Theory of first-order layering transitions in thin helium films

Thin liquid (Formula presented) films on graphite show evidence of layered growth with increasing number density via a succession of first-order phase transitions. These so-called "layering transitions" separate uniformly covering phases, such as monolayers and bilayers. The present work is a detailed theoretical study of such layering transitions using a Maxwell construction. We model the graphite surface by a strong substrate potential, and using a microscopic variational theory we obtain the uniform coverage solutions for liquid helium. For each layer, the theory yields the chemical potential (Formula presented) and surface tension (Formula presented) as functions of coverage (Formula presented), and from this we deduce (Formula presented). For each set of adjacent layers, we then obtain the crossing point in the curves of (Formula presented). In this way we obtain the values of (Formula presented), (Formula presented), and surface coverages for the transition. Particular attention is paid to the monolayer-bilayer transition.