Interface potentials and physical constraints

We derive a wall-interface potential V(Γ) for wetting phenomena, through minimization of the surface free energy under the constraint of fixed adsorption Γ. We show that the upper bound VBILB (Γ), previously proposed by Bukman et al. [Phys. Rev. B 47 (1993) 1577], is not the minimum. The actual minimum apparently coincides with the equilibrium value of the free energy. Thus, the constraint is too weak and we impose an additional physical constraint. This ensures that the decay length, associated with the approach of the order parameter towards the bulk value, does not exceed the bulk correlation length Ξ. The resulting free energy minimum is a boundary minimum and coincides with VBILB (Γ).