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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. 161, 057102 (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. [ABSTRACT FROM AUTHOR]

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye–Hückel theories. This equation of state underscores the pivotal role of ion–ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion–ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study presents a novel model to predict the electrical conductivity of multisalt electrolyte solutions by incorporating corrections to the ideal behavior due to relaxation and electrophoretic effects. The performance of the model is evaluated by comparing its predictions with the experimental data of 24 multisalt aqueous solutions. The comparison reveals good agreement for solutions with an ionic strength below 1 mol/L without adjusting any parameter to fit to the experimental data. However, the model tends to overestimate the molar conductivity at higher ionic strengths. The discrepancy is attributed to the neglect of the solvent structure and the formation of ion pairs. It has been speculated how the accuracy of the developed model could be improved in relation to these limitations. Furthermore, the performance of the model is rigorously tested in systems with ion complex formation. It has been demonstrated that when the distribution of ion complexes is calculated from a thermodynamic model and then used to predict the electrical conductivity with the developed model, a satisfactory level of accuracy is attained for these systems.

A new electrical conductivity model is developed for unassociated electrolyte solutions based on the Debye-Hückel-Onsager theory. In this model, we assume that a single cation and a single anion with their crystallographic ionic radii are in a continuum medium of the solvent(s). We compare the predictions of the developed model with the experimental measurements of binary 1:1, 2:1, 1:2, 2:2, 1:3, 3:1, 2:3, 3:2, 3:3, 1:4, and 2:4 aqueous solutions in the temperature range 273.15-373.15 K. Our results are in good agreement with the experimental data. An extension of the model was formulated to incorporate ion pairing, and its effectiveness was evaluated across three essential systems: 2:2 aqueous sulfate solutions, ionic liquid-co-solvent systems, and NaCl-water-1,4-dioxane solutions. This adaptation demonstrated a strong correlation with experimental data, highlighting the broad applicability.

The static permittivity is the most important physical property for thermodynamic models that account for the electrostatic interactions between ions. The measured static permittivity in mixtures containing electrolytes is reduced due to kinetic depolarization and reorientation of the dipoles in the electrical field surrounding ions. Kinetic depolarization may explain 25-75% of the observed decrease in the permittivity of solutions containing salts, but since this is a dynamic property, this effect should not be included in the thermodynamic modeling of electrolytes. Kinetic depolarization has, however, been ignored in relation to thermodynamic modeling, and authors have either neglected the effect of salts on permittivity or used empirical correlations fitted to the measured static permittivity, leading to an overestimation of the reduction in the thermodynamic static permittivity. We present a new methodology for obtaining the static permittivity over wide ranges of temperatures, pressures, and compositions for use within an equation of state for mixed solvents containing salts. The static permittivity is calculated from a new extension of the framework developed by Onsager, Kirkwood, and Fröhlich to associating mixtures. Wertheim's association model as formulated in the statistical associating fluid theory is used to account for hydrogen-bonding molecules and ion-solvent association. Finally, we compare the Debye-Hückel Helmholtz energy obtained using an empirical model with the new physical model and show that the empirical models may introduce unphysical behavior in the equation of state.

The static permittivity is a key property for describing solutions containing polar and hydrogen bonding compounds. However, the precise relationship between the molecular and dielectric properties is not well-established. Here we show that the relative permittivity at zero frequency (static permittivity) can be modeled simultaneously with thermodynamic properties. The static permittivity is calculated from an extension of the framework developed by Onsager, Kirkwood, and Fröhlich to associating mixtures. The thermodynamic properties are calculated from the cubic-plus-association (CPA) equation of state that includes the Wertheim association model as formulated in the statistical associating fluid theory (SAFT) to account for hydrogen bonding molecules. We show that, by using a simple description of the geometry of the association, we may calculate the Kirkwood g-factor as a function of the probability of hydrogen bond formation. The results show that it is possible to predict the static permittivity of complex mixtures over wide temperature and pressure ranges from simple extensions of well-established theories simultaneously with the calculation of thermodynamic properties.