Article | Published:

Geometric frustration in buckled colloidal monolayers

Nature volume 456, pages 898903 (18 December 2008) | Download Citation

Abstract

Geometric frustration arises when lattice structure prevents simultaneous minimization of local interaction energies. It leads to highly degenerate ground states and, subsequently, to complex phases of matter, such as water ice, spin ice, and frustrated magnetic materials. Here we report a simple geometrically frustrated system composed of closely packed colloidal spheres confined between parallel walls. Diameter-tunable microgel spheres are self-assembled into a buckled triangular lattice with either up or down displacements, analogous to an antiferromagnetic Ising model on a triangular lattice. Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model. This tunable soft-matter system provides a means to directly visualize the dynamics of frustration, thermal excitations and defects.

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Acknowledgements

We thank B. Chakraborty, R. D. Kamien, D. Li, A. J. Liu, C. D. Modes, T.-K. Ng, S. A. Rice, Y. Snir, T. A. Witten and Y. Zhou for discussions. This work was supported primarily by the NSF through MRSEC grant DMR-0520020 and partially by DMR-0804881 (NSF) and by NAG-2939 (NASA).

Author Contributions Y.H. and A.M.A. initialized the project. A.M.A. synthesized the particles. Y.H. conducted the experiments. Y.S. performed the simulations and provided the tiling model. Y.H. and Y.S. analysed and explained the experimental data. P.Y. characterized the particles. T.C.L. provided theoretical guidance. A.G.Y. provided experimental guidance. Y.H., Y.S., T.C.L. and A.G.Y. wrote the paper.

Author information

Author notes

    • Yilong Han
    •  & Yair Shokef

    These authors contributed equally to this work.

    • Yair Shokef

    Present address: Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.

Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA

    • Yilong Han
    • , Yair Shokef
    • , Ahmed M. Alsayed
    • , Peter Yunker
    • , Tom C. Lubensky
    •  & Arjun G. Yodh
  2. Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    • Yilong Han

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Corresponding authors

Correspondence to Yilong Han or Yair Shokef.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains a Supplementary Method, Supplementary Data, Supplementary References, Supplementary Figures S1-S6 with Legends and Supplementary Table 1.

Videos

  1. 1.

    Supplementary Movie S1

    This file contains Supplementary Movie S1: Raw experimental video at T = 24.7°C, corresponding to Fig. 2A.

  2. 2.

    Supplementary Movie S2

    This file contains Supplementary Movie S2: Labyrinth pattern at T = 24.7°C, corresponding to Fig. 2B.

  3. 3.

    Supplementary Movie S3

    This file contains Supplementary Movie S3: Thermal excitations and defects at T = 24.7°C, corresponding to Fig. 2C.

  4. 4.

    Supplementary Movie S4

    This file contains Supplementary Movie S4: Raw experimental video at T = 27.1°C, corresponding to Fig. 2D.

  5. 5.

    Supplementary Movie S5

    This file contains Supplementary Movie S5: Labyrinth pattern at T = 27.1°C, corresponding to Fig. 2E.

  6. 6.

    Supplementary Movie S6

    This file contains Supplementary Movie S6: Thermal excitations and defects at T = 27.1°C, corresponding to Fig. 2F.

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DOI

https://doi.org/10.1038/nature07595

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