Composition-dependence of relative static permittivity in ePPC-SAFT for mixed-solvent alkali halides

Yang, Fufang; Kontogeorgis, Georgios M.; de Hemptinne, Jean-Charles

doi:10.1016/j.fluid.2024.114103

Cited by 2 publications

(19 citation statements)

References 125 publications

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“…In the ePPC-SAFT model, − ,− the residual Helmholtz free energy is given as A res = A hc + A disp + A assoc + A polar + A NAHS + A MSA + A Born where the superscript hc denotes hard-chain, disp denotes dispersion, assoc denotes association, polar denotes multipolar as presented by refs − , NAHS denotes the nonadditive hard sphere as presented by ref . The NAHS term corrects for the combining rule of the diameters and is used in this work only for water–methanol, for which the parameter was obtained in previous work .…”

Section: Methodsmentioning

confidence: 99%

“…It has also been used for supplementing the Born term for the solvation effect, as suggested by Wu and Prausnitz, for introducing “additional association interactions between ions and solvent (water) molecules to represent interactions between charged ions and water”. In previous works, − Wertheim’s theory is used for the solvent–solvent, ion–solvent, and ion–ion associations. In our new association framework, it is used for the solvent–solvent and ion–solvent associations and is compared for the ion–ion association with Bjerrum’s theory, which will be introduced in Sections 2.1.2 and 2.1.3.…”

Section: Methodsmentioning

confidence: 99%

“…Table summarizes the modeling approaches for the association interactions. The modeling approach, Assoc-I-15, is from previous works, − in which the ion–ion and ion–solvent association sites are not distinctly labeled. Regarding the ion pairing approaches, the modeling approach using Wertheim’s theory is noted as IP-Wertheim (eq ) and that using Bjerrum’s is noted as IP-Bjerrum (eq ).…”

Section: Methodsmentioning

confidence: 99%

“…The relative static permittivity (RSP) is treated in the same way as in previous works. − For aqueous electrolyte solutions, the model presented by Schreckenberg et al (noted as the Schreckenberg model in the following) is used. In this model, the RSP is given as ε r = 1 + n solv V d v ( d T T − 1 ) where n solv is the number of moles of the solvent of volume V , d v and d T are parameters determined using the mixing rules: d v = ∑ solv n i d v , i ∑ solv n i d T = ∑ solv n i d T , i ∑ solv n i …”

Section: Methodsmentioning

confidence: 99%

“…In early electrolyte SAFT models, − ,, short-range ion–ion and ion–solvent interactions are usually accounted for using the dispersion interactions only. However, in recent works, ion association has been taken into account, − either in the association term or in the electrostatic term. In ref , a dissociation factor was introduced into the DH term in the ePC-SAFT model.…”

Section: Introductionmentioning

confidence: 99%

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Ion Pairing in ePPC-SAFT for Aqueous and Mixed-Solvent Alkali Halide Solutions

Yang,

Raeispour Shirazi,

Roa Pinto

et al. 2024

Ind. Eng. Chem. Res.

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Short-range ion−solvent and ion−ion interactions need to be taken into account in molecule-based electrolyte equations of state. The ePPC-SAFT (electrolyte polar perturbed chain statistical associating fluid theory) model consists of hard chain, dispersion, association, multipolar, nonadditive hard sphere, mean spherical approximation, and Born contributions. Using Wertheim's first-order thermodynamic perturbation theory for associating fluids to account for short-range cation−anion interactions offers significant advantages over models that use ion−ion dispersion interactions only. However, the ionic association framework assigns the same number of sites for ion−solvent and cation−anion interactions, assuming the formation of ion clusters. This work proposes a new association framework in which ion−ion and ion−solvent association sites are labeled, restricting the ion−ion association site number to one per ion to prevent the formation of larger ion clusters. This approach improves modeling accuracy compared to the original model, in which ion clustering was considered, without increasing the number of adjustable parameters. Furthermore, this work proposes a generalized Bjerrum theory with one adjustable parameter in the association strength function, as in Wertheim's theory, and proposes an analytical approximation for the Bjerrum integral to speed up calculations. This work uses Wertheim's theory for short-range ion−solvent interactions and compares Wertheim's theory and Bjerrum's theory for short-range ion−ion interactions, i.e., ion pairing. The new association framework with Wertheim's theory for both short-range ion−ion and ion−solvent associations is demonstrated to be significantly more accurate compared to Bjerrum's theory and slightly more accurate than the previous best practice. The model extends to mixed-solvent electrolyte solutions. Furthermore, the contributions of Helmholtz free energy terms and number of bonds of the ions are analyzed.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ion Pairing in ePPC-SAFT for Aqueous and Mixed-Solvent Alkali Halide Solutions

Yang,

Raeispour Shirazi,

Roa Pinto

et al. 2024

Ind. Eng. Chem. Res.

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Permittivity Modeling in Electrolyte PC-SAFT

Rueben,

Rehner,

Gross

et al. 2024

J. Chem. Eng. Data

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Accurately modeling the thermodynamic properties of electrolyte systems is key to designing decarbonized energy and chemical processes. For this purpose, a promising model class are electrolyte equations of state. These electrolyte equations of state require the relative static permittivity as an important input. The permittivity in solution deviates from the solvent permittivity, particularly at high ion concentrations. This deviation necessitates an approach to account for this dielectric decrement. This work presents a model for the dielectric decrement in the electrolyte equation of state ePC-SAFT. For this purpose, we extend ePC-SAFT by integrating our previous model for the relative static permittivity, based on perturbation theory. To account for the dielectric decrement, we obtain ion-specific permittivity parameters by adjusting to experimental mean ionic activity coefficients of water–salt mixtures. With a relative deviation of 4.1% averaged over all studied mixtures, the proposed approach accurately models mean ionic activity coefficients for lithium salts, sodium salts, potassium salts, and hydrogen halides. Moreover, the approach outperforms the common linear mixing approach based on the mole fraction. In this work, ePC-SAFT is implemented in the open-source software framework for equations of state FeOs and can be used as an easy-to-install Python package.

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Composition-dependence of relative static permittivity in ePPC-SAFT for mixed-solvent alkali halides

Cited by 2 publications

References 125 publications

Ion Pairing in ePPC-SAFT for Aqueous and Mixed-Solvent Alkali Halide Solutions

Ion Pairing in ePPC-SAFT for Aqueous and Mixed-Solvent Alkali Halide Solutions

Permittivity Modeling in Electrolyte PC-SAFT

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