Determining Hansen Solubility Parameters by a Rotated Ellipsoid-Based Method

In the Hansen solubility parameters (HSPs) space, the solubility region of solute was modeled as a rotated ellipsoid (SRE) which was centered at the HSPs of solute and arbitrarily oriented. The optimal SRE of solute, enclosing all good solvents, having the lowest number of outliers, and having the smallest volume, was determined by a novel method composed of an analytic-geometric model and an optimization procedure. The resultant SREs of sixteen materials described optimally the solubility behavior of the substances, i.e. enclosed lower numbers of outliers and/or had smaller volumes as compared with the corresponding SREs, solubility axis-aligned ellipsoids, and solubility spheres available so far. The results verified the validity of the novel method and demonstrated its advantages over the methods reported elsewhere, the problems in which and the underlying causes thereof were analyzed and explained.