Mixed Solvent Electrolyte Research Articles

An activity coefficient model for mixed-solvent electrolyte mixtures based on Gibbs–Duhem’s equation: A case study of mixtures of water, KCl and ethanol

Thermodynamic properties of mixtures with several fluid components and electrolytes are challenging to model. Models are needed to develop and improve a wide range of electrochemical systems such as fuel cells, lithium-ion batteries, and processes with ion-exchange membranes. In the literature, activity coefficients are extracted using fundamentally different experimental methods that rely on electrochemical cells, vapour pressure measurements, solubility measurements, etc. The reference states of the activity coefficients obtained from these methods are likely to differ. This makes it difficult to combine or compare activity coefficient models from different sources. In this work, we present a method using Gibbs–Duhem’s equation for the development of activity coefficient models of mixtures that are based on experimental data from different methods. We use the ternary mixture of KCl, H2O and ethanol as example. First, empirical expressions are developed for the logarithm of the activity coefficients of KCl and ethanol. The expression for the activity coefficient of H2O is next derived using Gibbs–Duhem’s equation. The resulting three activity coefficient models are fitted to available experimentally data from several sources, generating linear and relatively low-complexity activity coefficient models. The empirical activity coefficient models are next compared to the electrolyte cubic plus association (e-CPA) equation of state. The models give saturation pressures in ternary mixtures that have average absolute relative deviations for water/ethanol of 8.3/3.4% for the empirical model and 11.8/3.3% for e-CPA. Experimental data reduction procedures for concentration cells, formation cells, and vapour pressure measurements are discussed, and the freedom to choose the reference state and the consequences are highlighted.

Electron Transfer Dynamics at Dye-Sensitized SnO2/TiO2 Core/Shell Electrodes in Aqueous/Nonaqueous Electrolyte Mixtures.

The dynamics of photoinduced electron transfer were measured at dye-sensitized photoanodes in aqueous (acetate buffer), nonaqueous (acetonitrile), and mixed solvent electrolytes by nanosecond transient absorption spectroscopy (TAS) and ultrafast optical-pump terahertz-probe spectroscopy (OPTP). Higher injection efficiencies were found in mixed solvent electrolytes for dye-sensitized SnO2/TiO2 core/shell electrodes, whereas the injection efficiency of dye-sensitized TiO2 electrodes decreased with the increasing acetonitrile concentration. The trend in injection efficiency for the TiO2 electrodes was consistent with the solvent-dependent trend in the semiconductor flat band potential. Photoinduced electron injection in core/shell electrodes has been understood as a two-step process involving ultrafast electron trapping in the TiO2 shell followed by slower electron transfer to the SnO2 core. The driving force for shell-to-core electron transfer increases as the flat band potential of TiO2 shifts negatively with increasing concentrations of acetonitrile. In acetonitrile-rich electrolytes, electron injection is suppressed due to the very negative flat band potential of the TiO2 shell. Interestingly, a net negative photoconductivity in the SnO2 core is observed in mixed solvent electrolytes by OPTP. We hypothesize that an electric field is formed across the TiO2 shell from the oxidized dye molecules after injection. Conduction band electrons in SnO2 are trapped at the core/shell interface by the electric field, resulting in a negative photoconductivity transient. The overall electron injection efficiency of the dye-sensitized SnO2/TiO2 core/shell photoanodes is optimized in mixed solvents. The ultrafast transient conductivity data illustrate the crucial role of the electrolyte in regulating the driving forces for electron injection and charge separation at dye-sensitized semiconductor interfaces.

Phase diagrams of CoSO4-H2O and CoSO4-H2SO4-H2O systems for CoSO4·nH2O (n = 6,7) recovery by cooling and eutectic freeze crystallization

This paper reports the solid-liquid phase equilibria of the CoSO4-H2O and CoSO4-H2SO4-H2O systems at low temperatures. Binary and ternary phase diagrams, including the stable solid phases CoSO4·6H2O and CoSO4·7H2O were established using experimental data and thermodynamic modeling applying the mixed-solvent electrolyte (MSE) model. The results showed that the addition of H2SO4 shifts the eutectic temperature and concentration to lower values for cobalt sulfate and ice crystallization. The trends obtained from the experimental data and the modeling are consistent for the binary CoSO4-H2O system with good agreement, but the ternary CoSO4-H2SO4-H2O system shows some deviations. In general, the MSE model is shown to be reliable for inferring and establishing the phase diagram of the low-temperature system. The phase diagrams are helpful for designing the pathways of cooling crystallization and eutectic freeze crystallization and assessing the performance of the low-temperature crystallization process in the production of CoSO4 hydrates. In addition, some practical examples of cooling crystallization and eutectic freeze crystallization of CoSO4 solutions are provided.

