title: Universal Cyclic Topology in Polymer Networks.
abstract: Polymer networks invariably possess topological defects: loops of different orders which have profound effects on network properties. Here, we demonstrate that all cyclic topologies are a universal function of a single dimensionless parameter characterizing the conditions for network formation. The theory is in excellent agreement with both experimental measurements of hydrogel loop fractions and Monte Carlo simulations without any fitting parameters. We demonstrate the superposition of the dilution effect and chain-length effect on loop formation. The one-to-one correspondence between the network topology and primary loop fraction demonstrates that the entire network topology is characterized by measurement of just primary loops, a single chain topological feature. Different cyclic defects cannot vary independently, in contrast to the intuition that the densities of all topological species are freely adjustable. Quantifying these defects facilitates studying the correlations between the topology and properties of polymer networks, providing a key step in overcoming an outstanding challenge in polymer physics.
authors.affiliation: Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Rui
authors.initials: R
authors.lastname: Wang
authors.affiliation: Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Alfredo
authors.initials: A
authors.lastname: Alexander-Katz
authors.affiliation: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Jeremiah A
authors.initials: JA
authors.lastname: Johnson
authors.affiliation: Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Bradley D
authors.initials: BD
authors.lastname: Olsen