Multiscale Modeling of Aqueous Electric Double Layers.

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Force field for halide and alkali ions in water based on single-ion and ion-pair thermodynamic properties for a wide range of concentrations.

A classical non-polarizable force field for the common halide (F-, Cl-, Br-, and I-) and alkali (Li+, Na+, K+, and Cs+) ions in SPC/E water is presented. This is an extension of the force field developed by Loche et al. for Na+, K+, Cl-, and Br- (JPCB 125, 8581-8587, 2021): in the present work, we additionally optimize Lennard-Jones parameters for Li+, I-, Cs+, and F- ions. Li+ and F- are particularly challenging ions to model due to their small size. The force field is optimized with respect to experimental solvation free energies and activity coefficients, which are the necessary and sufficient quantities to accurately reproduce the electrolyte thermodynamics. Good agreement with experimental reference data is achieved for a wide range of concentrations (up to 4 mol/l). We find that standard Lorentz-Berthelot combination rules are sufficient for all ions except F-, for which modified combination rules are necessary. With the optimized parameters, we show that, although the force field is only optimized based on thermodynamic properties, structural properties are reproduced quantitatively, while ion diffusion coefficients are in qualitative agreement with experimental values.

Nature of Cations Critically Affects Water at the Negatively Charged Silica Interface.

Understanding the collective behavior of ions at charged surfaces is of paramount importance for geological and electrochemical processes. Ions screen the surface charge, and interfacial fields break the centro-symmetry near the surface, which can be probed using second-order nonlinear spectroscopies. The effect of electrolyte concentration on the nonlinear optical response has been semi-quantitatively explained by mean-field models based on the Poisson-Boltzmann equation. Yet, to explain previously reported ion-specific effects on the spectroscopic response, drastic ion-specific changes in the interfacial properties, including surface acidities and dielectric permittivities, or strong ion adsorption/desorption had to be invoked. Here, we use sum-frequency generation (SFG) spectroscopy to probe the symmetry-breaking of water molecules at a charged silica surface in contact with alkaline metal chloride solutions (LiCl, NaCl, KCl, and CsCl) at various concentrations. We find that the water response varies with the cation: the SFG response is markedly enhanced for LiCl compared to CsCl. We show that within mean-field models, neither specific ion-surface interactions nor a reduced dielectric constant of water near the interface can account for the variation of spectral intensities with cation nature. Molecular dynamics simulations confirm that the decay of the electrochemical potential only weakly depends on the salt type. Instead, the effect of different salts on the optical response is indirect, through the reorganization of the interfacial water: the salt-type-dependent alignment of water directly at the interface can explain the observations.

Nanomolar Surface-Active Charged Impurities Account for the Zeta Potential of Hydrophobic Surfaces.

The electrification of hydrophobic surfaces is an intensely debated subject in physical chemistry. We theoretically study the ζ potential of hydrophobic surfaces for varying pH and salt concentration by solving the Poisson-Boltzmann and Stokes equations with individual ionic adsorption affinities. Using the ionic surface affinities extracted from the experimentally measured surface tension of the air-electrolyte interface, we first show that the interfacial adsorption and repulsion of small inorganic ions such as H3O+, OH-, HCO3-, and CO32- cannot account for the ζ potential observed in experiments because the surface affinities of these ions are too small. Even if we take hydrodynamic slip into account, the characteristic dependence of the ζ potential on pH and salt concentration cannot be reproduced. Instead, to explain the sizable experimentally measured ζ potential of hydrophobic surfaces, we assume minute amounts of impurities in the water and include the impurities' acidic and basic reactions with water. We find good agreement between our predictions and the reported experimental ζ potential data of various hydrophobic surfaces if we account for impurities that consist of a mixture of weak acids (pKa = 5-7) and weak bases (pKb = 12) at a concentration of the order of 10-7 M.

Exploring the Absorption Spectrum of Simulated Water from MHz to Infrared.

Absorption spectra of liquid water at 300 K are calculated from both classical and density functional theory molecular dynamics simulation data, which together span from 1 MHz to hundreds of THz, agreeing well with experimental data qualitatively and quantitatively over the entire range, including the IR modes, the microwave peak, and the intermediate THz bands. The spectra are decomposed into single-molecular and collective components, as well as into components due to molecular reorientations and changes in induced molecular dipole moments. These decompositions shed light on the motions underlying the librational and translational (hydrogen-bond stretching) bands at 20 and 5 THz, respectively; interactions between donor protons and acceptor lone pair electrons are shown to be important for the line shape in both librational and translational regimes, and in- and out-of-phase librational dimer modes are observed and explored.

