Solubility Prediction via COSMO-RS

The COSMO-RS (Conductor-like Screening Model for Real Solvents) [63 (link),64 (link),65 (link),66 (link)] was applied for the theoretical characteristics of solid–liquid multi-component systems. This commonly used framework takes advantage of the first principle quantum chemistry computations augmented with statistical thermodynamics for assessments of thermodynamic properties including chemical activities. Although it was designed for liquid systems, the solid–liquid equilibria (SLE) can also be treated, if only fusion data are provided either from direct measurements or external computations. In the case of edaravone, both the melting temperature, T_m = 403.15 K, and heat of fusion H_fus = 29.91 kJ/mol are known [14 (link)] and as such were used for solubility computations. The fusion data are indispensable since the values of the chemical potential of the solute in the saturated conditions are determined by the activity of the pure solid phase, according to the fundamental formula: $$\ln \left({\mathrm{a}}_{\mathrm{i}}^{\mathrm{s}}\right)=\ln \left({\mathsf{\gamma }}_{\mathrm{i}}^{\mathrm{sat}}{\mathrm{x}}_{\mathrm{i}}^{\mathrm{sat}}\right)=-\frac{{\Delta }_{\mathrm{fus}}{G}_i^m\left(p,T\right)}{\mathrm{RT}}$$
where ${\Delta }_{\mathrm{fus}}{G}_i^m\left(p,T\right)$ is the partial molar Gibbs free energy of fusion at the solubility measurement conditions. Practically, solubility is commutated by iteratively solving the following equation: $$ln\left({\gamma }_i^{sat,i+1}{x}_i^{sat,i+1}\right)=\frac{1}{RT}\left({\mu }_i^{o,liq}-{\mu }_i^{\left(i\right)}\left({\gamma }_i^{sat,i}{x}_i^{sat,i}\right)+max\left(0,{\Delta }_{fus}{G}_i^m\left(p,T\right)\right)\right)$$
In the above equation superscripts i and i + 1 denote the values obtained in two subsequent iterations. The iterative cycle is repeated until convergence is achieved, which means that the computation is supposed to be interrupted if the difference in the computed solubility drops below a defined threshold value. The bulk phase used for solubility computations has the same composition as the solute-free solvent used in experimental measurements.