Calculation of Mixing Heat and Free Energy

According to the mean-field assumption, the mixing heat 

Pj2 is the number of pairs between solvent site 1 and monomer site 2, the mixing interactions in each pair B = Bi2— Bn + 522)/2. Each chain approximately holds q-2)r coordination sites, and each coordination site contains the probability of solvent occupation (f)], thus for N2 chains, 

This parameter has been called Flory-Huggins interaction parameter. Therefore, 

With the assumption of incompressible mixing in the lattice space, the mixing heat corresponds to the mixing enthalpy, and the Helmhotz free energy is equivalent to the Gibbs free energy. 

Merging the mixing entropy and the mixing heat into the mixing free energy, one can obtain 

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