Organic electrolyte solutions: Modeling of deviations from ideality within the binding mean spherical approximation

Abstract

Deviations from ideality in organic electrolyte solutions are described within the Binding Mean Spherical Approximation (BiMSA) theory, in which ions are regarded as charged hard spheres and unlike ions may associate to form an ion pair. Association is modeled within the Wertheim theory (as done in SAFT-type models). The model includes a mass action law with a thermodynamic association constant. The literature about the thermodynamic properties of this type of solution is reviewed. Besides, it is attempted to gain some insight into the solvation of ions by computing their Stokes hydrodynamic diameters from conductivity experiments, and by employing an original analysis introduced by Fawcett. The BiMSA model is used to represent the osmotic coefficient of 1-1 electrolytes in pure methanol, ethanol, 2-propanol, acetone and acetonitrile. The optimized cation sizes in the solvents are compared with their hydrodynamic diameters. The regressed association constants are compared with literature values derived from conductivity and vapor pressure experiments.

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“…(Fitting K to the experimental thermodynamic data slightly improves the fit for water and small alcohols, but introduces an additional adjustable parameter.) The results are consistent with those of Barthel and co-workers ,, and more recent work by Simonin and Bernard . Using eq and calculating from the solvent molecular volumes in Table ( ), the fitting parameter σ gives that falls within the expected range of zero and 1.…”

“…The insert in Figure shows that theory is semiquantitative at higher concentrations due to changes in the solvation-shell size. Wu and Lee and Simonin et al , showed that incorporation of concentration-dependent ionic sizes and solution dielectric constant yields excellent fits to experiment up to saturation but such fits require numerous additional adjustable parameters.…”

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“…20 Importantly, MSA provides an accurate representation of both thermodynamic and transport properties of electrolyte solutions using only the ionic diameters as the adjustable parameters. 21,22 MSA obeys the limiting law at low electrolyte concentrations similar to various empirical modifications of the DH theory. 23 Besides, further improvements can be accomplished by including the ion pairing effects.…”

“…Over the years, a number of thermodynamic models have been developed for electrolyte solutions beyond semiempirical modifications of the DH theory. , Among them, the mean-spherical approximation (MSA) represents a popular choice owing to its computational simplicity to describe the ion-size effects and electrostatic correlations . Importantly, MSA provides an accurate representation of both thermodynamic and transport properties of electrolyte solutions using only the ionic diameters as the adjustable parameters. , MSA obeys the limiting law at low electrolyte concentrations similar to various empirical modifications of the DH theory . Besides, further improvements can be accomplished by including the ion pairing effects .…”

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“…The MSA has been used to get an interpretation of the impact of sugars on ion properties in milk-based systems by taking into account electrostatic interactions and volume exclusion [30]. Lastly, the effect of temperature on the activity coefficients of various salts in water [31], and deviations from ideality in organic electrolyte solutions [32][33][34] (an industrially relevant topic nowadays) have been obtained in this framework.…”