Fowkes model of surface energy

[teqnick]

Hello
I need an answer for my Bachelor’s dissertation.
In Fowkes model of surface energy, work of adhesion is defined as the sum of geometric mean of dispersive and nondispersive forces.
In all articles, people say that the geometric mean comes from Berthelot combining rules, developed in 1898 and published in Comptes Rendus Chimie journal.

Unfortunately I was unable to get to this old article, so I am asking you, why the geometric mean was used in this theory?

Please help, and thank you.

 

[BigJDubs]

The Berthelot combining rules are a set of equations which describe the interactions between molecules in solution. The rules state that the interaction energy between two different molecules is equal to the geometric mean of the two individual energies. This means that the total energy of a system is equal to the product of the individual energies, divided by the square root of their product. This rule is used to accurately calculate the overall energy of a mixture of different molecules, and is especially useful when dealing with solutions of different substances. In Fowkes' model, the work of adhesion is the sum of the geometric mean of the dispersive and nondispersive forces. This equation gives a more accurate representation of the physical forces involved in the surface energy than if it was calculated using the individual forces alone.