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The K₄ crystal lattice, also known as the Laves graph, diamond twin, or triamond structure, is a remarkable geometric framework that, to date, has not been observed in nature. This lattice exhibits exceptional properties, including a very high level of symmetry comparable to that of diamond, intrinsic chirality—which means it exists in distinct right-handed and left-handed forms similar to many biological molecules—and an impressively low density. These attributes make the K₄ lattice a potential superstar in the world of metamaterials, with outstanding mechanical and optical properties. The only problem is it does not exist (yet).
Recent advancements in programmable self-assembly, particularly the utilization of DNA as smart building blocks, offer a viable pathway to fabricate such complex structures. This project aims to explore possible methodologies for the DNA-based self-assembly of the K₄ crystal and related structures through molecular simulations. Additionally, we will investigate the mechanical properties of these hypothetical metamaterials. The project will leverage a long-established collaboration with leading experimentalists in the field of programmable self-assembly at Brookhaven National Laboratory, ensuring a robust integration of theoretical and experimental insights.
References
Coxeter, H. S. M. (1955). On Laves' graph of girth ten. Canadian Journal of Mathematics, 7, 18–23. DOI:10.4153/CJM-1955-003-7
Sunada, T. (2008). Crystals that nature might miss creating. Notices of the American Mathematical Society, 55(2), 208–215. Retrieved from https://www.ams.org/journals/notices/200802/tx080200208p.pdf
Sunada, T. (2019). Diamond Twin. Retrieved from https://arxiv.org/abs/1904.07230
Fukunaga, T. M., Kato, T., Ikemoto, K., & Isobe, H. (2022). A minimal cage of a diamond twin with chirality. Proceedings of the National Academy of Sciences, 119(7). DOI:10.1073/pnas.2120160119
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