Flexible polymers under spherical confinement

We compute the free energy of confinement $\Delta F$ for a flexible self-avoiding polymer inside a spherical cavity. We find two different regimes depending on the degree of compression. For moderate confinement the free energy exhibits a power-law dependence on the diameter~$D$ of the cavity. At larger packing fraction $\phi$, however, the excluded-volume interactions between monomers dominate and the scaling law breaks down. We demonstrate that in the low density regime $\beta\Delta F$ scales as $(R_G/D)^{3/(3\nu-1)}$, where $R_G$ is the radius of gyration of the unconstrained polymer. This behavior differs from what is observed for confinement inside an infinitely long cylinder or between parallel plates, $\beta\Delta F \sim (R_G/D)^{1/\nu}$. On the basis of our results we revisit the problem of the escape through a hole of a spherically confined polymer and provide a corrected scaling prediction for the average escape time.