Long-chain limit of polymer-blend miscibility
= Long-chain limit of polymer-blend miscibility
{title2=$\chi_c=\tfrac12(N_A^{-1/2}+N_B^{-1/2})^2$}
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.