Prediction of thermodynamic properties of aqueous electrolyte solutions using equation of state

In this study, a predictive model is presented for estimation of second order thermodynamic properties of electrolyte solutions. In order to provide a comprehensive understanding, the capability of modified electrolyte PC‐SAFT up to high pressure and temperature has been studied. In addition to the first order derivative thermodynamic properties, the Gibbs free energy, enthalpy and heat capacity of aqueous electrolyte solutions at infinite dilution are predicted. Using new methodology, the dielectric constant is modified to keep the pressure, temperature, and ionic strength dependency. Our results show that the Born term has a significant contribution on prediction of second order derivative properties. Meanwhile the impact of temperature‐dependent solution dielectric constant on standard state heat capacity is studied. Finally, the isobaric heat capacity at various salt concentrations is predicted without any adjustable parameters. The results of this work indicate an acceptable agreement with experimental data especially at high pressure and temperature. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Solvent effects on esterification equilibria

Solvents are known to have strong impacts on the yields of equilibrium reactions. This work focuses on the thermodynamic investigation of these solvent effects on esterification reactions of acetic acid and propionic acid with ethanol. Esterification of acetic acid was performed in the solvents acetone, acetonitrile (ACN), dimethylformamide (DMF), and tetrahydrofurane as well as in mixtures thereof. ACN promotes the esterification of acetic acid, whereas it is strongly suppressed by DMF. The esterification of propionic acid was investigated with various reactant concentrations in acetone. The experimental equilibrium data in pure solvents and solvent mixtures were modeled using the thermodynamic equilibrium constant K_a and the reactant/product activity coefficients predicted by the perturbed chain‐statistical associating fluid theory (PC‐SAFT). For a given K_a, PC‐SAFT is able to predict the influence of the solvent and even solvent mixtures on the equilibrium concentrations of esterification in almost quantitative agreement with the experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3000–3011, 2015     

Study of solubility and swelling ratio in polymer‐CO2 systems using the PC‐SAFT equation of state

We use the PC‐SAFT equation of state to model the solubility of CO₂ in various homopolymers. We also model the swelling ratio of the PP (polypropylene)‐CO₂ mixture using PC‐SAFT and then compare the results with Sanchez‐Lacombe (S‐L) and Simha‐Somcynsky (S‐S) equations. The results show that PC‐SAFT can describe the solubility of CO₂ in polymers very well. We compare two sets of parameters in the PC‐SAFT equation, Gross et al.'s and Chen et al.'s. As for the swelling ratio, PC‐SAFT using Chen et al. parameters is better than S‐L equation, which is commonly used by early researchers in studying the solubility of CO₂ in polymers. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44804.     

Estimation of thermodiffusion coefficients in ternary associating mixtures

Following the non‐equilibrium thermodynamics formulation and taking into account the complexities in the structure of aqueous associating mixtures, expressions are proposed to estimate the thermodiffusion coefficients in ternary associating mixtures, such as water and alcohol mixtures. The model expressions are used to estimate the thermodiffusion coefficients in methanol–ethanol–water, dimethyl sulfoxide (DMSO)–ethanol–water and DMSO–t‐butanol–water mixtures at various concentrations. The perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state is used to obtain the mixture properties, such as the derivatives of the chemical potentials needed to evaluate the thermodiffusion coefficient expressions. The results show that at certain concentrations of one component, variation of the concentration of the other two components can cause a sign change in the thermodiffusion coefficients. While the model cannot be evaluated due to the lack of any pertinent experimental data, the model predictions may be used to choose suitable mixture compositions in space experiments to be performed onboard the International Space Station (ISS) in near future. © 2011 Canadian Society for Chemical Engineering     

An electrolyte CPA equation of state for mixed solvent electrolytes

Despite great efforts over the past decades, thermodynamic modeling of electrolytes in mixed solvents is still a challenge today. The existing modeling frameworks based on activity coefficient models are data‐driven and require expert knowledge to be parameterized. It has been suggested that the predictive capabilities could be improved through the development of an electrolyte equation of state. In this work, the Cubic Plus Association (CPA) Equation of State is extended to handle mixtures containing electrolytes by including the electrostatic contributions from the Debye–Hückel and Born terms using a self‐consistent model for the static permittivity. A simple scheme for parameterization of salts with a limited number of parameters is proposed and model parameters for a range of salts are determined from experimental data of activity and osmotic coefficients as well as freezing point depression. Finally, the model is applied to predict VLE, LLE, and SLE in aqueous salt mixtures as well as in mixed solvents. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2933–2950, 2015     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Application of Chebyshev polynomials to predict phase behavior of fluids containing asphaltene and associating components using SAFT equation of state

