Non-ideal Electrolyte Research Articles

An MPM-Based Phase-Field Simulation of Plating and Stripping of Lithium with a Solid Electrolyte Interphase

A methodology for performing phase-field simulations of plating and stripping in the presence of a solid electrolyte interphase (SEI) is presented and applied to a lithium metal electrode. Material point method (MPM) simulations are performed assuming a homogeneous SEI layer and are compared with experiment. Results are consistent with experiment for two electrolytes and confirm the dominance of the SEI layer in determining cell impedance. Notably, in some instances, the SEI potential drop greatly affected activation overpotential, differing from the applied potential. To accurately depict stripping current vs potential for SEI-free systems, the model considered non-ideal electrolyte effects: concentration-dependent salt activity coefficient, salt diffusion coefficient, and electrolyte conductivity. Conversely, systems with SEI layers displayed minimal non-ideal concentration-related electrolyte effects due to impedance originating primarily from the SEI. In plating scenarios, low SEI salt concentration negated the need for non-ideal SEI effects. However, for stripping, non-ideal salt-concentration dependent SEI effects were crucial in reproducing experimental behavior, owing to high salt concentration at the electrode/SEI interface.

Understanding the solvation structures of glyme-based electrolytes by machine learning molecular dynamics

Glyme-based electrolytes are of great interest for rechargeable lithium metal batteries due to their high stability, low vapor pressure, and non-flammability. Understanding the solvation structures of these electrolytes at the atomic level will facilitate the design of new electrolytes with novel properties. Recently, classical molecular dynamics (CMD) and ab initio molecular dynamics (AIMD) have been applied to investigate electrolytes with complex solvation structures. On one hand, CMD may not provide reliable results as it requires complex parameterization to ensure the accuracy of the classical force field. On the other hand, the time scale of AIMD is limited by the high cost of ab initio calculations, which causes that solvation structures from AIMD simulations depend on the initial configurations. In order to solve the dilemma, machine learning method is applied to accelerate AIMD, and its time scale can be extended dramatically. In this work, we present a computational study on the solvation structures of triglyme (G3) based electrolytes by using machine learning molecular dynamics (MLMD). Firstly, we investigate the effects of density functionals on the accuracy of machine learning potential (MLP), and find that PBE-D3 shows better accuracy compared to BLYP-D3. Then, the densities of electrolytes with different concentration of LiTFSI are computed with MLMD, which shows good agreement with experiments. By analyzing the solvation structures of 1 ns MLMD trajectories, we found that Li+ prefers to coordinate with a G3 and a TFSI− in equimolar electrolytes. Our work demonstrates the significance of long-time scale MLMD simulations for clarifying the chemistry of non-ideal electrolytes.