Nonlinear Electrophoresis of Highly Charged Nonpolarizable Particles.

Nonlinear field dependence of electrophoresis in high fields has been investigated theoretically, yet experimental studies have failed to reach consensus on the effect. In this Letter, we present a systematic study on the nonlinear electrophoresis of highly charged submicron particles in applied electric fields of up to several kV/cm. First, the particles are characterized in the low-field regime at different salt concentrations and the surface charge density is estimated. Subsequently, we use microfluidic channels and video tracking to systematically characterize the nonlinear response over a range of field strengths. Using velocity measurements on the single particle level, we prove that nonlinear effects are present at electric fields and surface charge densities that are accessible in practical conditions. Finally, we show that nonlinear behavior leads to unexpected particle trapping in channels.

Analytical Interfacial Layer Model for the Capacitance and Electrokinetics of Charged Aqueous Interfaces.

We construct an analytical model to account for the influence of the subnanometer-wide interfacial layer on the differential capacitance and the electro-osmotic mobility of solid-electrolyte interfaces. The interfacial layer is incorporated into the Poisson-Boltzmann and Stokes equations using a box model for the dielectric properties, the viscosity, and the ionic potential of mean force. We calculate the differential capacitance and the electro-osmotic mobility as a function of the surface charge density and the salt concentration, both with and without steric interactions between the ions. We compare the results from our theoretical model with experimental data on a variety of systems (graphite and metallic silver for capacitance and titanium oxide and silver iodide for electro-osmotic data). The differential capacitance of silver as a function of salinity and surface charge density is well reproduced by our theory, using either the width of the interfacial layer or the ionic potential of mean force as the only fitting parameter. The differential capacitance of graphite, however, needs an additional carbon capacitance to explain the experimental data. Our theory yields a power-law dependence of the electro-osmotic mobility on the surface charge density for high surface charges, reproducing the experimental data using both the interfacial parameters extracted from molecular dynamics simulations and fitted interfacial parameters. Finally, we examine different types of hydrodynamic boundary conditions for the power-law behavior of the electro-osmotic mobility, showing that a finite-viscosity layer explains the experimental data better than the usual hydrodynamic slip boundary condition. Our analytical model thus allows us to extract the properties of the subnanometer-wide interfacial layer by fitting to macroscopic experimental data.

Viscous interfacial layer formation causes electroosmotic mobility reversal in monovalent electrolytes.

We study the ion density, shear viscosity and electroosmotic mobility of an aqueous monovalent electrolyte at a charged solid surface using molecular dynamics simulations. Upon increasing the surface charge density, ions are displaced first from the diffuse layer to the outer Helmholtz layer, increasing its viscosity, and subsequently to the hydrodynamically stagnant inner Helmholtz layer. The ion redistribution causes both charge inversion and reversal of the electroosmotic mobility. Because of the surface-charge dependent interfacial hydrodynamic properties, however, the charge density of mobility reversal differs from the charge density of charge inversion, depending on the salt concentration and the chemical details of the ions and the surface. Mobility reversal cannot be described by an effective slip boundary condition alone - the spatial dependence of the viscosity is essential.

Water-separated ion pairs cause the slow dielectric mode of magnesium sulfate solutions.

We compare the dielectric spectra of aqueous MgSO4 and Na2SO4 solutions calculated from classical molecular dynamics simulations with experimental data, using an optimized thermodynamically consistent sulfate force field. Both the concentration-dependent shift of the static dielectric constant and the spectral shape match the experimental results very well for Na2SO4 solutions. For MgSO4 solutions, the simulations qualitatively reproduce the experimental observation of a slow mode, the origin of which we trace back to the ion-pair relaxation contribution via spectral decomposition. The radial distribution functions show that Mg2+ and SO42- ions form extensive water-separated-and thus strongly dipolar-ion pairs, the orientational relaxation of which provides a simple physical explanation for the prominent slow dielectric mode in MgSO4 solutions. Remarkably, the Mg2+-SO42- ion-pair relaxation extends all the way into the THz range, which we rationalize by the vibrational relaxation of tightly bound water-separated ion pairs. Thus, the relaxation of divalent ion pairs can give rise to widely separated orientational and vibrational spectroscopic features.

