Polymers with spatial or topological constraints: theoretical and computational results

TL;DR

This review summarizes theoretical and computational insights into polymers with spatial or topological constraints, focusing on entanglement effects, properties of fixed topologies, and their technological and biological implications.

Contribution

It provides an accessible overview of topological concepts, models, and methods for dense and entangled polymers, highlighting recent results and open problems.

Findings

Spatial confinement affects polymer entanglement.

Topological state influences polymer metric and entropic properties.

The review identifies key open problems in the field.

Abstract

In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide an accessible, non-specialist introduction to the main topological concepts, polymer models, and theoretical/computational methods used to investigate dense and entangled polymer systems. The main body of our review deals with: (i) the effect that spatial confinement has on the equilibrium topological entanglement of one or more polymer chains and (ii) the metric and entropic properties of polymer chains with fixed topological state. These problems have important technological applications and implications for the life-sciences. Both aspects, especially the latter, are amply covered. A number of selected open problems are finally highlighted.