On the surface tension theory of van der Waals and of Cahn and Hilliard

摘要: The following features of the theory van der Waals and Cahn Hilliard are proven to be true: It is possible find a local free energy, ψi, depending upon T density profile, that sums (over i) give total energy system; when minimized with respect exact equilibrium profile results. has form ψi = δi + μiρi, where ρi μi both depend entire profile. For surface tension σ given by hΣi(δi P) (h interaction range P pressure); grand canonical partition function Ξ for system κT InΞ − AhΣiδi (A area), equal chemical potential μ. Cahn‐Hilliard recovered making ``reasonable'' approximations δi.