Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions

A new method to calculate broadband dielectric spectra of solvents from molecular dynamics simulations demonstrated with polarizable force fields

Simulating the dielectric spectra of solvents requires the nuanced definition of inter- and intra-molecular forces. Non-polarizable force fields, while thoroughly benchmarked for dielectric applications, do not capture all the spectral features of solvents, such as water. Conversely, polarizable force fields have been largely untested in the context of dielectric spectroscopy but include charge and dipole fluctuations that contribute to intermolecular interactions. We benchmark non-polarizable force fields and the polarizable force fields AMOEBA03 and HIPPO for liquid water and find that the polarizable force fields can capture all the experimentally observed spectral features with varying degrees of accuracy. However, the non-polarizable force fields miss at least one peak. To diagnose this deficiency, we decompose the liquid water spectra from polarizable force fields at multiple temperatures into static and induced dipole contributions and find that the peak originates from induced dipole contributions. Broadening our inquiry to other solvents parameterized with the AMOEBA09 force field, we demonstrate good agreement between the experimental and simulated dielectric spectra of methanol and formamide. To produce these spectra, we develop a new computational approach to calculate the dielectric spectrum via the fluctuation dissipation theorem. This method minimizes the error in both the low and high frequency portions of the spectrum, improving the overall accuracy of the simulated spectrum and broadening the computed frequency range.

Dynamic Ion Correlations and Ion-Pair Lifetimes in Aqueous Alkali Metal Chloride Electrolytes

Electrolytes are central to many technological applications, as well as life itself. The behavior and properties of electrolytes are often described in terms of ion pairs, whereby ions associate as either contact ion pairs (in which ions are "touching") solvent-separated ion pairs (in which ions' solvent shells overlap) or solvent-solvent-separated ion pairs (in which ions' solvent shells are distinct). However, this paradigm is generally restricted to statistically averaged descriptions of solution structure and ignores temporal behavior. Here we elucidate the time-resolved dynamics of these ion-ion interactions in aqueous metal chloride electrolytes using the partial van Hove correlation function, based on polarizable molecular dynamics simulations. Our results show that the existence and persistence of ion pairs in aqueous metal chloride electrolytes should not be assumed a priori, but in fact are ion specific features of the solution with lifetimes on subpicosecond time scales.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Dielectric Response and Linear Absorption Spectroscopy of Ionic Systems

Time-dependent electric fields applied to ionic systems can induce both a dielectric and a conductive response, leading to the generation of macroscopic polarization and current, respectively. It has long been recognized that it is not possible to determine the two types of responses separately. However, this aspect is often not adequately accounted for in dielectric and absorption spectroscopies of ionic systems. To clarify this, we theoretically investigate the dielectric and conductive responses of ionic systems containing polyatomic ions based on linear response theory. We derive general expressions for the frequency-dependent dielectric functions, conductivity, and absorption coefficient, including those measured experimentally. Furthermore, we show that the dielectric and conductive responses cannot be uniquely distinguished even at the theoretical level and, therefore, cannot represent experimentally measured quantities. Instead, dielectric and absorption spectra of ionic systems should be expressed in terms of the generalized dielectric function that encompasses both dielectric and conductive responses. We propose a computational method to calculate this generalized dielectric function reliably. Model calculations on concentrated aqueous solutions of NaCl, a monatomic salt, and LiTFSI, a polyatomic salt, show that the dielectric and linear absorption spectra of the two systems based on the generalized dielectric function are significantly different from purely dielectric counterparts in the far-IR, terahertz, and lower-frequency regions. Moreover, the spectra are mainly determined by the autocorrelations of total dipole and total current, but dipole-current cross-correlation can also significantly contribute to the spectra of the LiTFSI solution. The present theoretical approach could be extended to nonlinear spectroscopy of ionic liquids and electrolyte solutions.

Microwave Dielectric Relaxation of Univalent and Bivalent Electrolyte Solutions

The microwave dielectric relaxation of aqueous solutions of univalent (KCl, NaCl, NaI) and bivalent (CaCl2, MgCl2) electrolytes at concentrations between 0.1 and 1 M at 25 °C was investigated using a vector network analyzer (0.5≤ ν ≤ 40 GHz). The spectra of these electrolyte systems are characterized by a symmetrical broadening of the main relaxation peak and were fitted using the Cole-Cole equation. In our analysis, we provide insights into the underlying physics of the relaxation events at microscopic and mesoscopic scales by using a 3D phase space trajectory that is based on the interactions of the relaxing dipole units with their surroundings and Frohlich's B function. The effect of the solutes on the H-bond network of water with increasing concentration is evident in the microwave dielectric spectra through decreasing dielectric strengths and relaxation times. It was found that the number of perturbed water molecules is higher in the case of bivalent electrolytes and appears to be proportional to the ionic radius. In our approach, the particular dependence between the broadening parameter α and the relaxation times τ reflects the rate of interactions between the elementary dipole units and their surroundings. We provide a quantitative analysis of the level of perturbation caused by the presence of ions in the hydrogen-bond network of water. It was found that the H-bonded network of water is highly perturbed in univalent systems compared to bivalent systems due to weaker bonded hydration shells. Finally, we found significant differences between the dielectric response of NaCl and NaI. The differences, originating in the counterions Cl- and I-, which are characterized by large ionic radii and consequently weaker electric fields in their vicinity, confirm that the effect of weakly hydrated ions should not be neglected in microwave dielectric spectra analysis.

