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Topics addressed include: laboratory double layers; ion-acoustic double layers; pumping potential wells; ion phase-space vortices; weak double layers; electric fields and double layers in plasmas; auroral double layers; double layer formation in a plasma; beamed emission from gamma-ray burst source; double layers and extragalactic jets; and electric potential between plasma sheet clouds.
Electrochemical interfaces still have remaining mysteries surrounding the interfacial region of the electrical double layer, despite being prevalent throughout the energy and water remediation industries. The electrical double layer is where many important dynamic processes such as catalysis and electron transfer occur. The goal of this work is to study the electrical double layer with two-dimensional infrared (2D IR) spectroscopy to experimentally access the details of the structural dynamics of this complex environment. However, there are several experimental challenges to applying 2D IR spectroscopy to this application, such as assuring the surface specificity of the spectrum, optimizing the signal strength while minimizing spectral distortions from dispersion and Fano line shapes, and selecting electrode materials that are both sufficiently IR compatible and conductive. Here we will discuss various considerations when designing 2D IR experiments of electrode interfaces utilizing several substrates and experimental configurations and demonstrate a robust method for 2D IR experiments of electrode interfaces under applied potential that combines nonconducting Si ATR wafers with conductive ITO and thin nanostructured films of plasmonically active Au functionalized with 3-mercapto-2-butanone (MCB). We show that layered electrodes on thin Si ATR wafers with MCB are sensitive to applied potential and that the distortions in the linear and 2D IR spectra are heavily dependent on the morphology of the Au surface.
In classical electric double layer (EDL) theory, co-ions—ions carrying the same charge as the electrode—are assumed to be excluded from the Stern layer because of electrostatic repulsion. However, ion pairing with adsorbed counterions may enable co-ions to access the EDL, a phenomenon that remains underexplored. Key questions therefore remain unresolved, including how deeply co-ions penetrate, how ion-specific properties govern them, and how ion pairing within the EDL differs from bulk solution. Here, in this study, we employ molecular dynamics simulations combined with well-tempered metadynamics to quantify co-ion penetration and ion-pairing thermodynamics at positively charged Mg-Al layered double hydroxide interfaces (σ = +20.6 μC/cm 2 ) in aqueous chloride electrolytes across 0.005–3 M range. We reveal a concentration-driven crossover: at dilute conditions, counterion–co-ion contact ion pairing (CIP) is thermodynamically unfavorable or only weakly favorable (ΔG CIP = +0.12 kcal/mol for Li + to −0.42 kcal/mol for K + ), leading to co-ion exclusion. As concentration increases (≥0.5 M), enhanced screening reduces surface repulsion and stabilizes CIP thermodynamics (ΔG CIP = −0.89 kcal/mol for Li + to −1.05 kcal/mol for K + at 3 M), enabling monovalent co-ions to penetrate the Stern layer following the hydration hierarchy K + > Na + > Li + , while divalent co-ions (Mg 2+ , Ca 2+ ) remain in the diffuse layer, forming only solvent-separated pairs. Comparison with bulk solution shows interfacial ion pairing is suppressed at low concentrations but converges to bulk-like thermodynamics at high concentrations, indicating surface effects vanish under strong screening. These results establish a quantitative framework linking ion-pairing thermodynamics to co-ion penetration and providing strategies to design electrochemical interfaces.
After examining the properties of Coulomb-collision resistivity, anomalous (collective) resistivity, and double layers, a hybrid anomalous-resistivity/double-layer model is introduced. In this model, beam-driven waves on both sides of a double layer provide electrostatic plasma-wave turbulence that greatly reduces the mobility of charged particles. These regions then act to hold open a density cavity within which the double layer resides. In the double layer, electrical energy is dissipated with 100 percent efficiency into high-energy particles, creating conditions optimal for the collective emission of polarized radio waves.
