Robust self-assembly of nonconvex shapes in two dimensions

Area of Science:

• Computational physics
• Materials science
• Biophysics

Background:

• Self-assembly is crucial for forming complex structures in nature and technology.
• Understanding the principles governing self-assembly of specific shapes is key to designing novel materials.
• The tobacco mosaic virus coat protein assembly provides a biological model for studying helical shell formation.

Purpose of the Study:

• To present efficient simulation methods for modeling the self-assembly of complex 2D shapes.
• To investigate the necessary conditions for robust self-assembly into a unique final state.
• To explore the role of shape geometry and boundary interactions in self-assembly.

Main Methods:

• Development of fast simulation techniques utilizing hybrid Monte Carlo algorithms.
• Modeling shapes with general boundary curves and employing volume/interpenetration interaction terms.
• Efficient energy evaluation using signed distance functions.

Main Results:

• Demonstration of robust self-assembly of a designed nonconvex 2D shape into a unique final state.
• Identification of essential prerequisites: blocking and matching boundary interactions.
• Highlighting the importance of shape nonconvexity and handedness for directed self-assembly.

Conclusions:

• Fast simulation methods enable efficient study of complex shape self-assembly.
• Specific geometric properties (nonconvexity, handedness) and boundary interactions (blocking, matching) are critical for predictable self-assembly.
• The findings provide a framework for designing and controlling self-assembly processes for targeted structures.