🔬 condensed matter

Shaping boundaries to control and transport topological defects in colloidal nematic liquid crystals

This study demonstrates that topographical patterning of boundaries can effectively control anchoring and topological defects in confined colloidal nematic liquid crystals, while dynamic shape-shifting of these boundaries enables the transformation and transport of such defects.

Original authors: Gerardo Campos-Villalobos, André F. V. Matias, Ethan I. L. Jull, Lisa Tran, Marjolein Dijkstra

Published 2026-05-29

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CC BY 4.0

Original authors: Gerardo Campos-Villalobos, André F. V. Matias, Ethan I. L. Jull, Lisa Tran, Marjolein Dijkstra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a box filled with thousands of tiny, rigid matchsticks floating in a liquid. If you shake the box gently, the matchsticks will eventually line up, all pointing in roughly the same direction. This organized state is called a nematic liquid crystal.

However, if you put these matchsticks into a container with a specific shape, they can get confused. They want to line up, but the walls of the container force them to bend or twist. When they can't satisfy both the desire to line up and the rules of the wall, they create "kinks" or "glitches" in their alignment. In the scientific world, these glitches are called topological defects. Think of them like a whirlpool in a calm river or a knot in a rope; they are points where the order breaks down.

For a long time, scientists could control these "knots" in molecular liquids (like those in your LCD screen) by chemically coating the walls to tell the molecules how to stand. But for larger, microscopic particles (colloids), this chemical trick doesn't work well. They usually just stick flat against the wall, no matter what you do.

The Big Idea: Shape is the New Chemistry
This paper says: "Forget the chemicals; let's change the shape of the walls."

The researchers discovered that if you carve the walls of the container into a wavy, bumpy pattern (like a sawtooth wave), you can force the matchsticks to stand up straight (perpendicular) instead of lying flat.

The Analogy: Imagine trying to park a long car in a garage.
- If the wall is smooth and flat, the car naturally parks parallel to it (Planar Anchoring).
- But if the wall has deep, sharp V-shaped grooves, the car is forced to park perpendicular to the wall to fit inside the groove (Homeotropic Anchoring).
- The matchsticks behave the same way. The "bumpy" wall creates a geometric trap that makes it energetically favorable for the rods to stand up. This happens purely because of the shape and the "crowding" of the particles, not because of any chemical glue.

Controlling the "Knots"
Once the researchers figured out how to make the rods stand up or lie down just by changing the wall's texture, they realized they could control the "knots" (defects) in the middle of the fluid.

Smooth Walls: The knots stay stuck to the edges.
Bumpy Walls: The knots get pushed into the center of the container.
Mixing It Up: By creating a wall that is smooth in some spots and bumpy in others, they could move the knots around like pieces on a chessboard. They could even make a knot appear or disappear just by changing the pattern of the wall.

The "Shape-Shifting" Future
The paper also runs computer simulations to predict what would happen if the walls could physically change shape in real-time (like a wall that ripples or morphs).

The Analogy: Imagine a river with whirlpools. If you could instantly reshape the riverbanks, you could push a whirlpool from one spot to another, or merge two whirlpools into one.
The researchers predict that by dynamically changing the shape of the container, they could "transport" these defects, moving them from one location to another without physically stirring the fluid.

Why This Matters (According to the Paper)
The authors suggest this is a powerful new way to:

Store Information: They demonstrated that by arranging the walls in specific patterns across multiple circular containers, they could create a "1" (a knot exists) or a "0" (no knot) in each container. By controlling the walls, they could flip these bits, effectively creating a memory system made of liquid crystals.
Move Particles: Since these "knots" can trap tiny particles, moving the knot by reshaping the wall could be used to transport those trapped particles to specific locations.

In Summary
This paper shows that you don't need complex chemistry to control how microscopic particles align. By simply carving the right patterns into the walls of their container, you can force them to stand up or lie down, and in doing so, you can create, destroy, and move the "knots" in their alignment. It's like being a conductor of a symphony, where the shape of the stage dictates how the musicians play, allowing you to compose complex patterns of order and chaos.

