Statistics and Geometrical Picture of Ring Polymer Melts and Solutions
arXiv:1202.1890 · doi:10.1103/PhysRevE.85.021806
Abstract
We present a detailed account of a recently proposed phenomenological theory for noncatenated ring polymer melts (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 spacial 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.
12 pages, 6 figures
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- Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect
- Segregated structure of ring polymer melts near the surface: Molecular dynamics simulation study
- Topological Constraints in Directed Polymer Melts