Monte Carlo Simulation for the Double Layer Structure of an Ionic Liquid Using a Dimer Model: A Comparison with the Density Functional Theory

Integrative studies of ionic liquid interface layers: bridging experiments, theoretical models and simulations

Ionic liquids (ILs) are a class of salts existing in the liquid state below 100 °C, possessing low volatility, high thermal stability as well as many highly attractive solvent and electrochemical capabilities, etc., making them highly tunable for a great variety of applications, such as lubricants, electrolytes, and soft functional materials. In many applications, ILs are first either physi- or chemisorbed on a solid surface to successively create more functional materials. The functions of ILs at solid surfaces can differ considerably from those of bulk ILs, mainly due to distinct interfacial layers with tunable structures resulting in new ionic liquid interface layer properties and enhanced performance. Due to an almost infinite number of possible combinations among the cations and anions to form ILs, the diversity of various solid surfaces, as well as different external conditions and stimuli, a detailed molecular-level understanding of their structure-property relationship is of utmost significance for a judicious design of IL-solid interfaces with appropriate properties for task-specific applications. Many experimental techniques, such as atomic force microscopy, surface force apparatus, and so on, have been used for studying the ion structuring of the IL interface layer. Molecular Dynamics simulations have been widely used to investigate the microscopic behavior of the IL interface layer. To interpret and clarify the IL structure and dynamics as well as to predict their properties, it is always beneficial to combine both experiments and simulations as close as possible. In another theoretical model development to bridge the structure and properties of the IL interface layer with performance, thermodynamic prediction & property modeling has been demonstrated as an effective tool to add the properties and function of the studied nanomaterials. Herein, we present recent findings from applying the multiscale triangle "experiment-simulation-thermodynamic modeling" in the studies of ion structuring of ILs in the vicinity of solid surfaces, as well as how it qualitatively and quantitatively correlates to the overall ILs properties, performance, and function. We introduce the most common techniques behind "experiment-simulation-thermodynamic modeling" and how they are applied for studying the IL interface layer structuring, and we highlight the possibilities of the IL interface layer structuring in applications such as lubrication and energy storage.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Application of surface complexation modeling on adsorption of uranium at water-solid interface: A review

Precise prediction of uranium adsorption at water-mineral interface is of great significance for the safe disposal of radionuclides in geologic environments. Surface complexation modeling (SCM) as a very useful tool has been extensively investigated for simulating adsorption behavior of metals/metalloids at water-mineral interface. Numerous studies concerning the fitting of uranium adsorption on various adsorbents using SCM are well documented, but the systematic and comprehensive review of uranium adsorption using various SCM is not available. In this review, we briefly summarized the rationale of SCM, including constant-capacitance-model (CCM), diffuse-layer-model (DLM), triple-layer-model (TLM); The recent progress in the application of SCM on the fitting of uranium adsorption towards metal (hydr)oxides, clay minerals and soil/sediments was reviewed in details. This review hopefully provides the beneficial guidelines for predicting the transport and fate of uranium in geologic environments beyond laboratory timescales.

Interfacial Layering in the Electric Double Layer of Ionic Liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly interacting environment, leading to the formation of discrete layers of charges at interfaces and spin-glass structure in the bulk. Here, we propose a simple theory that captures the coupling between steric and electrostatic forces in ionic liquids. The theory predicts the formation of discrete layers of charge at charged interfaces. Further from the interface, or at low polarization of the electrode, the model outputs slowly decaying oscillations in the charge density with a wavelength of a single ion diameter, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.

Off-center charge model revisited: Electrical double layer with multivalent cations

The off-center charge model of ions is a relatively simple model for introducing asymmetry in Coulomb interaction while retaining the simplicity and convenience of the spherical hard core geometry. A Monte Carlo simulation analysis of the planar electric double layer formed by this ionic model for 1+:1- valence systems [S. Lamperski et al., Langmuir 33, 11554-11560 (2017)] is extended to include solutions of multivalent (2+, 3+) hard spherical cations and single valence (1-) hard spherical anions near a uniformly charged, planar electrode. The solvent is modelled as a uniform dielectric continuum with a dielectric constant equal to that of the pure solvent, viz., the primitive model. Results are reported for the ion density, the cation charge profile, and the electrostatic potential profile at 1 mol/dm³ salt concentration. Additionally, the double layer potential drop, that is, the electrode potential, and the integral and the differential capacitances are computed as functions of the electrode surface charge density. The latter two quantities show an expected asymmetry as long as the cation valence is not too great and the charge of the off-center ion cannot approach too close to the electrode surface. It is unusual that the integral and differential capacitances are negative for high valence cations and a negatively charged electrode when the off-center charge is large and can be very near the surface of the electrode. The corresponding electrode potential versus surface charge density curve becomes non-monotonic and shows a change of slope, and thus the resultant integral and differential capacitances can become negative. This nonphysical result is the result of an incipient singularity when a large positive charge is too near a negatively charged electrode. Overall, the off-center charge model suggests a useful recipe to model electrical asymmetry within the broader context of the primitive model provided that the off-center charge is not too near the surface of the electrode.

