= Critical point of a Flory–Huggins polymer solution
{title2=$\phi_c=1/(1+\sqrt N),\quad\chi_c=(1+N^{-1/2})^2/2$}
For composition-independent $\chi$, the <spinodal> of <Flory–Huggins solution theory> is $2\chi=1/(N\phi)+1/(1-\phi)$. At its <thermodynamic critical point>, a second condition $-1/(N\phi^2)+1/(1-\phi)^2=0$ gives $1-\phi_c=\sqrt N\phi_c$, proving the displayed values. Hence $\phi_c\sim N^{-1/2}$ and $\chi_c-1/2\sim N^{-1/2}$. Under $\chi=C/T$, the <theta temperature> is $\Theta=2C$ and $T_c=\Theta/(1+N^{-1/2})^2$. Thus $T_c$ approaches a constant while $\Theta-T_c$ scales as $N^{-1/2}$. Converting $\chi_c$ to a temperature always requires a specified or inferred $\chi(T)$ law.
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