Hypothesis: The electrical double layer formed at the mineral/electrolyte interface is often modeled using mean-field approaches based on a continuum description of the solvent whose dielectric constant is assumed to decrease monotonically with decreasing distance to the surface. In contrast, molecular simulations show that the solvent polarizability oscillates near the surface similar to the water density profile - as shown previously, for example, by Bonthuis et al. (D.J. Bonthuis, S. Gekle, R.R. Netz, Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance, Phys Rev Lett 107(16) (2011) 166102). Here, we showed that molecular and mesoscale pictures agree by spatially averaging the dielectric constant obtained from molecular dynamics simulations over the distances relevant to the mean-field representation. In addition, the values of capacitances used to describe the electrical double layer in Surface Complexation Models (SCMs) of the mineral/electrolyte interface can be estimated using molecularly informed spatially averaged dielectric constants and positions of hydration layers. Experiments: First, we used molecular dynamics simulations to model the calcite 101¯4/electrolyte interface. Next, by using atomistic trajectories, we calculated the distance-dependent static dielectric constant and water density in the direction normal to the. Finally, we applied spatial compartmentalization consistent with the model of parallel-plate capacitors connected in series to estimate SCM capacitances. Findings: Computationally expensive simulations are required to determine the dielectric constant profile of interfacial water near the mineral surface. On the other hand, water density profiles are readily assessable from much shorter simulation trajectories. Our simulations confirmed that dielectric and water density oscillations at the interface are correlated. Here, we parametrized linear regression models to estimate the dielectric constant directly from the local water density. This is a significant computational shortcut compared to slowly converging calculations relying on total dipole moment fluctuations. The amplitude of the interfacial dielectric constant oscillation can exceed the dielectric constant of the bulk water, suggesting an ice-like frozen state, but only if there are no electrolyte ions. The interfacial accumulation of electrolyte ions causes a decrease in the dielectric constant due to the reduction of water density and re-orientation of water dipoles in ion hydration shells. Finally, we show how to use the computed dielectric properties to estimate SCM's capacitances.
We establish a solid/water interface model which treats ionic defects in solids and ions in water uniformly, allowing one to study the space charge layer and the electric double layer profiles under doping and pH effects.
In photoelectrochemical cells, promising devices for directly converting solar energy into storable chemical fuels, the spatial variation of the electrostatic potential across the semiconductor–electrolyte junction is the key parameter that determines the cell performance. In principle, electric field induced second harmonic generation (EFISH) provides a contactless in situ spectroscopic tool to measure the spatial variation of electrostatic potential. However, the total second harmonic generation (SHG) signal contains the contributions of the EFISH signals of semiconductor space charge layer and the electric double layer, in addition to the SHG signal of the electrode surface. The interference of these complex quantities hinders their analysis. In this work, to understand and deconvolute their contributions to the total SHG signals, bias-dependent SHG measurements are performed on the rutile TiO2(100)–electrolyte junction as a function of light polarization and crystal azimuthal angle (angle of the incident plane relative to the crystal [001] axis). A quadratic response between SHG intensity and the applied potential is observed in both the accumulation and depletion regions of TiO2. The relative phase difference and amplitude ratio are extracted at selected azimuthal angles and light polarizations. At 0° azimuthal angle and s-in–p-out polarization, the SHG intensity minimum has the best match with the TiO2 flatband potential due to the orthogonal relative phase difference between bias-dependent and bias-independent SHG terms. We further measure the pH-dependent flatband potential and probe the photovoltage under open circuit conditions using the EFISH technique, demonstrating the capability of this contactless method for measuring electrostatic potential at semiconductor–electrolyte junctions.
