Generalized stern models of the electric double layer considering the spatial variation of permittvity and finite size of ions in saturation regime

Elucidation of the pH-Dependent Electric Double Layer Structure at the Silica/Water Interface Using Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy

The silica/water interface is one of the most abundant charged interfaces in natural environments, and the elucidation of the water structure at the silica/water interface is essential. In the present study, we measured the interface-selective vibrational (χ(2)) spectra in the OH stretch region of the silica/water interface in a wide pH range of pH 2.0-12.0 while changing the salt concentration by heterodyne-detected vibrational sum-frequency generation spectroscopy. With the help of singular value decomposition analysis, it is shown that the imaginary part of the χ(2) (Imχ(2)) spectra can be decomposed into the spectra of the diffuse Gouy-Chapman layer (DL) and the compact Stern layer (SL), which enables us to quantitatively analyze the spectra of DL and SL separately. The salt-concentration dependence of the DL spectra at different pH values is analyzed using the modified Gouy-Chapman theory, and the pH-dependent surface charge density and the pKa value (4.8 ± 0.2) of the silica/water interface are evaluated. Furthermore, it is found that the pH-dependent change of the SL spectra is quantitatively explained by three spectral components that represent the three characteristic water species appearing in different pH regions in SL. The quantitative understanding obtained from the analysis of each spectral component in the Imχ(2) spectra provides a clear molecular-level picture of the electric double layer at the silica/water interface.

Effects of Cold Atmospheric Plasma Pre-Treatment of Titanium on the Biological Activity of Primary Human Gingival Fibroblasts

Cold atmospheric plasma treatment (CAP) enables the contactless modification of titanium. This study aimed to investigate the attachment of primary human gingival fibroblasts on titanium. Machined and microstructured titanium discs were exposed to cold atmospheric plasma, followed by the application of primary human gingival fibroblasts onto the disc. The fibroblast cultures were analyzed by fluorescence, scanning electron microscopy and cell-biological tests. The treated titanium displayed a more homogeneous and denser fibroblast coverage, while its biological behavior was not altered. This study demonstrated for the first time the beneficial effect of CAP treatment on the initial attachment of primary human gingival fibroblasts on titanium. The results support the application of CAP in the context of pre-implantation conditioning, as well as of peri-implant disease treatment.

Nonequilibrium Dynamics of Transient Autoelectrophoresis and Effect of Surface Heterogeneity

Nonuniform proton flux around a reactive Janus particle as a result of zone selective heterogeneous surface reaction leads to the formation of asymmetric electrical double layers (EDLs) which assists in generating a proximate electric field dipole around the Janus particle to initiate autoelectrophoretic migration. To estimate the force of the autoelectrophoretic motion of such Janus particles, a mathematical model is set up taking Poisson-Nernst-Plank (PNP) equations coupled with the Navier-Stokes (NS) equations with appropriate boundary conditions. To track the actual motion of these particles, we employ moving deforming mesh and fluid-structure interactions (fsi) of COMSOL Multiphysics while a finite element method is deployed for solving the set of modeled equations. At the outset, transient genesis of the electric field around the particle owing to the nonuniform proton flux has been explored. We further explore the detailed unsteady particle dynamics of the autoelectrophoretic motion with the help of fluid structure interaction physics. It has been observed that the concept of perfect ionic equilibrium in autoelectrophoretic motion is hard to achieve. The autoelectrophoretic particle undergoes continuous change in terms of the ionic concentration around it, speed of the particle, and the transient electric field gradient across the particle. The parametric variation of proton flux reveals that at a relatively lower proton flux a quasi-equilibrium state can be achieved, whereas for higher proton flux the phenomenon can be a pure nonequilibrium case. This parametric study has been done to support the transient dynamics. It has also been shown that the presence of chemical heterogeneity on the particle surface can alter the dynamics of the particle significantly, and the chemical heterogeneity can be used as a tool to control directionality and tuning speed of autoelectrophoretic motion.

Addition of Dioxane in Electrolyte Promotes (002)-Textured Zinc Growth and Suppressed Side Reactions in Zinc-Ion Batteries

The reversibility and cyclability of aqueous zinc-ion batteries (ZIBs) are largely determined by the stabilization of the Zn anode. Therefore, a stable anode/electrolyte interface capable of inhibiting dendrites and side reactions is crucial for high-performing ZIBs. In this study, we investigated the adsorption of 1,4-dioxane (DX) to promote the exposure of Zn (002) facets and prevent dendrite growth. DX appears to reside at the interface and suppress the detrimental side reactions. ZIBs with the addition of DX demonstrated a long-term cycling stability of 1000 h in harsh conditions of 10 mA cm^-2 with an ultrahigh cumulative plated capacity of 5 Ah cm^-2 and shows a good reversibility with an average Coulombic efficiency of 99.7%. The Zn//NH₄V₄O₁₀ full battery with DX achieves a high specific capacity (202 mAh g^-1 at 5 A g^-1) and capacity retention (90.6% after 5000 cycles), much better than that of ZIBs with the pristine ZnSO₄ electrolyte. By selectively adjusting the Zn²⁺ deposition rate on the crystal facets with adsorbed molecules, this work provides a promising modulation strategy at the molecular level for high-performing Zn anodes and can potentially be applied to other metal anodes suffering from instability and irreversibility.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Proton Discharge on a Gold Electrode from Triethylammonium in Acetonitrile: Theoretical Modeling of Potential-Dependent Kinetic Isotope Effects

