Blue phases as templates for 3D colloidal photonic crystals

10.1117/2.1201009.003168

Blue phases as templates for 3D colloidal photonic crystals Slobodan Zumer, Miha Ravnik, Tine Porenta, Gareth P. Alexander, and Julia M. Yeomans Intrinsic defect networks promote automatic assembly of ‘soft’ photonic crystals with possible application in electrically controlled lasing and other electro-optical devices. Crystals that can be easily manipulated and formed through self-assembly would clearly be of great interest for photonic applications that require easy tuning, for example, bandgaps, transmission, and lasing. Here, we focus our attention on ‘blue phase’ crystals, i.e., soft photonic crystals that undergo periodic 3D modulation of their molecular orientation. We propose to decorate blue phases with submicron spherical particles to form ‘colloidal’ crystals that can be easily controlled by external stimuli. Blue phases are liquid crystals whose chiral (left- or righthanded) molecules tend to orient with an intrinsic twist in two spatial directions, leading to large-scale ‘frustration’ and thus formation of a fully 3D crystalline arrangement. In blue phase I and II, the resulting lattices are arrays of double-twisted areas separated by defect lines that exhibit simple cubic and body-centered cubic symmetry, respectively.1 Their lattice constants, which are crucial for the wavelength of lasing, for example, are in the submicron range: see Figure 1(a) and (b). The structures may be understood in terms of energy balance between the energetically preferred double-twisted local ordering and the energetic cost of the large-scale defect network. In the past, exploitation of blue phases for applications such as electrically controlled lasing2, 3 was seriously handicapped by a narrow stability range of few degrees Kelvin. But we are now able to produce blue phases with an extended stability range of 40–50K,4, 5 which increases their usefulness. These developments spurred us to employ modeling and simulations to examine the possibility of using blue phases as templates for assembling 3D colloidal crystals. When dispersing particles with sizes that amount to only a fraction of the lattice constant, it is expected that they will adopt spatial positions exhibiting the same symmetry as the underlying orientational ordering lattice.

Figure 1. Networks of defect lines in blue phases I and II with surfaces that enclose the areas where the nematic order parameter is below a chosen value. The spatial dependences of the orientational ordering characterized by the nematic director fields are not shown. Eight unit cells are shown: (a) Blue phase I with surfaces corresponding to 40% of the bulk order parameter and 540nm unit cell and (b) blue phase II with surfaces corresponding to 20% of the bulk value and 350nm unit cell. Such a photonic crystal would have an advantage over pure blue phases because particles with specific optical, electric, and magnetic properties present possibilities for additional manipulation. Moreover, liquid crystal-based dispersions would stay soft and would also offer many more structural possibilities than ordinary, densely packed colloidal crystals. We applied our experience of trapping tiny colloidal particles to defect lines appearing in the orientational order of simple nonchiral ‘nematic’ liquid crystals.6 The particles perturb the orientational order in a complex way, leading to anisotropic, long-range effective interaction and consequently to numerous organizational arrangements of colloidal particles not present in simple liquids. We based our approach on the phenomenological Landau-de Gennes description and topological theory, which has proven to be extremely useful in dealing with nematic colloids.7, 8 The nematic free energy is extended by a chiral term.9 When a colloidal particle is added to a blue-phase liquid crystal, it is attracted to an energetically favorable defect Continued on next page

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Author Information Slobodan Zumer and Tine Porenta University of Ljubljana Ljubljana, Slovenia Slobodan Zumer is a professor of physics. In 2008 he also started his four-year term as president of the International Liquid Crystal Society. His research interests cover modeling, simulations, and theory of soft-matter systems, including liquid crystals, polymers, nematic elastomers, and colloids. Miha Ravnik and Julia M. Yeomans Oxford University Oxford, United Kingdom Figure 2. Three-dimensional blue phase colloidal crystal. Stable crystalline configuration based on a blue phase II defect network with two 150nm particles per body-centered cubic unit cell with a 350nm lattice constant. Eight cells are shown.

Gareth P. Alexander University of Pennsylvania Philadelphia, PA References

network. In other words, occupying a region previously covered by a defect line reduces the free-energy penalty caused by a network. As a result, the lattice of defect lines that characterizes the cholesteric (i.e., chiral nematic) blue phases forms an environment in which a 3D colloidal crystal can self-assemble. Colloidal particles localized on the deformed areas adopt a configuration that has the same symmetry as the defect lattice (see Figure 2). In summary, the assemblies described here constitute soft photonic crystals that can be easily manipulated by perturbing the liquid crystal matrix or colloidal particles. We expect that in the future, blue phases will be used to self-assemble complex structures needed for different ways of manipulating electromagnetic signals. To stimulate experimental studies of blue phase colloids and their applications, we plan to investigate the stability ranges of relevant structures and, in particular, their susceptibility to external stimuli.

1. D. C. Wright and N. D. Mermin, Crystalline liquids: the blue phases, Rev. Mod. Phys. 61, p. 385, 1989. 2. W. Cao, A. Munoz, P. Palffy-Muhoray, and B. Taheri, Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II, Nat. Mater. 1, p. 111, 2002. 3. Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, Large electro-optic Kerr effect in polymer-stabilized blue phases, Adv. Mater. 17, p. 96, 2005. 4. H. J. Coles and M. N. Pivnenko, Liquid crystal ‘blue phases’ with a wide temperature range, Nature 436, p. 997, 2005. 5. F. Castles, S. M. Morris, E. M. Terentjev, and H. J. Coles, Thermodynamically stable blue phase, Phys. Rev. Lett 104, p. 157801, 2010. 6. M. Skarabot, M. Ravnik, S. Zumer, U. Tkalec, I. Poberaj, D. Babic, and I. Musevic, Hierarchical self-assembly of nematic colloidal superstructures, Phys. Rev. E 77, p. 061706, 2008. 7. I. Musevic, M. Skarabot, U. Tkalec, M. Ravnik, and S. Zumer, Two-dimensional nematic colloidal crystals self-assembled by topological defects, Science 313, p. 954, 2006. 8. M. Ravnik and S. Zumer, Nematic colloids entangled by topological defects, Soft Matter 5, p. 269, 2009. 9. M. Ravnik, G. P. Alexander, J. M. Yeomans, and S. Zumer, Mesoscopic modeling of colloids in chiral nematics, Faraday Discuss. 144, p. 159, 2010.

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