= Symmetric Flory-Huggins polymer blend
{title2=$\chi_c=2/N$}
For two equal-site-volume polymers of chain length $N$, the mixing <free energy> per lattice site is $f/(k_BT)=[\phi\ln\phi+(1-\phi)\ln(1-\phi)]/N+\chi\phi(1-\phi)$. Each chain is one translating object, reducing the <entropy of mixing> per monomer by $N$ relative to the <regular solution model>. Its curvature is $f''/(k_BT)=1/[N\phi(1-\phi)]-2\chi$. The symmetric <thermodynamic critical point> has $\phi_c=1/2$ and $\chi_c=2/N$. Long chains can therefore demix under a very small unfavorable <Flory interaction parameter>.
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