The surface tension is related to the derivative of the Helmholtz energy by the equations
Note: Only when is equal to the surface (excess) Helmholtz energy per unit area. In general, for a multicomponent system it is not possible to define either an interfacial layer, or a Gibbs surface, for which this condition is satisfied. However, it is satisfied automatically when the system exhibits an adsorption azeotrope at which all the are zero.
For a one-component system, treated in terms of a Gibbs surface it is always possible to choose this surface so that , so that the surface tension is equal to the value of relative to this surface; on the other hand must always be positive for an interfacial layer so that and can never be equated.
The surface excess entropy is given by