Theory Of Electrolyte Solutions Research Articles

Comment on "Binding Debye-Hückel theory for associative electrolyte solutions" [J. Chem. Phys. 159, 154503 (2023)

It is argued that the Binding Debye-Hückel (BiDH) model proposed by Naseri Boroujeni et al. [J. Chem. Phys. 159, 154503 (2023)] might not be appropriate for the description of Monte Carlo simulation data obtained for primitive model electrolytes. The first reason is that the original Debye-Hückel (DH) theory is of low accuracy for describing deviations from ideality in concentrated solutions of strong salts. The DH framework is thus a poor basis for building a model including association. The second reason is that the mean-spherical approximation, without assumption of association, apparently predicts Monte Carlo (MC) data for primitive electrolytes better than BiDH. Thus, the BiDH model seems to be simply a way of compensating for the deficiencies of DH theory by assuming association.

Response to "Comment on 'Binding Debye-Hückel theory for associative electrolyte solutions'" [J. Chem. Phys. 159, 154503 (2023)

This Response addresses critiques raised about the Binding Debye-Hückel (BiDH) theory [Naseri Boroujeni et al., J. Chem. Phys. 159, 154503 (2023)] by Simonin and Bernard [J.-P. Simonin and O. Bernard, J. Chem. Phys. (2024)]. The critiques questioned the foundational framework of the Debye-Hückel (DH) theory, the relevance of ion pairing in primitive model fluids, and the accuracy of the BiDH model compared to mean spherical approximation model. Through a systematic rebuttal, supported by extensive literature review and comparison with Monte Carlo simulation data, this Response addresses these concerns. It demonstrates the efficacy of DH theory in describing real electrolyte solutions, validates the relevance of ion pairing in primitive model fluids, and establishes the BiDH model's accuracy in describing electrolyte properties.

Comparative Investigation of the Microstructure of MgCl2 Aqueous Solutions Using Different X-ray Scattering Sources, Raman Spectroscopy, and Atomistic Simulations.

Aqueous solutions of magnesium chloride (MgCl2(aq)) are often used to test advances in the theory of electrolyte solutions because they are considered an ideal strong 2:1 electrolyte. However, there is evidence that some ion association occurs in these solutions, even at low concentrations. Even a small ion-pairing constant can have a significant impact on the chemical speciation of ions, so it is important to determine whether ion pairing actually occurs. In this study, MgCl2(aq) with concentrations ranging from 1 to 35% was studied using three methods: X-ray scattering (XRS) with the Shanghai Synchrotron Radiation Facility (SSRF) and silver-anode laboratory sources, Raman spectroscopy, and molecular dynamics (MD) simulations with the COMPASS-II and Madrid force fields. XRS results were analyzed in the framework of PDF theory to obtain the reduced structure function F(Q) and the reduced pair distribution function G(r). The F(Q) values from synchrotron radiation and laboratory sources both showed that the tetrahedral hydrogen bonds in bulk water were destroyed with the increased MgCl2 concentration. The results of G(r) indicated that the main peaks centered at 2.05 and 2.80 Å can be ascribed to the interactions of Mg-O and O-O, respectively. The peak at 3.10 Å is attributed to the combined effect of O-O and Cl-O. By comparing the structural information on MgCl2 solution obtained from the two light sources, it was found that both SSRF and silver-anode laboratory sources can reflect the above-mentioned structural information on MgCl2 solution. The radial distribution function (RDF) obtained from MD simulations of MgCl2 solutions assigned the peaks at 2.0, 2.8, and 3.2 Å to the Mg-O, O-O, and Cl-O interatomic pairs, respectively. The decrease in the O-O coordination number confirms that the hydrogen-bonding network of water is disrupted by increasing MgCl2 observed by X-ray scattering. The proportion of Mg-Cl contact ion pairs gradually increases with MgCl2 concentration as does the coordination number. Raman spectroscopy results show that the bond type changes from double donor double acceptor (DDAA) to single donor-single acceptor (DA) with increasing concentration, providing explicit details of the hydrogen-bond evolution in the aqueous solution.

Binding Debye-Hückel theory for associative electrolyte solutions.

