Size-Dependent Interfacial Tension of Nanodroplets Revealed by In Situ Nuclear Magnetic Resonance Spectroscopy

Abstract

According to the Young–Laplace equation, the extreme curvature of nanodroplets (NDs) and nanobubbles (NBs) should generate immense internal pressure, which would theoretically necessitate their rapid dissolution. The long-term stability of NDs and NBs in practice therefore presents a fundamental challenge to classical thermodynamics, and bridging this gap requires an accurate determination of the internal pressure within these nanostructures. In this work, we demonstrate that by using in situ nuclear magnetic resonance (NMR) to monitor the ¹⁹F signal of perfluoropropane (C₃F₈) NDs in water during pressure reduction, we quantitatively determine the internal pressure of NDs. Our results reveal that the derived interfacial tension of nanodroplets is significantly lower than the macroscopic bulk value, exhibiting a pronounced size-dependent decrease below 180 nm. Furthermore, 2D exchange spectroscopy (EXSY) and spin saturation transfer difference (SSTD) spectroscopy confirm and quantify the bidirectional exchange of C₃F₈ molecules across the ND interface. Collectively, these thermodynamic and kinetic insights offer compelling evidence to decipher the stability of NDs and NBs. Beyond that, the established in situ NMR method provides a versatile paradigm for characterizing nanoscale multiphase systems.