experimental observations of correlated cation and anion distributions adsorbed at the muscovite (001)-aqueous electrolyte interface as a function of dissolved RbBr concentration ([RbBr]=0.01-5.8 M) using resonant anomalous X-ray reflectivity. Our results show alternating cation-anion layers in the EDL when [RbBr]≳100 mM, whose spatial extension (i. e., ~20 Å from the surface) far exceeds the dimension of the classical Stern layer. Comparison to RbCl and RbI electrolytes indicates that these behaviors are sensitive to the choice of co-ion. This new in-depth molecular-scale understanding of the EDL structure during transition from classical to non-classical regimes supports the development of realistic EDL models for technologies operating at high salinity such as water purification applications or modern electrochemical storage.

(Invited) Bridging the Gap between the Physics and Chemistry of Electric Double Layer

Classical models of electric double layer (EDL) are mostly concerned with ion distributions and their responses to the surface potential that can be regulated by changing either the voltage or the extent of surface ionization. With the help of adjustable parameters, classical EDL models are able to describe diverse physical phenomena including EDL capacitance and ion transport in good agreement with experimental measurements. However, major challenges remain in understanding chemical reactions within EDL important for the rational design and optimization of electrochemical processes such as energy storage and electrocatalysis. In this talk, I will present a molecular-thermodynamic model to predict the charging behavior of ionizable surfaces under various solution conditions. If a solid is non-conductive, the surface reactions can be reliably described with a Langmuir-type model coupled with liquid-state methods to account for the local thermodynamic non-ideality. When a solid is conductive, however, the electronic properties of different surface sites are intrinsically coupled with each other leading to highly correlated surface reactions. While the brute-force prediction of chemical equilibrium at an electrified surface is computationally prohibitive, a combination of the first-principles calculations and coarse-grained modeling provides complemental information that may be useful for diverse electrochemical applications.

Design of VN anode catalyst towards enhanced kinetics for vanadium flow batteries

The all-vanadium flow battery (VFB) constantly suffers from sluggish kinetics for the negative electrodes, restricting its operation ability at high current density. To develop an effective catalyst for anode materials, vanadium nitride (VN) is synthesized to decorate the carbon felt (VN-CF). The unique 1-dimension structure and mesoporous character of VN nanorods are beneficial to the mass transfer in the liquid phase. More importantly, by DFT calculation, VN demonstrates strong adsorption energy to the hydrated vanadium ions, thus effectively shortening the distance between reactants and the electrode and accelerating the electron transfer process, which could significantly improve the electrochemical kinetics, from the perspective of the classical electric double layer model theory. As a result, the VN-CF anode exhibits an energy efficiency up to 72.17% at a high current density of 200 mA cm−2, 3.84% higher than the pristine carbon felt electrode. Additionally, the VFB equipped with VN-CF electrode demonstrates superior cycling stability and high-capacity retention. This work provides an innovative idea to uncover the underlying catalytic mechanism of VN, which can also guide the research direction for the high-performance electrocatalyst of VFB in the future.

A review of transport models in charged porous electrodes

There is increased interest in many different processes based upon interactions between a charged solid surface and a liquid electrolyte. Energy storage in capacitive porous materials, ionic membranes, capacitive deionization (CDI) for water desalination, capacitive energy generation, removal of heavy ions from wastewater streams, and geophysical applications are some examples of these processes. Process development is driven by the production of porous materials with increasing surface area. Understanding of the physical phenomena occurring at the charged solid-electrolyte interface will significantly improve the design and development of more effective applied processes. The goal of this work is to critically review the current knowledge in the field. The focus is on concepts behind different models. We start by briefly presenting the classical electrical double layer (EDL) models in flat surfaces. Then, we discuss models for porous materials containing macro-, meso-, and micro-pores. Some of the current models for systems comprising two different pore sizes are also included. Finally, we discuss the concepts behind the most common models used for ionic transport and Faradaic processes in porous media. The latter models are used for simulation of electrosorption processes in porous media.

Gating ion and fluid transport with chiral solvent.