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Theory of electrolyte solutions in a slit charged pore: Effects of structural interactions and specific adsorption of ions.

In this paper, we present a continuation of our research on modeling electrolyte solutions within charged pores. We make use of the model developed by Blossey et al. [Phys. Rev. E 95, 060602 (2017)], which takes into account the structural interactions between ions through a bilinear form over the gradients of local ionic concentrations in the grand thermodynamic potential, as well as their steric interactions through the lattice gas model. The structural interactions may describe the effects of the molecular structure of ions at a phenomenological level. For example, these effects include steric effects due to non-spherical shapes of ions, their conformational lability, and solvent effects. In addition, we explore their specific interactions with the pore walls by incorporating external attractive potentials. Our primary focus is on observing the behavior of ionic concentration profiles and the disjoining pressure as the pore width changes. By starting with the local mechanical equilibrium condition, we derive a general expression for the disjoining pressure. Our findings indicate that considering the structural interactions of ions leads to a pronounced minimum on the disjoining pressure profiles at small pore widths. We attribute this minimum to the formation of electric double layers on the electrified surfaces of the pore. In addition, our results demonstrate that the inclusion of the attractive interactions of ions with the pore walls enhances this minimum and shifts it to smaller pore thicknesses. Our theoretical discoveries may be useful for those involved in supercapacitor electrochemical engineering, particularly when working with porous electrodes that have been infused with concentrated electrolyte solutions.

In memory of Hartmut Krienke

This brief essay is commemorated to Prof. Dr. Hartmut Krienke, well known scientist in the theory of electrolyte solutions. Prof. Dr. Hartmut Krienke passed away in Rostock at the age of 80 on October 28, 2023, surrounded by his family after a long illness. We express our deepest condolences to his family, colleagues and friends.

Minimum-modified Debye-Hückel theory for size-asymmetric electrolyte solutions with moderate concentrations

A minimum-modified Debye-Hückel (DH) theory for electrolytes with size asymmetry is developed. Compared with the conventional DH theory, the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation. This theory can distinguish the electrostatic energies and excess chemical potentials of ions with the same sizes but opposite charges, and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling. Compared with the hyper-netted chain theory, the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.

Real Electrolyte Solutions in the Functionalized Mean Spherical Approximation: A Density Functional Theory for Simple Electrolyte Solutions.

The equation of state based on the mean spherical approximation (MSA) can describe electrolyte solutions as a primitive model, where the ions are charged hard-sphere particles and the solvent is a continuum medium. In recent years, many propositions of the classical density functional theory (cDFT) for electrolyte solutions have been presented. One of these is the functionalized MSA (fMSA) which has proven to be a great functional approach of MSA to calculate the electric double layer structures. This work demonstrates how the fMSA theory can describe real electrolyte solutions (e.g., NaCl, KI, and LiBr) where hydration and solvent concentration effects are present. Experimental data of the mean activity coefficients of different simple salts were successfully reproduced. When the hydrated diameter and the electrolyte solution electric permittivity are used, the fMSA predicts a charge inversion on the electrostatic potential near a charged surface at high salt concentrations.

An Accurate Model for Estimating H2 Solubility in Pure Water and Aqueous NaCl Solutions

By employing a specific particle interaction theory and a high-precision equation of states for the liquid and vapor phases of H2, respectively, a new H2 solubility model in pure water and aqueous NaCl solutions is proposed in this study. The model established by fitting the experimental data of H2 solubility can be used to estimate H2 solubility in pure water at temperatures and pressures of 273.15–423.15 K and 0–1100 bar, respectively, and in salt solutions (NaCl concentration = 0–5 mol/kg) at temperatures and pressures of 273.15–373.15 K and 0–230 bar, respectively. By adopting the theory of liquid electrolyte solutions, the model can also be used to predict H2 solubility in seawater without fitting the experimental data of a seawater system. Within or close to experimental data uncertainty, the mean absolute percentage error between the model-predicted and experimentally obtained H2 solubilities was less than 1.14%.