The Double Layer Capacity of Non-Ideal Electrolyte Solutions – a Numerical Study

The capacity of electrochemical interfaces is an important characteristic of the adjacent electrode and electrolyte materials [5,2]. In order to interpret experimental results of capacity measurements, mathematical models resolving the space charge layer are necessary [3,4,6]. These are usually based on Poisson-Nernst-Planck-type equations, which – together with equilibrium conditions – allow for a numerical computation of the differential capacity. In recent research, progress has been made in the modeling of space charge layers, most notably with taking the solvation effect into account [1,3], which leads to a coupled Poisson-momentum equation system [2,3,4]∇(ε0(1+χ)∇φ) = -q(φ,p)∇p = -q(φ,p)∇φwhere φ is the electrostatic potential, p the (local) material pressure, and q the charge density.The electrolyte is mainly considered as ideal mixture, which yields for the chemical potential μα ∼ log (yα), where yα is the mole fraction of constituent Xα (α = 0, 1, ..., N), which in turn yields in thermodynamic equilibrium an analytic expression yα = yα(φ,p) and thus q = q(φ,p) via the incompressibility constraint.Non-idealities, for example Debye-Hückel-like activity coefficients [7,8], yield more complex representations μα = μα(yα) or even μα = μα(y1, ..., yN), whereby the equilibrium condition ∇μα + e0zα∇φ = 0 cannot be employed anymore to derive an explicit expression for yα. Instead, it remains an implicit (differential) equation, which has to be solved (numerically) together with the Poisson and the momentum equation.For different examples of non-ideal chemical potential functions, e.g. Debye-Hückel-like acitivity coefficients [7,8], we derive the corresponding boundary value problems. Some remarks on mathematical issues of the derivation are given throughout the presentation and we describe the general strategy how to solve the corresponding coupled, non-linear differential equation system. Subsequently we provide numerical results for the differential capacity and the corresponding space charge layers and investigate the impact of the non-ideality by comparison to ideal, incompressible solvation mixtures.[1] M. Landstorfer. Electrochemistry Communications, 92:56–59 (2018).[2] M. Landstorfer, C. Guhlke, and W. Dreyer. Electrochimica Acta, 201:187–219 (2016).[3] W. Dreyer, C. Guhlke, and M. Landstorfer. Electrochemistry Communications, 43(0):75–78 (2014).[4] W. Dreyer, C. Guhlke, and R. Muller. Phys. Chem. Chem. Phys., 15:7075–7086 (2013).[5] G. Valette. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 122(0):285–297 (1981).[6] C.-L. Li and J.-L. Liu. SIAM Journal on Applied Mathematics, 80(5):2003–2023 (2020).[7] P. Debye and E. Hückel. Physikalische Zeitschrift, 24:185–206 (1923).[8] K. S. Pitzer. Activity coefficients in electrolyte solutions. CRC press, 2018.

An integrated theoretical-experimental approach to understand facilitated proton transfer-electron transfer coupled reactions at thick-film modified electrodes

The main purpose of the current work is to generalize the analytical model for the facilitated proton transfer-electron transfer coupled reactions at thick organic film-modified electrodes, including ion pairing in the organic phase and considering non-ideal electrolyte solutions in both phases. The main equations to calculate half-wave potentials developed in this model allow the simulation of different chemical systems, comprising hydrophilic and hydrophobic neutral weak bases, at different experimental conditions such as pH, organic phase to aqueous phase volume ratio, and concentration ratios between the redox probe and the transferring protonated species. The model was checked against experimental voltammetric responses measured with the transfer of Tylosin A at the water|1,2-dichloroethene interface. Consequently, we present here an integrated theoretical-experimental approach in order to compare the results of our previous model [Zanotto et al. Electrochim. Acta 258 (2017) 727–734] with experimental data from Tylosin A and predicted half-wave potentials.

Ion transfer of weak acids across liquid | liquid interfaces

The main purpose of this paper is to develop a model for the ion transfer of weak acids across liquid|liquid interfaces including ion pairing and non-ideal electrolyte solutions to calculate the half-wave potential. The main equation derived in this model allows the simulation of different chemical systems, comprising multiple acid-base equilibria, hydrophilic and hydrophobic neutral weak acids, and different anions, including ion-pair formation in the organic phase. Hence, several representative chemical systems are analysed in detail in order to demonstrate the usefulness of the model. In addition, simple criteria to evaluate the presence of ion-pairs in the organic phase as well as the calculation of the apparent ion-pair formation constants are included.

