Measurement of the Chemical Potential of Thin Helium Films.

High-precision measurements of third sound velocities in atomically thin ^4He films on Ar, Ne, CO_2, and H_2 substrates in the T = OK limit reveal a periodic structure not corresponding to whole layers. We analyze the data in two extreme limits. First, treating the helium film as an incompressible, continuous fluid, the data indicate that the chemical potential has a contribution proportional to l^{-6}, where l is a layer coverage, which is modulated at intervals of.62 +/-.04 layers, and which weakens the van der Waals potential. Second, if we assume the potential is exactly the van der Waals potential, the data indicate the existence in the film of a damped smectic density wave with a periodicity of.54 +/-.04 layers, independent of substrate. The correct description of He films must lie between these extremes. We find the inert layer coverages to be 1 full layer on Ar, Ne, and CO_2, and.36 layers on H_2. Coverages scales were determined using helium adsorption isotherms. A self-consistent analysis method was developed based on the modified Brunauer-Emmet-Teller method for low coverages and the Fenkel-Halsey-Hill vapor pressure relation at high coverages. The analysis establishes the layer capacities for helium films and helium-substrate chemical potential constants, Gamma.