Theoretical determination of the thickness of a liquid-vapour interface

We compare eight possible definitions of the surface thickness for two density profiles. One definition is eliminated, and then the 10–90 thickness t is shown to be in satisfactory agreement with the other six. Our earlier work on the liquid-vapour interface is taken further, with a physical interpretation of the slowly varying density limit for the surface energy ∈; an improved estimate of t using experimental values of ∈ and the bulk energy; and an estimate of t using experimental values of ∈ and the surface tension. We obtain t ≈ 1.3d (d is the atomic diameter) for Ar, Kr and Xe near their triple points. A comparison is made with other estimates for t/d. These vary from 1 to above 3. Our results are in best agreement with Monte-Carlo simulations of the interface. The results for liquid 4He at zero temperature are discussed briefly.