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

Structure and Screening in Confined Electrolytes: The Role of Ion Association

The effect of ionic association on the structure and property of confined electrolytes is investigated using the classical density functional theory. We find that ionic association strongly affects the ion distribution, surface force, and screening behavior of confined electrolytes. The decay length ξ, which can describe the screening effect of high-concentration electrolytes, satisfies a scaling relationship ξ/λD ∼ (σ/λD)n, with λD being the Debye length and σ representing the ion diameter. We find that n = 1.5 in the nonassociation model, which is contributed by the charge correlation, but n = 3 in the association model, which is contributed by the density correlation. The ion association changes the concentration-dependent characteristics of the screening length by promoting the shift of the decay behavior from the charge-dominated regime to the density-dominated regime. Our result reveals the importance of ion association for electrolyte structure and screening behaviors.

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.

Electrical noise in electrolytes: a theoretical perspective

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and surface force balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. The fluctuations of such various observables arise from the same underlying microscopic dynamics of the ions and solvent molecules. In principle, the relevant length and time scales of these dynamics are encoded in the dynamic structure factors. However, modelling the latter for frequencies and wavevectors spanning many orders of magnitude remains a great challenge to interpret the experiments in terms of physical processes such as solvation dynamics, diffusion, electrostatic and hydrodynamic interactions between ions, interactions with solid surfaces, etc. Here, we highlight the central role of the charge-charge dynamic structure factor in the fluctuations of electrical observables in electrolytes and offer a unifying perspective over a variety of complementary experiments. We further analyze this quantity in the special case of an aqueous NaCl electrolyte, using simulations with explicit ions and an explicit or implicit solvent. We discuss the ability of the standard Poisson-Nernst-Planck theory to capture the simulation results, and how the predictions can be improved. We finally discuss the contributions of ions and water to the total charge fluctuations. This work illustrates an ongoing effort towards a comprehensive understanding of electrical fluctuations in bulk and confined electrolytes, in order to enable experimentalists to decipher the microscopic properties encoded in the measured electrical noise.

Solvent Effects on Structure and Screening in Confined Electrolytes

Using classical density functional theory, we investigate the influence of solvent on the structure and ionic screening of electrolytes under slit confinement and in contact with a reservoir. We consider a symmetric electrolyte with implicit and explicit solvent models and find that spatially resolving solvent molecules is essential for the ion structure at confining walls, excess ion adsorption, and the pressure exerted on the walls. Despite this, we observe only moderate differences in the period of oscillations of the pressure with the slit width and virtually coinciding decay lengths as functions of the scaling variable σ_{ion}/λ_{D}, where σ_{ion} is the ion diameter and λ_{D} the Debye length. Moreover, in the electrostatic-dominated regime, this scaling behavior is practically independent of the relative permittivity and its dependence on the ion concentration. In contrast, the crossover to the hard-core-dominated regime depends sensitively on all three factors.

The Membrane Potential Has a Primary Key Equation

It is common to say that the origin of the membrane potential is attributed to transmembrane ion transport, but it is theoretically possible to explain its generation by the mechanism of ion adsorption. It has been previously suggested that the ion adsorption mechanism even leads to potential formulae identical to the famous Nernst equation or the Goldman-Hodgkin-Katz equation. Our further analysis, presented in this paper, indicates that the potential formula based on the ion adsorption mechanism leads to an equation that is a function of the surface charge density of the material and the surface potential of the material. Furthermore, we have confirmed that the equation holds in all the different experimental systems that we have studied. This equation appears to be a key equation that governs the characteristics of the membrane potential in all systems.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

Coupled Interactions at the Ionic Graphene-Water Interface

We compute ionic free energy adsorption profiles at an aqueous graphene interface by developing a self-consistent approach. To do so, we design a microscopic model for water and put the liquid on an equal footing with the graphene described by its electronic band structure. By evaluating progressively the electronic and dipolar coupled electrostatic interactions, we show that the coupling level including mutual graphene and water screening permits one to recover remarkably the precision of extensive quantum simulations. We further derive the potential of mean force evolution of several alkali cations.

