Absence of anomalous underscreening in highly concentrated aqueous electrolytes confined between smooth silica surfaces

Ionic Associations and Hydration in the Electrical Double Layer of Water-in-Salt Electrolytes

Water-in-Salt-Electrolytes (WiSEs) are an exciting class of concentrated electrolytes finding applications in energy storage devices because of their expanded electrochemical stability window, good conductivity and cation transference number, and fire-extinguishing properties. These distinct properties are thought to originate from the presence of an anion-dominated ionic network and interpenetrating water channels for cation transport, which indicates that associations in WiSEs are crucial to understanding their properties. Currently, associations have mainly been investigated in the bulk, while little attention has been given to the electrolyte structure near electrified interfaces. Here, we develop a theory for the electrical double layer (EDL) of WiSEs, where we consistently account for the thermoreversible associations of species into Cayley tree aggregates. The theory predicts an asymmetric structure of the EDL. At negative voltages, hydrated Li+ dominates, and cluster aggregation is initially slightly enhanced before disintegration at larger voltages. At positive voltages, when compared to the bulk, clusters are strictly diminished. Performing atomistic molecular dynamics (MD) simulations of the EDL of WiSE provides EDL data for validation and bulk data for parametrization of our theory. Validating the predictions of our theory against MD showed good qualitative agreement. Furthermore, we performed electrochemical impedance measurements to determine the differential capacitance of the studied LiTFSI WiSE and also found reasonable agreement with our theory. Overall, the developed approach can be used to investigate ionic aggregation and solvation effects in the EDL, which, among other properties, can be used to understand the precursors for solid-electrolyte interphase formation.

Exceptionally Strong Double-Layer Barriers Generated by Polyampholyte Salt

Experiments using the surface force apparatus have found anomalously long-range interactions between charged surfaces in concentrated salt solutions. Ion clustering has been suggested as a possible origin of this behavior. In this work, we demonstrate that if such stable clusters indeed form, they are able to induce remarkably strong free energy barriers under conditions where a corresponding solution of simple salt provides negligible forces. Our cluster model is based on connected ions producing a polyampholyte salt containing a symmetric mixture of monovalent cationic and anionic polyampholytes. Ion distributions and surface interactions are evaluated utilizing statistical-mechanical (classical) polymer density functional theory, cDFT. In the Supporting Information, we briefly investigate a range of different polymer architectures (connectivities), but in the main part of the work, a polyampholyte ion is modeled as a linear chain with alternating charges, in which the ends carry an identical charge (hence, a monovalent net charge). These salts are able to generate repulsions, between similarly charged surfaces, of a remarkable strength, exceeding those from simple salts by orders of magnitude. The underlying mechanism for this is the formation of brush-like layers at the surfaces, i.e., the repulsion is strongly related to excluded volume effects, in a manner similar to the interaction between surfaces carrying grafted polymers. We believe our results are relevant not only to possible mechanisms underlying anomalously long-ranged underscreening in concentrated simple salt solutions but also for the potential use of synthesized polyampholyte salt as extremely efficient stabilizers of colloidal dispersions.

Quantification of solvation forces with amplitude modulation AFM

HYPOTHESIS

Interfacial solvation forces arise from the organisation of liquid molecules near solid surfaces. They are crucial to fundamental phenomena, spanning materials science, molecular biology, and technological applications, yet their molecular details remain poorly understood. Achieving a complete understanding requires imaging techniques, such as three-dimensional atomic force microscopy (3D AFM), to provide atomically resolved images of solid-liquid interfaces (SLIs). However, converting 3D AFM data into accurate tip-sample forces remains challenging, as the process of translating observables into forces is not straightforward.

EXPERIMENTS/SIMULATIONS

This study compares standard amplitude modulation AFM (AM-AFM) force reconstruction methods (FRMs) and identifies their limitations in reconstructing SLI forces. A novel numerical matrix-based FRM specifically designed for AM-AFM is then introduced, aiming to overcome the limitations and inaccuracies found in standard approaches. The new method is validated through simulations and experimental data obtained at the SLI of silicon oxide and water with 3D AFM.