Crystal Structures and Solution Chemical Properties of Two Lactate Complexes Mn[(C3H5O3)2(H2O)2]⋅H2O(s) and Cu(C3H5O3)2(s)

Trihydrated manganese lactate Mn[(C3H5O3)2(H2O)2]⋅H2O(s) and anhydrous copper lactate Cu(C3H5O3)2(s) were synthesized. Crystal structures of the two compounds were characterized by X-ray single crystal diffraction technique. The compositions, spatial structures and coordination modes of the two compounds were determined by analysis of their molecular structures and crystal structures. Lattice potential energies of the compounds were calculated by using the crystallographic data. Molar enthalpies of dissolution of these metal complexes in the ultrapure water were measured by an isoperibol solution-reaction calorimeter with an accuracy of ±0.3%. On the basis of Pitzer's electrolyte solution theory, infinite dilution molar enthalpies of dissolution and Pitzer's parameters of the two lactate complexes soluble in water at T = 298.15 K were calculated. The infinite dilution molar enthalpies (ΔsHm∞) of dissolution of the title compounds were combined with lattice potential energies (UPOT) by a designed thermodynamic cycle, and the average molar enthalpy of hydration of the common lactate ion was calculated to be (407.207 ± 0.038) kJ·mol−1. The mechanism of thermal decomposition or dehydration of the trihydrated manganese lactate was explored by TG-DSC technique, and the difference between molar enthalpies (ΔsHm) of dissolution of trihydrated manganese lactate and anhydrous copper lactate at the same concentration was revealed.

Crystal structure and solution thermodynamics of the lactate complex Zn[(C3H5O3)2(H2O)2]⋅H2O(s)

An important trihydrated lactate complex Zn[(C3H5O3)2(H2O)2]⋅H2O(s) was synthesized. Crystal structure was characterized by X-ray single crystal diffractometer, and molecular structure, spatial structure and coordination mode of the complex were determined. The lattice potential energy of the complex was calculated by crystal data. The enthalpy of dissolution of the compound in the water was measured by isoperibol reaction calorimeter with an accuracy of ±0.3%. According to the Pitzer electrolyte solution theory, molar enthalpy of dissolution at the infinite dilution and Pitzer parameters of the compound soluble in water at T = 298.15 K were calculated. Combined with molar enthalpy of dissolution in the infinite dilution (ΔsHm∞) and lattice potential energy (UPOT), enthalpy of hydration of lactate ion was calculated. Mechanism of thermal analysis or dehydration of the compound was explained by TG-DSC technique.

Experimental and Theoretical Study of Morphological and Charging Properties of Truncated Octahedron and Cubic Ceria Nanoparticles: Implications for Biomedical Applications

Ceria (CeO2) nanoparticles are known to be very often used in various applications from biomedicine to fuel cells. To optimize the applications, detailed information about the physicochemical properties such as size, shape, and charge of nanoparticles should be available. Therefore, in our study we performed a systematic study of ceria nanoparticles ranging from synthesis to comprehensive experimental and theoretical characterization. We synthesized ceria nanoparticles using two synthesis paths which led to the formation of two types of ceria nanoparticles. The structure and charging properties of both types of ceria nanoparticles were studied by using X-ray powder diffraction (XRD), high-resolution transmission electron microscopy (HR-TEM), particle charge detector (PCD) for surface charge density, and a ZetaPlus instrument for electrophoretic mobility measurements. The results suggested that in the case where hydrolysis of Ce(NO3)3 at room temperature was applied nanoparticles with morphology close to a spherical, more exactly truncated octahedron were synthesized. On the other hand, nanoparticles obtained by hydrothermal synthesis had characteristic cube-like morphology. Finally, for more complete understanding and interpretation of the studied system, we prepared a theoretical model based on the classical density functional theory for electrolyte solutions coupled with the surface charge regulation via the law of mass action. Even without using fitting parameters, the theory adequately describes the experimental data. All the results obtained in our study could serve as a basis for obtaining tuned and engineered ceria nanoparticles with optimized physicochemical properties which could lead to the improved applications of the nanotechnology in the biomedical research.

