Underscreening and hidden ion structures in large scale simulations of concentrated electrolytes

Immersed boundary method for dynamic simulation of polarizable colloids of arbitrary shape in explicit ion electrolytes

We develop a computational method for modeling electrostatic interactions of arbitrarily shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion electrolytes and nonionic solvents. Our method computes the nonuniform polarization charge distribution induced in a colloidal particle by both externally applied electric fields and local electric fields arising from other charged objects in the dispersion. This leads to expressions for electrostatic energies, forces, and torques that enable efficient molecular dynamics and Brownian dynamics simulations of colloidal dispersions in electrolytes, which can be harnessed to accurately predict structural and transport properties. We describe an implementation in which colloidal particles are modeled as rigid composites of small spherical beads that tessellate the surface of the particle. The electrostatics calculations are accelerated using a spectrally accurate particle-mesh-Ewald technique implemented on a graphics processing unit and regularized such that the electrostatic calculations are well-defined even for overlapping bodies. We illustrate the effectiveness of this approach with a comprehensive set of calculations: the induced dipole moments and forces for individual, paired, and lattice configurations of spherical colloids in an electric field; the induced dipole moment and torque for anisotropic particles subjected to an electric field; the equilibrium ion distribution in the double layer surrounding charged colloids; the dynamics of charged colloids; and the behavior of ions in the double layer of a polarizable colloid under the influence of an electric field.

Electric field induced associations in the double layer of salt-in-ionic-liquid electrolytes

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However, at large negative voltages, which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes more aggregated while screening the electrode charge from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

Cation valency in water-in-salt electrolytes alters the short- and long-range structure of the electrical double layer

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI)2], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI)2], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

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.

Minimal Coarse-Grained Models of Polar Solvent for Electrolytes: Stockmayer Versus Dumbbell

This study explores the potential of the dumbbell solvent as a minimal model for understanding electrolyte solutions in polar solvents. Our investigation involves a comparative analysis of the dumbbell model and the Stockmayer model, focusing on ion solvation and ion-ion correlations. We examine electrolytes containing symmetric monovalent salts dissolved in polar solvents while varying the ion density and solvent polarity. Both models predict an augmented solvent coordination number around ions as the solvent polarity increases, with the dumbbell solvent displaying a more pronounced effect. Notably, radial distribution functions (RDFs) between solvent and ions yield differing trends; Stockmayer models exhibit a nonmonotonic relationship due to strong dipole-dipole interactions at higher polarity, while RDFs for ions and dumbbell solvents consistently rise. In response to increased solvent polarity, Stockmayer solvents within the ion's solvation shell undergo continuous dipole orientation shifts, whereas the dumbbell solvent predominantly adopts pointing-away dipole orientations, diminishing pointing-to orientations. This underscores the significance of the interplay between the solvent molecular orientation and dipole rotation. Both models qualitatively predict ion pairing and clustering behaviors across varying solvent dipole strengths and salt concentrations. The Stockmayer solvent generally provides stronger electrostatic screening than the dumbbell solvent due to its neglect of the coupling between molecular orientation and dipole rotation. What's more, at a high dipole moment regime, ion-ion correlations in Stockmayer solvent can become stronger with increasing dipole moment due to stronger solvent-solvent correlations. This study underscores the effectiveness of the dumbbell solvent model in systematically elucidating the fundamental principles governing electrolytes and offers potential applications in the rational design of electrolyte systems.

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.

Giant Thermoelectric Response of Confined Electrolytes with Thermally Activated Charge Carrier Generation

The thermoelectric response of thermally activated electrolytes (TAEs) in a slit channel is studied theoretically and by numerical simulations. The term TAE refers to electrolytes whose charge carrier concentration is a function of temperature, as recently suggested for ionic liquids and highly concentrated aqueous electrolyte solutions. Two competing mechanisms driving charge transport by temperature gradients are identified. For suitable values of the activation energy that governs the generation of charge carriers, a giant thermoelectric response is found, which could help explain recent experimental results for nanoporous media infiltrated with TAEs.

Carrier Screening Controls Transport in Conjugated Polymers at High Doping Concentrations

Transport properties of doped conjugated polymers (CPs) have been widely analyzed with the Gaussian disorder model (GDM) in conjunction with hopping transport between localized states. These models reveal that even in highly doped CPs, a majority of carriers are still localized because dielectric permittivity of CPs is well below that of inorganic materials, making Coulomb interactions between carriers and dopant counterions much more pronounced. However, previous studies within the GDM did not consider the role of screening the dielectric interactions by carriers. Here we implement carrier screening in the Debye-Hückel formalism in our calculations of dopant-induced energetic disorder, which modifies the Gaussian density of states (DOS). Then we solve the Pauli master equation using Miller-Abrahams hopping rates with states from the resulting screened DOS to obtain conductivity and Seebeck coefficient across a broad range of carrier concentrations and compare them to measurements. Our results show that screening has significant impact on the shape of the DOS and consequently on carrier transport, particularly at high doping. We prove that the slope of Seebeck coefficient versus electric conductivity, which was previously thought to be universal, is impacted by screening and decreases for systems with small dopant-carrier separation, explaining our measurements. We also show that thermoelectric power factor is underestimated by a factor of ∼10 at higher doping concentrations if screening is neglected. We conclude that carrier screening plays a crucial role in curtailing dopant-induced energetic disorder, particularly at high carrier concentrations.

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.

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.

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

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.

Understanding specific ion effects and the Hofmeister series

Specific ion effects (SIE), encompassing the Hofmeister Series, have been known for more than 130 years since Hofmeister and Lewith's foundational work. SIEs are ubiquitous and are observed across the medical, biological, chemical and industrial sciences. Nevertheless, no general predictive theory has yet been able to explain ion specificity across these fields; it remains impossible to predict when, how, and to what magnitude, a SIE will be observed. In part, this is due to the complexity of real systems in which ions, counterions, solvents and cosolutes all play varying roles, which give rise to anomalies and reversals in anticipated SIEs. Herein we review the historical explanations for SIE in water and the key ion properties that have been attributed to them. Systems where the Hofmeister series is perturbed or reversed are explored, as is the behaviour of ions at the liquid-vapour interface. We discuss SIEs in mixed electrolytes, nonaqueous solvents, and in highly concentrated electrolyte solutions - exciting frontiers in this field with particular relevance to biological and electrochemical applications. We conclude the perspective by summarising the challenges and opportunities facing this SIE research that highlight potential pathways towards a general predictive theory of SIE.

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.

Ionic screening in bulk and under confinement

Recent experiments have shown that the repulsive force between atomically flat, like-charged surfaces confining room-temperature ionic liquids or concentrated electrolytes exhibits an anomalously large decay length. In our previous publication [J. Zeman, S. Kondrat, and C. Holm, Chem. Commun. 56, 15635 (2020)], we showed by means of extremely large-scale molecular dynamics simulations that this so-called underscreening effect might not be a feature of bulk electrolytes. Herein, we corroborate these findings by providing additional results with more detailed analyses and expand our investigations to ionic liquids under confinement. Unlike in bulk systems, where screening lengths are computed from the decay of interionic potentials of mean force, we extract such data in confined systems from cumulative charge distributions. At high concentrations, our simulations show increasing screening lengths with increasing electrolyte concentration, consistent with classical liquid state theories. However, our analyses demonstrate that-also for confined systems-there is no anomalously large screening length. As expected, the screening lengths determined for ionic liquids under confinement are in good quantitative agreement with the screening lengths of the same ionic systems in bulk. In addition, we show that some theoretical models used in the literature to relate the measured screening lengths to other observables are inapplicable to highly concentrated electrolytes.