Flory approximation
= Flory approximation
{c}
{title2=$\mathcal F/(k_BT)\sim R^2/(Nb^2)+vN^2/R^d$}
The <Flory approximation> balances the entropic cost of expanding an <ideal chain> against a mean-field <excluded volume> interaction. For $N$ segments of length $b$ in $d$ spatial dimensions, minimizing $R^2/(Nb^2)+vN^2/R^d$ gives $R^{d+2}\sim vN^3b^2$. This yields the scaling exponents $3/5$ in three dimensions and $3/4$ in two dimensions. It is a scaling approximation, not an exact numerical free energy or proof of critical exponents; confinement replaces $R^d$ by the accessible coil volume.