Ring polymers in the melt state: the physics of crumpling

Abstract

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 non-concatenated 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 multi-scale approach to show that melts of rings of total contour length $L_r$ can be {\it quantitatively} mapped onto melts of {\em interacting} lattice trees with gyration radii $⟨R_g^2(L_r)⟩\propto L_r^{2\nu }$ and $\nu =0.32\pm 0.01$.

10 pages (5 pages Main Paper + 5 pages Supplemental Material), 3 main figures + 5 Supplemental Figures

References in corpus (4)

• Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics
• Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: II. Dynamics
• Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: Towards the physics of crumpling
• Viscoelasticity and primitive path analysis of entangled polymer liquids: From f-actin to polyethylene

Cited by in corpus (54)

• Kremer-Grest models for commodity polymer melts: Linking theory, experiment and simulation at the Kuhn scale
• A Topologically Driven Glass in Ring Polymers
• Anomalous diffusion in fractal globules
• Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers
• Effects of topological constraints on globular polymers
• Characteristic time and length scales in melts of Kremer-Grest bead-spring polymers with wormlike bending stiffness
• Understanding the dynamics of rings in the melt in terms of annealed tree model
• On the Tree-Like Structure of Rings in Dense Solutions
• Polymer Physics by Quantum Computing
• Computational study of the cross-link and the entanglement contributions to the elastic properties of model PDMS networks
• Multiscale approach to equilibrating model polymer melts
• DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling
• Super-stretchable Elastomer from Cross-linked Ring Polymers
• Dynamics of Self-Threading Ring Polymers in a Gel
• Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure
• Computer simulations of melts of randomly branching polymers
• Conformational statistics of randomly-branching double-folded ring polymers
• Topological free volume and quasi-glassy dynamics in melt of ring polymers
• Beyond Flory theory: Distribution functions for interacting lattice trees
• Large scale chromosome folding is stable against local changes in chromatin structure
• Entanglement length scale separates threading from branching of unknotted and non-concatenated ring polymers in melts
• Computer simulations of randomly branching polymers: Annealed vs. quenched branching structures
• 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
• Many-body contacts in fractal polymer chains and fBm trajectories
• Topological analysis and the recovery of entanglements in polymer melts
• Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains
• From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers
• Computer simulations of melts of ring polymers with non-conserved topology: A dynamic Monte Carlo lattice model
• Viscoelasticity of model interphase chromosomes
• Dynamic Clustering of Active Rings
• Coalescence Model for Crumpled Globules Formed in Polymer Collapse
• Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts
• Multiscale equilibration of highly entangled isotropic model polymer melts
• Nuclear dynamical deformation induced hetero- and euchromatin positioning
• Density effects in entangled solutions of linear and ring polymers
• Marginally compact fractal trees with semiflexibility
• Marginally compact hyperbranched polymer trees
• Topology mediated organization of E.coli chromosome in fast growth conditions
• Supercoiled ring polymers under shear flow
• Amoeba Monte Carlo algorithms for random trees with controlled branching activity: efficient trial move generation and universal dynamics
• Merging 1D and 3D genomic information: Challenges in modelling and validation
• Topological Constraints in Directed Polymer Melts
• Nanorheology of active-passive polymer mixtures is topology-sensitive
• Towards a robust algorithm to determine topological domains from colocalization data
• Fractional Brownian motion meets topology: statistical and topological properties of globular macromolecules with volume interactions
• Computing Canonical Averages with Quantum and Classical Optimizers: Thermodynamic Reweighting for QUBO Models of Physical Systems
• Entropy of self-avoiding branching polymers: mean field theory and Monte Carlo simulations
• The configurational entropy of random trees
• Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"
• Configurational entropy of randomly double-folding ring polymers
• Randomly branching $\theta$-polymers in two and three dimensions: Average properties and distribution functions
• Coherent modeling of double-folded ring polymers and their underlying random tree structure