(Invited) Engineering Approaches to Lithium-Ion Cell Design

By far, most effort in lithium-ion technology is devoted to the development of new and improved materials such as intercalation compounds, electrolytes, and binders. However, as applications of lithium-ion technology have expanded, so has interest in designing batteries using existing chemistries. Notably, consumer electronics companies are maximizing energy density by using irregularly shaped cells, and in electric vehicle makers are producing battery packs that are thermally uniform in operation. The challenge of engineering models is to add value in the design process in a practical way. There has been some notable success in battery design based on the unit cell concept. A “unit cell” is defined as a discrete volume element that contains the material between the positive and negative current collectors. So, in a lithium-ion cell, the unit cell is comprised of the negative electrode coating, separator, and positive electrode coating. The unit cell encompasses all the electrochemistry and mass transfer processes that occur during the life of a lithium-ion cell. The behavior of a unit cell can be simulated by a number of different models depending on the objective of the study. The unit cell model serves as a building block for a full battery model which is constructed by connecting unit cells to current collectors. Simple unit cell models based on electric circuit analogs have proved the most successful because of the ease in which their parameters can be readily measured and they are computational efficient. Tables of parameters can be determined as functions of charge and discharge current, temperature, state of charge, and age, and then interpolation used to obtain values at intermediate points. Electric circuit models have been successfully used for scale-up from small to large cells and simulation of battery packs. Despite these successes, there is great interest in physics-based models, most notably the DUALFOIL model. The DUAL model (the lithium-ion portion of the DUALFOIL model) uses conservation of mass and energy, non-ideal electrolyte transport theory, Butler-Volmer kinetics, Fick’s law, Kirchoff’s law, and Ohm’s law to simulate mass and charge transport in a lithium-ion cell. In theory, the model can predict the effect of unit cell design variables such as porosity and electrode thickness, on performance; a number of academic studies have used the DUAL model for optimization. The model has been successful in representing the behavior of lithium-ion cells probably because the parameters are adjusted to fit data sets, though a recent study has reported some success in actually predicting cell performance using independently measured parameters. The difficulty in parameterizing the DUAL model makes it difficult for battery makers to use, and even more difficult for OEMs to use. Still, there is great interest in the DUALFOIL model and numerous enhancements have been made. The ever increasing computational power of computers and the widespread availability of the DUAL model make it highly likely that applications of this model will continue to expand. Today’s engineering models are fairly successful for simulation of charge and discharge behavior of lithium-ion cells. The growing acceptance of these models should create a positive feedback loop in which validated parameter sets drive use and use drives development of validated parameter sets, and so enable better designs of lithium-ion cells.

Analysis and modeling of alkali halide aqueous solutions

A new model is proposed for correlation and prediction of thermodynamic properties of electrolyte solutions. In the proposed model, terms of a second virial coefficient-type and of a KT-UNIFAC model are used to account for a contribution of binary interactions between ion and ion, and water and ion, respectively, with a Debye–Hückel term for electrostatic interactions. In a second approach of the model, additional parameters for interactions of ion pairs in the KT-UNIFAC are introduced as a correction to get better agreement with data. Structural parameters of ions used in the framework of UNIFAC or UNIQUAC are newly estimated using ionic radii for physically correct representation of the combinatorial part. Including temperature-dependent coefficients in the interaction parameters, significant improvements in accuracy are achieved for a wide range of temperatures. This work is focused on calculations for various electrolyte properties of alkali halide aqueous solutions such as mean ionic activity coefficients, osmotic coefficients, and salt solubilities. The model covers highly nonideal electrolyte systems such as lithium chloride, lithium bromide and lithium iodide, that is, systems that are very soluble in water, for example, up to more than 30 mol kg−1. Phase behaviors for the systems are analyzed at concentrations of salt up to the solubility in water at temperatures between 273 and 373 K by comparing calculated results with available experimental data and available models.

Ray-theory approach to electrical-double-layer interactions.

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress-associated with the ray contributions interacting nonlinearly-decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

Ionization of methyl orange in aqueous sodium chloride solutions

Ionization constants of sodium 4′-dimethylaminoazobenzene-4-sulphonate (methyl orange) were determined by means of spectrophotometric measurements in water and in aqueous sodium chloride solutions with molalities up to 2mol·kg−1 at temperatures between 278.15K and 333.15K. The temperature dependence of the thermodynamic acidity constant shows a slight curvature in accordance with published data. The influence of sodium chloride on the methyl orange deprotonation was assessed by the measurement of stoichiometric acidity constants in this ionic medium. The Pitzer theory, widely used in the evaluation of the excess free energy of non-ideal electrolyte solutions, was applied to the computation of the activity coefficients of the chemical species involved in the equilibria and a good fit of those equations to the experimental data was observed, at all temperatures under consideration.