Electrokinetic, electrochemical, and electrostatic surface potentials of the pristine water liquid-vapor interface

Although conceptually simple, the air-water interface displays rich behavior and is subject to intense experimental and theoretical investigations. Different definitions of the electrostatic surface potential as well as different calculation methods, each relevant for distinct experimental scenarios, lead to widely varying potential magnitudes and sometimes even different signs. Based on quantum-chemical density-functional-theory molecular dynamics (DFT-MD) simulations, different surface potentials are evaluated and compared to force-field (FF) MD simulations. As well explained in the literature, the laterally averaged electrostatic surface potential, accessible to electron holography, is dominated by the trace of the water molecular quadrupole moment, and using DFT-MD amounts to +4.35 V inside the water phase, very different from results obtained with FF water models which yield negative values of the order of -0.4 to -0.6 V. Thus, when predicting potentials within water molecules, as relevant for photoelectron spectroscopy and non-linear interface-specific spectroscopy, DFT simulations should be used. The electrochemical surface potential, relevant for ion transfer reactions and ion surface adsorption, is much smaller, less than 200 mV in magnitude, and depends specifically on the ion radius. Charge transfer between interfacial water molecules leads to a sizable surface potential as well. However, when probing electrokinetics by explicitly applying a lateral electric field in DFT-MD simulations, the electrokinetic ζ-potential turns out to be negligible, in agreement with predictions using continuous hydrodynamic models. Thus, interfacial polarization charges from intermolecular charge transfer do not lead to significant electrokinetic mobility at the pristine vapor-liquid water interface, even assuming these transfer charges are mobile in an external electric field.

Effects of surface rigidity and metallicity on dielectric properties and ion interactions at aqueous hydrophobic interfaces

Using classical molecular dynamics simulations we investigate the dielectric properties at interfaces of water with graphene, graphite, hexane and water vapor. For graphite we compare metallic and non-metallic versions. At the vapor-liquid water and hexane-water interfaces the laterally averaged dielectric profiles are significantly broadened due to interfacial roughness and only slightly anisotropic. In contrast, at the rigid graphene surface the dielectric profiles are strongly anisotropic and the perpendicular dielectric profile exhibits pronounced oscillations and sign changes. The interfacial dielectric excess, characterized by the shift of the dielectric-dividing-surface with respect to the Gibbs-dividing-surface, is positive for all surfaces, showing that water has an enhanced dielectric response at hydrophobic surfaces. The dielectric-dividing-surface positions vary significantly among the different surfaces, which points to pronounced surface-specific dielectric behavior. The interfacial repulsion of a chloride ion is shown to be dominated by electrostatic interactions for the soft fluid-fluid interfaces and by non-electrostatic Lennard-Jones interactions for the rigid graphene-water interface. A linear tensorial dielectric model for the ion-interface interaction with sharp dielectric interfaces located on the dielectric-dividing-surface positions works well for graphene but fails for vapor and hexane, because these interfaces are smeared out. The repulsion of chloride from the metallic and non-metallic graphite versions differs very little, which reflects the almost identical interfacial water structure and can be understood based on linear continuum dielectric theory. Interface flexibility shows up mostly in the non-linear Coulomb part of the ion-interface interaction, which changes significantly close to the interfaces and signals the breakdown of linear dielectric continuum theory.

The Role of Surface Chemistry in the Orientational Behavior of Water at an Interface

Molecular dynamics studies have demonstrated that molecular water at an interface, with either a gas or a solid, displays anisotropic orientational behavior in contrast to its bulk counterpart. This effect has been recently implicated in the like-charge attraction problem for colloidal particles in solution. Here, negatively charged particles in solution display a long-ranged attraction where continuum electrostatic theory predicts monotonically repulsive interactions, particularly in solutions with monovalent salt ions at low ionic strength. Anisotropic orientational behavior of solvent molecules at an interface gives rise to an excess interfacial electrical potential which we suggest generates an additional solvation contribution to the total free energy that is traditionally overlooked in continuum descriptions of interparticle interactions in solution. In the present investigation we perform molecular dynamics simulation based calculations of the interfacial potential using realistic surface models representing various chemistries as well as different solvents. Similar to previous work that focused on simple model surfaces constructed by using oxygen atoms, we find that solvents at more realistic model surfaces exhibit substantial anisotropic orientational behavior. We explore the dependence of the interfacial solvation potential on surface properties such as surface group chemistry and group density at silica and carboxylated polystyrene interfaces. For water, we note surprisingly good agreement between results obtained for a simple O-atom wall and more complex surface models, suggesting a general qualitative consistency of the interfacial solvation effect for surfaces in contact with water. In contrast, for an aprotic solvent such as DMSO, surface chemistry appears to exert a stronger influence on the sign and magnitude of the interfacial solvation potential. The study carries broad implications for molecular-scale interactions and may find relevance in explaining a range of phenomena in soft-matter physics and cell biology.

