Reformulated Mathematical Models for Correlating the Solubility of Solid Drugs in Supercritical Carbon Dioxide

Abstract

Solubility is the fundamental thermodynamic key parameter influencing supercritical technology in practice. In the literature, several solubility models are available to represent the solubility data. They are classified into several categories based on their origin and the background on which they were developed. Some important categories of solubility models are solvate complex models, mathematical models, and phase equilibrium models. Among them, mathematical models have shown good correlation efficiency for several solute-solvent systems. However, some do not comply with the fundamental phase rule in their functional form, which can cause them to be termed redundant models. Therefore, the current investigation aims to address the redundant nature of some mathematical models. Models considered in the work relate solubility as a function of temperature, pressure, and density in a nonlinear relationship (i.e., y₂ = f (T, P, ρ₁)). Reformulation was aimed at converting solubility models to a dimensionally consistent form in which the mole fraction of the solute is represented as a function of the reduced density of the solvent and the reduced temperature. Thus, all solubility models considered in the work are converted to y₂ = f(T_r, ρ_r). Further, existing models and reformulation models were tested with four standard solute-solvent systems namely, naphthalene-SCCO₂, anthracene-SCCO₂, phenanthrene-SCCO₂, and salicylic acid-SCCO₂. Finally, the comparison between the existing and the reformulated models was done in terms of global values of AARD%, R², R²_adj, and ΔΑΙC. From the results, it is quite clear that reformulated models are showing better results than the existing models.