Analysis of lanthanide extraction using dynamic interfacial tension measurement in the NaNO3 aqueous solution/tributyl phosphate system.

Mass transfer across liquid-liquid interfaces critically determines the efficiency of solvent extraction, yet its intrinsic kinetics remain poorly understood because conventional spectroscopic methods struggle to directly probe interfacial reactions. We hypothesized that dynamic interfacial tension (DIT) measurements, which capture real-time interfacial physicochemical changes, can reveal the kinetic mechanisms of lanthanide extraction without relying on spectroscopy. To test this hypothesis, we investigated the extraction of Pr, Sm, and Eu from aqueous nitrate solutions into tributyl phosphate (TBP) using time-resolved DIT measurements. Complementary electrical conductivity measurements were performed to identify the origin of interfacial tension changes. The time-dependent DIT profiles were analyzed using a pseudo-first-order temporal kinetic model, in which the time evolution follows a first-order differential form, while the effective rate constants exhibit higher-order dependences on nitrate and TBP concentrations. Forward and backward rate constants were obtained at different concentrations of NO3- and TBP to determine reaction orders and calculate interfacial equilibrium constants. The kinetic behavior was interpreted within a reaction-dominated to mixed reaction-transport regime, as supported by Damköhler analysis and solvent-variation experiments. Conductivity measurements indicate the presence of partially dissociated species in the organic phase, suggesting that electrocapillary contributions may coexist with interfacial compositional effects. Together, these results demonstrate the capability of DIT to quantify interfacial reaction kinetics in liquid-liquid extraction systems. Kinetic modeling showed that all three lanthanides follow third-order dependence on NO3- and second-order dependence on TBP. The interfacial equilibrium constants derived from DIT kinetics agreed well with independently obtained spectroscopic values, validating the method. These results demonstrate that DIT offers a robust, spectroscopy-independent approach for quantifying interfacial reaction kinetics, providing a broadly applicable platform for solvent extraction and other interfacial processes in analytical and physical chemistry.