Betamethasone sodium phosphate solubility in supercritical CO2: Application of Peng-Robinson EoS and density-based correlations

Drug components’ solubility in supercritical carbon dioxide (SC-CO₂) should be considered for the development of the pharmaceutical industry and the drug delivery field. Accurate experimental solubility computing in supercritical CO₂ would help identify the best working conditions and thermodynamic boundaries for drug processing with supercritical fluids. The prediction of drug solubility in supercritical CO₂ is generally approached through two different methodologies: thermodynamic modeling and empirical correlation. Thermodynamic models are based on fundamental thermodynamic principles and phase equilibrium rules. Semi-empirical equations develop a mathematical relationship between drug solubility and operational parameters (temperature and pressure or density) of the supercritical fluid. In spite of the acceptance of each of these procedures, more experimental drug solubility data are still required for improving modeling performances. For the first time and in the present communication, solubility of Betamethasone Sodium Phosphate ( BSP ) is measured and modeled using a set of eight semi-empirical equations and Peng-Robinson equation of state (PR EoS). Using an experimental set-up based on ultraviolet-visible spectroscopy, the drug solubility data, consisting of 24 measurements, were obtained at various temperatures (308-338 K) and pressures (120-270 bar). The results indicated that the BSP solubility is within the range of 0.32 × 10⁻⁶ to 8.43 × 10⁻⁶. Variations in temperature and pressure affected the solubility of BSP , and pressure showed a direct influence, but a cross-over behavior was identified at constant temperature. For thermodynamic modeling, the PR EoS showed satisfactory alignment with the experimental data, but the Chrastil model, as semi-empirical model, with an AARD = 7.22%, performed better. Also, to investigate the performance of the EoS and semi-empirical models, the comparison between the PR EoS and Bartle et al. model (as example of semi-empirical models) in the term of density-solubility was performed. Finally, the BSP /SC-CO₂ enthalpies were calculated.