Determination of the Contact Angle Based on the Casimir Effect

On a macroscopic scale, a nonreactive liquid partially covering a homogeneous solid surface will intersect the solid at an angle called the contact angle. For molten metals and semiconductors, the contact angle is materially dependent upon both the solid and liquid and typical values fall in the range 80-170 deg, depending on the crucible material. On a microscopic scale, there does not exist a precise and sharp contact angle but rather the liquid and solid surfaces merge smoothly and continuously. Consider the example of the so called detached Bridgman crystal growth process. In this technique, a small gap is formed between the growing crystal and the crucible. At the crystal/melt interface, a meniscus ring is formed. Its width can be in the range of a few micrometers, approaching a microscopic scale. It then becomes questionable to describe the shape of this meniscus by the contact angle. A more advanced treatment of the interface is needed and here we propose such a refined model. The interaction of the liquid surface with the solid can be calculated by considering two forces: a short-range repulsive force and a longer range (up to a few micrometers) Casimir or van der Waals force.