Hierarchical self-assembly of simple hard polyhedra into complex mesophases

Area of Science:

• Soft Matter Physics
• Materials Science
• Crystallography

Background:

• Hierarchically self-assembled mesophases (lamellar, gyroid, hexagonal, cholesteric) are common in nature.
• These structures are typically attributed to complex enthalpic interactions in block copolymers and surfactants.

Purpose of the Study:

• To investigate the self-assembly behavior of simple achiral hard particles with distorted tetrahedral shapes.
• To demonstrate spontaneous formation of mesophases and liquid crystal phases driven by excluded-volume interactions.
• To explore the role of particle shape in inducing geometric frustration and elastic deformation.

Main Methods:

• Extensive Monte Carlo simulations were employed.
• Analysis focused on excluded-volume interactions and particle shape effects.
• Shape descriptors like anisotropy and biaxiality were used to predict assembly behavior.

Main Results:

• Achiral hard particles with distorted tetrahedral shapes spontaneously self-assemble into diverse mesophases and liquid crystal phases.
• Unexpected chiral structures emerged due to geometric frustration in orientational ordering.
• Particle shape dictates the type of mesophase formed: rod-like particles yield cholesteric phases, plate-like particles form biaxial nematic and hexagonal phases, and anisotropic particles favor gyroid phases.

Conclusions:

• Geometric frustration, induced by particle shape, is a key driver for self-assembly in these systems.
• The interplay between shape, excluded-volume interactions, and elastic deformation governs mesophase formation.
• This framework aids in designing mesophases for applications in supramolecular chemistry, liquid crystals, colloid science, and nanoparticle assembly.