Polar liquids at charged interfaces: A dipolar shell theory

The structure of polar liquids and electrolytic solutions, such as water and aqueous electrolytes, at interfaces underlies numerous phenomena in physics, chemistry, biology, and engineering. In this work, we develop a continuum theory that captures the essential features of dielectric screening by polar liquids at charged interfaces, including decaying spatial oscillations in charge and mass, starting from the molecular properties of the solvent. The theory predicts an anisotropic dielectric tensor of interfacial polar liquids previously studied in molecular dynamics simulations. We explore the effect of the interfacial polar liquid properties on the capacitance of the electrode/electrolyte interface and on hydration forces between two plane-parallel polarized surfaces. In the linear response approximation, we obtain simple formulas for the characteristic decay lengths of molecular and ionic profiles at the interface.

Molecular dynamics simulations of the evaporation of hydrated ions from aqueous solution

Although important for atmospheric processes and gas-phase catalysis, very little is known about the hydration state of ions in the vapor phase. Here we study the evaporation energetics and kinetics of a chloride ion from liquid water by molecular dynamics simulations. As chloride permeates the interface, a water finger forms and breaks at a chloride separation of ≈ 2.8 nm from the Gibbs dividing surface. For larger separations from the interface, about 7 water molecules are estimated to stay bound to chloride in saturated water vapor, as corroborated by continuum dielectrics and statistical mechanics models. This ion hydration significantly reduces the free-energy barrier for evaporation. The effective chloride diffusivity in the transition state is found to be about 6 times higher than in bulk, which reflects the highly mobile hydration dynamics as the water finger breaks. Both effects significantly increase the chloride evaporation flux from the quiescent interface of an electrolyte solution, which is predicted from reaction kinetic theory.

Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon–lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer.

Dielectric response of thin water films: a thermodynamic perspective

The surface of a polar liquid presents a special environment for the solvation and organization of charged solutes, which differ from bulk behaviors in important ways. These differences have motivated many attempts to understand electrostatic response at aqueous interfaces in terms of a spatially varying dielectric permittivity, typically concluding that the dielectric constant of interfacial water is significantly lower than in the bulk liquid. Such analyses, however, are complicated by the potentially nonlocal nature of dielectric response over the short length scales of interfacial heterogeneity. Here we circumvent this problem for thin water films by adopting a thermodynamic approach. Using molecular simulations, we calculate the solvent's contribution to the reversible work of charging a parallel plate capacitor. We find good agreement with a simple dielectric continuum model that assumes bulk dielectric permittivity all the way up to the liquid's boundary, even for very thin (∼1 nm) films. This comparison requires careful attention to the placement of dielectric boundaries between liquid and vapor, which also resolves apparent discrepancies with dielectric imaging experiments.

Free energy calculations from molecular simulations reveal that water's interfacial dielectric response is well-described by bulk properties.

A molecular perspective on induced charges on a metallic surface

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

Effects of electrical image potentials and solvation energy on salt ions near a metallic or dielectric wall

Electrical image potentials near a metallic or a dielectric wall of higher dielectric constant than that of the solution are attractive, and therefore, could concentrate salt ions near the wall. In fact, ions in room temperature ionic liquids have been observed to precipitate near a metallic surface (but not near a nonmetallic surface). It will be argued that a likely reason for why precipitation of ions in salt water due to electrical image forces has not as yet been observed is that the solvation of the ions is reduced near the wall. This results in an energy barrier. This reduction occurs because of the large decrease near the wall of the dielectric constant of water normal to the wall. The conditions under which ions are able to get past the resulting energy barrier and concentrate at a solid wall, either as a result of a reduction in this barrier due to screening at high ion concentration or as a result of thermal activation over the barrier will be explored.

Electrification of water interface

The surface charge of a water interface determines many fundamental processes in physical chemistry and interface science, and it has been intensively studied for over a hundred years. We summarize experimental methods to characterize the surface charge densities developed so far: electrokinetics, double-layer force measurements, potentiometric titration, surface-sensitive nonlinear spectroscopy, and surface-sensitive mass spectrometry. Then, we elucidate physical ion adsorption and chemical electrification as examples of electrification mechanisms. In the end, novel effects on surface electrification are discussed in detail. We believe that this clear overview of state of the art in a charged water interface will surely help the fundamental progress of physics and chemistry at interfaces in the future.

