= Solution
Use polymer <volume fraction> $\phi$ and interaction parameter $\chi$, increasing toward poor-solvent conditions. The <Flory–Huggins solution theory> free energy per lattice site is
$$
\frac{f}{k_BT}=\frac\phi N\ln\phi+(1-\phi)\ln(1-\phi)+\chi\phi(1-\phi).
$$
The common-tangent construction gives the <binodal>; $f''=0$ gives the <spinodal>, $2\chi_s=1/(N\phi)+1/(1-\phi)$. Its critical point is $\phi_c=1/(1+\sqrt N)$, $\chi_c=\frac12(1+N^{-1/2})^2$. Above the binodal in this $\chi$ plot, the solution separates into polymer-poor and polymer-rich phases; between binodal and spinodal it is metastable, while inside the spinodal a homogeneous state is unstable.
The line $\chi=1/2$ is the <theta solvent> condition for a long dilute chain. Below it is the <good solvent> side; above it is the <poor solvent> side. Poor solvent does not imply that every composition is already phase separated. Independently, a homogeneous solution is dilute for $\phi\ll\phi^*$, <semidilute> for $\phi\gg\phi^*$ below close packing, and concentrated as $\phi$ approaches one.
\Image[/past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2007-polymer-phase-diagram.png]
{title=Solvent quality and phase separation in a polymer solution}
{description=Calculated Flory-Huggins binodal and spinodal for $N=1000$. Larger $\chi$ means poorer solvent quality; the dashed horizontal line is the dilute-chain theta condition. The concentration regimes are distinct from the coexistence boundaries.}
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