Predictive thermodynamic model for solvent extraction of Iron(III) by tri-n-butyl phosphate (TBP) from chloride media

Hydrometallurgical processes are crucial to reducing the environmental impact of metal recovery, yet dealing with iron impurities is a major challenge. This paper presents a semi-empirical predictive thermodynamic model for iron removal from chloride media by solvent extraction with tri-n-butyl phosphate (TBP). This model is built upon the OLI mixed-solvent electrolyte framework (OLI-MSE). It goes beyond traditional thermodynamic models by incorporating the non-ideality of both the aqueous and organic phases in a single, chemistry-based thermodynamic model. On top of the OLI-MSE framework lies the chemical model that depicts the extraction of Fe(III) by forming an ion pair between the FeCl4– anion and protonated TBP (TBPH+) in the organic phase. The iron(III)-containing ion pair in the organic phase is further stabilized by interactions with neutral TBP molecules. Developing the model required modeling the Fe(III) – chloride chemistry in the aqueous phase, optimizing the HCl extraction model, and fitting the parameters between FeCl4–, TBPH+, and TBP to experimental solvent extraction data. The resulting thermodynamic model can predict the solvent extraction of iron(III) from complex feed solutions by TBP in aliphatic diluents at all concentrations up to undiluted TBP. It can be used to calculate the equilibrium energies and composition, and the species present at equilibrium.

Theoretical considerations on single and mixed solvent electrolyte solutions

Theoretical considerations on single and mixed solvent electrolyte solutions

Understanding the Surprising Ionic Conductivity Maximum in Zn(TFSI)2 Water/Acetonitrile Mixture Electrolytes.

Aqueous electrolytes composed of 0.1 M zinc bis(trifluoromethylsulfonyl)imide (Zn(TFSI)2) and acetonitrile (ACN) were studied using combined experimental and simulation techniques. The electrolyte was found to be electrochemically stable when the ACN V% is higher than 74.4. In addition, it was found that the ionic conductivity of the mixed solvent electrolytes changes as a function of ACN composition, and a maximum was observed at 91.7 V% of ACN although the salt concentration is the same. This behavior was qualitatively reproduced by molecular dynamics (MD) simulations. Detailed analyses based on experiments and MD simulations show that at high ACN composition the water network existing in the high water composition solutions breaks. As a result, the screening effect of the solvent weakens and the correlation among ions increases, which causes a decrease in ionic conductivity at high ACN V%. This study provides a fundamental understanding of this complex mixed solvent electrolyte system.

Correlating the Solvating Power of Solvents with the Strength of Ion-Dipole Interaction in Electrolytes of Lithium-ion Batteries.

The solvation structure of Li+ plays a significant role in determining the physicochemical properties of electrolytes. However, to date, there is still no clear definition of the solvating power of different electrolyte solvents, and even the solvents that preferentially participate in the solvation structure remain controversial. In this study, we comprehensively discuss the solvating power and solvation process of Li+ ions using both experimental characterizations and computational calculations. Our findings reveal that the solvating power is dependent on the strength of the Li+-solvent (ion-dipole) interaction. Additionally, we uncover that anions tend to enter the solvation sheath in most electrolyte systems through Li+-anion (ion-ion) interaction, which is weakened by the shielding effect of solvents. The competition between the Li+-solvent and Li+-anion interactions ultimately determines the final solvation structures. This insight into the fundamental understanding of the solvation structure of Li+ ions provides inspiration for the design of multifunctional mixed-solvent electrolytes for advanced batteries.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State.

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.