The Power Spectrum of Ionic Nanopore Currents: The Role of Ion Correlations.

We calculate the power spectrum of electric-field-driven ion transport through nanometer-scale membrane pores using both linearized mean-field theory and Langevin dynamics simulations. Remarkably, the linearized mean-field theory predicts a plateau in the power spectral density at low frequency ω, which is confirmed by the simulations at low ion concentration. At high ion concentration, however, the power spectral density follows a power law that is reminiscent of the 1/ω(α) dependence found experimentally at low frequency. On the basis of simulations with and without ion-ion interactions, we attribute the low-frequency power-law dependence to ion-ion correlations. We show that neither a static surface charge density, nor an increased pore length, nor an increased ion valency have a significant effect on the shape of the power spectral density at low frequency.

Orientation-Induced Adsorption of Hydrated Protons at the Air-Water Interface.

The surface tension of the air-water interface increases upon addition of inorganic salts, implying a negative surface excess of ionic species. Most acids, however, induce a decrease in surface tension, indicating a positive surface excess of hydrated protons. In combination with the apparent negative charge at pure air-water interfaces derived from electrokinetic experiments, this experimental observation has been a source of intense debate since the mid-19th century. Herein, we calculate surface tensions and ionic surface propensities at air-water interfaces from classical, thermodynamically consistent molecular dynamics simulations. The surface tensions of NaOH, HCl, and NaCl solutions show outstanding quantitative agreement with experiment. Of the studied ions, only H3 O+ adsorbs to the air-water interface. The adsorption is explained by the deep potential well caused by the orientation of the H3 O+ dipole in the interfacial electric field, which is confirmed by ab initio simulations.

Interfacial layer effects on surface capacitances and electro-osmosis in electrolytes.

Many properties of the interfacial layer of water at surfaces differ significantly from those of bulk water. The consequences are most significant for the double-layer capacitance and the electrokinetic properties. We model the interfacial hydration layer by a modified dielectric constant and a modified local viscosity over a single interfacial width. Analytic expressions in the low-charge Debye-Hückel approximation are derived and shown to describe experimental surface capacitance and electro-osmotic data in a unified framework.

Optimization of classical nonpolarizable force fields for OH(-) and H3O(+).

We optimize force fields for H3O(+) and OH(-) that reproduce the experimental solvation free energies and the activities of H3O(+) Cl(-) and Na(+) OH(-) solutions up to concentrations of 1.5 mol/l. The force fields are optimized with respect to the partial charge on the hydrogen atoms and the Lennard-Jones parameters of the oxygen atoms. Remarkably, the partial charge on the hydrogen atom of the optimized H3O(+) force field is 0.8 ± 0.1|e|--significantly higher than the value typically used for nonpolarizable water models and H3O(+) force fields. In contrast, the optimal partial charge on the hydrogen atom of OH(-) turns out to be zero. Standard combination rules can be used for H3O(+) Cl(-) solutions, while for Na(+) OH(-) solutions, we need to significantly increase the effective anion-cation Lennard-Jones radius. While highlighting the importance of intramolecular electrostatics, our results show that it is possible to generate thermodynamically consistent force fields without using atomic polarizability.

Mechanosensitive channel activation by diffusio-osmotic force.

For ion channel gating, the appearance of two distinct conformational states and the discrete transitions between them are essential, and therefore of crucial importance to all living organisms. We show that the physical interplay between two structural elements that are commonly present in bacterial mechanosensitive channels--namely, a charged vestibule and a hydrophobic constriction--creates two distinct conformational states, open and closed, as well as the gating between them. We solve the nonequilibrium Stokes-Poisson-Nernst-Planck equations, extended to include a molecular potential of mean force, and show that a first order transition between the closed and open states arises naturally from the diffusio-osmotic stress caused by the ions and the water inside the channel and the elastic restoring force from the membrane.

Nanoscale pumping of water by AC electric fields.