Experimental study and theoretical simulation of fluid phase equilibrium in the subsystems of quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K

Abstract Underground brine known as one of special fluids existing in nature has been regarded as a kind of comprehensive mineral resource. After multi-step separation mining, it can realize the effective extraction and recovery of various mineral resources. Conducting a series of further studies on this kind of natural fluid, especially on the study of fluid phase equilibrium, will be of great significance to explore the rules of its geochemical evolution and formation, and to guide the follow-up fluid mineralization simulation. Based on the above considerations, stable phase equilibria and solubility data of unreported subsystems for quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K were determined by the method of isothermal dissolution equilibrium aiming at the compositions of the underground brine in western Sichuan Basin. The research contents in this work include two ternary systems (NaBr–SrBr2–H2O, KBr–SrBr2–H2O) and three quaternary systems (NaBr–KBr–SrBr2–H2O, NaBr–MgBr2–SrBr2–H2O, and KBr–MgBr2–SrBr2–H2O). The phase diagrams of listed above systems were all drawn by experimental data. The experimental results show that there are no solid solutions as well as any complex salts in the three ternary systems. These phase diagrams all contain two solid phase regions of crystallization, two isothermal dissolution curves and only one isothermal-isobaric invariant point. At 298 K, quaternary systems NaBr–KBr–SrBr2–H2O belongs to a simple type, and the phase diagram consists of only one isothermal-isobaric invariant point, three isothermal dissolution curves and three crystallization regions. In the phase diagram of quaternary system NaBr–MgBr2–SrBr2–H2O at 298 K, there are two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. In the quaternary systems KBr–MgBr2–SrBr2–H2O at 298 K, it was found that one complex salt (KBr·MgBr2·6H2O) formed and the phase diagram has two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. The solubilities of the above subsystems at 298 K were predicted accurately by referring to Pitzer's electrolyte solution theory. It was found that the predicted results were coincided basically with the experimental data.

Measurements and calculations of solid-liquid equilibria in two quaternary systems: LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K

Using the method of isothermal dissolution equilibrium, stable phase equilibria of unreported strontium-containing systems LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K have been studied in accordance with the compositions of the underground brine in western Sichuan Basin. The experimental results show that there are no solid solution and complex salt in two quaternary systems. The phase diagram of quaternary system LiCl–NaCl–SrCl2–H2O consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The quaternary system LiCl–KCl–SrCl2–H2O belongs to a simple type and the phase diagram consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The solubilities of salts in the above systems were accurately calculated with Pitzer electrolyte solution theory. It was found that the calculated phase diagrams coincided basically with the experimental phase diagrams by evaluated the accuracy through the experimental results. Meanwhile, the applicability of Pitzer parameters selected in this paper was validated.

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Using the method of isothermal dissolution equilibrium, stable phase equilibria of unreported strontium-containing systems LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K have been studied in accordance with the compositions of the underground brine in western Sichuan Basin. The experimental results show that there are no solid solution and complex salt in two quaternary systems. The phase diagram of quaternary system LiCl–NaCl–SrCl2–H2O consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The quaternary system LiCl–KCl–SrCl2–H2O belongs to a simple type and the phase diagram consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The solubilities of salts in the above systems were accurately calculated with Pitzer electrolyte solution theory. It was found that the calculated phase diagrams coincided basically with the experimental phase diagrams by evaluated the accuracy through the experimental results. Meanwhile, the applicability of Pitzer parameters selected in this paper was validated.

Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory

Three analytic results are proposed for a linear form of the modified Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is also made with the mean spherical approximation results. The linear theories predict a transition of the mean electrostatic potential from a Debye-H\"{u}ckel type damped exponential to a damped oscillatory behaviour as the electrolyte concentration increases beyond a critical value. The screening length decreases with increasing concentration when the mean electrostatic potential is damped oscillatory. A comparison is made with one set of recent experimental screening results for aqueous NaCl electrolytes.