Modeling phase equilibria and speciation in aqueous solutions of rare earth elements with hydroxide and organic ligands

A thermodynamic model has been developed for calculating speciation and phase equilibria in aqueous solutions of rare earth elements (REEs) with hydroxide, acetate, citrate, and oxalate anions. The computational framework is based on the Mixed-Solvent Electrolyte (MSE) framework, which has been previously used to establish a systematic treatment of binary and multicomponent systems containing REE sulfates and chlorides up to solid–liquid saturation at temperatures up to 300 °C. The model has been parametrized by performing a multi-property analysis of critically evaluated speciation and solubility data. For rare earth hydroxides, a comprehensive model has been developed for fourteen REEs (i.e., for yttrium and all lanthanides except promethium). The effect of the crystallinity of rare earth hydroxides on their solubility has been analyzed. Model parameters have been determined for two limiting cases, i.e., for crystalline and amorphous hydroxides, while recognizing that the hydroxides may span a range of degrees of crystallinity. For the organic ligands, the model has been established for neodymium with additional analysis for other selected REEs. The model accurately reproduces the effects of pH, temperature, and complexation with organic ligands on the behavior of rare earth elements in aqueous solutions. When coupled with previously developed models for inorganic rare earth salts, it provides a thermodynamic tool for the design and optimization of separation processes for the production and recycling of REEs and for predicting the properties of REEs in geological and biological settings.

Thermodynamic Modeling the Solid–Liquid Phase Equilibrium of a Water–Methanol–Potassium Dihydrogen Phosphate Ternary System with a Mixed-Solvent Electrolyte (MSE) Model

The solubility measurement of potassium dihydrogen phosphate (MKP) in a water–methanol system is of great significance for the salting-out crystallization of MKP. The solubility of MKP in the H2O–CH3OH solution was determined by the static equilibrium method in the range of 283.15–343.15 K, and the molar fraction of CH3OH varied from 0.0588 to 0.6923. The mixed-solvent electrolyte model (MSE) was used to regress the experimental results, and new parameters were obtained. Based on it, the thermodynamic model of the H2O–CH3OH–MKP system was established, which is in good agreement with the experimental results, with a relative average absolute deviation of 6.46%. Then, the change in the ion concentration and the activity coefficients in the system were predicted by the thermodynamic model. Finally, the Pixact Crystallization Monitoring (PCM) system and a scanning electron microscope (SEM) were used to observe the crystallization process and the morphology of MKP in the H2O–CH3OH system, respectively.

A comparative study of thermodynamic modeling and experimental measurement of precipitation titration curves for single- and multi-component sulfate systems

The current study is focused on the thermodynamic modeling and experimental measurement of metal hydroxide precipitation titration curves for the single- and multi-component sulfate systems. The systematic analytical model is developed based on Bromley-Zemaitis's theory and H. E. Wirth's theory to accurately predict the precipitation behavior of sulfate systems under different operating conditions and to simulate the precipitation titration curve. The titration curves established using the analytical model are compared with the curves built using the numerical mixed-solvent electrolyte model provided in OLI software along with the experimental measurement. The results demonstrate a good agreement between the analytical model, numerical model, and experimental approach while unveiling the limitations of the developed analytical model such as the disregard of multi-species ions, constant solution density, and constant water activity. The effect of three key operating parameters, namely initial solution pH, initial metal ion concentration, and reaction temperature, on the precipitation behaviors is investigated with emphasis on the ion interaction, precipitation pH, the amount of precipitant required, and species equilibrium.

Solid–Liquid Phase Equilibria in the Ternary MgCl2–NiCl2–H2O System at 303–323 K

For efficient nickel recovery from laterite nickel ore, an improved understanding of the solubility in ternary MgCl2–NiCl2–H2O systems is required. Herein, the stable phase equilibria in a ternary MgCl2–NiCl2–H2O system at 303, 313, and 323 K were studied using an isothermal dissolution equilibrium method. For this ternary system, the solubility and density were measured at different temperatures. The equilibrium solid phases were identified using X-ray diffraction, combined with the Schreinemakers’ method for wet residues. Based on the solubility data, the phase diagrams of the MgCl2–NiCl2–H2O system at 303, 313, and 323 K were plotted. At all investigated temperatures, the phase diagrams of this ternary system presented an invariant point, two isothermal dissolution curves, and three crystallization regions. Neither double salt nor solid solution was produced. The Mixed Solvent Electrolyte (MSE) model was applied to calculate the solubility for this ternary system. According to the comparison of phase diagram, the calculated data were in good agreement with the experimental values.