Why Dissolving Salt in Water Decreases Its Dielectric Permittivity

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters.

Dielectric relaxation and dielectric decrement in ionic acetamide deep eutectic solvents: Spectral decomposition and comparison with experiments

Frequency-dependent dielectric relaxation in three deep eutectic solvents (DESs), (acetamide+LiClO4/NO3/Br), was investigated in the temperature range, 329 ≤ T/K ≤ 358, via molecular dynamics simulations. Subsequently, decomposition of the real and the imaginary components of the simulated dielectric spectra was carried out to separate the rotational (dipole-dipole), translational (ion-ion), and ro-translational (dipole-ion) contributions. The dipolar contribution, as expected, was found to dominate all the frequency-dependent dielectric spectra over the entire frequency regime, while the other two components together made tiny contributions only. The translational (ion-ion) and the cross ro-translational contributions appeared in the THz regime in contrast to the viscosity-dependent dipolar relaxations that dominated the MHz-GHz frequency window. Our simulations predicted, in agreement with experiments, anion-dependent decrement of the static dielectric constant (ɛs ∼ 20 to 30) for acetamide (ɛs ∼ 66) in these ionic DESs. Simulated dipole-correlations (Kirkwood g factor) indicated significant orientational frustrations. The frustrated orientational structure was found to be associated with the anion-dependent damage of the acetamide H-bond network. Single dipole reorientation time distributions suggested slowed down acetamide rotations but did not indicate presence of any "rotationally frozen" molecule. The dielectric decrement is, therefore, largely static in origin. This provides a new insight into the ion dependence of the dielectric behavior of these ionic DESs. A good agreement between the simulated and the experimental timescales was also noticed.

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

We demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation-dissipation method for water and acetonitrile. We examine this method's trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

Time-resolved terahertz-Raman spectroscopy reveals that cations and anions distinctly modify intermolecular interactions of water

The solvation of ions changes the physical, chemical and thermodynamic properties of water, and the microscopic origin of this behaviour is believed to be ion-induced perturbation of water's hydrogen-bonding network. Here we provide microscopic insights into this process by monitoring the dissipation of energy in salt solutions using time-resolved terahertz-Raman spectroscopy. We resonantly drive the low-frequency rotational dynamics of water molecules using intense terahertz pulses and probe the Raman response of their intermolecular translational motions. We find that the intermolecular rotational-to-translational energy transfer is enhanced by highly charged cations and is drastically reduced by highly charged anions, scaling with the ion surface charge density and ion concentration. Our molecular dynamics simulations reveal that the water-water hydrogen-bond strength between the first and second solvation shells of cations increases, while it decreases around anions. The opposite effects of cations and anions on the intermolecular interactions of water resemble the effects of ions on the stabilization and denaturation of proteins.

Dielectric Properties of Water in Charged Nanopores

In this study, we examine the spectral dielectric properties of liquid water in charged nanopores over a wide range of frequencies (0.3 GHz to 30 THz) and pore widths (0.3 to 5 nm). This has been achieved using classical molecular dynamics simulations of hydrated Na-smectite, the prototypical swelling clay mineral. We observe a drastic (20-fold) and anisotropic decrease in the static relative permittivity of the system as the pore width decreases. This large decrement in static permittivity reflects a strong attenuation of the main Debye relaxation mode of liquid water. Remarkably, this strong attenuation entails very little change in the time scale of the collective relaxation. Our results indicate that water confined in charged nanopores is a distinct solvent with a much weaker collective nature than bulk liquid water, in agreement with recent observations of water in uncharged nanopores. Finally, we observe remarkable agreement between the dielectric properties of the simulated clay system against a compiled set of soil samples at various volumetric water contents. This implies that saturation may not be the sole property dictating the dielectric properties of soil samples, rather that the pore-size distribution of fully saturated nanopores may also play a critically important role.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛ_r) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛ_r, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛ_r show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛ_r. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛ_r. Moreover, even in simulations with constant ɛ_r for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

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.

