Ring polymers in melts and solutions: scaling and crossover

Abstract

We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many body effects of topological origin in dense systems. We predict that although the compact statistics with the Flory exponent $\nu =1/3$ is realized for very long chains, most practical cases fall into the crossover regime with the apparent exponent $\nu =2/5$ during which the system evolves toward a topological dense-packed limit.

4 pages, 3 figures

Cited by in corpus (30)

• From a melt of rings to chromosome territories: The role of topological constraints in genome folding
• Ring polymers in the melt state: the physics of crumpling
• Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: Towards the physics of crumpling
• Anomalous diffusion in fractal globules
• Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers
• Threading Dynamics of Ring Polymers in a Gel
• Slowing down of ring polymer diffusion caused by inter-ring threading
• Effect of Topology on the Conformations of Ring Polymers
• Ring conformations in bidisperse blends of ring polymers
• On the Tree-Like Structure of Rings in Dense Solutions
• Statistics and Geometrical Picture of Ring Polymer Melts and Solutions
• Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure
• Topological free volume and quasi-glassy dynamics in melt of ring polymers
• Entanglement length scale separates threading from branching of unknotted and non-concatenated ring polymers in melts
• Persistence Homology Of Entangled Rings
• Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect
• Segregated structure of ring polymer melts near the surface: Molecular dynamics simulation study
• Conformational properties of complex polymers: rosette versus star-like structures
• Ejection dynamics of a ring polymer out of a nanochannel
• Coalescence Model for Crumpled Globules Formed in Polymer Collapse
• Ring polymers in crowded environment: conformational properties
• Marginally compact fractal trees with semiflexibility
• Density effects in entangled solutions of linear and ring polymers
• Unraveling the glass-like dynamic heterogeneity in ring polymer melts: From semi-flexible to stiff chain
• Topological Constraints in Directed Polymer Melts
• Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization
• Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"
• Quantifying the mobility of chromatin during embryogenesis: Nuclear size matters
• Hydrodynamic Inflation of Ring Polymers under Shear
• Effective Hamiltonian of topologically stabilized polymer states