Correlation Equation for Predicting Attachment Efficiency (α) of Organic Matter-Colloid Complexes in Unsaturated Porous Media

Naturally occurring polymers such as organic matter have been known to inhibit aggregation and promote mobility of suspensions in soil environments by imparting steric stability. This increase in mobility can significantly reduce the water filtering capacity of soils, thus jeopardizing a primary function of the vadose zone. Improvements to classic filtration theory have been made to account for the known decrease in attachment efficiency of electrostatically stabilized particles, and more recently, of sterically stabilized particles traveling through simple and saturated porous media. In the absence of an established unsaturated transport expression, and in the absence of applicable theoretical approaches for suspensions with asymmetric and nonindifferent electrolytes, this study presents an empirical correlation to predict attachment efficiency (α) for electrosterically stabilized suspensions in unsaturated systems in the presence of nonideal electrolytes. We show that existing models fall short in estimating polymer-coated colloid deposition in unsaturated media. This deficiency is expected given that the models were developed for saturated conditions where the mechanisms controlling colloid deposition are significantly different. A new correlation is derived from unsaturated transport data and direct characterization of microspheres coated with natural organic matter over a range of pH and CaCl(2) concentrations. The improvements to existing transport models include the following: adjustment for a restricted liquid-phase in the medium, development of a quantitative term to account for unsaturated transport phenomena, and adjustments in the relative contribution of steric stability parameters based on direct measurements of the adsorbed polymer layer characteristics. Differences in model formulation for correlations designed for saturated systems and the newly proposed correlation for unsaturated systems are discussed, and the performance of the new model against a comprehensive set of experimental observations is evaluated.

Ionization of Acetic Acid in Aqueous Potassium Chloride Solutions

Stoichiometric ionization constants of acetic acid were determined in the temperature range (10 to 40) °C, from potentiometric titrations in aqueous potassium chloride solutions with molalities up to 3 mol·kg–1. The electrochemical cell was calibrated in terms of hydrogen ion concentration, and the calculations were performed by means of the SUPERQUAD computer program. The Pitzer theory, widely used in the evaluation of the excess free energy of nonideal electrolyte solutions, was applied to the calculation of the activity coefficient of each chemical species involved in the equilibria, and a good fit was observed at all temperatures. From these results, Pitzer interaction coefficients for potassium acetate were determined. This model was also used to calculate the chloride ion activity coefficient in acetate buffer systems with added potassium chloride, at ionic strengths higher than 0.1 mol·kg–1, the limit of validity of the Bates–Guggenheim convention.

The Semi-Ideal Solution Theory for Mixed Ionic Solutions at Solid−Liquid−Vapor Equilibrium

The semi-ideal solution theory has been presented to describe the changes in thermodynamic properties accompanying the process of mixing the nonideal electrolyte solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) at constant activities of NY and H2O, including concentration, chemical potential, activities of all M(i)X(i), Gibbs free energy, enthalpy, entropy, thermal properties, and volumetric properties. The theory states that, under the conditions of equal activities of NY and H2O, the average hydration numbers characterizing the ion-solvent interactions have the same values in the mixture as in the subsystems and the process of mixing these nonideal electrolyte solutions is as simple as that of mixing the ideal solutions if the contributions from the ion-ion interactions to the solvent activity are assumed to be the same in the mixture as in its subsystems, which has been justified by the calculations of the Pitzer equation. Therefore, a series of novel linear equations are established for the thermodynamic properties accompanying the process of mixing these nonideal solutions as well as mixing the ideal solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) of equal mole fractions of NY and H2O. From these equations, the widely applied empirical Zdanovskii's rule is derived theoretically, and the important constant in the McKay-Perring equation under isopiestic equilibrium is determined theoretically, which has been substantiated by comparisons with the experimental results for 18 mixtures reported in the literature. Isopiestic measurements have been made for the systems BaCl2-LaCl3-H2O, NaCl-BaCl2-LaCl3-H2O, and NaCl-LaCl3-BaCl2.2H2O(sat)-H2O at 298.15 K. The results are used to test the novel linear concentration relations, and the agreement is excellent. The novel predictive equation for the activity coefficient of M(i)X(i) in M1X1-M2X2-(NY)sat-H2O has been compared with the calculations of the Pitzer equation, and the agreement is good.

