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.

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.

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.

Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction.

The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this analysis disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K+, Na+, Cl-, and Br- in the complete parameter space of all Lennard-Jones interactions using standard mixing rules. No extra-thermodynamic assumption is necessary for the simultaneous optimization of the four ion pairs. After an optimization with respect to the experimental solvation free energy and activity, the force fields reproduce the concentration-dependent density, ionic conductivity, and dielectric constant with high accuracy. The force field is fully transferable between simple point charge/extended and transferable intermolecular potential water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and standard Coulomb interactions.

Interfacial, Electroviscous, and Nonlinear Dielectric Effects on Electrokinetics at Highly Charged Surfaces.

The dielectric constant and the viscosity of water at the interface of hydrophilic surfaces differ from their bulk values, and it has been proposed that the deviation is caused by the strong electric field and the high ion concentration in the interfacial layer. We calculate the dependence of the dielectric constant and the viscosity of bulk electrolytes on the electric field and the salt concentration. Incorporating the concentration and field-dependent dielectric constant and viscosity in the extended Poisson-Boltzmann and Stokes equations, we calculate the electro-osmotic mobility. We compare the results to literature experimental data and explicit molecular dynamics simulations of OH-terminated surfaces and show that it is necessary to additionally include the presence of a subnanometer wide interfacial water layer, the properties of which are drastically transformed by the sheer presence of the interface. We conclude that the origin of the anomalous behavior of aqueous interfacial layers cannot be found in electrostriction or electroviscous effects caused by the interfacial electric field and ion concentration. Instead, it is primarily caused by the intrinsic ordering and orientation of the interfacial water layer.

Ionic Surfactants at Air/Water and Oil/Water Interfaces: A Comparison Based on Molecular Dynamics Simulations.

Ionic surfactants are known to build up higher interfacial pressures at oil/water interfaces than at air/water interfaces for the same surfactant bulk concentration. Here, we systematically investigate this effect through atomistic molecular dynamics (MD) simulations of surfactant-loaded air/water and oil/water interfaces. Two prototypical ionic surfactants, C12TAB and sodium dodecyl sulfate (SDS), are studied and found to give consistent results, which are also robust with respect to variations in the simulation force field. The simulations reproduce the experimental interfacial pressure data on a semiquantitative level and reveal that the influence of oil on the surfactants' in-plane distribution is a major contribution to the observed effect, albeit insufficient to be the sole reason. The simulations are further analyzed with regard to surfactant/oil cooperative/competitive effects that have been invoked recently as an explanation. However, the interfacial orientation of oil molecules, a presumable indicator for such behavior, is found to display changes only for high levels of surfactant coverage.

Energy transfer within the hydrogen bonding network of water following resonant terahertz excitation.

Energy dissipation in water is very fast and more efficient than in many other liquids. This behavior is commonly attributed to the intermolecular interactions associated with hydrogen bonding. Here, we investigate the dynamic energy flow in the hydrogen bond network of liquid water by a pump-probe experiment. We resonantly excite intermolecular degrees of freedom with ultrashort single-cycle terahertz pulses and monitor its Raman response. By using ultrathin sample cell windows, a background-free bipolar signal whose tail relaxes monoexponentially is obtained. The relaxation is attributed to the molecular translational motions, using complementary experiments, force field, and ab initio molecular dynamics simulations. They reveal an initial coupling of the terahertz electric field to the molecular rotational degrees of freedom whose energy is rapidly transferred, within the excitation pulse duration, to the restricted translational motion of neighboring molecules. This rapid energy transfer may be rationalized by the strong anharmonicity of the intermolecular interactions.

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.

Macroscopic conductivity of aqueous electrolyte solutions scales with ultrafast microscopic ion motions.

Despite the widespread use of aqueous electrolytes as conductors, the molecular mechanism of ionic conductivity at moderate to high electrolyte concentrations remains largely unresolved. Using a combination of dielectric spectroscopy and molecular dynamics simulations, we show that the absorption of electrolytes at ~0.3 THz sensitively reports on the local environment of ions. The magnitude of these high-frequency ionic motions scales linearly with conductivity for a wide range of ions and concentrations. This scaling is rationalized within a harmonic oscillator model based on the potential of mean force extracted from simulations. Our results thus suggest that long-ranged ionic transport is intimately related to the local energy landscape and to the friction for short-ranged ion dynamics: a high macroscopic electrolyte conductivity is thereby shown to be related to large-amplitude motions at a molecular scale.

