Thermodynamic Interaction within a Region of Uniform Average Segment Concentration

An important departure from the previous theory arises from the fact that portions only of the polymer molecules, and never an entire molecule, occur within a volume element. It will be recalled that, in the estimation of the total number of configurations in the entire solution, one segment (the first one in the chain) of each molecule was allowed the opportunity to locate in any vacant cell of the lattice. 

Let there be bx segments from both molecules in the volume element 5F. The number of permissible arrangements of them, subject to the restriction discussed above, is simply 

The free energy of mixing polymer segments with solvent in the volume element 5F, obtained from 5(AaSm ) in conjunction with a term kTxi niV representing the standard state free energy of mixing (see Eq. 20), is 

The volume fraction V2 appearing here and in the following equations refers to the volume element and not to the solution as a whole. 

The chemical potential of the solvent in the volume element, obtained by differentiating Eq. (40), is 

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