Long-chain limit of polymer-blend miscibility (${\chi }_c=\frac{1}{2}(N_A^{-1/2}+N_B^{-1/2}{)}^2$)

Connecting segments into chains reduces their independent translational mixing entropy per segment by factors $1/N_A$ and $1/N_B$. Consequently the tolerable positive contact penalty tends to zero as both chains become long. Equal chain lengths have ${\chi }_c=2/N$; favorable unlike interactions can still produce a miscible polymer pair.