Wetting morphologies and apparent line tension of nanodroplets on soft substrates

The size dependence of contact angles for small droplets on solid substrates is typically attributed to line tension. While previous studies have shown that the apparent line tension on rigid substrates is wettability-dependent, the influence of substrate stiffness on line tension for soft, deformable substrates remains elusive. Here, we experimentally demonstrate that the apparent line tension on soft substrates exhibits a clear dependence on substrate stiffness. Using atomic force microscopy to image ionic liquid nanodroplets on polydimethylsiloxane substrates with varying cross-linking densities, we find that the contact angles depend on both the droplet contact radius and the substrate stiffness. Analysis based on the modified Young's equation for soft substrates yields negative apparent line tensions ranging from -5.9 × 10^-11 to -3.5 × 10^-10 J m^-1, in good agreement with theoretical predictions and previous experimental results on rigid substrates. Notably, the absolute value of the apparent line tension decreases on softer substrates, revealing a direct coupling between substrate elasticity and the thermodynamic excess free energy in the three-phase confluence region.