Predicting the distribution coefficient in the solvent extraction of rare earth elements

Rare earth elements (REEs) comprise the 15 lanthanides, scandium, and yttrium, and are critical to many modern technologies. Solvent extraction is the most common method for REEs separation, with the distribution coefficient (log D ) influenced by factors such as extractant type, pH, temperature, and diluent properties. This study analyzes intercept differences of adjacent lanthanides in log D vs. pH plots using experimental data and proposes a new model to predict log D behavior based on thermodynamic principles. A gradual decrease in ionic radius across the lanthanide series, correlated with atomic number, was observed. Predictions from the model were found to be in reasonable agreement with available experimental data. The model considers ionic size trends and equilibrium behavior, providing a physically meaningful alternative to purely empirical methods. Additionally, a thermodynamic interpretation using Gibbs free energy was introduced to further validate the consistency between model predictions and equilibrium behavior. The model enables improved prediction of REEs behavior in solvent extraction systems without the need for extensive experimental calibration. In addition, the framework may assist in optimizing extraction process parameters for selective separation of target REEs.