Abstract
We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size from atoms to micron-scale polymers and interact through mechanisms as different as hydrogen bonds and covalent forces. A combination of statistical mechanics and quantum mechanics shows that one can capture the physics that governs the assembly of these networks by resolving only the geometry and strength of building-block interactions. The resulting framework reproduces a broad range of phenomena seen experimentally, including periodic and nonperiodic networks in thermal equilibrium, and nonperiodic supercooled and glassy networks away from equilibrium. Our results show how simple “design criteria” control the assembly of a wide variety of networks and suggest that kinetic trapping can be a useful way of making functional assemblies.
- Received 12 November 2013
DOI:https://doi.org/10.1103/PhysRevX.4.011044
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Published by the American Physical Society
Popular Summary
Carbon atoms, microscopic stars made of polymerized DNA, and organic molecules can all form polygon networks, despite the fact that these building blocks differ in size by orders of magnitude and possess interactions as different as hydrogen bonds and covalent forces. Are there, then, “rules” that govern network assembly that transcend the apparent differences between building blocks? If so, mastery of such rules may one day allow us to “program” building blocks in order to self-assemble materials on demand. In this paper, we show that these networks and their self-assembly dynamics can indeed be reproduced by a model that resolves only the geometry of building blocks and the strength of their interactions, suggesting that these two parameters are more important than the atomic and chemical details of the building blocks themselves.
The central element of our work is the demonstration, using quantum mechanics and statistical mechanics, that the thermodynamics of molecular polygon formation—polygons being the key microscopic element of self-assembled networks—can be captured by a “patchy-particle” model containing no explicit chemical detail. Each material system can be related to a patchy particle with a particular patch size and binding energy. Large-scale self-assembly of patchy particles proceeds through their diffusion-driven association, and, because particles’ polygon-forming tendencies are similar to those of the real building blocks, this self-assembly reproduces the phenomena seen in experiments.
These phenomena include the formation of periodic and nonperiodic polygon networks in thermal equilibrium, similar to what is seen in the case of graphene and a silica bilayer, respectively. As nonequilibrium structures, we have observed honeycomb polycrystals, similar to those formed by a certain covalently associating molecule; a polygon network that evolves as time progresses to a honeycomb one, similar to what is seen within a hydrogen-bonding bimolecular system; and nonperiodic glassy networks, similar to those seen in experiments involving covalently associating organic molecules.
Our results suggest a unifying and practically useful framework for understanding and engineering large-scale structural assemblies.