Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

Abstract

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion-ion interactions are included at the centre of a Mie core; the ion-water interactions are also modelled with a Mie potential without an explicit treatment of iondipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion-ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion-solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.

Modelling and prediction of the thermophysical properties of aqueous mixtures of choline geranate and geranic acid (CAGE) using SAFT-γ Mie

“…In the SAFT-g Mie group-contribution approach 17,18 molecules are represented as associating hetero-segmented chains consisting of fused spherical segments that interact via Mie potentials of variable range 24 with short-range directional interactions incorporated by embedding square-well association sites on any given segment. The total Helmholtz free energy A of a mixture of n components at a given temperature T, volume V, and composition vector N ¼ (N 1 , N 2 , ., N n ), where N j denotes the number of molecules of component j, is obtained as the sum of six contributions arising from a perturbation approach: 17,18,20 A ¼ A ideal + A monomer + A chain + A association + A Born + A ion . (1) Here, A ideal represents the contribution of the ideal gas mixture of non-interacting particles and point charges, and A monomer , A chain and A association are the usual residual non-electrostatic terms describing the change in free energy associated with the monomer spherical segments interacting through Mie potentials, the contribution due to fusing monomer spherical segments into molecular chains, and the contribution due to molecular association through the short-ranged square-well sites, respectively.…”

“…The diameter required for the calculation of the Born term of the COO À group is obtained following the method proposed by Rashin and Honig; 29 i.e., s Born COO À ¼ 1:07s COO À : The dispersion energy 3 kk between ions is calculated using the polarisability a 0 and the ionisation potential I (electron affinity) of the COO À functional group by applying eqn (10), as for previous models developed for ionic groups. 20 The values used for the polarisability and the electron affinity are reported in Table 1. The unlike dispersion energy for the COO À -Na + pair is also obtained with eqn (10), using the experimental values of a 0 and I shown in Table 1, and the unlike interactions between H 2 O and Na + are take from ref.…”

“…The unlike dispersion energy for the COO À -Na + pair is also obtained with eqn (10), using the experimental values of a 0 and I shown in Table 1, and the unlike interactions between H 2 O and Na + are take from ref. 20. The unlike dispersion energy parameters between COO À and the alkyl groups are given the same values as those between COOH and the alkyl groups.…”

“…As with other ions, the COO À -K + unlike ion-ion dispersion energy is obtained with eqn (10), using the experimental values of a 0 and I given in Table 1, and the unlike interactions between H 2 O and K + are taken from ref. 20. The concentration dependence of the osmotic and activity coefficient of several aqueous solutions of potassium acetate at standard conditions are shown in Fig.…”

“…19 Of particular relevance to this discussion is the fact that charged compounds can be accounted for in the methodology. 20,21 Furthermore, the SAFT-g Mie approach has the added advantage of maintaining a direct link between the molecular model and the corresponding macroscopic equilibrium properties, which allows it to be used for the development of force-eld parameters for use in molecular simulation, 22,23 from which structural, interfacial and transport properties can also be studied.…”