The discharge of protons on electrode surfaces, known as the Volmer reaction, is a ubiquitous reaction in heterogeneous electrocatalysis and plays an important role in renewable energy technologies. Recent experiments with triethylammonium (TEAH⁺) donating the proton to a gold electrode in acetonitrile demonstrate significantly different Tafel slopes for TEAH⁺ and its deuterated counterpart, TEAD⁺. As a result, the kinetic isotope effect (KIE) for the hydrogen evolution reaction changes considerably as a function of applied potential. Herein a vibronically nonadiabatic approach for proton-coupled electron transfer (PCET) at an electrode interface is extended to heterogeneous electrochemical processes and is applied to this system. This approach accounts for the key effects of the electrical double layer and spans the electronically adiabatic and nonadiabatic regimes, as found to be necessary for this reaction. The experimental Tafel plots for TEAH⁺ and TEAD⁺ are reproduced using physically reasonable parameters within this model. The potential-dependent KIE or, equivalently, isotope-dependent Tafel slope is found to be a consequence of contributions from excited electron-proton vibronic states that depend on both isotope and applied potential. Specifically, the contributions from excited reactant vibronic states are greater for TEAD⁺ than for TEAH⁺. Thus, the two reactions proceed by the same fundamental mechanism yet exhibit significantly different Tafel slopes. This theoretical approach may be applicable to a wide range of other heterogeneous electrochemical PCET reactions.

Theory of the Double Layer in Water-in-Salt Electrolytes

One challenge in developing the next generation of lithium-ion batteries is the replacement of organic electrolytes, which are flammable and most often contain toxic and thermally unstable lithium salts, with safer, environmentally friendly alternatives. Recently developed water-in-salt electrolytes (WiSEs), which are nonflammable, nontoxic, and also have enhanced electrochemical stability, are promising alternatives. In this work, we develop a simple modified Poisson-Fermi theory for WiSEs, which demonstrates the fine interplay between electrosorption, solvation, and ion correlations. The phenomenological parameters are extracted from molecular dynamics simulations, also performed here. The theory reproduces the WiSEs' electrical double-layer structure with remarkable accuracy.

High-Frequency Nanocapacitor Arrays: Concept, Recent Developments, and Outlook

We have developed a measurement platform for performing high-frequency AC detection at nanoelectrodes. The system consists of 65 536 electrodes (diameter 180 nm) arranged in a sub-micrometer rectangular array. The electrodes are actuated at frequencies up to 50 MHz, and the resulting AC current response at each separately addressable electrode is measured in real time. These capabilities are made possible by fabricating the electrodes on a complementary metal-oxide-semiconductor (CMOS) chip together with the associated control and readout electronics, thus minimizing parasitic capacitance and maximizing the signal-to-noise ratio. This combination of features offers several advantages for a broad range of experiments. First, in contrast to alternative CMOS-based electrical systems based on field-effect detection, high-frequency operation is sensitive beyond the electrical double layer and can probe entities at a range of micrometers in electrolytes with high ionic strength such as water at physiological salt concentrations. Far from being limited to single- or few-channel recordings like conventional electrochemical impedance spectroscopy, the massively parallel design of the array permits electrically imaging micrometer-scale entities with each electrode serving as a separate pixel. This allows observation of complex kinetics in heterogeneous environments, for example, the motion of living cells on the surface of the array. This imaging aspect is further strengthened by the ability to distinguish between analyte species based on the sign and magnitude of their AC response. Finally, we show here that sensitivity down to the attofarad level combined with the small electrode size permits detection of individual 28 nm diameter particles as they land on the sensor surface. Interestingly, using finite-element methods, it is also possible to calculate accurately the full three-dimensional electric field and current distributions during operation at the level of the Poisson-Nernst-Planck formalism. This makes it possible to validate the interpretation of measurements and to optimize the design of future experiments. Indeed, the complex frequency and spatial dependence of the data suggests that experiments to date have only scratched the surface of the method's capabilities. Future iterations of the hardware will take advantage of the higher frequencies, higher electrode packing densities and smaller electrode sizes made available by continuing advances in CMOS manufacturing. Combined with targeted immobilization of targets at the electrodes, we anticipate that it will soon be possible to realize complex biosensors based on spatial- and time-resolved nanoscale impedance detection.