In this work, a thermodynamic model based on statistical association fluid theory (SAFT) is developed to predict the phase behavior of mixtures containing asphaltene contents. The SAFT equation of state is a good candidate for closing that gap between statistical mechanic models and the classical models dominated by cubic equation of state. A robust, fast and accurate computational algorithm based on Chebyshev polynomial approximation is developed to calculate the density and hence fugacity using SAFT equation of state in order to perform phase equilibrium calculations. Application of Chebyshev polynomials to approximate pressure-density function leads to an interpolation error of degree 10⁻¹³. Application of the proposed algorithm to calculate density of binary systems composed of ethanol and toluene shows an average relative deviation of 0.143% in the temperature range 283.15-353.15 K and for pressures up to 45 MPa. The proposed model is developed to predict the precipitation behavior of petroleum fluids containing asphaltene. The effect of pressure, temperature and solvent concentration on the amount of asphaltene precipitation is investigated. A good agreement with an AAD of 2.593% is observed between experimental and predicted amount of asphaltene precipitate. The model is also tested to investigate the effect of temperature and solvent concentration on asphaltene onset pressures (upper and lower). Again, an excellent agreement is observed between experimental and predicted values of the asphaltene onset pressure at different temperatures and solvent concentrations with an average 0.705% relative error. The accuracy of the proposed model is compared with WinProp software using Peng-Robinson equation of state with average 53.132% and 8.657% relative errors for the amount of asphaltene precipitate and onset pressure, respectively.     

Prediction of Hydrate Phase Equilibria in Aqueous Solutions of Salt and Organic Inhibitor Using a Combined Equation of State and Activity Coefficient‐Based Model

A thermodynamic model based on combination of the Valderrama modification of the Patel‐Teja equation of state with non‐density dependent mixing rules and a modification of a Debye‐Hückel electrostatic term is extended to systems containing salt and organic inhibitor by correcting the properties of the aqueous phase such as dielectric constant, density and molecular weight. A linear mixing rule is used for determining the dielectric constant of salt‐free mixture by introducing an interaction parameter (in dielectric constant mixing rule), which is tuned using the freezing point data of aqueous solutions containing salt and organic inhibitor. The binary interaction parameter between salt and organic inhibitor is adjusted using water vapour pressure data in the presence of salt and organic inhibitor. The predicted hydrate dissociation conditions are in acceptable agreement with the experimental data, demonstrating the reliability of the model developed in this work.     

Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT)

A semi-empirical equation of state for the freely jointed square-well chain fluid is developed. This equation of state is based on Wertheim’s thermodynamic perturbation theory (TPT) and the statistical associating fluid theory (SAFT). The compressibility factor and radial distribution function of square-well monomer are obtained from Monte Carlo simulations. These results are correlated using density expansion. In developing the equation of state the exact analytical expressions are adopted for the second and third virial coefficients for the compressibility factor and the first two terms of the radial distribution function, while the higher order coefficients are determined from regression using the simulation data. In the limit of infinite temperature, the present equation of state and the expression for the radial distribution function are represented by the Carnahan-Starling equation of state. This semi-empirical equation of state gives at least comparable accuracy with other empirical equation of state for the square-well monomer fluid. With the new SAFT equation of state from the accurate expressions for the monomer reference and covalent terms, we compare the prediction of the equation of state to the simulation results for the compressibility factor and radial distribution function of the square-well monomer and chain fluids. The predicted compressibility factors for square well chains are found to be in a good agreement with simulation data. The high accuracy of the present equation of state is ascribed to the fact that rigorous simulation results for the reference fluid are used, especially at low temperatures and low densities. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

Effects of ultrasonic assisted processing and clay nanofiller on dielectric properties and lithium ion transport mechanism of poly(methyl methacrylate) based plasticized polymer electrolytes

Lithium ion conducting solid polymer electrolyte (SPE) films consisted of poly(methyl methacrylate) (PMMA) matrix with lithium perchlorate as a dopant ionic salt, poly(ethylene glycol) as plasticizer and montmorillonite clay as inorganic nanofiller have been prepared by classical solution casting and high intensity ultrasonic assisted solution casting methods. The X‐ray diffraction study confirmed the amorphous structure of all these PMMA‐based solid electrolytes and the clay nanosheets existed in exfoliated form in their amorphous phase. Dielectric relaxation spectroscopy had been employed for the investigation of complex dielectric function, ac electrical conductivity, electric modulus, and impedance spectra of these electrolytes over the frequency range from 20 Hz to 1 MHz. It was observed that the dielectric properties and ionic conductivity of the electrolytes strongly depended on the sample preparation methods, and also had changes with addition of the clay nanofiller. Temperature‐dependent dielectric study of the electrolyte films confirmed that their dc ionic conductivity and conductivity relaxation time values obeyed the Arrhenius behavior. This study also revealed that the lithium ion transportation in the ion–dipolar complexes of these electrolytes occurred through hopping mechanism and it was correlated with the conductivity relaxation time. Preparation of these electrolyte films through ultrasonic assisted solution casting method increased the ionic conductivity by more than one order of magnitude in comparison to that of the classical solution casting method, which revealed that the former was a novel method for the preparation of these SPEs of relatively enhanced ionic conductivity. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42188.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Thermodynamics of protein aqueous solutions: From the structure factor to the osmotic pressure