Shear Viscosity of Aqueous Electrolyte Solutions

The kinematic shear viscosity of aqueous electrolyte solutions has been studied. The temperature dependence of this parameter is shown to be described by an exponential formula at T < Td and a formula of the argon-like type at T > Td, where Td is the temperature of the dipole ordering, in the whole considered concentration interval. Main attention is focused on the peculiarities in the temperature and concentration dependences of the shear viscosity in the argon-like interval. It is shown that the root-like concentration dependence can appear, only if the Debye theory of dilute electrolyte solutions is applicable. Beyond its validity domain, the series expansion of the kinematic shear viscosity in the concentration parameter should have an analytical character. The latter behavior is inherent in the concentration dependence of the shear viscosity in the majority of experiments. The error of reproducing the experimental data did not exceed the experimental one, i.e. it was smaller than 4–5%.

A generalized Debye-Hückel theory of electrolyte solutions

We propose a generalized Debye-Hückel (DH) theory by using a recent Poisson-Fermi model that accounts for the steric, correlation, and polarization effects of ions and water treated as nonuniform spheres with interstitial voids. The generalized DH theory reduces to the classical one when these effects are not considered. The Debye length is also generalized to include the steric effect. The new theory yields an electrolyte (analytical) equation of state for calculating the activity coefficient of aqueous electrolyte solutions, which is of fundamental importance in thermodynamic modeling for a variety of chemical and biological systems. Results obtained by the analytical equation well fit experimental data for eight 1:1 and six 2:1 electrolytes with only three adjustable parameters. By contrast, the DH models extended from the classical DH theory such as the Pitzer model can have several to great many parameters due to explosive combinations of wide ranges of composition, temperature, and pressure.

BASIC CHARACTERISTICS OF THE COMPLEX CITRATE ELECTROLYTES ON THE BASIS OF IRON (III) FOR OBTAINING THIN-LAYER GALVANIC COATINGS

The article presents the results of studies of basic parameters of complex citrate electrolytes based on iron (III) for the application of ternary alloys with cobalt and molybdenum. The aim of the work was to determine the performance of the electrolyte, such as stability, viscosity, electrical conductivity and buffer capacity, as well as to establish the dependence of their change under the action of an important external factor - temperature. Using the conductometric method, it was found that with an increase in temperature the electrical conductivity of electrolytes predictably grows, and the solutions under study are strong electrolytes. The obtained values of the activation energy of conductivity are in the range of 694–965 J/mol. The dependence of the viscosity of electrolytes on temperature is established, the change of which also agrees with the fundamentals of the theory of electrolyte solutions. Based on the results obtained, the activation energy of the molecular jump is determined. Titrimetric studies evaluated the buffer properties of citrate electrolytes and compared the results obtained with the properties of known electrolytes for electrodeposition of electroplated coatings with alloys of a different composition.

Mineral solubilities of salts in the three quaternary systems: LiCl–NaCl–MgCl2–H2O, LiCl–KCl–MgCl2–H2O and Li2SO4–K2SO4–MgSO4–H2O at 288.15 K

In this paper, the stable phase equilibria of the quaternary systems LiCl–NaCl–MgCl2–H2O, LiCl–KCl–MgCl2–H2O and Li2SO4–K2SO4–MgSO4–H2O were studied at 288.15 K using an isothermal dissolution equilibrium method and the solubility of each system was measured. Based on experimental solubility data, the dry salt diagrams and the diagrams of water-content vs composition of three quaternary systems were plotted. In addition to the single salts, there is a double salt LiCl·MgCl2·7H2O formation at 288.15 K in quaternary system LiCl–NaCl–MgCl2–H2O. In quaternary system LiCl–KCl–MgCl2–H2O, there are two kinds of double salt LiCl·MgCl2·7H2O and KCl·MgCl2·6H2O. It has been found that LiCl has a strong salting-out effect on both NaCl and KCl, which result in NaCl and KCl having larger crystallization regions in each phase diagram. At 288.15 K, the phase diagram of quaternary system Li2SO4–K2SO4–MgSO4–H2O has phase fields of single salt Li2SO4·H2O, K2SO4 and MgSO4·7H2O, and that of double salts K2SO4·MgSO4·6H2O and Li2SO4·K2SO4. The solubilities of the three quaternary systems at 288.15 K were calculated by using the Pitzer electrolyte solution theory model. The parameters involved but not previously reported were obtained by using the solubility data of ternary subsystems and the method of multivariate linear regression. The results show that the calculated results are in good agreement with the experimental results.