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Mutually tangled colloidal knots and induced defect loops in nematic fields

Nature Materials volume 13, pages 258–263 (2014)Cite this article

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Abstract

Colloidal dispersions in liquid crystals can serve as asoft-matter toolkit for the self-assembly of composite materials with pre-engineered properties and structures that are highly dependent on particle-induced topological defects1,2,3. Here, we demonstrate that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them. In particular, by taking advantage of two-photon photopolymerization techniques to make knot-shaped microparticles, we show that the interplay of the topologies of the knotted particles, the nematic field and the induced defects leads to knotted, linked and other topologically non-trivial field configurations4,5,6,7,8,9,10,11,12. These structures match theoretical predictions made on the basis of the minimization of the elastic free energy and satisfy topological constraints4,5. Our approach may find uses in self-assembled topological superstructures of knotted particles linked by nematic fields, in topological scaffolds supporting the decoration of defect networks with nanoparticles1, and in modelling other physical systems exhibiting topologically analogous phenomena12,13,14,15,16.

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Figure 1: Photopolymerized knotted particles and their arrays.
Figure 2: A trefoil knot particle with tangential boundary conditions in an aligned liquid crystal.
Figure 3: A colloidal trefoil knot with perpendicular surface boundary conditions.
Figure 4: A colloidal knot T(5,3) with tangential boundary conditions.
Figure 5: Torus knot T(5,2) particles with tangential boundary conditions.

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Acknowledgements

We thank G. Alexander, B. Chen, N. Clark, S. Čopar, M. Dennis, W. Irvine, R. Kamien, T. Lubensky, I. Muševič, L. Radzihovsky and B. Senyuk for discussions. M.R., S.Ž. and I.I.S. acknowledge the hospitality of the KITP programme ‘Knotted Fields’ and the Isaac Newton Institute’s programme ‘Mathematics of Liquid Crystals’, during which this work was discussed. We acknowledge the support of the National Science Foundation Grants DMR-0847782 (R.V., B.L., I.I.S.), DMR-0820579 (A.M., I.I.S.) and DGE-0801680 (A.M., I.I.S.), as well as the SLO ARRS program P1-0099, EU FP7 CIG FREEFLUID, SLO ARRS grant Z1-5441, and the Center of Excellence NAMASTE (M.R., S.Ž.).

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Authors and Affiliations

  1. Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

    Angel Martinez, Brice Lucero, Rayshan Visvanathan & Ivan I. Smalyukh

  2. Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA

    Angel Martinez & Ivan I. Smalyukh

  3. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia

    Miha Ravnik & Slobodan Žumer

  4. Jozef Stefan Institute, Jamova 39, Ljubljana 1000, Slovenia

    Slobodan Žumer

  5. Department of Electrical, Computer, and Energy Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA

    Ivan I. Smalyukh

  6. Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA

    Ivan I. Smalyukh

Authors
  1. Angel Martinez
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Contributions

A.M., B.L., R.V. and I.I.S. performed experimental work and analysed experimental results. A.M. built the two-photon polymerization set-up. M.R. and S.Ž. carried out numerical modelling of the structures of defects and fields. A.M. and I.I.S. experimentally reconstructed the director fields induced by colloids and compared them with theoretical results by modelling 3PEF-PM images. M.R., S.Ž. and I.I.S. analysed models of director fields and defects satisfying topological constraints. A.M., M.R. and I.I.S. wrote the manuscript. I.I.S. conceived and designed the project.

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Correspondence to Ivan I. Smalyukh.

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Martinez, A., Ravnik, M., Lucero, B. et al. Mutually tangled colloidal knots and induced defect loops in nematic fields. Nature Mater 13, 258–263 (2014). https://doi.org/10.1038/nmat3840

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