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Updated: May 23, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Statistics and geometrical picture of ring polymer melts and solutions
1Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan. sakaue@phys.kyushu-u.ac.jp
Abstract:
We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts [Sakaue, Phys. Rev. Lett. 106, 167802 (2011)]. A basic assumption lies in the implementation of the noncatenation constraint via the effective excluded-volume effect, from which a geometrical picture of melts emerges. The result captures many of the salient features observed so far, including (i) the overall spatial size of rings, (ii) the coordinate number, i.e., the number of rings surrounding a given ring, (iii) the topological length scale as a function of the molecular weight, and (iv) the effect of the chain stiffness and concentration. We also suggest a geometrical interpretation of the topological length scale, which may shed some light on the entanglement concept in polymeric systems.
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