Estimates of Electrical Conductivity from Molecular Dynamics Simulations: How to Invest the Computational Effort

Electrical Conductivity of Subsurface Ocean Analogue Solutions from Molecular Dynamics Simulations

Investigating the habitability of ocean worlds is a priority of current and future NASA missions. The Europa Clipper mission will conduct approximately 50 flybys of Jupiter's moon Europa, returning a detailed portrait of its interior from the synthesis of data from its instrument suite. The magnetometer on board has the capability of decoupling Europa's induced magnetic field to high precision, and when these data are inverted, the electrical conductivity profile from the electrically conducting subsurface salty ocean may be constrained. To optimize the interpretation of magnetic induction data near ocean worlds and constrain salinity from electrical conductivity, accurate laboratory electrical conductivity data are needed under the conditions expected in their subsurface oceans. At the high-pressure, low-temperature (HPLT) conditions of icy worlds, comprehensive conductivity data sets are sparse or absent from either laboratory data or simulations. We conducted molecular dynamics simulations of candidate ocean compositions of aqueous NaCl under HPLT conditions at multiple concentrations. Our results predict electrical conductivity as a function of temperature, pressure, and composition, showing a decrease in conductivity as the pressure increases deeper into the interior of an icy moon. These data can guide laboratory experiments at conditions relevant to icy moons and can be used in tandem to forward-model the magnetic induction signals at ocean worlds and compare with future spacecraft data. We discuss implications for the Europa Clipper mission.

Effect of K+ Force Fields on Ionic Conductivity and Charge Dynamics of KOH in Ethylene Glycol

Predicting ionic conductivity is crucial for developing efficient electrolytes for energy storage and conversion and other electrochemical applications. An accurate estimate of ionic conductivity requires understanding complex ion-ion and ion-solvent interactions governing the charge transport at the molecular level. Molecular simulations can provide key insights into the spatial and temporal behavior of electrolyte constituents. However, such insights depend on the ability of force fields to describe the underlying phenomena. In this work, molecular dynamics simulations were leveraged to delineate the impact of force field parameters on ionic conductivity predictions of potassium hydroxide (KOH) in ethylene glycol (EG). Four different force fields were used to represent the K+ ion. Diffusion-based Nernst-Einstein and correlation-based Einstein approaches were implemented to estimate the ionic conductivity, and the predicted values were compared with experimental measurements. The physical aspects, including ion-aggregation, charge distribution, cluster correlation, and cluster dynamics, were also examined. A force field was identified that provides reasonably accurate Einstein conductivity values and a physically coherent representation of the electrolyte at the molecular level.

Computing Accurate True Self-Diffusion Coefficients and Shear Viscosities Using the OrthoBoXY Approach

In a recent paper [Busch, J.; Paschek, D. J. Phys. Chem. B 2023, 127, 7983-7987], we have shown that for molecular dynamics (MD) simulations using orthorhombic periodic boundary conditions with "magic" box length ratios of Lz/Lx = Lz/Ly = 2.7933596497, the self-diffusion coefficients Dx and Dy in x- and y-directions are independent of the system size. They both represent the true self-diffusion coefficient D0 = (Dx + Dy)/2, while the shear viscosity can be calculated from diffusion coefficients in x-, y-, and z-directions, using η = kBT·8.1711245653/[3πLz(Dx + Dy - 2Dz)]. In this contribution, we test this "OrthoBoXY" approach by its application to a variety of different systems: liquid water, dimethyl ether, methanol, triglyme, water/methanol mixtures, water/triglyme mixtures, and imidazolium-based ionic liquids. The chosen systems range from small-sized molecular liquids to complex mixtures and ionic liquids, while spanning a viscosity range of almost 3 orders of magnitude. We assess the efficiency of the method for computing true self-diffusion and viscosity data and provide simple formulas for estimating the required MD simulation lengths and sizes for delivering reliable data with targeted uncertainty levels. Our analysis of the system size dependence of statistical uncertainties for both the viscosity and the self-diffusion coefficient leads us to the conclusion that it is preferable to extend the simulation length instead of increasing the system size. MD simulations consisting of 768 molecules or ion pairs seem to be perfectly adequate.

Evidence for Complex Dynamics in Glassy Fast Ion Conductors: The Case of Sodium Thiosilicates

Classical molecular dynamics is used to study the dynamics of alkali ions in a promising fast ion conductor glass system, i.e., Na2S-SiS2. Diffusion in such thiosilicates is found to display various salient features of alkali silicates, i.e., channel-like diffusion with typical length scales emerging as the temperature is decreased to the glassy state, and Arrhenius behavior for both Na ion diffusivity and calculated conductivity. The dynamics appears, however, to be largely heterogeneous as manifested by fast and slow Na ion motion at intermediate times, both in the high-temperature liquid and in the glassy state. In the former, a diffusion-limited regime is found due to the increased motion of the network-forming species that limits the Na ion dynamics, whereas at low temperatures, the typical dynamical heterogeneities are recovered as observed close to the glass transition.

