Microcontact and macrocontact angles and the drop stability on a bare surface

The microscopic approach of ref I regarding the shape and stability of a liquid drop on a bare solid surface is extended to include the structuring of the liquid near the solid surface. It is supposed that the liquid molecules near the solid. form a monolayer, which is characterized by a surface number density and short- and long-range interactions with the solid. The rest of the drop is considered as a continuous medium with only long-range interactions with the solid. Two kinds of droplets, cylindrical (two-dimensional) and axisymmetrical (three-dimensional), were examined for two types of interaction potentials similar to the London-van der Waals and the Lennard-Jones ones. The microcontact angle, theta(0), that the drop profile makes with the solid surface is dependent on the microscopic parameters of the model (strength of intermolecular interactions, densities of liquid and solid phases, hard core radius, etc.), whereas in the previous continuum picture of ref 1, it was constant and equal to 180degrees. All drop characteristics, such as stability, shape, and macroscopic contact angle, become functions of theta(0) and a certain parameter a dependent on the model interaction parameters. There are two domains in the plane theta(0)-a for the drop stability, separated by a critical curve. In the first domain, the drop can have any height, h(m), at its apex and is always stable. In the second domain, h(m) is limited by a critical value, h, which depends on a and theta(0), and drops with h(m) > h(c) cannot exist. The drop shape depends on whether the point (theta(0), a) on the theta(0)-a plane is far from the critical curve or near it. In the first case, the drop profile has a large circular part, while in the second case, the shape is almost planar. By extrapolating for sufficiently large drops the spherical part to the solid surface, one can obtain the macroscopic (apparent) contact angle, which is accessible experimentally. In the region near the solid surface, the tangent to the profile makes with the solid surface an angle that varies rapidly between the microcontact angle, theta(0), and the macroscopic contact angle,theta(m).