Solution
= Solution
The <polymer overlap concentration> corresponds to about one chain per coil volume. Approximating the occupied volume of one statistical segment by $a^3$ gives
$$
\boxed{\phi^*\sim\frac{Na^3}{R_\theta^3}=N^{-1/2}=0.0316.}
$$
Thus the site-volume model predicts overlap at a few percent volume fraction. A separately specified molecular segment volume or a coil-volume prefactor would change this numerical prefactor.