FINDINGS

The proposed matrix-based FRM, differently from standard FRMs, can reconstruct the full SLI interaction at the atomic scale, with no loss of information deriving from the specific choice of AFM experimental parameters or the force functional form. This method unlocks the full spectrum of physical phenomena encoded in the tip-sample interaction at the SLI in AFM experiments, greatly advancing our understanding of interfacial properties and their effects on colloid science, including nanoparticle interactions and molecular self-assembly.

Mesoscopic theory for a double layer capacitance in concentrated ionic systems

The effect of oscillatory decay in charge density in concentrated ionic solutions and ionic liquids on the double-layer capacitance is studied within the framework of a mesoscopic theory. Only Coulomb and steric forces between the ions that are present in all ionic systems are taken into account. We show that the charge oscillations lead to a rescaled distance between the electrode and the virtual monolayer of counterions in the Helmholtz capacitance, and the scaling factor depends on the period of the charge oscillations. Our very simple formula for large density of ions and small voltages can serve as a reference point for the double layer capacitance in concentrated ionic solutions and ionic liquids, and can help to disentangle the universal and specific contributions to the capacitance in particular systems.

Beyond the Debye-Hückel limit: Toward a general theory for concentrated electrolytes

The phenomenon of underscreening in concentrated electrolyte solutions leads to a larger decay length of the charge-charge correlation than the prediction of Debye-Hückel (DH) theory and has found a resurgence of both theoretical and experimental interest in the chemical physics community. To systematically understand and investigate this phenomenon in electrolytes requires a theory of concentrated electrolytes to describe charge-charge correlations beyond the DH theory. We review the theories of electrolytes that can transition from the DH limit to concentrations where charge correlations dominate, giving rise to underscreening and the associated Kirkwood Transitions (KTs). In this perspective, we provide a conceptual approach to a theoretical formulation of electrolyte solutions that exploits the competition between molecular-informed short-range (SR) and long-range interactions. We demonstrate that all deviations from the DH limit for real electrolyte solutions can be expressed through a single function ΣQ that can be determined both theoretically and numerically. Importantly, ΣQ can be directly related to the details of SR interactions and, therefore, can be used as a tool to understand how differences in representations of interaction can influence collective effects. The precise function form of ΣQ can be inferred through a Gaussian field theory of both the number and charge densities. The resulting formulation is validated by experiment and can accurately describe the collective phenomenon of screening in concentrated bulk electrolytes. Importantly, the Gaussian field theory predictions of the screening lengths appear to be less than ∼1 nm at concentrations above KTs.

Long-Range Surface Forces in Salt-in-Ionic Liquids

Ionic liquids (ILs) are a promising class of electrolytes with a unique combination of properties, such as extremely low vapor pressures and nonflammability. Doping ILs with alkali metal salts creates an electrolyte that is of interest for battery technology. These salt-in-ionic liquids (SiILs) are a class of superconcentrated, strongly correlated, and asymmetric electrolytes. Notably, the transference numbers of the alkali metal cations have been found to be negative. Here, we investigate Na-based SiILs with a surface force apparatus, X-ray scattering, and atomic force microscopy. We find evidence of confinement-induced structural changes, giving rise to long-range interactions. Force curves also reveal an electrolyte structure consistent with our predictions from theory and simulations. The long-range steric interactions in SiILs reflect the high aspect ratio of compressible aggregates at the interfaces rather than the purely electrostatic origin predicted by the classical electrolyte theory. This conclusion is supported by the reported anomalous negative transference numbers, which can be explained within the same aggregation framework. The interfacial nanostructure should impact the formation of the solid electrolyte interphase in SiILs.