Using molecular dynamics simulations we demonstrate pumping of water through a carbon nanotube by time-dependent electric fields. The fields are generated by electrodes with oscillating charges in a broad gigahertz frequency range that are attached laterally to the tube. The key ingredient is a phase shift between the electrodes to break the spatiotemporal symmetry. A microscopic theory based on a polarization-dragging mechanism accounts quantitatively for our numerical findings.

Unraveling the combined effects of dielectric and viscosity profiles on surface capacitance, electro-osmotic mobility, and electric surface conductivity.

We calculate the electro-osmotic mobility and surface conductivity at a solid-liquid interface from a modified Poisson-Boltzmann equation, including spatial variations of the dielectric function and the viscosity that where extracted previously from molecular dynamics simulations of aqueous interfaces. The low-dielectric region directly at the interface leads to a substantially reduced surface capacitance. At the same time, ions accumulate into a highly condensed interfacial layer, leading to the well-known saturation of the electro-osmotic mobility at large surface charge density regardless of the hydrodynamic boundary conditions. The experimentally well-established apparent excess surface conductivity follows from our model for all hydrodynamic boundary conditions without additional assumptions. Our theory fits multiple published sets of experimental data on hydrophilic and hydrophobic surfaces with striking accuracy, using the nonelectrostatic ion-surface interaction as the only fitting parameter.

Profile of the static permittivity tensor of water at interfaces: consequences for capacitance, hydration interaction and ion adsorption.

We derive the theoretical framework to calculate the dielectric response tensor and determine its components for water adjacent to hydrophilic and hydrophobic surfaces using molecular dynamics simulations. For the nonpolarizable water model used, linear response theory is found to be applicable up to an external perpendicular field strength of ∼2 V/nm, which is well beyond the experimental dielectric breakdown threshold. The dipole contribution dominates the dielectric response parallel to the interface, whereas for the perpendicular component it is essential to keep the quadrupole and octupole terms. Including the space-dependent dielectric function in a mean-field description of the ion distribution at a single charged interface, we reproduce experimental values of the interfacial capacitance. At the same time, the dielectric function decreases the electrostatic part of the disjoining pressure between two charged surfaces, unlike previously thought. The difference in interfacial polarizability between hydrophilic and hydrophobic surfaces can be quantized in terms of the dielectric dividing surface. Using the dielectric dividing surface and the Gibbs dividing surface positions to estimate the free energy of a single ion close to an interface, ion-specific adsorption effects are found to be more pronounced at hydrophobic surfaces than at hydrophilic surfaces, in agreement with experimental trends.

Short-Range Cooperative Slow-down of Water Solvation Dynamics Around SO4 2--Mg2+ Ion Pairs.

The presence of ions affects the structure and dynamics of water on a multitude of length and time scales. In this context, pairs of Mg2+ and SO4 2- ions in water constitute a prototypical system for which conflicting pictures of hydration geometries and dynamics have been reported. Key issues are the molecular pair and solvation shell geometries, the spatial range of electric interactions, and their impact on solvation dynamics. Here, we introduce asymmetric SO4 2- stretching vibrations as new and most specific local probes of solvation dynamics that allow to access ion hydration dynamics at the dilute concentration (0.2 M) of a native electrolyte environment. Highly sensitive heterodyne 2D-IR spectroscopy in the fingerprint region of the SO4 2- ions around 1100 cm-1 reveals a specific slow-down of solvation dynamics for hydrated MgSO4 and for Na2SO4 in the presence of Mg2+ ions, which manifests as a retardation of spectral diffusion compared to aqueous Na2SO4 solutions in the absence of Mg2+ ions. Extensive molecular dynamics and density functional theory QM/MM simulations provide a microscopic view of the observed ultrafast dephasing and hydration dynamics. They suggest a molecular picture where the slow-down of hydration dynamics arises from the structural peculiarities of solvent-shared SO4 2--Mg2+ ion pairs.

Dielectric profile of interfacial water and its effect on double-layer capacitance.

The framework for deriving tensorial interfacial dielectric profiles from bound charge distributions is established and applied to molecular dynamics simulations of water at hydrophobic and hydrophilic surfaces. In conjunction with a modified Poisson-Boltzmann equation, the trend of experimental double-layer capacitances is well reproduced. We show that the apparent Stern layer can be understood in terms of the dielectric profile of pure water.