Basic Assumptions of Flory-Huggins Lattice Theory

2 Basic Assumptions of Flory-Huggins Lattice Theory 

Assuming polymer solutions are located in the lattice space, with each lattice site containing the coordination number q, one can assign the solvent molecules to those single sites with the number Nj, and each polymer chain to occupy consecutive connected sites with the number of r, as illustrated in Fig. 8.3. The number of polymer chains is N2. Supposing that the size of each chain unit is comparable with one solvent molecule, as given by 

Note that the actual size difference between the chain unit and the solvent can be corrected later. 

Chain units are assumed to homogeneously distribute in the lattice space, which is valid only for concentrated polymer solutions. In dilute solution, as we know, polymer chain units are heterogeneously distributed in the solution as in the relatively isolated coils. 

In the lattice space, the bonds formed by the neighboring chain units orient randomly, and the volume exclusion simply implies the next chain units cannot overlap with the previous one. As illustrated in Fig. 8.4, in the coordination sites of the second chain unit, the third unit along the chain sequence can choose anyone of the coordination sites except for the one occupied by the first unit. Such a situation is similar with the non-reversing random walks, with each step of walks containing q— 1 possible directions. 

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