Experimental Activity Coefficients Research Articles

An Electrolyte Non-random-UNIQUAC Model for Thermodynamic Modeling of Binary and Multicomponent Aqueous Electrolyte Systems

An Electrolyte non-random-UNIQUAC (NR-UNIQUAC) local composition model is developed for calculation of the excess Gibbs energy and activity coefficients for binary and the multicomponent electrolyte solutions. A new expression for the energies of the reference cells in the random state is used and a modified version of the UNIQUAC model is provided. The high efficiency of the presented model is demonstrated through the correlation of the available experimental data for various electrolyte solutions. Obtained results are compared with those of Electrolyte-UNIQUAC-NRF model. The correlation of data was carried out using two different approaches, the single system correlation and the global optimization of the interaction parameters. In the single fitting approach, two adjustable binary interaction parameters of the model are regressed using the experimental mean activity coefficient data of binary solutions. In the global approach, the anion-water and cation–anion interaction energy parameters of different ions are calculated via simultaneous correlation of the mean activity coefficient data of the forty-nine binary electrolyte solutions. In both approaches, the adjustable parameters are calculated in a wide range of electrolyte concentrations and at different temperatures, so that these parameters can be used to predict the osmotic coefficient data of many binary systems. Moreover, the solubility and osmotic coefficient data of ternary electrolyte solutions were predicted using the previously obtained binary parameters. Using the present model, the predicted data for the binary and multicomponent electrolyte solutions are in good agreement with the experimental data. When compared to Electrolyte-UNIQUAC-NRF model, the present model is more accurate. Additionally, the presence of salt–salt interaction parameters in the electrolyte-NR-UNIQUAC model can further improve its efficiency when experimental data for a ternary system is available.

A Simple G-Excess Model for Concentrated Aqueous Electrolyte Solutions

A simple yet accurate thermodynamic model was developed here to represent the nonideal behavior of single electrolytes in water at very high molalities and within a wide temperature range. The present model was obtained from an analytical expression of the excess Gibbs free energy (G-excess) which comprises three major contributions; in this context, a chemical term in the model handles the most predominant short-range ion–solvent interactions by means of a chemical equilibrium approach based on a stepwise ion solvation, whereas another term in the model of physical nature also contributes in describing the aforementioned interactions by incorporating a simple Margules equation, and last, a continuum-solvent term given by the explicit mean-spherical-approximation (MSA) expression serves to account for long-range ion–ion forces. The resulting G-excess model was applied to the representation of experimental mean ionic activity coefficients and osmotic coefficients of various representative aqueous electrolyte solutions: AgNO3, CaCl2, HCl, HClO4, HF, HNO3, KF, KOH, LiBr, LiCl, LiNO3, NaCNS, NaOH, NH4NO3, ZnBr2, and ZnCl2 salts in water at 25 °C (and from 0 up to 300 °C only in the case of KOH) and at high concentrations (up to 83.263 M). The results indicated a very good agreement between the experimental data and those calculated using the present G-excess model for the majority of the electrolyte solutions considered here.

Application of trihexyltetradecylphosphonium dicyanamide ionic liquid for various types of separations problems: Activity coefficients at infinite dilution measurements utilizing GLC method

In this work, the ionic liquid trihexyltetradecylphosphonium dicyanamide [P 6 6 6 14] [DCA] was evaluated as a potential extraction solvent for organic compounds. The assessment was done based on the solute retention data obtained by gas liquid chromatography (GLC) for 33 solutes: (alkanes, alkenes, ketones, alcohols, alkynes, aromatic hydrocarbons, tetrahydrofuran, thiophene, acetonitrile and water). The experiment was conducted at a series of four temperatures (313.15–343.15) K at 10 K intervals. Experimental activity coefficients at infinite dilution data acquired over the investigated temperature range was then utilized to compute the thermodynamic functions at infinite dilution including partial molar excess enthalpy, ΔH1E,∞, Gibbs free energy, ΔG1E,∞ and entropy term, TrefΔS1E,∞. The selectivity and capacity values for some of the separation challenges (heptane/thiophene, water/butanol and heptane/benzene) were computed from the γ13∞ data and in contrast to the other phosphonium based ionic liquids in the literature. The selectivity and capacity data shows that the investigated ionic liquid can be utilized in the separation of heptane/thiophene or water/butan-1-ol mixtures.