Interplay of Interfacial Viscosity, Specific-Ion, and Impurity Adsorption Determines Zeta Potentials of Phospholipid Membranes

Ion-specific induced changes of the ζ-potential of phospholipid vesicles are commonly used to quantify the affinity of different ions to the lipid interface. The negative ζ-potential of zwitterionic net-neutral phospholipid vesicles in neat water, which changes sign and increases in solutions of NaCl or KCl, is a phenomenon consistently observed in experiments but not fully understood theoretically. Using atomistic molecular dynamics simulations in the presence of applied electric fields which drive electroosmotic flows, in combination with an electrostatic continuum model based on the modified Poisson-Boltzmann and Helmholtz-Smoluchowski equations, we study the electrokinetic and electrostatic properties as well as the specific ion affinities to the phospholipid-water interface, in order to resolve these puzzling observations. Our modified continuum equations account for the dielectric profile at the lipid-water interface, ion-specific interactions between ions and the lipid-water interface, and the interfacial viscosity profile, which are all extracted from our atomistic simulations and rather accurately predict ion-density and electrostatic-potential distributions as well as ζ-potentials in comparison with our atomistic simulations. Our continuum model can explain experimental ζ-potentials only when we assume minute amounts of surface-active anionic impurities in the aqueous solution. In fact, the amount of impurities needed to explain the experimental data increases linearly with the salt concentration, suggesting that surface-active species, which might be already present in the lab water or lipid samples, could further be introduced through the added salt.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Confinement-Controlled Aqueous Chemistry within Nanometric Slit Pores

In this Focus Review, we put the spotlight on very recent insights into the fascinating world of wet chemistry in the realm offered by nanoconfinement of water in mechanically rather rigid and chemically inert planar slit pores wherein only monolayer and bilayer water lamellae can be hosted. We review the effect of confinement on different aspects such as hydrogen bonding, ion diffusion, and charge defect migration of H⁺(aq) and OH^-(aq) in nanoconfined water depending on slit pore width. A particular focus is put on the strongly modulated local dielectric properties as quantified in terms of anisotropic polarization fluctuations across such extremely confined water films and their putative effects on chemical reactions therein. The stunning findings disclosed only recently extend wet chemistry in particular and solvation science in general toward extreme molecular confinement conditions.

Confined Water's Dielectric Constant Reduction Is Due to the Surrounding Low Dielectric Media and Not to Interfacial Molecular Ordering

Liquid water confined within nanometer-sized channels exhibits a surprisingly low dielectric constant along the direction orthogonal to the channel walls. This is typically assumed to result from a pronounced heterogeneity across the sample: the dielectric constant would be bulk-like everywhere except at the interface, where it would be dramatically reduced by strong restrictions on interfacial molecules. Here we study the dielectric properties of water confined within graphene slit channels via classical molecular dynamics simulations. We show that the permittivity reduction is not due to any important alignment of interfacial water molecules, but instead to the long-ranged anisotropic dipole correlations combined with an excluded-volume effect of the low-dielectric confining material. The bulk permittivity is gradually recovered only over several nanometers due to the impact of long-range electrostatics, rather than structural features. This has important consequences for the control of, e.g., ion transport and chemical reactivity in nanoscopic channels and droplets.

Assessing long-range contributions to the charge asymmetry of ion adsorption at the air-water interface

Anions generally associate more favorably with the air–water interface than cations. In addition to solute size and polarizability, the intrinsic structure of the unperturbed interface has been discussed as an important contributor to this bias. Here we assess quantitatively the role that intrinsic charge asymmetry of water's surface plays in ion adsorption, using computer simulations to compare model solutes of various size and charge. In doing so, we also evaluate the degree to which linear response theory for solvent polarization is a reasonable approach for comparing the thermodynamics of bulk and interfacial ion solvation. Consistent with previous works on bulk ion solvation, we find that the average electrostatic potential at the center of a neutral, sub-nanometer solute at the air–water interface depends sensitively on its radius, and that this potential changes quite nonlinearly as the solute's charge is introduced. The nonlinear response closely resembles that of the bulk. As a result, the net nonlinearity of ion adsorption is weaker than in bulk, but still substantial, comparable to the apparent magnitude of macroscopically nonlocal contributions from the undisturbed interface. For the simple-point-charge model of water we study, these results argue distinctly against rationalizing ion adsorption in terms of surface potentials inherent to molecular structure of the liquid's boundary.