Internal configuration and electric potential in planar negatively charged lipid head group region in contact with ionic solution

The lipid bilayer composed of negatively charged lipid 1-palmitoyl-3-oleoyl-sn-glycero-3-phosphatidylserine (POPS) in contact with an aqueous solution of monovalent salt ions was studied theoretically by using the mean-field modified Langevin-Poisson-Boltzmann (MLPB) model. The MLPB results were tested by using molecular dynamic (MD) simulations. In the MLPB model the charge distribution of POPS head groups is theoretically described by the negatively charged surface which accounts for negatively charged phosphate groups, while the positively charged amino groups and negatively charged carboxylate groups are assumed to be fixed on the rod-like structures with rotational degree of freedom. The spatial variation of relative permittivity, which is not considered in the well-known Gouy-Chapman (GC) model or in MD simulations, is thoroughly derived within a strict statistical mechanical approach. Therefore, the spatial dependence and magnitude of electric potential within the lipid head group region and its close vicinity are considerably different in the MLPB model from the GC model. The influence of the bulk salt concentration and temperature on the number density profiles of counter-ions and co-ions in the lipid head group region and aqueous solution along with the probability density function for the lipid head group orientation angle was compared and found to be in qualitative agreement in the MLPB and MD models.

Resolving Anomalies in Predicting Electrokinetic Energy Conversion Efficiencies of Nanofluidic Devices

We devise a new approach for capturing complex interfacial interactions over reduced length scales, towards predicting electrokinetic energy conversion efficiencies of nanofluidic devices. By embedding several aspects of intermolecular interactions in continuum based formalism, we show that our simple theory becomes capable of representing complex interconnections between electro-mechanics and hydrodynamics over reduced length scales. The predictions from our model are supported by reported experimental data, and are in excellent quantitative agreement with molecular dynamics simulations. The present model, thus, may be employed to rationalize the discrepancies between low energy conversion efficiencies of nanofluidic channels that have been realized from experiments, and the impractically high energy conversion efficiencies that have been routinely predicted by the existing theories.

Membrane potential generated by ion adsorption

It has been widely acknowledged that the Goldman-Hodgkin-Katz (GHK) equation fully explains membrane potential behavior. The fundamental facet of the GHK equation lies in its consideration of permeability of membrane to ions, when the membrane serves as a separator for separating two electrolytic solutions. The GHK equation describes that: variation of membrane permeability to ion in accordance with ion species results in the variation of the membrane potential. However, nonzero potential was observed even across the impermeable membrane (or separator) separating two electrolytic solutions. It gave rise to a question concerning the validity of the GHK equation for explaining the membrane potential generation. In this work, an alternative theory was proposed. It is the adsorption theory. The adsorption theory attributes the membrane potential generation to the ion adsorption onto the membrane (or separator) surface not to the ion passage through the membrane (or separator). The computationally obtained potential behavior based on the adsorption theory was in good agreement with the experimentally observed potential whether the membrane (or separator) was permeable to ions or not. It was strongly speculated that the membrane potential origin could lie primarily in the ion adsorption on the membrane (or separator) rather than the membrane permeability to ions. It might be necessary to reconsider the origin of membrane potential which has been so far believed explicable by the GHK equation.

Influence of nanoparticle-membrane electrostatic interactions on membrane fluidity and bending elasticity

The aim of this work is to investigate the effect of electrostatic interactions between the nanoparticles and the membrane lipids on altering the physical properties of the liposomal membrane such as fluidity and bending elasticity. For this purpose, we have used nanoparticles and lipids with different surface charges. Positively charged iron oxide (γ-Fe2O3) nanoparticles, neutral and negatively charged cobalt ferrite (CoFe2O4) nanoparticles were encapsulated in neutral lipid 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine and negatively charged 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine lipid mixture. Membrane fluidity was assessed through the anisotropy measurements using the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene. Though the interaction of both the types of nanoparticles reduced the membrane fluidity, the results were more pronounced in the negatively charged liposomes encapsulated with positively charged iron oxide nanoparticles due to strong electrostatic attractions. X-ray photoelectron spectroscopy results also confirmed the presence of significant quantity of positively charged iron oxide nanoparticles in negatively charged liposomes. Through thermally induced shape fluctuation measurements of the giant liposomes, a considerable reduction in the bending elasticity modulus was observed for cobalt ferrite nanoparticles. The experimental results were supported by the simulation studies using modified Langevin-Poisson-Boltzmann model.