The development of modern membranes for ionic separations and energy-storage devices such as supercapacitors depends on the description of ions at solid interfaces, as is often provided by the electrical double layer (EDL) model. The classical EDL model ignores, however, important factors such as possible spatial organization of solvent at the interface and the influence of the solvent on the spatial dependence of the electrochemical potential; these effects in turn govern electrokinetic phenomena. Here we provide a molecular-level understanding of how solvent structure can dictate ionic distributions at interfaces using a model system of a polar, aprotic solvent, propylene carbonate, in its enantiomerically pure and racemic forms, at a silica interface. We link the interfacial structure to the tuning of ionic and fluid transport by the chirality of the solvent and the salt concentration. The results of nonlinear spectroscopic experiments and electrochemical measurements suggest that the solvent exhibits lipid-bilayer-like interfacial organization, with a structure that is dependent on the solvent chirality. The racemic form creates highly ordered layered structure that dictates local ionic concentrations, such that the effective surface potential becomes positive in a wide range of electrolyte concentrations. The enantiomerically pure form exhibits weaker ordering at the silica surface, which leads to a lower effective surface charge induced by ions partitioning into the layered structure. The surface charge in silicon nitride and polymer pores is probed through the direction of electroosmosis that the surface charges induce. Our findings add a new dimension to the nascent field of chiral electrochemistry, and emphasize the importance of including solvent molecules in descriptions of solid-liquid interfaces.

The electrical impedance of carbon xerogel hierarchical electrodes

Many electrodes used in energy storage devices are produced by grinding a micro- and meso- or macro-porous material into a powder and depositing it on a flat substrate, which leads to a hierarchical structure. At the largest scale the structure is that of a flat layer; the intermediate structure is that of porous grains; the smallest scale is that of the microporous skeleton that makes up the grains.The paper uses electrical impedance spectroscopy to investigate both experimentally and through mathematical modelling how electric charges are stored and transported in such structure. The paper focuses on electrodes produced with a variety of carbon xerogels soaked with KCl solutions. Nonane adsorption is used during the electrode preparation to selectively block the micropores, and discriminate their contribution from that of larger pores. The impedance data are analysed with a mathematical model built on the Poisson–Boltzmann equation for charge storage and on the Nernst–Planck equation for ion transport, which accounts for the hierarchical structure of the electrodes.The equilibrium charge storage in large pores is found to be quantitatively described by the classical electric double layer. In micropores, however, non-ideality of the electrolyte has to be invoked to account for the measured capacitance, hinting at ion desolvation. As for the charge transport, each structural level is found to have a characteristic frequency, above which the storage of electric charges is transport-limited at the considered scale. The hierarchical structure of the electrode is responsible for salient characteristics of the impedance. In particular the Warburg regime, with impedance proportional to (iω)−1/2, is observed when transport is rate-limiting at one scale only. In hierarchical electrodes, an additional regime is observed with impedance proportional to (iω)−1/4 when transport limitations are present at two scales simultaneously.

Engineering a passivating electric double layer for high performance lithium metal batteries

In electrochemical devices, such as batteries, traditional electric double layer (EDL) theory holds that cations in the cathode/electrolyte interface will be repelled during charging, leaving a large amount of free solvents. This promotes the continuous anodic decomposition of the electrolyte, leading to a limited operation voltage and cycle life of the devices. In this work, we design a new EDL structure with adaptive and passivating properties. It is enabled by adding functional anionic additives in the electrolyte, which can selectively bind with cations and free solvents, forming unique cation-rich and branch-chain like supramolecular polymer structures with high electrochemical stability in the EDL inner layer. Due to this design, the anodic decomposition of ether-based electrolytes is significantly suppressed in the high voltage cathodes and the battery shows outstanding performances such as super-fast charging/discharging and ultra-low temperature applications, which is extremely hard in conventional electrolyte design principle. This unconventional EDL structure breaks the inherent perception of the classical EDL rearrangement mechanism and greatly improve electrochemical performances of the device.

Reply to the 'Comment on "Can bulk nanobubbles be stabilized by electrostatic interaction?"' by S. Koshoridze and Y. Levin, Phys. Chem. Chem. Phys., 2022, 24, DOI: 10.1039/D1CP04406K.