Thermodynamic properties of infinitely diluted solutions of organic solutes in in silico designed task-specific ionic liquid

New experimental infinite dilution activity coefficients (IDACs) of 45 different molecular solutes (alkanes, cycloalkanes, alkenes, alkynes, aromatics, alcohols, ethers, ketones, thiophene, acetonitrile, pyridine and 1-nitropropane) in the novel ionic liquid 1-(3-cyanopropyl)-1-methyl pyrrolidinium thiocyanate are presented. The considered IL has been in silico designed in our previous work by using empirical group contribution method for IDAC calculation. The experimental results shown in this paper are discussed in terms of the strength and the chemical nature of mutual interactions between the IL and the molecular solutes. An effect of nitrile group is elucidated by means of comparison of the measured data with those reported in the literature for non-functionalized counterpart of the studied IL. Furthermore, an impact of the studied “task-specific” cation on the infinite dilution selectivity in thiophene/n-octane separation problem is highlighted. The entire data set presented herein is analyzed using linear solvation-energy relationship (LSER), regular solution theory and conductor-like screening model for real solvents (COSMO-RS).

Activity coefficients at infinite dilution of various organic solutes in the deep eutectic solvent (tetramethylammonium chloride + 1,6 hexanediol in the 1:1 molar ratio)

Deep eutectic solvents (DESs) have emerged as potential green and low-cost substitutes to ionic liquids in various chemical processes. In this study, experimental activity coefficients at infinite dilution for 22 organic solutes were measured in the DES consisting of tetramethylammonium chloride and 1,6 hexanediol (1:1 molar ratio) by gas-liquid chromatography at four temperatures within the range of (313.15–343.15) K at 101.3 kPa. The effect of the molecular structure of the solute on limiting activity coefficient was also examined. From infinite dilution activity coefficients, limiting partial molar excess enthalpies, entropies and Gibbs free energies were calculated to gain insight into solute-DES interactions. It emerged that the strongest soulte-DES interactions were associated with pyridine, thiophene and methyl acetate. Subsequently, limiting selectivities and capacities were calculated for various separation problems to evaluate the potential use of the DES as a separation agent. The best separation performance of the investigated DES was obtained for mixtures consisting of n-alkanes and thiophene or pyridine. For this reason, it was concluded that the DES (tetramethylammonium chloride + 1,6 hexanediol in the 1:1 molar ratio) is a credible candidate to be considered for the denitrogenation as well as the desulphurisation of transportation fuels.

Activity Coefficients at Infinite Dilution of Various Solutes in Tetrapropylammonium Bromide + 1,6-Hexanediol Deep Eutectic Solvent

The present work focuses on the application of a deep eutectic solvent (DES) to the separation of liquid mixtures. Experimental activity coefficients at infinite dilution γ13∞ of 23 organic solutes...

Revisiting electrolyte thermodynamic models: Insights from molecular simulations

Pitzer and electrolyte nonrandom two‐liquid (eNRTL) models are the two most widely used electrolyte thermodynamic models. For aqueous sodium chloride (NaCl) solution, both models correlate the experimental mean ionic activity coefficient (γ±) data satisfactorily up to salt saturation concentration, that is, ionic strength around 6 m. However, beyond 6 m, the model extrapolations deviate significantly and diverge from each other. We examine this divergence by calculating the mean ionic activity coefficient over a wide range of concentration based on molecular simulations and Kirkwood–Buff theory. The asymptotic behavior of the activity coefficient predicted by the eNRTL model is consistent with the molecular simulation results and supersaturation experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3728–3734, 2018

Tetramethylammonium chloride + glycerol deep eutectic solvent as separation agent for organic liquid mixtures: Assessment from experimental limiting activity coefficients

Solute retention data acquired by gas-liquid chromatography were used to determine the activity coefficients at infinite dilution for 24 organic solutes in the deep eutectic solvent (DES) consisting of tetramethylammonium chloride and glycerol in a molar ratio of 1.001:2. The organic solutes included alk-1-anes, alk-1-enes, alk-1-ynes, cycloalkanes, alkanols, alkylbenzenes, ketones, esters and heterocyclics. The measurements were undertaken at four different temperatures, viz T = (313.15, 323.15, 333.15 and 343.15) K with an estimated uncertainty of ±3.8%. From the experimental infinite dilution activity coefficient data, the values of partial molar excess enthalpy at infinite dilution were calculated using Gibbs Helmholtz relationship. Limiting selectivity and capacity values were also calculated from experimental limiting activity coefficients and compared to those of other separation agents, including other deep eutectic solvents, ionic liquids and industrial molecular agents. Results obtained in this study indicate that tetramethylammonium chloride + glycerol DES can potentially be used as an alternative solvent for nitrogen and sulphur removal from transportation fuels as well as the separation of cycloalkanes, aromatics and esters from light alkanols.

