Calculating the surface tension between a flat solid and a liquid: a theoretical and computer simulation study of three topologically different methods

We discuss three topologically different methods for calculating the surface tension between a flat solid and a liquid from theoretical and computer simulation viewpoints. The first method, commonly used in experiments, measures the contact angle at which a static droplet of liquid rests on a solid surface. We present a new analysis algorithm for this method and explore the effects of line tension on the contact angle. The second method, commonly used computer simulations, uses the pressure tensor through the virial in a system where a thick, infinitely extended slab of liquid rests on a solid surface. The third method, which is original to this paper and is closest to the thermodynamic definition of surface tension, applies to a spherical solid in contact with liquid in which the flat solid is recovered by extrapolating the sphere radius to infinity. We find that the second and third methods agree with each other, while the first method systematically underestimates surface tension values.