Ionic screening in bulk and under confinement

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.

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.

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.

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.

Long-Lived Weak Ion Pairs in Ionic Liquids: An Insight from All-Atom Molecular Dynamics Simulations

The microstructure and local dynamics of ions in room-temperature ionic liquids (RTILs) have drawn a lot of attention due to their extensive potential applications in numerous fields. It is well-known that the widely used definitions of ion pairs (IPs) cannot reflect the full picture of RTILs. In this study, we find a universal residence time (τ_MR), which is regardless of the number of counterions in the first solvation shell in RTILs. Inspired by this, we propose a weak IP (WIP) model from a spatiotemporal perspective and demonstrate that the WIPs are long-lived and that their lifetimes obey a log-normal distribution, which is different from the literature. In addition, the electrostatic interactions are the main factors in the formation of WIPs, and the reorientations of ions are vital to the ruptures of WIPs. This research provides a new perspective for understanding the microstructural and dynamical properties of RTILs.

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.

MDSuite: comprehensive post-processing tool for particle simulations

Particle-Based (PB) simulations, including Molecular Dynamics (MD), provide access to system observables that are not easily available experimentally. However, in most cases, PB data needs to be processed after a simulation to extract these observables. One of the main challenges in post-processing PB simulations is managing the large amounts of data typically generated without incurring memory or computational capacity limitations. In this work, we introduce the post-processing tool: MDSuite. This software, developed in Python, combines state-of-the-art computing technologies such as TensorFlow, with modern data management tools such as HDF5 and SQL for a fast, scalable, and accurate PB data processing engine. This package, built around the principles of FAIR data, provides a memory safe, parallelized, and GPU accelerated environment for the analysis of particle simulations. The software currently offers 17 calculators for the computation of properties including diffusion coefficients, thermal conductivity, viscosity, radial distribution functions, coordination numbers, and more. Further, the object-oriented framework allows for the rapid implementation of new calculators or file-readers for different simulation software. The Python front-end provides a familiar interface for many users in the scientific community and a mild learning curve for the inexperienced. Future developments will include the introduction of more analysis associated with ab-initio methods, colloidal/macroscopic particle methods, and extension to experimental data.

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

Recent surface forces apparatus experiments that measured the forces between two mica surfaces and a series of subsequent theoretical studies suggest the occurrence of universal underscreening in highly concentrated electrolyte solutions. We performed a set of systematic Atomic Force Spectroscopy measurements for aqueous salt solutions in a concentration range from 1 mM to 5 M using chloride salts of various alkali metals as well as mixed concentrated salt solutions (involving both mono- and divalent cations and anions), that mimic concentrated brines typically encountered in geological formations. Experiments were carried out using flat substrates and submicrometer-sized colloidal probes made of smooth oxidized silicon immersed in salt solutions at pH values of 6 and 9 and temperatures of 25 °C and 45 °C. While strong repulsive forces were observed for the smallest tip-sample separations, none of the conditions explored displayed any indication of anomalous long range electrostatic forces as reported for mica surfaces. Instead, forces are universally dominated by attractive van der Waals interactions at tip-sample separations of ≈2 nm and beyond for salt concentrations of 1 M and higher. Complementary calculations based on classical density functional theory for the primitive model support these experimental observations and display a consistent decrease in screening length with increasing ion concentration.

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Colloidal Systems in Concentrated Electrolyte Solutions Exhibit Re-entrant Long-Range Electrostatic Interactions due to Underscreening

Surface force measurements have revealed that at very high electrolyte concentrations as well as in neat and diluted ionic liquids and deep eutectic solvents, the range of electrostatic interactions is far greater than the Debye length. Here, we explore the consequences of this underscreening for soft-matter and colloidal systems by investigating the stability of nanoparticle dispersions, the self-assembly of ionic surfactants, and the thickness of soap films. In each case, we find clear evidence of re-entrant properties due to underscreening at high salt concentrations. Our results show that underscreening in concentrated electrolytes is a general phenomenon and is not dependent on confinement by macroscopic surfaces. The stability of systems at very high salinity due to underscreening may be beneficially applied to processes that currently use low-salinity water.