Disentangle the intrinsic line tension from the nano-corrugations induced by surface lateral roughness

Line tension of the contact line plays an important role in microscopic wetting, but its understanding remains vague and the reported values are far from convergence. We note in most studies the contact lines are treated as smooth lines as the droplets are considered as smooth spherical caps. Here using helium ion microscopy, we confirm ubiquitous nano-corrugations along the contact lines even on smooth solids like mica. The corrugation size is correlated with the lateral roughness, which represents the lateral characteristic size of the solid roughness elements. A remodified Young's equation for line tension is therefore derived by including the corrugations and the droplet deformation in the surface energy calculations. By applying the remodified Young's equation, the nonlinear relationship between the apparent contact angle and the droplet radius reported in experiments can be well explained, and a converged line tension value is given around 10⁻¹⁰ J/m.