Increasing the Prediction Efficiency of Hansen Solubility Parameters in Supercritical Fluids

Abstract

This work describes a simplified method developed for calculating the Hansen parameters (HSPs) for scCO₂-polar modifier solvent mixtures. The method consists in fitting 2^nd order equations on the calculated values of HSPs of pure components in function of pressure and temperature. It has been proved that these equations are suitable for the characterization of the above system. The current work also proposes a modified representation method, which eliminates the shortcomings of the original ternary Teas diagram, normally used for the representation of the Hansen parameters. On the one hand, the Teas diagram uses quantities without any physical meaning and, on the other hand, the illustration of the solubility information is distorted because it does not take into account the differences of the Hildebrand parameters of different solvents. The factors we have chosen to represent on the ternary diagram possess physical meaning (cohesion energy density partitions). The distortion was eliminated by extending the Teas diagram to a prismatic three dimensional representation. We proved that the Hansen-ellipsoid from the Cartesian coordinate system (d_d = f (δ_H, d_p)) is transformed in an ellipsoid also in the new coordinate system (the transformation is pseudo-isomorphic). Nonetheless, the suggested corrections improve the accuracy of the Hansen method, in some cases the interactions between the solvents and the dissolved materials are still not predicted with sufficient accuracy. Most probably a thermodynamic-based correction of the values of the HSPs of small molecules could lead to a significant improvement of the predictive ability of the newly developed method.