NaCl aggregation in water at elevated temperatures and pressures: Comparison of classical force fields

The properties of water vary dramatically with temperature and density. This can be exploited to control its effectiveness as a solvent. Thus, supercritical water is of keen interest as solvent in many extraction processes. The low solubility of salts in lower density supercritical water has even been suggested as a means of desalination. The high temperatures and pressures required to reach supercritical conditions can present experimental challenges during collection of required physical property and phase equilibria data, especially in salt-containing systems. Molecular simulations have the potential to be a valuable tool for examining the behavior of solvated ions at these high temperatures and pressures. However, the accuracy of classical force fields under these conditions is unclear. We have, therefore, undertaken a parametric study of NaCl in water, comparing several salt and water models at 200 bar-600 bar and 450 K-750 K for a range of salt concentrations. We report a comparison of structural properties including ion aggregation, hydrogen bonding, density, and static dielectric constants. All of the force fields qualitatively reproduce the trends in the liquid phase density. An increase in ion aggregation with decreasing density holds true for all of the force fields. The propensity to aggregate is primarily determined by the salt force field rather than the water force field. This coincides with a decrease in the water static dielectric constant and reduced charge screening. While a decrease in the static dielectric constant with increasing NaCl concentration is consistent across all model combinations, the salt force fields that exhibit more ionic aggregation yield a slightly smaller dielectric decrement.

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.

Correlation Length in Concentrated Electrolytes: Insights from All-Atom Molecular Dynamics Simulations

We study the correlation length of the charge-charge pair correlations in concentrated electrolyte solutions by means of all-atom, explicit-solvent molecular dynamics simulations. We investigate LiCl and NaI in water, which constitute highly soluble, prototypical salts for experiments, as well as two more complex, molecular electrolyte systems of lithium bis(trifluoromethane)sulfonimide (LiTFSI), a salt commonly employed in electrochemical storage systems, in water, and in an organic solvent mixture of dimethoxyethane and dioxolane. Our simulations support the recent experimental observations as well as theoretical predictions of a nonmonotonic behavior of the correlation length with increasing salt concentration. We observe a Debye-Hückel like regime at low concentration, followed by a minimum reached when d/λ_D ≃ 1, where λ_D is the Debye correlation length and d is the effective ionic diameter, and an increasing correlation length with salt concentration in very concentrated electrolytes. As in the experiments, we find that the screening length in the concentrated regime follows a universal scaling law as a function d/λ_D for all studied salts. However, the scaling exponent is significantly lower than the experimentally measured one and lies in the range of the theoretical predictions based on much simpler electrolyte models.

Dielectric Decrement for Aqueous NaCl Solutions: Effect of Ionic Charge Scaling in Nonpolarizable Water Force Fields

We investigate the dielectric constant and the dielectric decrement of aqueous NaCl solutions by means of molecular dynamic simulations. We thereby compare the performance of four different force fields and focus on disentangling the origin of the dielectric decrement and the influence of scaled ionic charges, as often used in nonpolarizable force fields to account for the missing dynamic polarizability in the shielding of electrostatic ion interactions. Three of the force fields showed excessive contact ion pair formation, which correlates with a reduced dielectric decrement. In spite of the fact that the scaling of charges only weakly influenced the average polarization of water molecules around an ion, the rescaling of ionic charges did influence the dielectric decrement, and a close-to-linear relation of the slope of the dielectric constant as a function of concentration with the ionic charge was found.

Simulations of Nanoseparated Charged Surfaces Reveal Charge-Induced Water Reorientation and Nonadditivity of Hydration and Mean-Field Electrostatic Repulsion

We perform atomistic simulations of nanometer-separated charged surfaces in the presence of monovalent counterions at fixed water chemical potential. The counterion density profiles are well described by a modified Poisson-Boltzmann (MPB) approach that accounts for nonelectrostatic ion-surface interactions, while the effects of smeared-out surface-charge distributions and dielectric profiles are found to be relatively unimportant. The simulated surface interactions are for weakly charged surfaces well described by the additive contributions of hydration and MPB repulsions, but already for a moderate surface charge density of σ = -0.77 e/nm² this additivity breaks down. This we rationalize by a combination of different effects, namely, counterion correlations as well as the surface charge-induced reorientation of hydration water, which modifies the effective water dielectric constant as well as the hydration repulsion.

Ion Hydration and Ion Pairing as Probed by THz Spectroscopy

Ion hydration is of pivotal importance for many fundamental processes. Various spectroscopic methods are used to study the retardation of the hydration bond dynamics in the vicinity of anions and cations. Here we introduce THz-FTIR spectroscopy as a powerful method to answer the open questions. We show through dissection of THz spectra that we can pinpoint characteristic absorption features that can be attributed to the rattling modes of strongly hydrating ions within their hydration cages as well as vibrationally induced charge fluctuations in the case of weakly hydrating ions. Further analysis yields information on anion-cation cooperativity, the size of the dynamic hydration shell, as well as the lifetimes of these collective ion-hydration water modes and their connecting thermal bath states. Our study provides evidence for a non-additive behavior, thus questioning the simplified Hofmeister model. THz spectroscopy enables ion pairing to be observed and quantified at a high salt concentration.

