Modelling of the thermodynamic and solvation properties of electrolyte solutions with the statistical associating fluid theory for potentials of variable range

Theoretical and practical investigation of ion-ion association in electrolyte solutions

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.

Spectroscopic and Computational Study of ZnCl2-Methanol Low-Melting-Temperature Mixtures

Alcoholic electrolyte mixtures have wide applications in industries. In this study, a series of mixtures composed of ZnCl2 and methanol (MeOH) with ZnCl2 mol % from 6.7 to 25 were prepared, and their spectral, structural, and thermodynamic properties were studied using infrared (IR) spectroscopy, differential scanning calorimetry (DSC), and density functional theory (DFT) calculations. The DFT-assisted analysis of excess spectra, supported by 2D-correlation spectroscopy, led to the identification of the major constituents of ZnCl2-MeOH mixtures, namely, MeOH monomer, MeOH dimer, and ZnCl2-3MeOH complex, produced after dissociation of MeOH trimer which represents the bulk methanol. The Hirshfeld charge analysis showed that in the competition between the O-H···Cl hydrogen bond (H-bond) and Zn ← O coordination bond to transfer charge in ZnCl2-MeOH complexes, the latter always dominates, making MeOH positively charged. The phase diagram of the binary system showed the presence of V-shaped glass transition temperatures (Tg), characteristic of low-melting mixture solvents (LoMMSs). The present study provides insights into the microscopic properties of the system and sheds light on the understanding of the general principles to prepare deep-eutectic solvents (DESs) or LoMMSs using inorganic salts and alcoholic compounds.

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.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Current Trends in Predictive Methods and Electrolyte Equations of State

Over the past 20-30 years, the development of thermodynamic models for electrolyte solutions has experienced remarkable progress. While in the first half of the 20th century, the thermodynamic models were essentially based on the continuum electrostatic approach, nowadays equations of state and predictive methods have been adapted to deal with electrolyte solutions. Given this panorama, in this mini-review, the recent advances in predictive methods and electrolyte equations of state are examined, as well as their performance in predicting activity coefficients and solid-liquid phase equilibrium data. Although this mini-review aims to shed light on the current progress in predictive methods and electrolyte equations of state, it also provides valuable references and information to the several models and theories that form the backbone of the thermodynamics of electrolyte solutions.

Molecular theory of the static dielectric constant of dipolar fluids

The link between the static dielectric constant and the microscopic intermolecular interactions is the Kirkwood g₁ factor, which depends on the orientational structure of the fluid. Over the years, there have been several attempts to provide an accurate description of the orientational structure of dipolar fluids using molecular theories. However, these approaches were either limited to mean-field approximations for the pair correlation function or, more recently, limited to adjusting the orientational dependence to simulation data. Here, we derive a theory for the dielectric constant of dipolar hard-sphere fluids using the augmented modified mean-field approximation. Qualitative agreement is achieved throughout all relevant thermodynamic states, as demonstrated by a comparison with simulation data from the literature. Excellent quantitative agreement can be obtained using a single empirical scaling factor, the physical origin of which is analyzed and accounted for. In order to predict the dielectric constant of the Stockmayer fluid (Lennard-Jones plus dipole potential), we use an adjusted version of the expression for the dipolar hard-sphere fluid. Comparing theoretical predictions with newly generated simulation data, we show that it is possible to obtain excellent agreement with simulation by performing the calculations at a corresponding state using the same scaling factor. Finally, we compare the theoretical orientational structure of the Stockmayer fluid with that obtained from simulations. The simulated structure is calculated following a post-processing methodology that we introduce by deriving an original expression that relates the proposed theory to the histogram of relative dipole angles.

Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulphuric, and carbonic acids

The distribution of ionic species in electrolyte systems is important in many fields of science and engineering, ranging from the study of degradation mechanisms to the design of systems for electrochemical energy storage. Often, other phenomena closely related to ionic speciation, such as ion pairing, clustering and hydrogen bonding, which are difficult to investigate experimentally, are also of interest. Here, we develop an accurate molecular approach, accounting for reactions as well as association and ion pairing, to deliver a predictive framework that helps validate experiment and guides future modelling of speciation phenomena of weak electrolytes. We extend the SAFT-VRE Mie equation of state [D. K. Eriksen et al., Mol. Phys., 2016, 114, 2724-2749] to study aqueous solutions of nitric, sulphuric, and carbonic acids, considering complete and partially dissociated models. In order to incorporate the dissociation equilibria, correlations to experimental data for the relevant thermodynamic equilibrium constants of the dissociation reactions are taken from the literature and are imposed as a boundary condition in the calculations. The models for water, the hydronium ion, and carbon dioxide are treated as transferable and are taken from our previous work. We present new molecular models for nitric acid, and the nitrate, bisulfate, sulfate, and bicarbonate anions. The resulting framework is used to predict a range of phase behaviour and solution properties of the aqueous acids over wide ranges of concentration and temperature, including the degree of dissociation, as well as the activity coefficients of the ionic species, and the activity of water and osmotic coefficient, density, and vapour pressure of the solutions. The SAFT-VRE Mie models obtained in this manner provide a means of elucidating the mechanisms of association and ion pairing in the systems studied, complementing the experimental observations reported in the literature.

On the "Born" term used in thermodynamic models for electrolytes

In the literature, many expressions for the Helmholtz or Gibbs energy of electrolyte solutions have included a term that takes into account the variation of the solution permittivity with the composition of solution (e.g., within the statistical-associated fluid theory formalism). This contribution is often called the "Born" term because it was inspired by the classic expression established by Born to describe the solvation energy of an ion. The present work is an attempt to get more physical insight into this semiempirical "Born" term. The way in which it has been used in the literature is briefly examined, and its typical magnitude is evaluated. Next, it is proposed to use the nonprimitive mean spherical approximation model to calculate the chemical potential of an ion in a solution composed of charged hard spheres (HSs) (the ions) and dipolar HSs (the solvent). The cation and the anion are monovalent monoatomic ions of equal diameter. The dipoles have a different size and mimic water molecules. The theoretical expressions for this model were found to fulfill the Gibbs-Duhem relation, which suggests that they are correct. A rescaled ion-dipole contribution is introduced, in a form that is suitable for inclusion in electrolyte models. It is compared with a "Born" term expressed in the same framework. It is found that the former is in general not well estimated by the latter. The two might even be of opposite signs in the case of ions of sufficiently small size.

On the use of molecular-based thermodynamic models to assess the performance of solvents for CO2 capture processes: monoethanolamine solutions

Predictive models play an important role in the design of post-combustion processes for the capture of carbon dioxide (CO₂) emitted from power plants. A rate-based absorber model is presented to investigate the reactive capture of CO₂ using aqueous monoethanolamine (MEA) as a solvent, integrating a predictive molecular-based equation of state: SAFT-VR SW (Statistical Associating Fluid Theory-Variable Range, Square Well). A distinctive physical approach is adopted to model the chemical equilibria inherent in the process. This eliminates the need to consider reaction products explicitly and greatly reduces the amount of experimental data required to model the absorber compared to the more commonly employed chemical approaches. The predictive capabilities of the absorber model are analyzed for profiles from 10 pilot plant runs by considering two scenarios: (i) no pilot-plant data are used in the model development; (ii) only a limited set of pilot-plant data are used. Within the first scenario, the mass fraction of CO₂ in the clean gas is underestimated in all but one of the cases, indicating that a best-case performance of the solvent can be obtained with this predictive approach. Within the second scenario a single parameter is estimated based on data from a single pilot plant run to correct for the dramatic changes in the diffusivity of CO₂ in the reactive solvent. This parameter is found to be transferable for a broad range of operating conditions. A sensitivity analysis is then conducted, and the liquid viscosity and diffusivity are found to be key properties for the prediction of the composition profiles. The temperature and composition profiles are sensitive to thermodynamic properties that correspond to major sources of heat generation or dissipation. The proposed modelling framework can be used as an early assessment of solvents to aid in narrowing the search space, and can help in determining target solvents for experiments and more detailed modelling.