Electric double layer capacitors (EDLCs) are prominent energy storage systems that constitute the foundation of more reliable and sustainable energy infrastructures. Modern EDLCs often incorporate ionic liquids (ILs) as a key component in their electrolytes, leveraging the high electrochemical stability of ILs to enhance device performance. The performance and functionality of these capacitors also hinge on the interfacial behavior of ILs at electrode surfaces, which remain insufficiently understood. Here, we performed synchrotron infrared nanospectroscopy (SINS) in combination with density functional theory (DFT) calculations to investigate the electric double layers (EDLs) of three imidazolium-based ILs in a custom-designed graphene liquid cell. This approach revealed new insights into the dynamics of IL EDLs and the underpinning factors originating from the IL structures. Variations in anion size and structure were found to tune the ILs’ ability to form EDLs with compact and closely-correlated ion arrangements, which are critical for enhancing their capacitive performance. These findings highlight the intricate interactions between ions governed by their structures and charge behaviors, which underscores the opportunities for targeted design of IL-based electrolytes to optimize EDLC functionality.
Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational—that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson–Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.
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Significance For centuries the double layer at the solid/electrolyte interface has been a central concept in electrochemistry. Today, it is still crucial for virtually all renewable energy storage and conversion technologies. Here, the double-layer formation is probed by THz spectroscopy with ultrabright synchrotron light as a source. Our results capture the molecular details of double-layer formation at positively/negatively charged Au electrodes for an NaCl electrolyte. We reveal a contrasting response applying positive versus negative bias, which is dictated by the interfacial water network and rationalized by accompanying molecular dynamics simulations and electronic-structure calculations. While Na + is directly attracted toward the negatively charged electrode, stripping of the Cl − hydration shell is observed only at larger potential values.
For many slow solar-fuel-forming reactions, the accumulation of photogenerated minority carriers on the photoelectrode surface leads to light-induced band edge unpinning, affecting the junction properties by decreasing band bending in the semiconductor space charge layer and increasing the driving force of surface reactions in the electric double layer. In this study, we demonstrate a contactless operando electric field-induced second harmonic generation (EFISH) method for measuring the band bending change (δΔΦ SCR L ) on photoelectrodes upon photoexcitation. For ndoped rutile TiO 2 water oxidation photoanodes at pH 7, δΔΦ SCR L increases at more positive potentials or higher illumination power density until it reaches saturation values. We show that under fast mass transport conditions, δΔΦ SCR L is exclusively attributed to the accumulated charged rate-determining species that can be regarded as temporary surface states, and the relationship between the photocurrent and δΔΦ SCR L can be well modeled by assuming that hole trap states function as the reaction center. Kinetic isotope experiments identify proton-coupled electron transfer as the rate-determining step and suggest a possible chemical nature of the key intermediate. We demonstrate that light-induced band edge unpinning is a beneficial feature under high illumination conditions for oxygen evolution reaction on TiO 2 because it maintains the photon-to-current conversion efficiency by enhancing the surface reaction driving force, shedding light on the actual device application.
Complex electrical conductivity is increasingly used to monitor subsurface processes associated with microbial activities because microbial cells mostly have surface charges and thus electrical double layers. Although highly saline environments are frequently encountered in coastal and marine sediments, there are limited data available on the complex conductivity associated with microbial activities under a high-salinity condition. Therefore, we have developed the spectral responses of complex conductivity of sand associated with bacterial growth and biofilm formation under a highly saline condition of approximately 1% salinity and approximately 2 S/m pore water conductivity with an emphasis on relaxation behavior. A column test is performed, in which the model bacteria Shewanella oneidensis MR-1 are stimulated for cell growth and biofilm formation in a sand pack, whereas the complex conductivity is monitored from 0.01 Hz to 10 kHz. The test results indicate that the real conductivity increases in the early stage due to the microbial metabolites and the increased surface conduction with cell growth but soon begin to decrease because of the reduction of charge passages due to bioclogging. However, the imaginary conductivity significantly increases with time, and clear bell-shaped relaxation behaviors are observed with the peak frequency of 0.1–1 Hz, associated with the double-layer polarization of cells and electrically conductive pili and biofilms. The Cole-Cole relaxation model appears to capture such relaxation behaviors well, and the modeling results indicate gradual increases in normalized chargeability and decreases in relaxation time during bacterial growth and biofilm formation in the highly saline condition. Comparison with previous literature confirms that the high-salinity condition further increases the normalized chargeability, whereas it suppresses the phase shift and thus the imaginary conductivity. Our results suggest that the complex conductivity can effectively capture microbial biomass formation in sands under a highly saline condition.
