Development of predictive distribution coefficient model for organic-inorganic hybrid nanoparticles (pKD-nano model) applied for technologies using liquid-liquid distribution equilibria

May 26, 2026

Author

Yuta Akiwa, Masaru Watanabe, Hiroshi Inomata, R. L. Smith, Jr., Masaki Ota*, Research Center of Supercritical Fluid Technology, Graduate School of Engineering (& Graduate School of Environmental Studies), Tohoku University

Keywords

Organic-Inorganic hybrid nanoparticles, Liquid-Liquid equilibria, Extraction and separation, Chemical engineering model, Distribution coefficient, Solubility

Abstract

A new thermodynamic chemical-engineering model called “predictive distribution coefficient model (pKD-nano model) for organic-inorganic hybrid nanoparticles (HNP)” was developed for application to technologies using liquid-liquid distribution phenomena on single or multiple solid solutes. This pKD-nano model took the Hildebrand solubility parameter (or the entropy-based solubility parameter, which is so-called eSP, defined in our previous work) into account of the concept and the model is very convenient and useful for general users. Due to the lack of volatility of HNPs caused by their high molecular mass, only SPs (or eSPs) between a single solute and multiple solvents were used for this model constructions without taking volatility of HNP into account. In this pKD-nano model, the Gauss function was adopted for use in expressing (the saturated) solubility of HNP in each liquid phase as a function of SP value (or eSP value) in each liquid phase. The obtained experimental distribution coefficient data in batch systems, which was analyzed by the UV-vis spectroscopy in each liquid phase, gave a good agreement with the theoretically calculated data with the pKD-nano model. In the future, this model would be used for application to liquid-liquid distribution equilibrium technologies.

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