Modeling of mixed-solvent electrolyte systems

Abstract

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 () and an association energy (). These two parameters are optimized by fitting experimental activity coefficient and liquid density data, for all alkali halide salts simultaneously, in the range 298K to 423K. The model is subsequently tested on a large number of available experimental data, including salting out of Methane/Ethane/CO 2 /H 2 S. 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).

110th Anniversary: Theory of Activity Coefficients for Lithium Salts in Aqueous and Nonaqueous Solvents and in Solvent Mixtures

“…Our attribution of the upturn in ln f ± at high salt concentrations to the excluded volume of the ions and their solvation shell results from the solvation effects reported by other researchers. (8,12,44,63) With higher ion association there are fewer solute particles and, as eq 23 shows, association moderates the increase in activity coefficients by reducing repulsive interactions. This finding is consistent with previous research on activity coefficients of weak electrolytes.…”

“…Several authors have experimentally characterized the thermodynamic activities of mixed-solvent electrolytes and a few microscale models have been presented based on pertinent molecular interactions. (10,12,18,19) In solvent mixtures, experimental and theoretical research has long ago shown that polarizable solvents and those with strong specific interactions preferentially solvate ions. (20−22) As a result of preferential solvation, activity coefficients of salts in a solvent mixture are not simple averages of pertinent single-solvent electrolyte properties.…”

Predicting activity coefficients with the Debye–Hückel theory using concentration dependent static permittivity

“…It has becoming accepted that a Born‐type equation 39 shall be included in order to describe the ion‐solvent interactions when modeling an electrolyte solution, with either the Debye–Hückel or the mean spherical approximation theory 22,23,29,37,40‐48 . It has been shown 22,35 that a full version of the Debye–Hückel theory naturally contains a contribution for the ion‐solvent interactions, which is essentially equivalent to the Born equation used in most of the aforementioned references 45 .…”

On the “Born” term used in thermodynamic models for electrolytes

“…The effect of solvent-solvent forces is taken into account in SAFT models through the Wertheim association term. Lastly, the contribution from ion-solvent forces is often implicitly described by inserting a so-called "Born" term [10][11][12][13] , which has been proposed as an extension of the formula provided by Born to calculate ion solvation energies in solution.…”

“…Besides this exception, many models have accounted for the effect of ion-solvent forces by adding an independent "Born" term to the Helmholtz or Gibbs energy, or directly to the chemical potential of an ion. This has been the case of models based on the Peng-Robinson equation of state (EOS) 8,20 , on the cubic-plus-association (CPA) EOS 21,22 , on the Soave-Redlich-Kwong (SRK) EOS 23 , on the electrolyte-NRTL model 3,24,25 , and on SAFTtype equations [10][11][12][13] . Another case is the II+IW model 26,27 in which the chemical potential of an ion comprises an ion-ion (II), and an ion-solvent (IW), interaction term.…”