We report the results of constant-potential molecular dynamics simulations of the double layer interface between molten 2LiF–BeF 2 (FLiBe) and 23LiF–6NaF–21KF (FLiNaK) fluoride mixtures and idealized solid electrodes. Employing methods similar to those used in studies of chloride double layers, we compute the structure and differential capacitance of molten fluoride electric double layers as a function of applied voltage. The role of molten salt structure is probed through comparisons between FLiBe and FLiNaK, which serve as models for strong and weak associate-forming salts, respectively. In FLiBe, screening involves changes in Be–F–Be angles and alignment of the oligomers parallel to the electrode, while in FLiNaK, the electric field is screened mainly by rearrangement of individual ions, predominantly the polarizable potassium cation.
Oxide-water interfaces underpin ion separation, catalysis, and electrochemical energy technologies, where the electrical double layer (EDL) controls adsorption, transport, and reactivity. Yet, the molecular-scale link between pH-dependent surface protonation, hydration-layer structure, and counter-ion adsorption remains poorly defined. Here, we combine in situ crystal truncation rod (CTR) and resonant anomalous X-ray reflectivity (RAXR) with streaming potential measurements and ab initio molecular dynamics (AIMD) simulations to resolve the chemical and structural evolution of the EDL at the single-crystal alumina (012)-water interface in 10 mM Rb+ over pH 3-12. CTR measurements reveal two distinct adsorbed water layers at ~2.2 and ~3.5 Å above the surface that each shift toward the substrate at transition pHs near 6.5 and 10.6, respectively, directly reflecting changes in primary hydration layer structure in response to the deprotonation of bridging and terminal aluminol groups. RAXR shows a 10-fold increase in Rb+ coverage and a decrease in mean adsorption height from ~3.5 to ~2.7 Å with increasing pH, indicating enhanced counter-ion binding accompanied by Stern layer contraction. Streaming potential measurements demonstrate that the zeta potential, i.e., potential at the hydrodynamic shear plane, is positive at pH 3 and becomes negative at pH ≥3.5. This negative charge magnitude increases with increasing pH, consistent with progressive surface deprotonation at higher pH. AIMD identifies inner- and outer-sphere Rb+ complexes whose adsorption heights and coordination geometries depend sensitively on the protonation state of surface oxygens, providing atomistic support for the experimentally inferred trends. These measurements establish two discrete, site-specific pH transitions in hydration-layer structure that track aluminol (de)protonation and quantitatively link them to a pH-driven contraction of the Stern layer (increasing Rb+ coverage and decreasing adsorption height). This provides a direct structural basis for connecting surface acid-base chemistry to ion binding distances at an oxide-water interface.
Recently, we studied the phase behavior of ionic fluids under confinement using the classical density functional theory within the framework of the restricted primitive model. Additionally, the theoretical results indicate that narrowing the pore size may lead to a drastic reduction in the electric double layer capacitance, while increasing the surface electrical potential would improve the ionic accessibility of micropores. In this work, we extend the theoretical investigation to systems containing size-asymmetric electrolytes that may exhibit a vapor-liquid like phase transition in the bulk phase. The effects of pore size and surface electric potential on the phase diagram and microscopic structures of the confined electrolytes were studied over a broad range of parameters. We found that decreasing the pore size or increasing the surface potential could destabilize the liquid phase in micropores, and capillary evaporation could occur regardless of the size asymmetry between cations and anions. Compared to that in a symmetric ionic system, the vapor-liquid phase separation is more likely to take place as the size asymmetry becomes more pronounced. The phase transition would alter the “accessibility” of ions to micropores and lead to coexisting micropores with different surface charge densities as identified by Monte Carlo simulation.
