Jones and Devonshire cellular model

The energy of interaction between two molecules is expressed by Leimard-Jones relation [A.3.44], This interaction is limited to the molecule s z nearest neighbors. 

This number z is the coordination index linked to the cell geometry. We shall suppose that the molecules occupy the sites of a cubic lattice with centered faces, and therefore the coordination index is z = 12. 

The volume of liquid is divided into cells centered on each molecule, whose near neighbors occupy the medium from the vertices of a cube with side length la . Each molecule which is a near neighbor of the original one thus belongs to four cells, and each cell contains 1 + 12/4 = 4 molecules. Hence, the volume of the cell is such that  

The translational canonical partition function with interactions can be written, on the basis of expression [A.3.38], taking account only of the z molecules that are near neighbors of each molecule /.  

On the basis of relation [A.3.24], using f ) to denote the double sum appearing in the previous relation, the canonical partition function becomes  

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Thus, the Lennard-Jones and Devonshire cellular model can be used to calculate thermodynamic functions with only two adjustable parameters. In section 1.7, however, we shall demonstrate that the results obtained are very... 

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