Technical Summary: Shaping Boundaries to Control and Transport Topological Defects in Colloidal Nematic Liquid Crystals

Problem Statement
Colloidal liquid crystals composed of anisotropic rod-like particles exhibit topological defects (TDs) when confined, which arise from the frustration of the nematic director field by boundary conditions. While the anchoring of molecular liquid crystals can be precisely tuned via surface functionalization to control defect states, this approach is difficult to apply to microscale colloidal systems. In colloidal systems, entropic arguments typically favor planar anchoring near flat and structured walls, making the achievement of homeotropic (perpendicular) anchoring elusive. Consequently, there is a lack of methods to control the anchoring type and, by extension, the resulting defect configurations in colloidal nematics without chemical modification.

Methodology
The authors employ a multi-faceted approach combining three distinct methods to investigate the relationship between boundary geometry and anchoring:

Monte Carlo (MC) Simulations: Hard discorectangles (rods with length $L$ and diameter $D$ ) were simulated in 2D rectangular and circular confinements. The boundaries were modeled with sinusoidal-triangular wave patterns characterized by amplitude ( $a$ ) and periodicity ( $p$ ). The packing fraction was fixed to ensure stable nematic phases.
Landau-de Gennes (LdG) Theory: A continuum theory for hard colloidal rods was used to minimize the grand potential and predict equilibrium director fields and defect structures under various boundary conditions.
Experiments: Fluorescently labeled silica rods ( $L/D \approx 9.4$ ) were sedimented into rectangular and circular confinement wells fabricated on glass coverslips using contact photolithography. The wells featured undulated boundaries with varying amplitudes and fixed periodicity.

Key Contributions and Results

Geometric Control of Anchoring: The study demonstrates that purely geometric patterning of boundaries can induce a transition from planar to homeotropic anchoring in hard colloidal rods, driven solely by entropy. In rectangular confinement, increasing the amplitude of undulations on the boundary walls eliminates disclination lines associated with planar anchoring, replacing them with homeotropic alignment.
Anchoring Phase Diagram: By systematically varying the reduced amplitude ( $a/D$ $a / D$ ) and period ( $p/D$ $p / D$ ), the authors mapped the anchoring behavior.
- Planar Anchoring: Occurs at low amplitudes or small periods where rods align tangentially.
- Homeotropic Anchoring: Occurs at high amplitudes and periods where rods align perpendicularly to the boundary.
- Bistability: An intermediate region exists where the system exhibits bistability, with rods switching between planar and homeotropic states or coexisting in spatially heterogeneous domains.
Entropic Mechanism: The transition is rationalized analytically by calculating the accessible area for rods in perpendicular versus tangential orientations. The free energy minimization reveals that the preference for homeotropic anchoring arises when the accessible area for perpendicular alignment exceeds that for tangential alignment, a condition governed by the geometric parameters $a$ , $p$ , and the rod aspect ratio $L/D$ .
Defect Manipulation in Circular Confinement:
- Planar vs. Homeotropic: In circular confinement, planar anchoring yields a bipolar configuration with two $+1/2$ defects at the poles. Homeotropic anchoring also results in a bipolar state but with reversed defect orientation and smaller separation; at intermediate radii, transient fluctuations allow the merging of defects into a single $+1$ defect.
- Hybrid Anchoring: By patterning the boundary with alternating 60° slices of planar and homeotropic anchoring, the authors demonstrated precise control over defect charge and location. A single homeotropic slice induces a $+1/2$ defect opposite to it, while alternating slices create a central $-1/2$ defect.
Defect Transport and Information Storage: The authors predict that dynamically shape-shifting boundaries can transport topological defects between adjacent circular cavities. By modulating boundary conditions in a system of overlapping circles, specific defect configurations (labeled as binary bits, e.g., 111, 100, 010) can be reversibly reconfigured. This suggests a mechanism for controlled defect transport and potential information storage.

Significance and Claims
The paper claims to establish that topographical patterning is a robust, purely entropic mechanism for controlling anchoring in colloidal liquid crystals, overcoming the limitations of planar anchoring typically found in such systems. The work provides a geometric phase diagram for anchoring transitions and demonstrates that boundary shape alone can dictate the symmetry, arrangement, and stability of topological defects.

The authors highlight that while the dynamic transport of defects via shape-shifting boundaries is currently a prediction based on MC simulations and LdG theory, it offers a pathway for the controlled manipulation of colloidal particles trapped by defects. They suggest that future experimental realization could utilize responsive materials, such as liquid crystal elastomers, to create dynamic topographies. The study positions these findings as a step toward tailoring defect configurations for applications in photonic devices, mechanical property tuning, and active matter systems, without relying on chemical surface functionalization.

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