We investigated the effect of the adsorbed ions on the stability of nanobubbles suspended in the liquid in a recent article published in Physical Chemistry Chemical Physics. We calculated the electrostatic pressure using the classical electrical double layer (EDL) theory and pointed out that the electrostatic pressure is overestimated in previous theories due to the overlook of the stress in the diffusive double layer. Recently, S. I. Koshoridze and Yu. K. Levin questioned our calculations and results based on their intuition that diffusive ions in the EDL will drift and, therefore, not contribute to hydrostatic pressure. In this reply, we explain why mobile ions can also produce hydrostatic pressure from a hydrodynamic perspective.

Structure of interfaces on mechanically renewed Sn, Pb, and Sn-Pb electrodes in acetonitrile solutions of surface inactive electrolytes

• Ideal polarizability regions of Sn and Pb electrodes in AN solutions were found. • Zero charge potentials of Sn and Pb in AN solutions were determined. • Time changes of capacitance curves are observed on Sn-Pb electrode after renewal. • It is shown that Pb atoms are squeezed out to the surface layer of Sn-Pb electrode. • Time effects on renewable Sn-Pb/AN solutions interface were analyzed in detail. The electrical double layer (EDL) structure of mechanically renewed electrodes of Sn, Pb, and Sn-Pb alloy (1 at.% Pb) is studied in acetonictrile (AN) solutions of LiClO 4 by the impedance method and cyclic voltammetry. The potential regions are found in which these electrodes can be considered in good approximation as ideal polarizable. In these solutions, the potentials of zero charge ( E σ = 0 ) on Sn and Pb electrodes are found to be –0.37 ± 0.02 and –0.59 ± 0.02 V (vs. aqueous SCE), respectively. The experimental dependences of the capacitance on the potential are shown to be in good agreement with the classical EDL model of Gouy–Chapman–Stern–Grahame. Based on the results of capacitance measurements carried out on renewed Sn-Pb electrodes, it is found that as the time of exposure of the renewed alloy surface to electrolyte increases, the C vs. E curves indicate that the concentration of lead atoms in the surface layer of alloy also increases, i.e., Pb is the surface-active component of these alloys. By analyzing the observed time effects, the surface coverage of Sn-Pb electrode by lead atoms (θ) is calculated in different time ( t ) after the renewal. It is shown that the θ vs. t dependences well agree with the model proposed earlier that describes the process of surface segregation of atoms of the surface-active component of eutectic alloys by the mechanism of surface diffusion. The kinetics of process of surface segregation of lead atoms on the mechanically renewed Sn-Pb electrode is compared for AN and aqueous solutions. The increase in θ is found to proceed slower in AN solutions than in aqueous solutions of the similar composition. The main reason for the differences observed is proposed.

Ion correlations drive charge overscreening and heterogeneous nucleation at solid–aqueous electrolyte interfaces

Classical electrical double layer (EDL) models are foundational to the representation of atomistic structure and reactivity at charged interfaces. An important limitation to these models is their dependence on a mean-field approximation that is strictly valid for dilute aqueous solutions. Theoretical efforts to overcome this limitation are severely impeded by the lack of visualization of the structure over a wide range of ion concentration. Here, we report the salinity-dependent evolution of EDL structure at negatively charged mica-water interfaces, revealing transition from the Langmuir-type charge compensation in dilute salt solutions to nonclassical charge overscreening in highly concentrated solutions. The EDL structure in this overcharging regime is characterized by the development of both lateral positional correlation between adsorbed ions and vertical layering of alternating cations and anions reminiscent of the structures of strongly correlated ionic liquids. These EDL ions can spontaneously grow into nanocrystalline nuclei of ionic compounds at threshold ion concentrations that are significantly lower than the bulk solubility limit. These results shed light on the impact of ion cooperativity that drives heterogeneous nonclassical behaviors of the EDL in high-salinity conditions.

