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Topological colloids
Bohdan Senyuk, Qingkun Liu, Sailing He, Randall D. Kamien, Robert B. Kusner, Tom C. Lubensky, Ivan I. Smalyukh
TL;DR
The paper fabricates silica particles with handlebody topology and studies their induced nematic defects. It shows that the established convention cannot properly assign and sum nematic defect charges, motivating a new charge-assignment procedure tested against observed configurations.
Problem
The established convention fails to properly describe hedgehog charges in nematic textures.
Method
The study fabricates silica particles with handlebody topology and examines their structures in liquid-crystal cells using bright-field microscopy, PM, and 3PEF-PM.
Results
The authors demonstrate that the old convention is incapable of properly assigning and summing charges due to defects and textures in nematic liquid crystals.
Takeaways & Limitations
The study establishes a new charge-assignment procedure for defects and textures in nematic liquid crystals.
Takeaways & Limitations
The structures can be unstable in the bulk of uniformly aligned nematic liquid crystals.
Abstract
from arXiv · showhide
Abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable - homeomorphic - to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal - a fluid made of rod-like molecules that spontaneously align along the so-called "director" - these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincare-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices, through new types of self-assembly, to the experimental study of low-dimensional topology.
METHODS SUMMARY
The study fabricates silica colloids with handlebody topology and introduces them into nematic liquid-crystal cells with controlled surface alignment. Optical manipulation and three-dimensional nonlinear imaging are used to study particle-induced director structures.
- Fabrication: Silica handlebodies are fabricated by patterning and etching ring structures in deposited silica layers, then releasing the particles into water.The process uses sacrificial aluminium, photoresist patterning, plasma etching, and aluminium removal.
- Sample preparation: Surface treatment with DMOAP establishes perpendicular boundary conditions for the nematic director on the colloids.The treated particles are redispersed in methanol before nematic liquid crystal is added.
- Sample preparation: The particles are dispersed in pentyl cyanobiphenyl and infiltrated into ITO-glass cells with either perpendicular or in-plane director alignment.Cell gaps are defined by glass spacers, while polyimide coating provides in-plane alignment.
- Imaging and manipulation: Holographic optical tweezers provide optical manipulation, while three-photon excitation fluorescence polarizing microscopy images the director field.The integrated setup uses an inverted microscope, a spatial light modulator, and tunable femtosecond excitation.
Supplementary Information
The supplementary experiments characterize handlebody colloids in nematic liquid crystals using optical manipulation and three-dimensional imaging. They show topology-dependent interior defects, conserved total charge, and a scope boundary imposed by instability in bulk aligned nematics.
- Imaging: Three-photon excitation fluorescence polarizing microscopy reconstructs three-dimensional director fields from polarization-dependent fluorescence.Maximum fluorescence occurs when excitation polarization is parallel to n(r), with intensity varying approximately as cos^6 α.
- Director structures: Each handlebody hole commonly contains either a hyperbolic hedgehog point defect or a half-integer disclination loop.Both configurations are observed across colloidal tori with ring diameters from 5 to 10 μm.
- Multistability: Optical tweezers can switch the interior structure between hyperbolic point-defect and disclination-loop configurations.The two configurations are described as bistable, while point defects undergo Brownian motion elastically confined to the hole center.
- Topological charge: The total hedgehog charge of disclination loops and point defects remains conserved during transformations and can sum to zero for multi-particle configurations.The supplementary text states that the conventional charge assignment fails for certain nematic textures, motivating a new assignment and summation procedure.
- Limitations: The observed structures are unstable in the bulk of uniformly aligned nematic liquid crystals, although confinement or twisted director configurations may stabilize them.Some additional configurations are hindered by the high elastic free energy of director distortions.