A discussion of the paper “Electrostatic repulsion between particles in cement suspensions: domain of validity of linearized Poisson–Boltzmann equation for nonideal electrolytes” by R.J. Flatt and P. Bowen

In this discussion paper, the authors comment on a study of the electrostatic repulsion between particles in cement suspensions by Flatt and Bowen (2003). The commentator applauds the original authors for departing from the usual practice of treating pore solution as ideal and symmetrical electrolytes. Instead, they have treated them as noninteger symmetric electrolytes. This has allowed the authors to approach the real world situation more closely. The commentator describes some misgivings about the methodology and asks the authors to clear up some of these concerns. The author concludes by asking four questions: what potential should be used to calculate the electrostatic repulsion at the initial stages of hydration? Where should the solid-liquid interface boundary be placed? And how is this interface located? Also, how will the number density of cement hydration products effect the electrostatic repulsion.

Reply to the discussion by S. Chatterji of the paper “Electrostatic repulsion between particles in cement suspensions: domain of validity of linearized Poisson–Boltzmann equation for nonideal electrolytes”

In this discussion paper, the original authors reply to a comment on their 2003 study of the electrostatic repulsion between particles in cement suspensions. The original authors departed from the usual practice of treating pore solution as ideal and symmetrical electrolytes. Instead, they treated them as noninteger symmetric electrolytes. This has allowed the authors to approach the real world situation more closely. The commentator had asked four questions: What potential should be used to calculate the electrostatic repulsion at the initial stages of hydration? Where should the solid-liquid interface boundary be placed? And how is this interface located? Also, how will the number density of cement hydration products effect the electrostatic repulsion? In this discussion, Flatt and Bowen address each of these questions, emphasizing practical approaches to the concerns raised.

Electrostatic repulsion between particles in cement suspensions: Domain of validity of linearized Poisson–Boltzmann equation for nonideal electrolytes

To understand the dispersion of cement particles by superplasticizers, proper quantification of the possible mechanisms involved (electrostatic, steric, and depletion forces) is required. This is an important objective to help understand the origin of unexpected incompatibilities between some cement and superplasticizer combinations and more generally predict the rheological behavior. The relative importance of the electrostatic interaction with respect to steric hindrance is currently under much debate. The debate centered on this topic has not fully explored how the nonideal electrolyte found in cement suspensions effects the simplified Debye–Hückel approximation for evaluation of electrostatic repulsion. In this article, the nonideality of the cement aqueous phase—suspension electrolyte—has been taken into account based on solubility equilibria of the possible ionic species present in typical cement suspensions. By replacing the normally assumed symmetric electrolyte (1:1, 2:2, or 3:3) with a noninteger symmetric electrolyte, the simple Debye–Hückel approach has been shown to remain valid for negative potentials down to around 30 mV. Significant deviations are found for positive potentials greater than 10 mV.