Cations and anions have different affinities for the air-water interface. The intrinsic orientation of surface molecules suggests such an asymmetry, but the bias is dominated by solvent response that is spatially local and significantly nonlinear.

Correlation function approach for diffusion in confined geometries

This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nanochannel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.

Surface Tension of Dielectric-Air Interfaces

Analytical and semianalytical expressions for the surface tension of dielectric-air interfaces are presented after considering local and nonlocal dielectric effects near interfaces. It is shown that the nonlocal effects of dielectrics are significant for highly polar dielectric fluids such as water. Far from the interface, nonlocal dielectric effects are shown to cause not only the oscillatory potential of the mean force but also a reversal of sign at intermediate distances.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution

Over the past few decades, the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in aqueous solution. Examples include nucleic acids and colloidal particles in the bulk solution and under confinement, and biological liquid-liquid phase separation. This observation is at odds with the intuitive expectation of an interparticle repulsion that decays monotonically with distance. Although attraction between like-charged particles can be rationalized theoretically in the strong-coupling regime, e.g., in the presence of multivalent counterions, recurring accounts of long-range attraction in aqueous solution containing monovalent ions at low ionic strength have posed an open conundrum. Here, we show that the behavior of molecular water at an interface-traditionally disregarded in the continuum electrostatics picture-provides a mechanism to explain the attraction between like-charged objects in a broad spectrum of experiments. This basic principle will have important ramifications in the ongoing quest to better understand intermolecular interactions in solution.

The Born model can accurately describe electrostatic ion solvation

The solvation free energies of ions in water are consistent with the Born linear response model if the centre on which the ion–water repulsion force acts is moved from the oxygen atom towards the hydrogens.

Giant Axial Dielectric Response in Water-Filled Nanotubes and Effective Electrostatic Ion-Ion Interactions from a Tensorial Dielectric Model

Molecular dynamics simulations in conjunction with effective medium theory are used to investigate dielectric effects in water-filled nanotubes. The resulting effective axial dielectric constant shows a divergent increase for small nanotube radii that depends on the nanotube length, while the effective radial dielectric constant decreases significantly for thin nanotubes. By solving Poisson's equation for an anisotropic dielectric medium in cylindrical geometry, we show that the axial ion-ion interaction depends for small separations primarily on the radial dielectric constant, not on the axial one. This means that electrostatic ion-ion interactions in thin water-filled nanotubes are on the linear dielectric level significantly enhanced due to water confinement effects at small separations, while at large separations the outside medium dominates. If the outside medium is metallic, then the ion-ion interaction decays exponentially for large ion separation.

Aqueous Nanoclusters Govern Ion Partitioning in Dense Polymer Membranes

The uptake and sorption of charged molecules by responsive polymer membranes and hydrogels in aqueous solutions is of key importance for the development of soft functional materials. Here, we investigate the partitioning of simple monatomic (Na⁺, K⁺, Cs⁺, Cl^-, I^-) and one molecular ion (4-nitrophenolate; NP^-) within a dense, electroneutral poly(N-isopropylacrylamide) membrane using explicit-water molecular dynamics simulations. Inside the predominantly hydrophobic environment, water distributes in a network of polydisperse water nanoclusters. The average cluster size determines the mean electrostatic self-energy of the simple ions, which preferably reside deeply inside them; we therefore find substantially larger partition ratios K ≃10^-1 than expected from a simple Born picture using a uniform dielectric constant. Despite their irregular shapes, we observe that the water clusters possess a universal negative electrostatic potential with respect to their surroundings, as is known for aqueous liquid-vapor interfaces. This potential, which we find concealed in cases of symmetric monatomic salts, can dramatically impact the transfer free energies of larger charged molecules because of their weak hydration and increased affinity to interfaces. Consequently, and in stark contrast to the simple ions, the molecular ion NP^- can have a partition ratio much larger than unity, K ≃10-30 (depending on the cation type) or even 10³ in excess of monovalent salt, which explains recent observations of enhanced reaction kinetics of NP^- reduction catalyzed within dense polymer networks. These results also suggest that ionizing a molecule can even enhance the partitioning in a collapsed, rather hydrophobic gel, which strongly challenges the traditional simplistic reasoning.