and the total solution volume is
N¼N 1 þrN 2 (8.2)Note that the actual size difference between the chain unit and the solvent can be
corrected later.
8.2.2.2 Concentrated Solution
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.
8.2.2.3 Flexible Chain
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
q1 possible directions.
8.2.2.4 Mean-Field Assumption
According to the Helmhotz mixing free energy
DFmix¼DUmTDSm (8.3)The increase of entropyDSmdue to the mixing of multiple components benefits
the decrease of free energy, favoring the mixing process.
Fig. 8.4 Illustration of a
flexible polymer chain with
2-3 bond randomly oriented
in the lattice space but the
third chain unit not
overlapping with the first one
8.2 Flory-Huggins Lattice Theory of Polymer Solutions 151