Ionic liquids-mediated interactions between nanorods

Surface forces mediated by room-temperature ionic liquids (RTILs) play an essential role in diverse applications including self-assembly, lubrication, and electrochemical energy storage. Therefore, their fundamental understanding is critical. Using molecular simulations, we study the interactions between two nanorods immersed in model RTILs at rod-rod separations where both structural and double layer forces are important. The interaction force between neutral rods oscillates as the two rods approach each other, similar to the classical structural forces. Such oscillatory force originates from the density oscillation of RTILs near each rod and is affected by the packing constraints imposed by the neighboring rods. The oscillation period and decay length of the oscillatory force are mainly dictated by the ion density distribution near isolated nanorods. When charges are introduced on the rods, the interaction force remains short-range and oscillatory, similar to the interactions between planar walls mediated by some protic RTILs reported earlier. Nevertheless, introducing net charges to the rods greatly changes the rod-rod interactions, e.g., by delaying the appearance of the first force trough and increasing the oscillation period and decay length of the interaction force. The oscillation period and decay length of the oscillatory force and free energy are commensurate with those of the space charge density near an isolated, charged rod. The free energy of rod-rod interactions reaches local minima (maxima) at rod-rod separations when the space charges near the two rods interfere constructively (destructively). The insight on the short-range interactions between nanorods in RTILs helps guide the design of novel materials, e.g., ionic composites based on rigid-rod polyanions and RTILs.

Atomistic simulations of cation hydration in sodium and calcium montmorillonite nanopores

During the last four decades, numerous studies have been directed to the swelling smectite-rich clays in the context of high-level radioactive waste applications and waste-liners for contaminated sites. The swelling properties of clay mineral particles arise due to hydration of the interlayer cations and the diffuse double layers formed near the negatively charged montmorillonite (MMT) surfaces. To accurately study the cation hydration in the interlayer nanopores of MMT, solvent-solute and solvent-clay surface interactions (i.e., the solvation effects and the shape effects) on the atomic level should be taken into account, in contrast to many recent electric double layer based methodologies using continuum models. Therefore, in this research we employed fully atomistic simulations using classical molecular dynamics (MD) simulations, the software package GROMACS along with the CLAYFF forcefield and the SPC/E water model. We present the ion distributions and the deformation of the hydrated coordination structures, i.e., the hydration shells of Na⁺ and Ca²⁺ in the interlayer, respectively, for MMT in the first-layer, the second-layer, the third-layer, the fourth-layer, and the fifth-layer (1W, 2W, 3W, 4W, and 5W) hydrate states. Our MD simulations show that Na⁺ in Na-MMT nanopores have an affinity to the ditrigonal cavities of the clay layers and form transient inner-sphere complexes at about 3.8 Å from clay midplane at water contents less than the 5W hydration state. However, these phenomena are not observed in Ca-MMT regardless of swelling states. For Na-MMT, each Na⁺ is coordinated to four water molecules and one oxygen atom of the clay basal-plane in the first hydration shell at the 1W hydration state, and with five to six water molecules in the first hydration shell within a radius of 3.1 Å at all higher water contents. In Ca-MMT, however each Ca²⁺ is coordinated to approximately seven water molecules in the first hydration shell at the 1W hydration state and about eight water molecules in the first hydration shell within a radius of 3.3 Å at all higher hydration states. Moreover, the MD results show that the complete hydration shells are nearly spherical with an orthogonal coordination sphere. They could only be formed when the basal spacing d₀₀₁ ≥ 18.7 Å, i.e., approximately, the interlayer separation h ≥ 10 Å. Comparison between DFT and MD simulations shows that DFT failed to reproduce the outer-sphere complexes in the Stern-layer (within ∼5.0 Å from the clay basal-plane), observed in the MD simulations.

Importance of Ion Packing on the Dynamics of Ionic Liquids during Micropore Charging

Molecular simulations of the diffusion of EMIM(+) and TFSI(-) ions in slit-shaped micropores under conditions similar to those during charging show that in pores that accommodate only a single layer of ions, ions diffuse increasingly faster as the pore becomes charged (with diffusion coefficients even reaching ∼5 × 10(-9) m(2)/s), unless the pore becomes very highly charged. In pores wide enough to fit more than one layer of ions, ion diffusion is slower than in the bulk and changes modestly as the pore becomes charged. Analysis of these results revealed that the fast (or slow) diffusion of ions inside a micropore during charging is correlated most strongly with the dense (or loose) ion packing inside the pore. The molecular details of the ions and the precise width of the pores modify these trends weakly, except when the pore is so narrow that the ion conformation relaxation is strongly constrained by the pore walls.