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.

Unraveling the Origin of the Apparent Charge of Zwitterionic Lipid Layers.

The structure of water molecules in contact with zwitterionic lipid molecules is of great biological relevance, because biological membranes are largely composed of such lipids. The interaction of the interfacial water molecules with the amphiphilic lipid molecules drives the formation of membranes and greatly influences various processes at the membrane surface, as the field that arises from the aligned interfacial water molecules masks the charges of the lipid headgroups from the approaching metabolites. To increase our understanding of the influence of water molecules on biological processes we study their structure at the interface using sum-frequency generation spectroscopy and molecular dynamics simulations. Interestingly, we find that water molecules at zwitterionic lipid molecules are mainly oriented by the field arising between the two oppositely charged molecular moieties within the lipid headgroups.

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.

Breakdown of Linear Dielectric Theory for the Interaction between Hydrated Ions and Graphene.

Many vital processes taking place in electrolytes, such as nanoparticle self-assembly, water purification, and the operation of aqueous supercapacitors, rely on the precise many-body interactions between surfaces and ions in water. Here we study the interaction between a hydrated ion and a charge-neutral graphene layer using atomistic molecular dynamics simulations. For small separations, the ion-graphene repulsion is of nonelectrostatic nature, and for intermediate separations, van der Waals attraction becomes important. Contrary to prevailing theory, we show that nonlinear and tensorial dielectric effects become non-negligible close to surfaces, even for monovalent ions. This breakdown of standard isotropic linear dielectric theory has important consequences for the understanding and modeling of charged objects at surfaces.

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.

Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity.

On the basis of the Poisson-Boltzmann equation in cylindrical coordinates, we calculate the conductivity of a single charged nanotube filled with electrolyte. The conductivity as a function of the salt concentration follows a power-law, the exponent of which has been controversially discussed in the literature. We use the co-ion-exclusion approximation and obtain the crossover between different asymptotic power-law behaviors analytically. Numerically solving the full Poisson-Boltzmann equation, we also calculate the complete diagram of exponents as a function of the salt concentration and the pH for tubes with different radii and p Ka values. We apply our theory to recent experimental results on carbon nanotubes using the p Ka as a fit parameter. In good agreement with the experimental data, the theory shows power-law behavior with the exponents 1/3 at high pH and 1/2 at low pH, with a crossover depending on salt concentration, tube radius and p Ka.

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.

The effects of ion adsorption on the potential of zero charge and the differential capacitance of charged aqueous interfaces.

Using a box profile approximation for the non-electrostatic surface adsorption potentials of anions and cations, we calculate the differential capacitance of aqueous electrolyte interfaces from a numerical solution of the Poisson-Boltzmann equation, including steric interactions between the ions and an inhomogeneous dielectric profile. Preferential adsorption of the positive (negative) ion shifts the minimum of the differential capacitance to positive (negative) surface potential values. The trends are similar for the potential of zero charge; however, the potential of zero charge does not correspond to the minimum of the differential capacitance in the case of asymmetric ion adsorption, contrary to the assumption commonly used to determine the potential of zero charge. Our model can be used to obtain more accurate estimates of ion adsorption properties from differential capacitance or electrocapillary measurements. Asymmetric ion adsorption also affects the relative heights of the characteristic maxima in the differential capacitance curves as a function of the surface potential, but even for strong adsorption potentials the effect is small, making it difficult to reliably determine the adsorption properties from the peak heights.

Charged Surface-Active Impurities at Nanomolar Concentration Induce Jones-Ray Effect.

The electrolyte surface tension exhibits a characteristic minimum around a salt concentration of 1 mM for all ion types, known as the Jones-Ray effect. We show that a consistent description of the experimental surface tension of salts, bases, and acids is possible by assuming charged impurities in the water with a surface affinity typical for surfactants. Comparison with experimental data yields an impurity concentration in the nanomolar range, well below the typical experimental detection limit. Our modeling reveals salt-screening enhanced impurity adsorption as the mechanism behind the Jones-Ray effect: for very low salt concentration added salt screens the  electrostatic repulsion between impurities at the surface, which dramatically increases impurity adsorption and thereby reduces the surface tension.