An analytical expression for the structure factor for globular proteins in aqueous solution is presented. This expression was obtained considering a potential given by the sum of a hard core, a van der Waals attractive, and a screened Coulomb contribution. Experimental data of small angle x‐ray scattering for bovine serum albumin (BSA) in aqueous solutions containing sodium salts at different protein concentrations and pH values are also presented. The developed expression for the structure factor describes accurately these experimental data provided a dependence of the attractive parameter on protein concentration is established. An expression for the osmotic pressure was derived from the structure factor. With attractive parameters adjusted from x‐ray scattering data, the osmotic pressure of BSA aqueous solutions could be predicted with very good agreement with experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2871–2880, 2015     

Polyelectrolyte behaviour of acrylonitrile methallylsulphonate copolymers in dimethylformamide

The properties in organic solvent (DMF) of two ionic copolymers are investigated and compared to those of polyelectrolytes in aqueous solutions. First, the viscometric behaviour is disccussed: it is demonstrated that [η] varies linearly with $\text{C}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}{}_{\mathrm{T}}$, where C_T is the ionic concentration of the solution. At infinite salt concentration we obtain data in agreement with unperturbed dimensions. Using isoionic dilution, we deduce ø_p, the osmotic coefficient. From osmometry, the dependence of ø_p on the concentration is obtained and compared to the theoretical value. In the presence of neutral salt, the osmotic pressure is determined as a function of salt and polymer concentrations. The results are interpreted in terms of a Donnan equilibrium.     

Ionic salt permeability through phase‐separated membranes composed of amphoteric polymers

Amphoteric copolymers composed of hydrophilic poly(dimethyl acrylamide) and hydrophobic poly(dimethyl siloxane) formed phase‐separated membranes. The hydrophilic and hydrophobic components formed continuous phase‐separated domains in the membranes. The hydrated poly(dimethyl acrylamide) domains formed membrane‐spanning pathways, which permitted an ionic salt to permeate the membranes. The permeability of the ionic salt through the amphoteric copolymer membranes was studied. On the basis of the results, the mechanism of salt transport could be explained by the free‐volume theory, which was used for the analysis of diffusive transport in the hydrated, homogeneous membranes. The diffusion coefficient of the ionic salt increased exponentially as the volume ratio of the hydrophilic polymer to water [(1 − H)/H, where H is the degree of hydration] decreased in the membrane. It was possible to postulate that the diffusion of the ionic salt through the membranes was dependent on the free‐volume fractions of water and hydrophilic poly(dimethyl acrylamide) domains in the membranes. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Correlation of the mean activity coefficient of aqueous electrolyte solutions using an equation of state

Accurate calculation of thermodynamic properties of electrolyte solution is essential in the design and optimization of many processes in chemical industries.A new electrolyte equation of state is developed for aqueous electrolyte solutions.The Carnahan–Starling repulsive model and an attractive term based on square-well potential are adopted to represent the short range interaction of ionic and molecular species in the new electrolyte EOS.The long range interaction of ionic species is expressed by a simplified version of Mean Spherical Approximation theory(MSA).The new equation of state also contains a Born term for charging free energy of ions.Three adjustable parameters of new e EOS per each electrolyte solution are size parameter,square-well potential depth and square-well potential interaction range.The new e EOS is applied for correlation of mean activity coefficient and prediction of osmotic coefficient of various strong aqueous electrolyte solutions at 25 °C and 0.1 MPa.In addition,the extension of the new e EOS for correlation of mean activity coefficient and solution density of a few aqueous electrolytes at temperature range of 0 to 100 °C is carried out.     

Accurate thermodynamic modeling of ionic liquids/metal salt mixtures: Application to carbon monoxide reactive absorption

For the first time, a theoretical semipredictive approach based on the soft‐Statistical Associating Fluid Theory equation of state is presented to model the complexation reaction between carbon monoxide (CO) in a combined ionic liquid (IL) plus a copper(I) metallic salt media in terms of the gas solubility as a function of temperature, pressure, and composition. Two different degrees of molecular approximation are tested. In the first approach, the IL‐metal salt mixture is treated as a single compound whose parameters are modified according to the concentration of the metallic salt. In the second approach, both compounds are treated as independent species, enhancing the predictive capability of the model. The complexation between CO molecules and the metal salt is reproduced by adding specific cross‐association interaction sites that simulate the reaction. The density of the doped IL and the CO solubility are described in quantitative agreement with the experimental data at different operating conditions. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3532–3543, 2017     

Structure–property relationship of sodium deoxycholate based poly(ester ether)urethane ionomers for biomedical applications

New sodium deoxycholate based poly(ester ether)urethane ionomers were prepared for the development of biomedical materials. A structure–property relationship in the tested biomaterials was established by cross‐examination of the dynamic mechanical and dielectric properties, attenuated total reflection–Fourier transform infrared investigation, thermogravimetric analysis, and surface morphology characterization. A stronger ionic interaction and solvation capacity of the ions and a higher ionic conductivity were manifested in the case of poly(ethylene oxide)‐rich segments than for poly(propylene oxide)‐rich segments in these polyurethane ionomers. The molecular and ionic interactions of the bile‐salt moiety with different polyether cosoft segments influenced chain packing and conformation, supramolecular organization, and the resulting surface morphological microstructures of the polyurethane biomembranes. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42921.