Diffuse layer near the zero charge point in the case of non-ideal electrolyte solutions

A theoretical analysis of the diffuse layer in solutions of a 1:1 electrolyte near the zero charge point was carried out without using the ideal solution concept. Accordance with the Gibbs adsorption equation demands fulfilment of the equality of the cross concentration derivatives of the chemical potentials of cations and anions. An expression was found for the differential capacity of the diffuse layer at the zero charge point as a function of the concentration derivatives of the chemical potentials of cations and anions. On this basis, and on the basis of Trasatti and coworkers' idea of using the ideally polarizable electrode as a constant reference electrode, it was shown that there exists the possibility, in principle, of finding experimentally the derivatives of the chemical potentials of ions with respect to both the cation concentration and the anion concentration. A plausible explanation for conserving the Parsons-Zobel dependence in the non-ideal solutions is given.

Generalized Maxwell-Wagner response in dispersive silver borophosphate glasses

The dielectric response of a glass-forming system (Ag2O∶B2O3∶P2O5) has been measured in the frequency range from 10−3–105 Hz and over temperatures in the range 150–400 K for three different compositions. The dynamic behaviour of the conductance and capacitance in these glasses has been observed to follow fractional power-law dependencies on frequency which obey the generalized Maxwell-Wagner relationships. The power-law dispersions for the bulk and the surface layer of the non-ideal solid electrolyte 0.6Ag2O∶xB2O3∶(0.4−x) P2O5 have been modelled mathematically using frequency-dependent resistive and capacitive elements in a conventional equivalent network. It is shown that controlled substitution of B2O3 in the glassy network influences the response and introduces an imperfect charge transport, the quasi-d.c. process of limited charge transport in place of bulk conduction, at higher frequencies, and affects the diffusion barrier at the electrodes to make them, weakly, more conductive at the lowest frequencies. The magnitudes of the activation energies of conduction indicate thermally activated localized hopping of silver ions between neighbouring sites in a structure that is modified by the addition of boron oxide.

Nonequilibrium thermodynamics of nonlinear diffusion flux in a nonideal electrolyte solution.

The nonlinear diffusion-dispersion flux of the total mole concentrations in nonideal electrolyte solution is represented by a Korteweg--de Vries (KdV) type of equation in equilibrium. With small perturbations of the KdV equation's coefficients, we can obtain its nonequilibrium steady-state flux. One finding is that the nonequilibrium flux is separated into the nonlinear wave propagation and the diffusion process for entropy production. By means of the perturbation procedure, we further studied the individual chemical component fluxes. The major finding is that in the stationary state, the macroscaled space fluxes between individual components still remain in the no-total-flux system. From this finding, it follows that there is a hierarchy in the thermodynamical flux. Then we obtain Onsager's relations in the nonlinear form and the entropy production for each hierarchy of the flux.

Thermodynamics of ion association in the mean spherical approximation

A free energy minimization procedure is presented for the evaluation of the association equilibrium of nonideal electrolytes in the mean spherical approximation (MSA). This model is applied to electrostatic Bjerrum association of 2-2 electrolytes in water, to chemical association of 1-1 electrolytes in low dielectric constant media, and to weak electrolytes in water. The present model is also applicable to mixtures of associating electrolytes

GENERAL LINEARIZED MATRIX THEORY OF ELECTROCHEMICAL MASS TRANSFER WITH APPLICATIONS TO ELECTRODE PROCESSES AND ION EXCHANGE

Abstract A general linearized matrix theory for electrochemical mass transfer is presented. The accuracy of the theory when applied to cases where electric current exists is tested by comparing results with exact calculations of the effect of ionic migration on limiting currents at a rotating disk electrode with laminar flow and at a flat plate electrode adjacent to a stagnant fluid film. Application of the theory is further illustrated by using it to calculate the effect of ionic migration on limiting currents in a turbulent, law-of-the-wall boundary layer. Finally, the theory is used to evaluate commonly used “film-model” methods for generalizing binary mass-transfer correlations to multicomponent nonideal mixtures. For this last purpose, a film-model generalization method was developed for nonideal electrolyte mixtures. The method is equivalent to that used by Krishnamurthy and Taylor (1985) for mass-transfer in nonideal nonelectrolyte mixtures. Results using the film-model method are compared to matri...