Entropy of binary mixing

While Fig. 4.1 shows the mixing of two small molecules of equal molecular volumes, similar mixing is possible if one or both of the species are polymers. In the more general case, the lattice site volume Vq is defined by the smallest units (solvent molecules or monomers), and larger molecules 

Regular solutions are mixtures of low molar mass species with Aa = Ab= 1. Polymer solutions are mixtures of macromolecules (Aa = A 1) with the low molar mass solvent defining the lattice (Ab = 1). Polymer blends are mixtures of macromolecules of different chemical species (Aa 1 and Ab 1). 

The entropy S is determined as the product of the Boltzmann constant k and the natural logarithm of the number of ways H to arrange molecules 

The number of translational states of a given single molecule is simply the number of independent positions that a molecule can have on the lattice, which is equal to the number of lattice sites. In a homogeneous mixture of A and B, each molecule has 

For a single molecule of species A, the entropy change on mixing is 

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