Ring polymers in the melt state: the physics of crumpling

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for nonconcatenated unknotted rings, which are known to crumple and segregate and which have been implicated as models for the generic behavior of interphase chromosomes. Here we use a computationally efficient multiscale approach to show that melts of rings of total contour length L-r can be quantitatively mapped onto melts of interacting lattice trees with gyration radii < R-g(2) (L-r)> proportional to L-r(2 nu) and nu = 0.32 +/- 0.01.