Developing an accurate empirical correlation for predicting anti-cancer drugs' dissolution in supercritical carbon dioxide

This study introduces a universal correlation based on the modified version of the Arrhenius equation to estimate the solubility of anti-cancer drugs in supercritical carbon dioxide (CO2). A combination of an Arrhenius-shape term and a departure function was proposed to estimate the solubility of anti-cancer drugs in supercritical CO2. This modified Arrhenius correlation predicts the solubility of anti-cancer drugs in supercritical CO2 from pressure, temperature, and carbon dioxide density. The pre-exponential of the Arrhenius linearly relates to the temperature and carbon dioxide density, and its exponential term is an inverse function of pressure. Moreover, the departure function linearly correlates with the natural logarithm of the ratio of carbon dioxide density to the temperature. The reliability of the proposed correlation is validated using all literature data for solubility of anti-cancer drugs in supercritical CO2. Furthermore, the predictive performance of the modified Arrhenius correlation is compared with ten available empirical correlations in the literature. Our developed correlation presents the absolute average relative deviation (AARD) of 9.54% for predicting 316 experimental measurements. On the other hand, the most accurate correlation in the literature presents the AARD = 14.90% over the same database. Indeed, 56.2% accuracy improvement in the solubility prediction of the anti-cancer drugs in supercritical CO2 is the primary outcome of the current study.