Electric double layer force between charged surfaces: effect of solvent polarization

In this paper, we develop a theory to delineate the consequences of finite solvent polarization in electric double layer interaction or the osmotic pressure between two similar or oppositely charged surfaces. We use previously published Langevin-Bikerman equations to calculate this electric double layer interaction force or the osmotic pressure between the charged surfaces. The osmotic pressure between oppositely charged surfaces is found to be much larger than that between similarly charged surfaces, and for either case, the influence of solvent polarization ensures a larger pressure than that predicted by the Poisson-Boltzmann (PB) model. We derive distinct scaling relationships to explain the increase of the pressure as a function of the separation between the surfaces, the solvent polarizability, and the number density of water molecules. Most importantly, we demonstrate that our theory can successfully reproduce the experimental results of interaction force between similar and oppositely charged surfaces, by accounting for the large under-prediction made by the corresponding PB model.

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

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

Interaction between dipolar lipid headgroups and charged nanoparticles mediated by water dipoles and ions

In this work, a theoretical model describing the interaction between a positively or negatively charged nanoparticle and neutral zwitterionic lipid bilayers is presented. It is shown that in the close vicinity of the positively charged nanoparticle, the zwitterionic lipid headgroups are less extended in the direction perpendicular to the membrane surface, while in the vicinity of the negatively charged nanoparticle, the headgroups are more extended. This result coincides with the calculated increase in the osmotic pressure between the zwitterionic lipid surface and positively charged nanoparticle and the decrease of osmotic pressure between the zwitterionic lipid surface and the negatively charged nanoparticle. Our theoretical predictions agree well with the experimentally determined fluidity of a lipid bilayer membrane in contact with positively or negatively charged nanoparticles. The prospective significance of the present work is mainly to contribute to better understanding of the interactions of charged nanoparticles with a zwitterionic lipid bilayer, which may be important in the efficient design of the lipid/nanoparticle nanostructures (like liposomes with encapsulated nanoparticles), which have diverse biomedical applications, including targeted therapy (drug delivery) and imaging of cancer cells.

Stability of membranous nanostructures: a possible key mechanism in cancer progression

Membranous nanostructures, such as nanovesicles and nanotubules, are an important pool of biological membranes. Recent results indicate that they constitute cell-cell communication systems and that cancer development is influenced by these systems. Nanovesicles that are pinched off from cancer cells can move within the circulation and interact with distant cells. It has been suggested and indicated by experimental evidence that nanovesicles can induce metastases from the primary tumor in this way. Therefore, it is of importance to understand better the mechanisms of membrane budding and vesiculation. Here, a theoretical description is presented concerning consistently related lateral membrane composition, orientational ordering of membrane constituents, and a stable shape of nanovesicles and nanotubules. It is shown that the character of stable nanostructures reflects the composition of the membrane and the intrinsic shape of its constituents. An extension of the fluid mosaic model of biological membranes is suggested by taking into account curvature-mediated orientational ordering of the membrane constituents on strongly anisotropically curved regions. Based on experimental data for artificial membranes, a possible antimetastatic effect of plasma constituents via mediation of attractive interaction between membranous structures is suggested. This mediated attractive interaction hypothetically suppresses nanovesiculation by causing adhesion of buds to the mother membrane and preventing them from being pinched off from the membrane.

Redefining electrical double layer thickness in narrow confinements: effect of solvent polarization

In this paper we delineate the consequences of field-dependent solvent polarization in the electric double layer (EDL) electrostatic potential distribution, and the effective EDL thickness in narrow nanofluidic confinements with thick (or overlapping) EDLs. The EDL, formed at the interface between a charged substrate and an electrolyte solution, induces a large electric field spanning across few nanometer distances from the interface. As a result, a polar solvent like water gets polarized, making its relative permittivity a function of the EDL electric field. This affects the overall EDL electrostatic potential distribution and most importantly, leads to a significant reduction of the effective EDL thickness, with the extent of the reduction being dictated by the value of field independent EDL thickness, strength of the solvent polarization, and the substrate-liquid interfacial electrostatic potential. Such a finding will necessitate redefining the classical EDL thickness, which will be of overwhelming significance in nanofluidic transport.

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.

Adhesion of osteoblasts to a nanorough titanium implant surface

This work considers the adhesion of cells to a nanorough titanium implant surface with sharp edges. The basic assumption was that the attraction between the negatively charged titanium surface and a negatively charged osteoblast is mediated by charged proteins with a distinctive quadrupolar internal charge distribution. Similarly, cation-mediated attraction between fibronectin molecules and the titanium surface is expected to be more efficient for a high surface charge density, resulting in facilitated integrin mediated osteoblast adhesion. We suggest that osteoblasts are most strongly bound along the sharp convex edges or spikes of nanorough titanium surfaces where the magnitude of the negative surface charge density is the highest. It is therefore plausible that nanorough regions of titanium surfaces with sharp edges and spikes promote the adhesion of osteoblasts.