Wave mechanics in an ionic liquid mixture

Experimental measurements of interactions in ionic liquids and concentrated electrolytes over the past decade or so have revealed simultaneous monotonic and oscillatory decay modes. These observations have been hard to interpret using classical theories, which typically allow for just one electrostatic decay mode in electrolytes. Meanwhile, substantial progress in the theoretical description of dielectric response and ion correlations in electrolytes has illuminated the deep connection between density and charge correlations and the multiplicity of decay modes characterising a liquid electrolyte. The challenge in front of us is to build connections between the theoretical expressions for a pair of correlation functions and the directly measured free energy of interaction between macroscopic surfaces in experiments. Towards this aim, we here present measurements and analysis of the interactions between macroscopic bodies across a fluid mixture of two ionic liquids of widely diverging ionic size. The measured oscillatory interaction forces in the liquid mixtures are significantly more complex than for either of the pure ionic liquids, but can be fitted to a superposition of two oscillatory and one monotonic mode with parameters matching those of the pure liquids. We discuss this empirical finding, which hints at a kind of wave mechanics for interactions in liquid matter.

Detecting underscreening and generalized Kirkwood transitions in aqueous electrolytes

We establish the connection between the measured small angle x-ray scattering signal and the charge-charge correlations underlying Kirkwood transitions (KTs) in 1:1, 2:1, and 3:1 aqueous electrolytes. These measurements allow us to obtain underscreening lengths for bulk electrolytes independently verified by theory and simulations. Furthermore, we generalize the concept of KTs beyond those theoretically predicted for 1:1 electrolytes, which involves the inverse screening length, a0, and the inverse periodicity length, Q0. Above the KTs, we find a universal scaling of a0∝c-ζ/3 and Q0 ∝ c1/3 for the studied electrolyte solutions, where ζ is the ionic strength factor.

Cluster Formation Induced by Local Dielectric Saturation in Restricted Primitive Model Electrolytes

Experiments using the Surface Force Apparatus (SFA) have found anomalously long-ranged charge-charge underscreening in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be a possible origin of this behavior. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric constant, εr, is unable to resolve the anomalous underscreening seen in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric "constant" in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged density correlations between charged surfaces, at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric constant remains uniform does not display similar clusters, even with εr equal to the low saturated value at ion contact. Hence, the observed behaviors are not simply due to an enhanced Coulomb interaction. In the latter case, cluster growth is counteracted by long-ranged repulsions between like-charged ions within clusters; this is an effect that is considerably reduced when the dielectric response drop is local. Our results imply that long-ranged interactions in these systems are mainly due to cluster-cluster correlations, rather than large electrostatic screening lengths.

An efficient method to establish electrostatic screening lengths of restricted primitive model electrolytes

We present a novel, and computationally cheap, way to estimate electrostatic screening lengths from simulations of restricted primitive model (RPM) electrolytes. We demonstrate that the method is accurate by comparisons with simulated long-ranged parts of the charge density, at various Bjerrum lengths, salt concentrations and ion diameters. We find substantial underscreening in low dielectric solvent, but with an "aqueous" solvent, there is instead overscreening, the degree of which increases with ion size. Our method also offers a possible path to (future) more accurate classical density functional treatments of ionic fluids.

Disparate External Electric Field Effect on the Adsorption and Shear Behavior of Monovalent and Trivalent Ions in Electrolyte Solution

Reducing friction is of great interest, and an external potential applied to the friction pair can regulate lubricity. Electrochemical atomic force microscopy (EC-AFM) is used to study the tribological and adsorption behavior of monovalent and trivalent ionic solutions between charged surfaces. An opposite trend of coefficient of friction (COF) and normal force that varies with the applied electric potential is witnessed. Direct force measurements and theoretical models have disclosed that, for the NaCl solution, the negative electric field reduces the COF by increasing cation adsorption. As for LaCl3 solution, the positive electric field promotes the primary adsorption of anions on HOPG, resulting in the disappearance of the attractive ion-ion correlation between the trivalent ions, thereby reducing the COF. The shear behavior of adsorbed ions in electrolyte solution is sensitive to their valence, because of their different surface force contribution. The study further provides a framework to optimize the design of hydration lubrication.

