Resolving the Apparent Line Tension of Sessile Droplets and Understanding its Sign Change at a Critical Wetting Angle.

Despite strenuous research efforts for more than one century, identifying the magnitude and sign of the apparent line tension for a liquid-solid-gas system remains an elusive goal. Herein we accurately determine the apparent line tension from the size-dependent contact angle of sessile nanodrops on surfaces with different wetting properties via atomic force microscopy measurements and molecular dynamics simulations. We show that the apparent line tension has a magnitude of 10^{-11}-10^{-10}  J/m, in good agreement with theoretical predictions. Furthermore, while it is positive and favors shorter contact lines for droplets on very lyophilic surfaces, the apparent line tension changes its sign and favors longer contact lines on surfaces with an apparent contact angle higher than a critical value. By analyzing the density and the potential energy of liquid molecules within the sessile droplet, we demonstrate that the sign of the apparent line tension is a thermodynamic property of the liquid-solid-gas system rather than the local effect of intermolecular interactions in the three-phase confluence region.