Determination of Abraham Model Correlations for Solute Transfer into Propyl Acetate Based on Experimental Activity Coefficient and Solubility Data

Experimental infinite dilution activity coefficients, gas-to-liquid partition coefficients, and molar solubility data have been measured for numerous organic solutes dissolved in propyl acetate. Results of our experimental measurements, combined with published solubility data retrieved from the published literature, have been used to derive Abraham model correlations for describing solute transfer into propyl acetate. The derived Abraham model correlations describe the experimental data to within 0.11 log10 units. Calculation of Abraham model solute descriptors for boscalid was illustrated using our derived solute transfer correlations into propyl acetate. Predictions using the calculated solute descriptors indicate that boscalid would show significant partitioning into the skin and fat tissues in the body, and would exhibit considerable baseline toxicity towards the eight aquatic organisms (five fish species and three water flea species).

Measurements of activity coefficient at infinite dilution for organic solutes in tetramethylammonium chloride + ethylene glycol deep eutectic solvent using gas-liquid chromatography

Deep eutectic solvents (DESs) are considered as the new ionic liquids (ILs) analogues that have emerged as potential alternative ‘green’ solvents, for a diversity of applications. In this study, a type III DES based on ammonium salt was investigated as an alternative solvent to currently employed conventional organic solvents in separation processes. Activity coefficients at infinite dilution, γ13∞ for 19 organic solutes in the tetramethylammonium chloride + ethylene glycol DES were measured by the gas-liquid chromatography (GLC) method at four temperatures in the range from (313.15–343.15) K. Experimental measurements were undertaken with an overall uncertainty of ±5.4%. The effect of the structure of the solutes on γ13∞ was also investigated. For all investigated solutes, Gibbs helmholtz relationship was utilised to derive partial molar excess enthalpy values at infinite dilution (ΔHiE,(∞)) from experimental limiting activity coefficient data. From selectivity (Sij∞) and capacity (kj∞) values at infinte dilution, it was concluded that the investigated DES has the potential to replace a number of industrial solvents for the separation of various industrial mixtures.

Preferential solvation, ion pairing, and dynamics of concentrated aqueous solutions of divalent metal nitrate salts.

We have investigated the characteristics of preferential solvation of ions, structure of solvation shells, ion pairing, and dynamics of aqueous solutions of divalent alkaline-earth metal nitrate salts at varying concentration by means of molecular dynamics simulations. Hydration shell structures and the extent of preferential solvation of the metal and nitrate ions in the solutions are investigated through calculations of radial distribution functions, tetrahedral ordering, and also spatial distribution functions. The Mg2+ ions are found to form solvent separated ion-pairs while the Ca2+ and Sr2+ ions form contact ion pairs with the nitrate ions. These findings are further corroborated by excess coordination numbers calculated through Kirkwood-Buff G factors for different ion-ion and ion-water pairs. The ion-pairing propensity is found to be in the order of Mg(NO3)2 < Ca(NO3)2 < Sr(NO3)2, and it follows the trend given by experimental activity coefficients. It is found that proper modeling of these solutions requires the inclusion of electronic polarization of the ions which is achieved in the current study through electronic continuum correction force fields. A detailed analysis of the effects of ion-pairs on the structure and dynamics of water around the hydrated ions is done through classification of water into different subspecies based on their locations around the cations or anions only or bridged between them. We have looked at the diffusion coefficients, relaxation of orientational correlation functions, and also the residence times of different subspecies of water to explore the dynamics of water in different structural environments in the solutions. The current results show that the water molecules are incorporated into fairly well-structured hydration shells of the ions, thus decreasing the single-particle diffusivities and increasing the orientational relaxation times of water with an increase in salt concentration. The different structural motifs also lead to the presence of substantial dynamical heterogeneity in these solutions of strongly interacting ions. The current study helps us to understand the molecular details of hydration structure, ion pairing, and dynamics of water in the solvation shells and also of ion diffusion in aqueous solutions of divalent metal nitrate salts.

Modeling of mixed-solvent electrolyte systems

Models for mixed-solvent strong electrolytes, using an equation of state (EoS) are reviewed in this work. Through the example of ePPC-SAFT (that includes a Born term and ionic association), the meaning and the effect of each contribution to the solvation energy and the mean ionic activity coefficient are investigated. The importance of the dielectric constant is critically reviewed, with a focus on the use of a salt-concentration dependent function. The parameterization is performed using two adjustable parameters for each ion: a minimum approach distance (σMSA) and an association energy (εAB). These two parameters are optimized by fitting experimental activity coefficient and liquid density data, for all alkali halide salts simultaneously, in the range 298 K–423 K. The model is subsequently tested on a large number of available experimental data, including salting out of Methane/Ethane/CO2/H2S. In all cases the deviations in bubble pressures were below 20% AADP. Predictions of vapor-liquid equilibrium of mixed solvent electrolyte systems containing methanol, ethanol are also made where deviations in bubble pressures were found to be below 10% (AADP).