Molecular thermodynamic model for solvent extraction of mineral acids by tri-n-butyl phosphate (TBP)

Removal or recovery of acids by solvent extraction is highly relevant for recycling, process control, and wastewater decontamination, especially in the hydrometallurgical industry. The construction and optimization of such processes would benefit from a molecular thermodynamic model that can predict liquid–liquid equilibria. Past attempts resulted in models that were not very predictive. Therefore, a new approach was followed and demonstrated for the extraction of the mineral acids (inorganic acids) HNO3, HCl, H2SO4, H3PO4, and H3AsO4 by tri–n–butyl phosphate (TBP). The semi-empirical OLI Mixed-Solvent Electrolyte (MSE) framework was used to construct the thermodynamic model for calculating the liquid–liquid equilibria. Contrary to previous attempts, this framework allows the description of both the aqueous and organic phases in one model, and it can accurately deal with the non-ideal behavior of concentrated electrolyte solutions. The best agreement between calculated and experimental distribution data was achieved by assuming that the extraction of mineral acids occurs via protonation of TBP and coextraction of the anions. At very high acid concentrations, also neutral acid molecules are transferred to the organic phase. The high accuracy of the thermodynamic model for all mineral acid systems considered in this study is an indication that this approach for modeling liquid–liquid equilibria is a universal one. Furthermore, the extraction of mineral acids can be predicted in mixed-acid systems and acid-salt systems that were not used to construct the model.

Volatility of boric acid in water: New experimental data below 373.15 K and reassessment of equilibrium constant models

A data review for vapour liquid equilibrium (VLE) of the boric acid/ water system is conducted from different databases and authors. A void of information for the distribution coefficient for boric acid into the liquid and vapour phases at temperatures below 373.15 K is identified. New experimental data is measured in this work to fill the lack of distribution coefficients values for temperatures below 373.15 K. Values calculated from mathematical correlations for the distribution coefficient are compared with the experimental data. Besides, mixed solvent electrolyte thermodynamic model (MSE) has been computed for VLE equilibrium based on a gamma–phi formulation; thus, it includes a calculation of the speciation equilibrium for boric acid in aqueous solutions. Nevertheless, actual parameters used in MSE model are not adapted to represent the distribution coefficient at temperatures below 500 K. Consistency is evaluated between experimental data and thermodynamic correlations. The correlation presented by Plyasunov (2011) is identified as the correlation that represents the experimental data with less variation among the collected correlations. Finally, a modification in the parameters of volatility for MSE model is proposed to obtain a similar representation of the distribution coefficient than the correlation proposed by Plyasunov (2011).

Quantifying selective solvent transport under an electric field in mixed-solvent electrolytes.

Electrolytes in lithium-ion batteries comprise solvent mixtures, but analysis of ion transport is always based on treating the solvents as a single-entity. We combine electrophoretic NMR (eNMR) measurements and molecular dynamics (MD) simulations to quantify electric-field-induced transport in a concentrated solution containing LiPF6 salt dissolved in an ethylene carbonate/ethyl methyl carbonate (EC/EMC) mixture. The selective transport of EC relative to EMC is reflected in the difference between two transference numbers, defined as the fraction of current carried by cations relative to the velocity of each solvent species. This difference arises from the preferential solvation of cations by EC and its dynamic consequences. The simulations reveal the presence of a large variety of transient solvent-containing clusters which migrate at different velocities. Rigorous averaging over different solvation environments is essential for comparing simulated and measured transference numbers. Our study emphasizes the necessity of acknowledging the presence of four species in mixed-solvent electrolytes.

A Benchmark Database for Mixed-Solvent Electrolyte Solutions: Consistency Analysis Using E-NRTL

Modeling of thermodynamic properties of mixed-solvent electrolyte solutions is challenging. Reliable experimental data are essential for any model development and parametrization. In this work, a benchmark database for (water + methanol/ethanol + alkali halide) mixed-solvent electrolyte solutions is presented. The available experimental data of mean ionic activity coefficient (MIAC) and vapor–liquid equilibrium (VLE) are comprehensively collected and critically evaluated for 61 data sets of 23 solutions. The resulting benchmark database includes 1413 data records from 32 data sets for 13 solutions. The evaluated data sets of the relevant aqueous electrolyte solutions are also presented. A consistent E-NRTL model that satisfies the Gibbs–Duhem equation is utilized for analyzing the data, reconciling the MIAC and VLE data. Based on the database, recommended parameters are obtained for the E-NRTL model.