Structure of an electric double layer containing a 2:2 valency dimer electrolyte

The structure of a planar electric double layer formed by a 2:2 valency dimer electrolyte in the vicinity of a uniformly charged planar hard electrode is investigated using density functional theory and Monte Carlo simulations. The dimer electrolyte consists of a mixture of charged divalent dimers and charged divalent monomers in a dielectric continuum. A dimer is constructed by two tangentially tethered rigid spheres, one of which is divalent and positively charged and the other neutral, whereas the monomer is a divalent and negatively charged rigid sphere. The density functional theory reproduces well the simulation results for (i) the singlet distributions of the various ion species with respect to the electrode, and (ii) the mean electrostatic potential. Comparison with earlier results for a 2:1/1:2 dimer electrolyte shows that the double layer structure is similar when the counterion has the same valency.

The tail effect on the shape of an electrical double layer differential capacitance curve

The differential capacitance curve for the double layer formed by an electrolyte dissolved in a solvent is commonly believed to be parabolic-like with a minimum at low electrolyte charge concentration and low electrode surface charge density, and independent of electrolyte concentration at high electrolyte concentrations and high electrode charge and would be, in the absence of solvent effects, featureless at these latter conditions. This is the prediction of the popular Gouy-Chapman-Stern theory. In contrast, for an ionic liquid this curve can have a single or a double hump (or a bell or camel shape). Fedorov et al. [Electrochem. Commun. 12, 296 (2010)]10.1016/j.elecom.2009.12.019 have related these humps, particularly the double hump, to the neutral tails of ions in many ionic liquids. Evidence presented here shows, however, that such humps are general features of the differential capacitance of a double layer, whether it be formed by ions with or without a neutral tail. The presence of a double or single hump results from the magnitude of the electrolyte charge concentration. For both spherical ions or non-spherical ions consisting of charged heads and neutral tails, the shape of the differential capacitance transforms continuously from a double hump to a single hump as the electrolyte concentration is increased.

Microscopic Insights into the Electrochemical Behavior of Nonaqueous Electrolytes in Electric Double-Layer Capacitors

Electric double-layer capacitors (EDLCs) are electrical devices that store energy by adsorption of ionic species at the inner surface of porous electrodes. Compared with aqueous electrolytes, ionic liquid and organic electrolytes have the advantage of larger potential windows, making them attractive for the next generation of EDLCs with superior energy and power densities. The performance of both ionic liquid and organic electrolyte EDLCs hinges on the judicious selection of the electrode pore size and the electrolyte composition, which requires a comprehension of the charging behavior from a microscopic view. In this Perspective, we discuss predictions from the classical density functional theory (CDFT) on the dependence of the capacitance on the pore size for ionic liquid and organic electrolyte EDLCs. CDFT is applicable to electrodes with the pore size ranging from that below the ionic dimensionality to mesoscopic scales, thus unique for investigating the electrochemical behavior of the confined electrolytes for EDLC applications.

On the Atomistic Nature of Capacitance Enhancement Generated by Ionic Liquid Electrolyte Confined in Subnanometer Pores

The capacitance enhancement experimentally observed in electrodes with complex morphology of random subnanometer wide pores is an intriguing phenomena, yet the mechanisms for such enhancement are not completely understood. Our atomistic molecular dynamics simulations demonstrate that in subnanometer slit-geometry nanopores, a factor of 2 capacitance enhancement (compared to a flat electrode) is possible for the 1-ethyl-3-methylimidazolium (EMIM)-bis(trifluoro-methylsulfonyl)imide (TFSI) ionic liquid electrolyte. This capacitance enhancement is a result of a fast charge separation inside the nanopore due to abrupt expulsion of co-ions from the pore while maintaining an elevated counterion density due to strong screening of electrostatic repulsive interactions by the conductive pore. Importantly, we find that the capacitance enhancement can be very asymmetric. For the negatively charged 7.5 Å wide pore, the integral capacitance is 100% larger than on a flat surface; however, on the positive electrode, almost no enhancement is observed. Detailed analysis of structure and composition of electrolyte inside nanopores shows that the capacitance enhancement and the shape of differential capacitance strongly depend on the details of the ion chemical structure and a delicate balance of ion-surface and ion-ion interactions.