The electric properties of AOT reverse micelles by molecular dynamics simulations

Reverse micelles (RMs) are the main component of a reverse microemulsion. The ionic RMs of sodium and calcium bis(2-ethylhexyl)sulfosuccinate (AOTNa and AOT2Ca, respectively), and water clusters of different size in isooctane were simulated by the united-atom molecular dynamics method. The radial density profiles characterized the local structure. The local electric potential and the electric field were calculated to describe the electric layer (EL). The behavior of these functions differs principally from the related quantities in the classical electric double layer. The decrease in the size of RMs leads to a noticeable compression of the EL. The value of the local electric field near the surface of the RM increases significantly with the replacement of Na+ counterions by Ca2+. The mutual compensation of the contributions from water and ions calculated separately was revealed, which results in poor sensitivity of the electric properties of the RMs to salt addition. The mean-square dipole moment was calculated for all considered aggregates. It was shown that this quantity strongly depends on the aggregate size as could be expected due to its fluctuation nature. Comparison of the mean-square dipole moment value obtained by the atomistic simulation with the one obtained within the primitive model witnesses that the strong overestimation of the dielectric permittivity of confined water in the primitive model of the RM leads to a significant decrease in the value of the micellar mean-square dipole moment.

Preferential Adsorption in Mixed Electrolytes Confined by Charged Amorphous Silica

Preferential ion adsorption in mixed electrolytes plays a crucial role in many practical applications, such as ion sensing and separation and in colloid science. Using all-atom molecular dynamics simulations of aqueous NaCl, CaCl2, and NaCl-CaCl2 solutions confined by charged amorphous silica, we show that Na+ ions can adsorb preferentially over Ca2+ ions, depending on the surface structure. We propose that this occurs when the local surface structure sterically hinders the first hydration shell of the Ca2+ ion. Introducing a protrusion metric as a function of protrusion of deprotonated silanols, ion-specificity is successfully predicted on isolated, vicinal, and geminal silanols alike, provided that no other deprotonated silanols are found nearby. Furthermore, we introduce a new strategy to analyze the results as a function of distance from the surface. This approach effectively removes surface roughness effects allowing for direct comparison with classical electric double layer theory and distinction of specifically adsorbed ions and electrostatically adsorbed ions.

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.

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.

Charge inversion and external salt effect in semi-permeable membrane electrostatics

Understanding the electrostatics of a charged semi-permeable plasma membrane is central to quantifying the membrane potential jump and the membrane osmotic pressure that play key roles in a myriad of biological processes ranging from control of intracellular calcium and apoptosis in cancer cells to regulation of cell-antibody or cell-vesicle interactions. In this study, we demonstrate a most remarkable charge inversion (CI) like electrostatics in the cytosol (cell) side of a negatively-charged plasma membrane for the case when the membrane is permeable to a cation and impermeable to an anion. This CI like electrostatics implies a switching of the sign of electrostatic potential from negative to positive from the membrane-cytosol interface to locations deep within the cytosol. Classical electric double layer (EDL) studies have reported such electrostatics manifesting switching of the sign of the electrostatic potential primarily during the occurrence of the CI phenomenon in presence multivalent counterions or ions with finite sizes – here, on the contrary, we witness such an effect on account of the combined influence of the specific sign of the charge and the specific permeability behavior of the cell membrane. We further demonstrate the role of an external permeable salt (both cations and anions of the salt permeate through the membrane) in the membrane electrostatics – presence of the salt invariably lowers the effect of semipermeability by either completely eradicating the CI like electrostatics phenomenon or by substantially reducing the membrane potential jump. Finally, we study the disjoining pressure triggered by the membrane-semipermeability-induced asymmetry in ionic distribution and show the distinct influences of the CI like electrostatics and external salt effects on the disjoining pressure.

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.

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.

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.

Effective permittivity of nanocomposites from 3D charge transport simulations

ABSTRACTThe effective permittivity and stored energy in nanocomposites incorporating dielectric and conducting nanofillers are computed by simulating bipolar charge injection, transport, attachment, and recombination through amorphous polymer using a self‐consistent 3D particle‐in‐cell model with nanofillers treated as extensions to the classical electrical double layer. Effective permittivities computed using an energy conserving scheme is shown to have excellent agreement with the Lichtenecker, Bruggeman, and Maxwell‐Garnett mixing rules especially at low volume fraction, low permittivity contrast, and small Clausius‐Mossotti factor, and lie well within the Wiener bounds. The energy conserving scheme with Maxwell‐Garnett E field interpolation combines the best of the Maxwell‐Garnett and fundamental Lichtenecker rules and results in broad validity over the entire volume fraction range. Computed stored energies show monotonic increase with dielectric fillers and a peak at 25 vol % for conducting fillers, attributed to the competing effects of higher energy with increasing E field modification and lower energy with decreasing binder volume. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43300.