Three-dimensional crystals of adaptive knots

Area of Science:

• Soft matter physics
• Liquid crystal science
• Topological matter

Background:

• Theoretical postulates by Gauss and Kelvin suggested field knots could mimic particle behavior.
• Experimental realization of field knots was limited to transient states or required complex conditions, preventing self-assembly.
• Previous attempts failed to create stable, self-assembling three-dimensional crystalline structures from field knots.

Purpose of the Study:

• To introduce and characterize energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals.
• To investigate the self-assembly behavior of these knots into crystalline structures.
• To explore the topological robustness and reconfigurability of these novel knot structures.

Main Methods:

• Utilized energy-minimizing numerical modeling to understand knot formation and stability.
• Employed optical imaging techniques to observe individual knots and their collective behavior.
• Investigated the topological properties and response to external stimuli.

Main Results:

• Successfully created stable, micrometer-sized knots in helical fields of chiral liquid crystals.
• Observed that these knots are spatially localized, freely diffusing, and self-assemble into crystalline lattices with open and closed structures.
• Demonstrated the robustness of these topological knots and their ability to be reconfigured by weak stimuli.

Conclusions:

• Energetically stable field knots can be realized in chiral liquid crystals, mimicking particle-like behavior.
• These knots self-assemble into ordered crystalline structures, offering a new paradigm for topological matter.
• The findings pave the way for applications in areas like displays and advanced materials due to their stability and reconfigurability.