The <polymer overlap concentration> is reached when the number of chains per coil area is of order one. If $n_c$ is the chain number per unit interfacial area, then $n_c^*R^2\sim1$. Equivalently, the monomer area fraction is $\phi^*\sim N\ell^2/R^2$, assuming an occupied monomer area of order $\ell^2$. Below this scale coils are mostly separate; above it they interpenetrate.

Solution

Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A4 / d / i / Solution

 Solution (source code)