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Disjoining Pressure Decay Length in Room-Temperature Ionic Liquids: A Molecular Simulation Study

We present all-atom molecular simulations to investigate the behavior of 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) in negatively charged carbon nanopores of different widths (h = 5÷15 nm) and lengths (l = 4÷10 nm). The goal of our study was to determine how the disjoining pressure varies as a function of the pore width at different lengths and to understand the influence of edge effects. Our results show that the edge effect decreases as the pore length increases. Using an exponential function, we can approximate the disjoining pressure at large pore widths and use this approximation to estimate the decay length that can correlate with the electrostatic screening length. The results agreed well with those of previous experimental studies.

Reexpansion of charged nanoparticle assemblies in concentrated electrolytes

Electrostatic forces in solutions are highly relevant to a variety of fields, ranging from electrochemical energy storage to biology. However, their manifestation in concentrated electrolytes is not fully understood, as exemplified by counterintuitive observations of colloidal stability and long-ranged repulsions in molten salts. Highly charged biomolecules, such as DNA, respond sensitively to ions in dilute solutions. Here, we use non-base-pairing DNA-coated nanoparticles (DNA-NP) to analyze electrostatic interactions in concentrated salt solutions. Despite their negative charge, these conjugates form colloidal crystals in solutions of sufficient divalent cation concentration. We utilize small-angle X-ray scattering (SAXS) to study such DNA-NP assemblies across the full accessible concentration ranges of aqueous CaCl2, MgCl2, and SrCl2 solutions. SAXS shows that the crystallinity and phases of the assembled structures vary with cation type. For all tested salts, the aggregates contract with added ions at low salinities and then begin expanding above a cation-dependent threshold salt concentration. Wide-angle X-ray scattering (WAXS) reveals enhanced positional correlations between ions in the solution at high salt concentrations. Complementary molecular dynamics simulations show that these ion-ion interactions reduce the favorability of dense ion configurations within the DNA brushes below that of the bulk solution. Measurements in solutions with lowered permittivity demonstrate a simultaneous increase in ion coupling and decrease in the concentration at which aggregate expansion begins, thus confirming the connection between these phenomena. Our work demonstrates that interactions between charged objects continue to evolve considerably into the high-concentration regime, where classical theories project electrostatics to be of negligible consequence.

Scaling perspectives of underscreening in concentrated electrolyte solutions

We present a scaling view of underscreening observed in salt solutions in the range of concentrations greater than about 1 M, in which the screening length increases with concentration. The system consists of hydrated clusters of positive and negative ions with a single unpaired ion as suggested by recent simulations. The environment of this ion is more hydrated than average which leads to a self-similar situation in which the size of this environment scales with the screening length. The prefactor involves the local dielectric constant and the cluster density. The scaling arguments as well as the cluster model lead to scaling of the screening length with the ion concentration, in agreement with observations.

A screening of results on the decay length in concentrated electrolytes

Screening of electrostatic interactions in room-temperature ionic liquids and concentrated electrolytes has recently attracted much attention as surface force balance experiments have suggested the emergence of unanticipated anomalously large screening lengths at high ion concentrations. Termed underscreening, this effect was ascribed to the bulk properties of concentrated ionic systems. However, underscreening under experimentally relevant conditions is not predicted by classical theories and challenges our understanding of electrostatic correlations. Despite the enormous effort in performing large-scale simulations and new theoretical investigations, the origin of the anomalously long-range screening length remains elusive. This contribution briefly summarises the experimental, analytical and simulation results on ionic screening and the scaling behaviour of screening lengths. We then present an atomistic simulation approach that accounts for the solvent and ion exchange with a reservoir. We find that classical density functional theory (DFT) for concentrated electrolytes under confinement reproduces ion adsorption at charged interfaces surprisingly well. With DFT, we study confined electrolytes using implicit and explicit solvent models and the dependence on the solvent's dielectric properties. Our results demonstrate how the absence vs. presence of solvent particles and their discrete nature affect the short and long-range screening in concentrated ionic systems.

