Ring polymers in two-dimensional melts double-fold around randomly branching “primitive shapes”

Drawing inspiration from the concept of the "primitive path" of a linear chain in melt conditions, we introduce here a numerical protocol which allows us to detect, in an unambiguous manner, the "primitive shapes" of ring polymers in two-dimensional melts. Then, by analysing the conformational properties of these primitive shapes, we demonstrate that they conform to the statistics of two-dimensional branched polymers (or, trees) in the same melt conditions, in agreement with seminal theoretical work by Khokhlov, Nechaev and Rubinstein. Results for polymer dynamics in light of the branched nature of the rings are also presented and discussed.