The solvation environments of Li + in conventional nonaqueous battery electrolytes, such as LiPF 6 in mixtures of ethylene carbaronate (EC) and ethyl methyl carbonate (EMC), are often used to rationalize transport properties and solid electrolyte interphase (SEI) formation. Solvation environments in the compact electrical double layer (EDL) next to the electrode, also known as the Helmholtz layer, determine (partially) what species can react to form the SEI, with bulk solvation environments often being used as a proxy. Here, we develop and test a theory of cation solvation in the Helmholtz layer of nonaqueous Li-ion battery electrolytes. First, we validate the theory against bulk and diffuse EDL atomistic molecular dynamics (MD) simulations of LiPF 6 EC/EMC mixtures as a function of surface charge, where we find the theory can qualitatively capture the solvation environments. Next, we turn to the Helmholtz layer, where we find the main effect of the solvation structures next to the electrode is an apparent reduction in the number of binding sites between Li + and the solvents, again where we find reasonable agreement with our developed theory. Finally, by solving a simplified version of the theory, we find that the probability of Li + binding to each solvent remains equal to the bulk probability, suggesting that the bulk solvation environments are a reasonable place to start when understanding battery electrolytes. Our developed formalism can be parametrized from bulk MD simulations and used to predict the solvation environments in the Helmholtz layer through reducing the number of available coordination sites, which can be used to determine what could react and form the SEI.
Energy generation through nanofluidics is a topic of great nanotechnological relevance. In this work, we conduct all-atom molecular dynamics (MD) simulations of the transport of water and ions in a pressure-driven flow in nanochannels grafted with charged polyelectrolyte (PE) brushes and discover the possibility of simultaneous electrokinetic energy generation and flow enhancement (henceforth denoted as the electroslippage effect). Such PE-brush-functionalized nanochannels have been recently shown to demonstrate an overscreening (OS) effect (characterized by the presence of a greater number of screening counterions within the PE brush layer than needed to screen the PE brush charges), a consequent presence of excess coions within the PE brush-free bulk, and a coion-driven electroosmotic (EOS) transport in the presence of small to moderate applied axial electric fields. Here, however, we find that the streaming current, which represents the current generated by the flow-driven downstream advection of the charge imbalance present within the electric double layer (EDL) that screen the PE brush charges, is governed by the migration of the counterions. This stems from the fact that the highest contribution to the overall streaming current arises from the region near the PE brush-water interface (where there is an excess of counterions), while the brush-free bulk yields a hitherto unreported, but small, coion-dictated streaming current. This downstream advection of the charge imbalance (and the resultant counterion-driven streaming current) eventually leads to the development of an electric field (streaming electric field) in the direction that is opposite to the direction of the counterion-driven streaming current. The streaming current and the streaming electric field interact to generate the electrokinetic energy. Equally importantly, this streaming electric field induces an EOS transport, which becomes coion-driven, due to the presence of excess coions in the brush-free bulk. For the case of nanochannels grafted with negatively charged PE brushes, the streaming electric field will be in a direction that is opposite to the pressure-driven transport, and hence the coion (or anion) driven EOS flow, will be in the same direction as the pressure-driven transport. On the other hand, for the case of nanochannels grafted with positively charged PE brushes, the streaming electric field will be in the same direction as the pressure-driven flow, and hence the coion (or cation) driven EOS flow, will again be in the same direction as the pressure-driven flow. Therefore, whenever there occurs the presence of the OS and the resulting coion-driven EOS transport in PE brush grafted nanochannels, regardless of the sign of the charges of the PE brushes, this EOS transport will always aid the pressure-driven transport and will cause the most fascinating increase in the net volume flow rate across the nanochannel cross section, which is the electroslippage effect.