Prediction of solubility of active pharmaceutical ingredients by semi- predictive Flory Huggins/Hansen model

In this work, solubility of four Active Pharmaceutical Ingredients (APIs) including Butyl Paraben, Fenoxycarb, Fenofibrate and Risperidone were predicted using Hansen Flory Huggins model using two different scenarios. In the first method, activity coefficient of APIs were obtained through fitting the experimental activity coefficients of solvents at particular temperature of 293K, then components solubility in entire temperature range of study was predicted. In the second scenario, the model parameters were adjusted using experimental data of two selected solvents, then components solubility were predicted in other solvents. In order to check the physical meanings of obtained values, Molecular Dynamic (MD) simulations was utilized and the results were compared. Finally the predictive capabilities of two Hansen Flory Huggins models were compared to temperature-dependent NRTL-SAC model.

Electrolyte-UNIQUAC-NRF Model Based on Ion Specific Parameters for the Correlation of Mean Activity Coefficients of Electrolyte Solutions

The Electrolyte-UNIQUAC-NRF excess Gibbs function was applied to estimate ion specific adjustable parameters of various salts by global optimization of the experimental activity coefficients of 54 electrolyte solutions. Twenty-three ion specific parameters were obtained for water and several cations and anions. The estimated individual ion parameters have been used to predict osmotic coefficient of electrolyte solutions. By using only the specific values for ions, the anion–cation and ion–water interaction parameters of different salts can be precisely estimated. Consequently, the interaction parameters of sparingly insoluble salts without experimental activity data can be easily calculated. For a case study, the solubility of CaSO4 was predicted in relatively good agreement with experimental values over a wide range of temperatures up to 473.18 K.

Apparent Henry’s law constants of furan in different n-alkanes and alcohols at temperatures from 293 to 323 K

Green chemical compounds with high added value can be obtained after pyrolysis of lignocellulosic biomass. This biomass is playing a major role in the chemical sectors as a substitution material. This study is focused on one of these compounds, furan. High selectivity of a solvent is the most important criteria for an optimised extraction. In other words, for the selected solvent, activity coefficients of the compounds to be separated must be different. Therefore, experimental activity coefficients of compounds of interest in different solvents are necessary. In this paper, apparent Henry’s law constants of furan in different n-alkane and alcohol solvents have been measured at temperatures from 293 to 323K using the inert gas stripping method to analyse their potential for furan extraction. Besides, if the value of limiting activity coefficient is close to one, it is an indicator of its suitability for the compound extraction.

Parameterization of a coarse-grained model with short-ranged interactions for modeling fuel cell membranes with controlled water uptake.

The design of polymer electrolyte membranes with controlled water uptake is of high importance for high-performance fuel cells, because the water content of the membranes modulates their conductivity, chemical stability and mechanical strength. The water activity aw controls the equilibrium water uptake of a system. Predicting aw of materials is currently a daunting challenge for molecular simulations, because calculations of water activity require grand canonical simulations that are extremely expensive even with classical non-polarizable force fields. Moreover, force fields do not generally reproduce aw of solutions. Here, we first present a general strategy to parameterize force fields that reproduce the experimental aw of solutions, and then implement that strategy to re-parameterize the interactions in FFcomp, a coarse-grained model for hydrated polyphenylene oxide/trimethylamine chloride (PPO/TMACl) membranes in which the TMA cation is attached to the PPO backbone and the Cl anion is in the mobile water nanophase. Coarse-grained models based on short-ranged potentials successfully model fuel cell membranes and other concentrated aqueous electrolyte solutions because electrostatic interactions are highly screened in these systems. The new force field, FFpvap, differs from the original FFcomp only in the parameters of the ion-ion interactions, yet it reproduces aw in TMACl solutions with accuracy within 0.5 and 3% of the experimental value in all the concentration range relevant to the operation of fuel cell membranes. We find that the heat needed to vaporize water in solutions with as little as five water molecules per ion pair is essentially the same as in pure water, despite the strong water-ion interactions and their impact on the water activity. We review the literature to demonstrate that this is independent of the model and a general feature of water solutions. FFpvap reproduces the radial distribution functions and captures well the relative diffusivities of water and ions in the ionic solution as predicted by the reference atomistic GAFF-TIP4P/2005 model, while providing a hundred-fold gain in computing efficiency with respect to the atomistic model. With the backbone fragments inherited from FFcomp, the new FFpvap force field can be used to model hydrated polymer electrolyte membranes and advance the design of fuel cell membranes with controlled water uptake and conductivity.

