Theory of first-order layering transitions in thin helium films

Abstract

Thin liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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 $\mu$ and surface tension $\alpha$ as functions of coverage $n$, and from this we deduce $\mu \left(\alpha \right)$. For each set of adjacent layers, we then obtain the crossing point in the curves of $\mu \left(\alpha \right)$. In this way we obtain the values of $\mu$, $\alpha$, and surface coverages for the transition. Particular attention is paid to the monolayer-bilayer transition.