The overlap concentration, $c^{**},$ which separates the dilute solution regime from

the semi$-$dilute regime can be estimated by space$-$filling arguments as the concentration at

which individual coil volumes begin to fill space. Derive an expression for $c^{**}$ in terms of

$R_g$ and $M$ and indicate how $c^{**}$ scales with $M$ in $$ solvent.

Based on the result above, specify the scaling relationship between $c^{**}$ and $.$