= Solution
The <Flory–Huggins solution theory> treats a <polymer solution> as an incompressible lattice mixture, with one <solvent> <molecule> occupying one site and one chain occupying $N$ connected sites. Thus the supplied $f$ is naturally the mixing <free energy> per lattice site; if a site has volume $v_0$, the free-energy density is $f/v_0$.
The term $k_BT(\phi/N)\ln\phi$ is the <polymer> translational <entropy of mixing> contribution. There are only $1/N$ as many independently translating chains as <monomers>, which explains the factor $1/N$. The term $k_BT(1-\phi)\ln(1-\phi)$ is the <solvent> <entropy of mixing> contribution. Both lower the mixing <free energy> for $0<\phi<1$.
The term $k_BT\chi\phi(1-\phi)$ is the mean-field excess interaction contribution from replacing like contacts with <polymer>–<solvent> contacts. In the simplest energetic lattice model,
$$
\chi=\frac{z}{k_BT}\left[\epsilon_{ps}-\frac{\epsilon_{pp}+\epsilon_{ss}}2\right],
$$
where $z$ counts neighboring contacts and the $\epsilon_{ij}$ are pair contact energies. Positive $\chi$ penalizes unlike contacts and can favor demixing. Because chain connectivity suppresses the <polymer>'s translational mixing <entropy>, relatively modest unfavorable interactions can cause separation of long chains. More general effective $\chi$ can also include entropic effects.
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