Computation of Electrical Conductivities of Aqueous Electrolyte Solutions: Two Surfaces, One Property

In this work, we computed electrical conductivities under ambient conditions of aqueous NaCl and KCl solutions by using the Einstein-Helfand equation. Common force fields (charge q = ±1 e) do not reproduce the experimental values of electrical conductivities, viscosities, and diffusion coefficients. Recently, we proposed the idea of using different charges to describe the potential energy surface (PES) and the dipole moment surface (DMS). In this work, we implement this concept. The equilibrium trajectories required to evaluate electrical conductivities (within linear response theory) were obtained by using scaled charges (with the value q = ±0.75 e) to describe the PES. The potential parameters were those of the Madrid-Transport force field, which accurately describe viscosities and diffusion coefficients of these ionic solutions. However, integer charges were used to compute the conductivities (thus describing the DMS). The basic idea is that although the scaled charge describes the ion-water interaction better, the integer charge reflects the value of the charge that is transported due to the electric field. The agreement obtained with experiments is excellent, as for the first time electrical conductivities (and the other transport properties) of NaCl and KCl electrolyte solutions are described with high accuracy for the whole concentration range up to their solubility limit. Finally, we propose an easy way to obtain a rough estimate of the actual electrical conductivity of the potential model under consideration using the approximate Nernst-Einstein equation, which neglects correlations between different ions.

Theoretical Investigation of the Structure and Physicochemical Properties of Alkaline and Alkaline Earth Metal Perchlorate Solutions in Sulfolane

To assess the possibility of using solutions of perchlorates of alkali and alkaline earth metals in sulfolane as electrolytes for electrochemical energy storage devices with metal negative electrodes, the physicochemical properties of 0.5 M solutions of Me(ClO₄)_n (Me = Li, Na, K, Mg, and Ca) in sulfolane were simulated by the method of molecular dynamics. The density, viscosity, conductivity, self-diffusion coefficients, and transport numbers are calculated. Satisfactory agreement between the calculated and experimentally measured properties of 0.5 M solutions of LiClO₄ and NaClO₄ in sulfolane suggests that the calculated values of the physicochemical properties of solutions of K, Mg, and Ca perchlorates are also close to real values. The study of the structure of solvate complexes of salts of alkali and alkaline earth metals with sulfolane by quantum chemical and molecular dynamics modeling showed that the first solvate shell of metal cations consists of sulfolane molecules. Regardless of the nature of the cation, sulfolane is coordinated to the metal cation by only one oxygen atom. Based on the analysis of the calculated values of the physicochemical properties of solutions of metal perchlorates in sulfolane, it can be concluded that they can be used as electrolyte systems of electrochemical energy storage devices with negative electrodes made of alkali and alkaline earth metals.

How Temperature, Pressure, and Salt Concentration Affect Correlations in LiTFSI/EMIM-TFSI Electrolytes: A Molecular Dynamics Study

Classical polarizable molecular dynamics simulations have been performed for LiTFSI solutions in the EMIM-TFSI ionic liquid. Different temperature or pressure values and salt concentrations have been examined. The structure and dynamics of the solvation shell of Li+ cations, diffusion coefficients of ions, conductivities of the electrolytes, and correlations between motions of ions have been analyzed. The results indicated that regardless of the conditions, significant correlations are present in all systems. The degree of correlations depends mainly on the salt fraction in the electrolyte and is much less affected by temperature and pressure changes. A positive correlation between motions of Li+ cations and TFSI anions, leading to the occurrence of negative Li+ transference numbers, exists for all conditions, although temperature and pressure changes affect the speed of anion exchange in Li+ solvation shells.

Efficient Parametrization of Force Field for the Quantitative Prediction of the Physical Properties of Ionic Liquid Electrolytes

The prediction of transport properties of room-temperature ionic liquids from nonpolarizable force field-based simulations has long been a challenge. The uniform charge scaling method has been widely used to improve the agreement with the experiment by incorporating the polarizability and charge transfer effects in an effective manner. While this method improves the performance of the force fields, this prescription is ad hoc in character; further, a quantitative prediction is still not guaranteed. In such cases, the nonbonded interaction parameters too need to be refined, which requires significant effort. In this work, we propose a three-step semiautomated refinement procedure based on (1) atomic site charges obtained from quantum calculations of the bulk condensed phase; (2) quenched Monte Carlo optimizer to shortlist suitable force field candidates, which are then tested using pilot simulations; and (3) manual refinement to further improve the accuracy of the force field. The strategy is designed in a sequential manner with each step improving the accuracy over the previous step, allowing the users to invest the effort commensurate with the desired accuracy of the refined force field. The refinement procedure is applied on N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide (DEME-TFSI), a front-runner as an electrolyte for electric double-layer capacitors and single-molecule-based devices. The transferability of the refined force field is tested on N,N-dimethyl-N-ethyl-N-methoxyethoxyethylammonium bis(trifluoromethanesulfonyl)imide (N_112,2O2O1-TFSI). The refined force field is found to be better at predicting both structural and transport properties compared to the uniform charge scaling procedure, which showed a discrepancy in the X-ray structure factor. The refined force field showed quantitative agreement with structural (density and X-ray structure factor) and transport properties-diffusion coefficients, ionic conductivity, and shear viscosity over a wide temperature range, building a case for the wide adoption of the procedure.

MeTFSI (Me = Li, Na) Solvation in Ethylene Carbonate and Fluorinated Ethylene Carbonate: A Molecular Dynamics Study

Classical and ab initio molecular dynamics (MD) simulations have been performed for electrolytes based on LiTFSI and NaTFSI solutions in ethylene carbonate and its mono- and difluoro derivatives. Differences between electrolytes with Li⁺ or Na⁺ ions and the effect of fluorination on the structure and transport properties have been analyzed. The observed differences are related to the strength of Me⁺-carbonate binding, which is weaker for the Na⁺ cation and/or fluorinated solvents. Infrared spectra have been computed from ab initio MD and density functional tight binding (DFTB) MD trajectories. The changes of vibrational frequencies have been related to the local structure of the electrolyte and to interactions between salt cations and solvent molecules. The frequency shifts obtained from the AIMD simulations agree with experimental data, whereas DFTB underestimates Na⁺-carbonate interactions.