Measurement of the Curvature-Dependent Surface Tension in Nucleating Colloidal Liquids

The curvature dependence of the surface tension is central to the nucleation of liquids, but remains difficult to access experimentally and predict theoretically. This curvature dependence arises from the curvature-dependent molecular structure, which, for small nuclei, can deviate significantly from that of the planar liquid interface. Simulations and density functional theory have been used to predict this curvature dependence, however with contradicting results. Here, we provide the first direct measurement of the curvature-dependent surface tension in nucleating colloidal liquids. We employ critical Casimir forces to finely adjust colloidal particle interactions and induce liquid nucleation, and image individual nuclei at the particle scale to measure their curvature-dependent surface tension directly from thermally excited surface distortions. Using continuum models, we elucidate the interplay between nucleus structure, particle pair potential, and surface tension. Our results reveal a 20% lower surface tension for nuclei of critical size compared to bulk liquids, leading to 3 orders of magnitude higher nucleation rates, thus highlighting the importance of surface tension curvature corrections for accurate prediction of nucleation rates.