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.

Impact of secondary structure and hydration water on the dielectric spectrum of poly-alanine and possible relation to the debate on slaved versus slaving water

Using extensive molecular dynamics simulations of a single eight-residue alanine polypeptide in explicit water, we investigate the influence of α-helix formation on the dielectric spectrum. For this, we project long equilibrium trajectories into folded and unfolded states and thereby obtain dielectric spectra representative for disordered as well α-helical conformations without the need to change any other system parameter such as pH or temperature. The absorption spectrum in the α-helical state exhibits a feature in the sub-GHz range that is significantly stronger than in the unfolded state. As we show by an additional decomposition into peptide and water contributions, this slow dielectric mode, the relaxation time of which matches the independently determined peptide rotational relaxation time, is mostly caused by peptide polarization correlations, but also contains considerable contributions from peptide-water correlations. In contrast, the peptide spectral contribution shows no features in the GHz range where bulk water absorbs, not even in the peptide-water correlation part, we conclude that hydration water around Ala8 is more influenced by peptide polarization relaxation effects than the other way around. A further decomposition into water-self and water-collective polarization correlations shows that the dielectric response of hydration water is, in contrast to electrolyte solutions, retarded and that this retardation is mostly due to collective effects, the self relaxation of hydration water molecules is only slightly slowed down compared to bulk water. We find the dynamic peptide-water polarization cross correlations to be rather long-ranged and to extend more than one nanometer away from the peptide-water interface into the water hydration shell, in qualitative agreement with previous simulation studies and recent THz absorption experiments.

Barrier-induced dielectric counterion relaxation at super-low frequencies in salt-free polyelectrolyte solutions

Based on the thermally activated diffusion of counterions over the barrier of the electrostatic binding potential, we construct a scaling theory for the slow dielectric response in dilute and semi-dilute polyelectrolyte solutions. The theory is based on an analytic evaluation of the mean-escape time of a single counterion from the surface of a polyelectrolyte chain and uses a variational expression for the electrostatic potential of a charged cylinder including counterion condensation. This mean-escape time shows a range of characteristic power-law dependencies on the polyelectrolyte length and the polyelectrolyte monomer concentration. The existence of this novel dielectric mode at super-low frequencies reflects the wide spectrum of experimental findings for the super-low-frequency dielectric relaxation mode and thereby helps to reconcile conflicting interpretations of experimental data in terms of conventional scaling laws. We also devise a scaling theory for the counterion condensation of finite-length polyelectrolyte chains at finite concentration, which allows us to include polyelectrolyte charge renormalization in dilute as well as semi-dilute solutions in a unified theoretical framework.

Bulk and interfacial liquid water as a transient network

The special macroscopic properties of liquid water stem from its structure as a complex network of molecules connected by hydrogen bonds. While the dynamics of single molecules within this network has been extensively investigated, only little attention has been paid to the closed loops (meshes) of hydrogen-bonded molecules which determine the network topology. Using molecular dynamics simulations we analyze the size, shape, geometrical arrangement, and dynamical stability of loops containing up to 10 hydrogen bonds. We find that six-membered loops in liquid water even at room temperature retain a striking similarity with the well-known structure of ice. Analyzing the network dynamics we find that rings of more than five hydrogen bonds are stabilized compared to a random collection containing the same number of single bonds. We finally show that in the vicinity of hydrophobic and hydrophilic interfaces loops arrange in a preferred orientation.

Dielectric response of the water hydration layer around spherical solutes

We calculate the local dielectric function ɛ(r) inside the hydration layer around a spherical solute (i) from molecular dynamics simulations including explicit solutes and (ii) theoretically using the nonlocal dielectric function of bulk water which includes the radial electric field, but not the explicit solute. The observed agreement between the two concepts shows that while ɛ(r) is strongly different from bulk, this difference is not due to restructuring of the hydrogen bond network but is mostly a consequence of the field geometry. The dielectric response differs for anions and cations, yielding a natural explanation for the well-known charge asymmetry of ionic solvation in agreement with experimental data.

A new lattice Monte Carlo simulation for dielectric saturation in ion-containing liquids

We develop a new, rapid method for the lattice Monte Carlo simulation of ion-containing liquids that accounts for the effects of the reorganization of solvent dipoles under external electrostatic fields. Our results are in reasonable agreement with the analytical solutions to the dielectric continuum theory of Booth for single ions, ion pairs, and ionic cross-links. We also illustrate the substantial disparity between the dielectric functions for like and unlike charges on the nanometer scale. Our simulation rationalizes the experimental data for the dependence of the bulk dielectric value of water on ion concentrations in terms of saturated dipoles near ions.