Ion adsorption and hydration forces: a comparison of crystalline mica vs. amorphous silica surfaces

Hydration forces are ubiquitous in nature and technology. Yet, the characterization of interfacial hydration structures and their dependence on the nature of the substrate and the presence of ions have remained challenging and controversial. We present a systematic study using dynamic Atomic Force Microscopy of hydration forces on mica surfaces and amorphous silica surfaces in aqueous electrolytes containing chloride salts of various alkali and earth alkaline cations of variable concentrations at pH values between 3 and 9. Our measurements with ultra-sharp AFM tips demonstrate the presence of both oscillatory and monotonically decaying hydration forces of very similar strength on both atomically smooth mica and amorphous silica surfaces with a roughness comparable to the size of a water molecule. The characteristic range of the forces is approximately 1 nm, independent of the fluid composition. Force oscillations are consistent with the size of water molecules for all conditions investigated. Weakly hydrated Cs+ ions are the only exception: they disrupt the oscillatory hydration structure and induce attractive monotonic hydration forces. On silica, force oscillations are also smeared out if the size of the AFM tip exceeds the characteristic lateral scale of the surface roughness. The observation of attractive monotonic hydration forces for asymmetric systems suggests opportunities to probe water polarization.

Structure and anomalous underscreening in ethylammonium nitrate solutions confined between two mica surfaces

The observation of long-range interactions across ionic liquids and highly concentrated electrolytes, extending far beyond the Debye-Hückel prediction and beyond the range predicted in liquid state theory, has been called 'anomalous underscreening'. A number of theoretical and experimental works have explored this phenomenon over recent years, although its origin is not yet fully understood. Most of the experimental studies of anomalous underscreening until now involved aprotic ionic liquids, and so it is of interest to explore interactions in protic ionic liquids where the distribution of charge in the fluid is different in nature. Here we present direct measurements of the interaction force as a function of separation distance, measured using a surface force balance, across solutions of a protic ionic liquid ethylammonium nitrate (EAN) and its mixtures with water over a range of volume fractions from 10 vol% to 100 vol% EAN. The results reveal intricate details about near-surface ordering and dynamics at the EAN-mica interface as well as anomalous underscreening consistent with that observed in the past with aprotic ionic liquids.

Underscreening in concentrated electrolytes: re-entrant swelling in polyelectrolyte brushes

Hypersaline environments are ubiquitous in nature and are found in myriad technological processes. Recent empirical studies have revealed a significant discrepancy between predicted and observed screening lengths at high salt concentrations, a phenomenon referred to as underscreening. Herein we investigate underscreening using a cationic polyelectrolyte brush as an exemplar. Poly(2-(methacryloyloxy)ethyl)trimethylammonium (PMETAC) brushes were synthesised and their internal structural changes and swelling response was monitored with neutron reflectometry and spectroscopic ellipsometry. Both techniques revealed a monotonic brush collapse as the concentration of symmetric monovalent electrolyte increased. However, a non-monotonic change in brush thickness was observed in all multivalent electrolytes at higher concentrations, known as re-entrant swelling; indicative of underscreening. For all electrolytes, numerical self-consistent field theory predictions align with experimental studies in the low-to-moderate salt concentration regions. Analysis suggests that the classical theory of electrolytes is insufficient to describe the screening lengths observed at high salt concentrations and that the re-entrant polyelectrolyte brush swelling seen herein is consistent with the so-called regular underscreening phenomenon.

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.

Anomalous Underscreening in the Restricted Primitive Model

Underscreening is a collective term for charge correlations in electrolytes decaying slower than the Debye length. Anomalous underscreening refers to phenomenology that cannot be attributed alone to steric interactions. Experiments with concentrated electrolytes and ionic fluids report anomalous underscreening, which so far has not been observed in simulation. We present Molecular Dynamics simulation results exhibiting anomalous underscreening that can be connected to cluster formation. A theory that accounts for ion pairing confirms the trend. Our results challenge the classic understanding of dense electrolytes impacting the design of technologies for energy storage and conversion.