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<p>Fivefold symmetry is incompatible with the translational periodicity of two-dimensional crystalline lattices. Nonetheless, aperiodic tilings, such as those introduced by Penrose and anticipated in Islamic geometric art, have demonstrated that local fivefold symmetry and long-range order can coexist without periodic repetition. Inspired by these mathematical constructs, recent advances in surface science have enabled the study of molecular self-assembly in two dimensions using molecules with intrinsic fivefold symmetry. In particular, penta-substituted derivatives of corannulene—rigid, bowl-shaped molecules resembling hard pentagons—exhibit intriguing self-assembly behavior on metal surfaces. Scanning tunneling microscopy (STM) reveals that these molecules organize into dense monolayers with stripe and rotator packing motifs reminiscent of theoretically predicted pentagonal tilings. Subtle variations in chirality and substitution patterns lead to diverse plane group symmetries (<i>pm</i>, <i>p1</i>, <i>p2gg</i>), domain boundaries, and packing densities. The balance between molecular geometry, chirality, and substrate interactions governs the emergence of ordered phases. These findings deepen our understanding of symmetry frustration, quasiperiodicity, and the transition between local and global order in molecular monolayers, with implications for the design of functional nanostructured materials.</p>

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Two-dimensional crystallization of pentagonal symmetric molecules

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月18日

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  • Karl-Heinz Ernst

摘要

Fivefold symmetry is incompatible with the translational periodicity of two-dimensional crystalline lattices. Nonetheless, aperiodic tilings, such as those introduced by Penrose and anticipated in Islamic geometric art, have demonstrated that local fivefold symmetry and long-range order can coexist without periodic repetition. Inspired by these mathematical constructs, recent advances in surface science have enabled the study of molecular self-assembly in two dimensions using molecules with intrinsic fivefold symmetry. In particular, penta-substituted derivatives of corannulene—rigid, bowl-shaped molecules resembling hard pentagons—exhibit intriguing self-assembly behavior on metal surfaces. Scanning tunneling microscopy (STM) reveals that these molecules organize into dense monolayers with stripe and rotator packing motifs reminiscent of theoretically predicted pentagonal tilings. Subtle variations in chirality and substitution patterns lead to diverse plane group symmetries (pm, p1, p2gg), domain boundaries, and packing densities. The balance between molecular geometry, chirality, and substrate interactions governs the emergence of ordered phases. These findings deepen our understanding of symmetry frustration, quasiperiodicity, and the transition between local and global order in molecular monolayers, with implications for the design of functional nanostructured materials.