Dielectric constant prediction of pure organic liquids and their mixtures with water based on interpretable machine learning

The thermodynamic properties of mixed-solvent electrolytes are functions of pressure, temperature, and composition (PTC), and are generally considered to be characterized by their dielectric constant. In this work, an interpretable dielectric constant model is proposed based on a machine learning algorithm. The model combines machine learning algorithms, Abraham Solvation Parameters (ASP) and SHapley Additive exPlanations (SHAP) methods to accurately predict the dielectric constants of pure organic liquids and their mixtures with water, the significance of each feature and its impact on the results are explained. The predictions demonstrate extremely low mean square errors, and the effect of each feature on the dielectric constant is clearly characterized. This model provides the ability to accurately predict the dielectric constant for any pure organic liquids and their mixtures with water, and can analyze the sensitivity and influence of each feature to the dielectric constant. Furthermore, this work extends the application of the Abraham solvation parameter to prediction of solution properties. The interpretability of the model will make this a great resource to direct the prediction of physical and chemical properties of materials.

Activity Coefficients and Solubilities of NaCl in Water-Methanol Solutions from Molecular Dynamics Simulations.

We obtain activity coefficients and solubilities of NaCl in water-methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung-Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz-Berthelot combining rules were adopted for the unlike-pair interactions of Na+, Cl-, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na+ and Cl- from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.

Redox Flow Capacitive Deionization in a Mixed Electrode Solvent of Water and Ethanol

In redox flow electrode capacitive deionization (FCDI), the solubility of the redox electrolyte and flowability of the carbon slurry have a great influence on the salt removal rate and energy consumption. In this work, a mixed solvent electrolyte is proposed for FCDI, which consists of iodide/triiodide redox couples and a carbon slurry in a mixed solvent of water and ethanol (1:1). At a current density of 5 mA cm−2, the salt removal rate in the mixed solvent can reach up to 2.72 μg cm−2 s−1, which is much higher than the value of 1.74 μg cm−2 s−1 and 2.37 μg cm−2 s−1 obtained in aqueous and ethanol solutions, respectively. This is attributed to the fast transport of ions during the redox reaction in organic solvents and the excellent flowability of the carbon slurry under aqueous conditions, which can provide more reaction sites for iodide/triiodide redox reactions and faster electron transportation. This unique FCDI with organic and aqueous mixed solvent electrolytes provides a new perspective for the development of redox flow electrochemical desalination.

Eutectic freeze crystallization for recovery of NiSO4 and CoSO4 hydrates from sulfate solutions

In this study, eutectic freeze crystallization (EFC) was investigated to recover NiSO4 and CoSO4 hydrates from aqueous and dilute sulfuric acid solutions of metal sulfates. Binary phase diagrams were established using a combination of thermodynamic modeling and experimental data. The mixed-solvent electrolyte (MSE) model was employed to model solid–liquid phase equilibria. The predicted binary phase diagrams from the model were in good agreement with the experimental results. Experimental eutectic temperatures and eutectic metal sulfate concentrations for the NiSO4-H2O and CoSO4-H2O systems are −3.3 °C and 20.8 wt% and −2.9 °C and 19.3 wt%, respectively. For NiSO4-H2SO4-H2O and CoSO4-H2SO4-H2O systems, the eutectic temperature and eutectic metal sulfate concentration decrease with increasing H2SO4 concentration. Batch experiments were performed to study the EFC of different sulfate solutions, including 25- wt% NiSO4 in H2O, 20- wt% NiSO4 in 0.5 mol/kg H2SO4, 25- wt% CoSO4 in H2O, and 20- wt% CoSO4 in 0.5 mol/kg H2SO4. The results show that controlling the supersaturation allows high-quality ice and salt crystals to be recovered as separate phases under eutectic conditions, with the crystalline salts in the form of heptahydrates. This study shows that EFC can be a promising alternative to evaporative crystallization for recovering NiSO4 and CoSO4 hydrates from sulfate solutions.