Universal Cyclic Topology in Polymer Networks

Universal Cyclic Topology in Polymer Networks.

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 a...

Topology Evolution in Polymer Modification

A recent numerical method has opened new opportunities in multidimensional population balance modeling. Here, this method is applied to a full three-dimensional population balance model (PBM) describing branching topology evolution driven by chain end to backbone coupling. This process is typical for polymer modification reactions, e.g., in polyethylene, where initially linear polymer chains un...

Enzyme-regulated topology of a cyclic peptide brush polymer for tuning assembly.

Norbornenyl cyclic elastin-like peptides were polymerized via ring opening metathesis polymerization (ROMP) to generate thermally responsive brush polymers. The thermally-responsive nature of the materials could be attenuated by the addition of a proteolytic enzyme that causes the cyclic peptide side chains to be linearized.

String Topology and Cyclic Homology

This book is devoted to some recent developments in our understanding of the topology of free loop spaces of manifolds. The contributions are based on three lecture courses given by the authors at a summer school at Almeŕıa, Spain, in the summer of 2003. The two parts treat rather different facets of the theory, and I will try to give some perspective on each of them in turn. The free loop spac...

The Universal Hopf Cyclic Theory