L. Tubiana, E. Orlandini and C. Micheletti
Multiscale entanglement in ring polymers under spherical confinement
Phys. Rev. Lett., 2011, 107, 188302
Link to arXiv preprint , Link to online article

Abstract
The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length, $l_k$, depends on the ring contour length, $L_c$ and the radius of the confining sphere, $R_c$. In the no- and strong-confinement cases we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of $l_k$, $L_c$ and $R_c$ that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalise the multiscale character of the entanglement that emerges with increasing confinement.