Local composition-regular solution theory for analysis of pharmaceutical solubility in mixed-solvents

Local composition regular solution theory (LC-RST) model was developed by introducing non-equal i–j and j–i parameters into regular solution theory (RST) to account for specific molecular interactions. The LC-RST model was applied to the correlation of solubilities of active pharmaceutical ingredients (API) in hydrogen bond donor (HBD) – hydrogen bond acceptor (HBA) mixed-solvent systems. In the assessment of 32 API-mixed-solvent systems that contained 11 different APIs and 1947 data, it was determined that the LC-RST model had a logarithmic average relative deviation (ARDln) in solubility of 0.028, the Wilson model had an ARDln value of 0.24 and the purely predictive RST model had an ARDln value of 1.29. Partial molar excess enthalpies and entropies of the API in the mixed-solvents determined from the LC-RST model allowed estimation of API solubility regions where specific interactions occur between API and HBD-HBA complex molecules. In the correlation scheme, component numbers were designated as API molecule (1) – HBD molecule (2) - HBA molecule (3) and systems were grouped according to HBD molecule interactions with the API (pro-solvent, anti-solvent, synergistic with HBA molecule). Phenomenological parameter sensitivity analysis of the LC-RST model showed that dominant specific interactions tended to be 1–2 or 2–1 molecules for pro-solvent groupings, 2–3 or 2–3 molecules for anti-solvent groupings and all i–j and j-–i molecular pairs for synergistic HBD-HBA molecule groupings. Based on parameters determined from a given API-mixed-solvent system, the LC-RST model allows qualitative prediction of solubilities for other systems. The LC-RST model is simple to apply and it retains inherent predictive characteristics of regular solution theory.

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