 Solution

The correlation length in a semidilute solution is the concentration blob size. Below it a chain retains isolated good-solvent statistics; beyond it concentration fluctuations are screened and many chains interpenetrate. It is a local scale, not the total chain radius. If a blob contains $g$ segments,Eliminating $g$ gives the good-solvent concentration-blob scalingUsing the supplied segment size and concentration,Here $g\simeq 316$ and $N/g\simeq 32$, so there are many segments within each blob and several dozen blobs per chain. Also $\varphi /{\varphi }^{\ast }\simeq 16$, consistent with a semidilute estimate rather than isolated coils. The cancellation of $N$ from $\xi$ is physical: once chains are long enough, the local concentration sets the mesh scale. As throughout the scaling argument, numerical amplitudes are not determined by the given data.