Electrostatic contribution to line tension in a wedge-shaped contact region

In the wetting problems of very small scales, such as in nanotubes and nanoparticles, the contribution of line tension potentially becomes significant. In contrast to the molecular contribution, there rarely exists any literature that systematically considers the electrical contribution to the line tension in wetting. In this paper, the electrical double layer around a wedge-shaped confinement (which represents the region of the three-phase contact of an electrolyte droplet on a charged, or ionizable, substrate) is analyzed. An exact analytical solution for the linearized Poisson-Boltzmann equation is obtained for both the constant surface charge and the constant surface potential conditions. Comprehensive analytical formulas of the line tension are derived. An equation for predicting the contact angle is also shown, considering the dependence of the electrostatic line tension on the contact angle. It is exhibited that the line tension can have either a positive or a negative value depending on the sign of the surface charge density. It is demonstrated that the magnitude of the line tension is comparable or (potentially) greater than that of the molecular contribution. To corroborate the results of the linear theory, the nonlinear Poisson-Boltzmann equation is solved numerically. The results of the nonlinear theory show reasonable agreement with those of the linear theory.