Topological and physical links in soft matter systems

Area of Science:

• Soft Matter Physics
• Polymer Science
• Materials Science

Background:

• Linking, a form of topological entanglement, is prevalent in diverse soft matter systems.
• Recent theoretical and experimental progress enables the study of these entanglements and their effects.

Purpose of the Study:

• To review the current state-of-the-art in the study of linking and topological entanglement in soft matter.
• To organize and present key concepts, models, and applications in this rapidly expanding field.

Main Methods:

• Conceptual review of topological and physical linking.
• Discussion of physical models for polymer entanglements.
• Examination of entanglements in various systems like liquid crystals and biological molecules.

Main Results:

• Comprehensive overview of linking phenomena from synthetic molecules to biological systems.
• Detailed exploration of models for linear and circular polymer entanglements.
• Analysis of entanglements in non-filamentous systems such as liquid crystals and fluids.

Conclusions:

• Linking is a fundamental property influencing soft matter behavior.
• Significant progress has been made in understanding and quantifying topological entanglement.
• Future research directions and open challenges in the field are identified.