Predicting the thermodynamic properties and dielectric behavior of electrolyte solutions using the SAFT-VR+DE equation of state

Modeling Henry's law and phase separations of water-NaCl-organic mixtures with solvation and ion-pairing

Empirical measurements of solution vapor pressure of ternary acetonitrile (MeCN) H2O-NaCl-MeCN mixtures were recorded, with NaCl concentrations ranging from zero to the saturation limit, and MeCN concentrations ranging from zero to an absolute mole fraction of 0.64. After accounting for speciation, the variability of the Henry's law coefficient at vapor-liquid equilibrium (VLE) of MeCN ternary mixtures decreased from 107% to 5.1%. Solute speciation was modeled using a mass action solution model that incorporates solute solvation and ion-pairing phenomena. Two empirically determined equilibrium constants corresponding to solute dissociation and ion pairing were utilized for each solute. When speciation effects were considered, the solid-liquid equilibrium of H2O-NaCl-MeCN mixtures appear to be governed by a simple saturation equilibrium constant that is consistent with the binary H2O-NaCl saturation coefficient. Further, our results indicate that the precipitation of NaCl in the MeCN ternary mixtures was not governed by changes in the dielectric constant. Our model indicates that the compositions of the salt-induced liquid-liquid equilibrium (LLE) boundary of the H2O-NaCl-MeCN mixture correspond to the binary plateau activity of MeCN, a range of concentrations over which the activity remains largely invariant in the binary water-MeCN system. Broader comparisons with other ternary miscible organic solvent (MOS) mixtures suggest that salt-induced liquid-liquid equilibrium exists if: (1) the solution displays a positive deviation from the ideal limits governed by Raoult's law; and (2) the minimum of the mixing free energy profile for the binary water-MOS system is organic-rich. This work is one of the first applications of speciation-based solution models to a ternary system, and the first that includes an organic solute.

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.

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.

Thermodiffusion: The physico-chemical mechanics view

Thermodiffusion in liquids (the Soret effect) has several unusual properties. In particular, transport can occur with or against a temperature gradient depending on the case. Numerous empirical correlations have been proposed with mixed success or range of applicability. Here, we show that physicochemical mechanics, derived from the Smoluchowski equation as a description of diffusive transport phenomena, is in accord with the experimental and simulated thermodiffusion data from colloidal beads and biomacromolecules to ionic solutions and ultracold fluid mixtures. It yields a simple formula for the Soret coefficient S_T based on the reference molar entropy including non-ideality. Hydrodynamic and local non-equilibrium effects are discussed but not included as these are apparently not a major contribution for the wide range of solutes under the near-equilibrium experimental conditions considered here.

Solute displacement in the aqueous phase of water-NaCl-organic ternary mixtures relevant to solvent-driven water treatment

Twelve water miscible organic solvents (MOS): acetone, tetrahydrofuran, isopropanol, acetonitrile, dimethyl sulfoxide, 1,4-dioxane, dimethylacetamide, N-methyl-2-pyrrolidone, trifluoroethanol, isopropylamine, dimethylformamide, and dimethyl ether (DME) were used to produce ternary mixtures of water-NaCl-MOS relevant to MOS-driven fractional precipitation. The aqueous-phase composition of the ternary mixture at liquid-liquid equilibrium and liquid-solid endpoint was established through quantitative nuclear magnetic resonance and mass balance. The results highlight the importance of considering the hydrated concentrations of salts and suggest that at high salt concentrations and low MOS concentration, the salt concentration is governed by competition between the salt ions and MOS molecules. Under these conditions a LS phase boundary is established, over which one mole of salt is replaced by one mole of MOS (solute displacement). At higher MOS concentrations, MOS with higher water affinity deviate from the one-to-one solute exchange but maintain a LS boundary with a homogenous liquid phase, while MOS with lower water affinity form a liquid-liquid phase boundary. DME is found to function effectively as an MOS for fractional precipitation, precipitating 97.7% of the CaSO₄ from a saturated solution, a challenging scalant. DME-driven water softening recycles the DME within the system improving the atom-efficiency over existing seawater desalination pretreatments by avoiding chemical consumption.