Calculation of Solid−Liquid Work of Adhesion Patterns from Combining Rules for Intermolecular Potentials

Abstract

The thermodynamic work of solid−liquid adhesion is a well-defined property. Their phenomenological patterns relating to surface tensions, however, have not been well-characterized. We employed a hard sphere model to determine the solid−liquid work of adhesion patterns from a mean-field theory through calculations of the liquid−vapor, solid−vapor, and solid−liquid interfacial tensions. By plotting the work of adhesion with the liquid−vapor interfacial tension, we constructed curves that appear to behave in a very regular manner for a variety of combining rules; the curves shift regularly when we increase the strength of solid−solid interaction and hence the solid−vapor surface tension. Contact angle patterns were also constructed via Young's equation. We found that, except Berthelot's rule, the (9:3), Steele, and (12:6) combining rules yield essentially similar adhesion patterns. The regularity of the patterns is remarkable and in reasonable agreement with recent experimental findings. We have shown that macroscopic experimental adhesion and contact angle patterns can, in principle, be reproduced from consideration of only intermolecular forces. The exact patterns depend on the choice of the combining rules.