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Fractionalization of interstitials in curved colloidal crystals

Nature Materials volume 11, pages 948–951 (2012)Cite this article

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Abstract

Understanding the effect of curvature and topological frustration in crystals yields insights into the fragility of the ordered state. For instance, a one-dimensional crystal of identical charged particles can accommodate an extra particle (interstitial) if all the particle positions are readjusted, yet in a planar hexagonal crystal interstitials remain trapped between lattice sites and diffuse by hopping1,2,3. Using optical tweezers operated independently of three-dimensional imaging, we inserted interstitials in a lattice of similar colloidal particles sitting on flat or curved oil/glycerol interfaces, and imaged the ensuing dynamics. We find that, unlike in flat space, the curved crystals self-heal through a collective particle rearrangement that redistributes the increased density associated with the interstitial. This process can be interpreted in terms of the out-of-equilibrium interaction of topological defects with each other and with the underlying curvature. Our observations suggest the existence of particle fractionalization on curved surface crystals.

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Figure 1: Curved crystals and topological defects.
Figure 2: Interstitials in flat space and interstitial absorption by grain boundaries.
Figure 3: Interstitial fractionalization.

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Acknowledgements

We acknowledge discussions with S. Sacanna, A. D. Hollingsworth, A. Grosberg, D. Nelson, T. Witten and V. Vitelli. This work was supported by Rhodia, the English speaking union and the MRSEC Program of the National Science Foundation under Award Number DMR-0820054 (WTMI), the National Science Foundation grant DMR-0808812 (MJB), the MRSEC Program of the National Science Foundation under Award Number DMR-0820341 and NSF DMR 1105417 (PMC). W.T.M.I. and M.J.B. acknowledge hospitality from the Aspen Center for Physics.

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Authors and Affiliations

  1. James Franck Institute, University of Chicago, 929 E 57th street, Chicago, Illinois 60637, USA

    William T. M. Irvine

  2. Physics Department, Syracuse University, Syracuse, New York 13244-1130, USA

    Mark J. Bowick

  3. Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA

    Paul M. Chaikin

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  1. William T. M. Irvine
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  2. Mark J. Bowick
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  3. Paul M. Chaikin
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Contributions

M.J.B., P.M.C. and W.T.M.I. designed the research. W.T.M.I. and P.M.C. designed the experimental system. W.T.M.I. developed the apparatus for simultaneous confocal imaging and optical tweezing, performed experiments, wrote analysis software and analyzed data. W.T.M.I., M.J.B. and P.M.C. wrote the manuscript.

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Correspondence to William T. M. Irvine, Mark J. Bowick or Paul M. Chaikin.

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The authors declare no competing financial interests.

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Irvine, W., Bowick, M. & Chaikin, P. Fractionalization of interstitials in curved colloidal crystals. Nature Mater 11, 948–951 (2012). https://doi.org/10.1038/nmat3429

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