The implementation of ion-based ePC-SAFT EOS for calculation of the mean activity coefficient of single and mixed electrolyte solutions

Following our previous work (Journal of Molecular Liquids 221 (2016) 904–913), the modified perturbed chain statistical associating fluid theory (ePC-SAFT) incorporated with Debye-Huckel term has been applied to calculate some thermodynamic properties of single and mixed electrolyte solutions. The applicability of this model has been investigated by calculation of the mean ionic activity and osmotic coefficients of electrolyte solutions as well as the water activity of regarded systems at different temperatures. Firstly, water-ion hydration has been taken into account independently by two individual strategies, i.e. ions can be considered as non-associating and associating compounds distinctly. Afterwards, a new set of ion parameters containing 31 common ions has been estimated using the experimental mean ionic activity coefficients and liquid densities of 78 binary electrolyte solutions in both strategies. The optimized parameters which have been utilized for prediction of single-salt aqueous electrolyte solutions MIACs up to 373.15 K are global and transferable to different salts. Eventually, it can be observed that not only the density of aqueous electrolyte solutions, but also MIACs, osmotic coefficients and water activity of single and mixed salt solutions are satisfactorily calculated by considering ions as association compounds over a wide range of temperature and salt concentration.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Vapor Pressure of Aqueous Solutions of Electrolytes Reproduced with Coarse-Grained Models without Electrostatics.

The vapor pressure of water is a key property in a large class of applications from the design of membranes for fuel cells and separations to the prediction of the mixing state of atmospheric aerosols. Molecular simulations have been used to compute vapor pressures, and a few studies on liquid mixtures and solutions have been reported on the basis of the Gibbs Ensemble Monte Carlo method in combination with atomistic force fields. These simulations are costly, making them impractical for the prediction of the vapor pressure of complex materials. The goal of the present work is twofold: (1) to demonstrate the use of the grand canonical screening approach ( Factorovich , M. H. J. Chem. Phys. 2014 , 140 , 064111 ) to compute the vapor pressure of solutions and to extend the methodology for the treatment of systems without a liquid-vapor interface and (2) to investigate the ability of computationally efficient high-resolution coarse-grained models based on the mW monatomic water potential and ions described exclusively with short-range interactions to reproduce the relative vapor pressure of aqueous solutions. We find that coarse-grained models of LiCl and NaCl solutions faithfully reproduce the experimental relative pressures up to high salt concentrations, despite the inability of these models to predict cohesive energies of the solutions or the salts. A thermodynamic analysis reveals that the coarse-grained models achieve the experimental activity coefficients of water in solution through a compensation of severely underestimated hydration and vaporization free energies of the salts. Our results suggest that coarse-grained models developed to replicate the hydration structure and the effective ion-ion attraction in solution may lead to this compensation. Moreover, they suggest an avenue for the design of coarse-grained models that accurately reproduce the activity coefficients of solutions.

Activity Coefficients at Infinite Dilution of Organic Solutes and Water in Tributylethylphosphonium Diethylphosphate Using Gas–Liquid Chromatography: Thermodynamic Properties of Mixtures Containing Ionic Liquids

In this work, new set of experimental activity coefficients at infinite dilution, γ13∞ for 51 various organic solutes such as alkanes, 1-alkenes, 1-alkynes, cycloalkanes, aromatic hydrocarbons, alcohols, thiophene, ethers, ketones, acetonitrile, pyridine, 1-nitropropane, and water in tributylethylphosphonium diethylphosphate, [P2,4,4,4][DEP] have been measured in temperature range T = (328.15 to 368.15) K by gas–liquid chromatography, GLC. From experimental data the partial molar excess Gibbs free energies ΔG1E,∞, enthalpies ΔH1E,∞, and entropies TrefΔS1E,∞ at infinite dilution were calculated. Additionally the gas–liquid partition coefficients, KL were determined. Moreover, capabilities of the studied ionic liquid in several liquid–liquid extraction processes are evaluated by selectivity and capacity at infinite dilution. These parameters were compared to the values from the recent literature for other ionic liquids with phosphonium cation or diethylphosphate anion. Additionally, basic thermophysical cha...