Twist renormalization in molecular crystals driven by geometric frustration

Area of Science:

• Materials Science
• Crystallography
• Soft Matter Physics

Background:

• Symmetry principles typically forbid twist in bulk crystalline structures.
• Twisted molecular crystals are prevalent, formed by approximately 25% of organic substances, yet remain poorly understood.
• The ubiquity of twisted crystals presents a paradox within established crystallographic theories.

Purpose of the Study:

• To investigate the phenomenon of twisted molecular crystals.
• To explain the formation and behavior of twisted crystals using a geometric frustration model.
• To reconcile the existence of twisted single crystals with fundamental symmetry principles.

Main Methods:

• Modeling molecular constituents as uniaxially twisted cubes.
• Employing a renormalization group (RG) approach to simulate crystal growth and evolution.
• Analyzing morphology, response functions, and residual energy during crystal assembly.
• Experimental verification using silicone rubber models.

Main Results:

• The renormalization group approach predicts the gradual untwisting of rod-like frustrated crystals.
• Experimental models confirmed the theoretical predictions of crystal untwisting.
• A mechanism for the scale-dependent conveyance of twist in crystalline structures was identified.

Conclusions:

• Twisted molecular crystals can be understood as geometrically frustrated assemblies.
• The renormalization group approach provides a theoretical framework for explaining crystal twisting.
• The study reconciles the existence of twisted crystals as a finite size effect, resolving a long-standing paradox.