Guiding Self-Organization with Topological Defects in Nematic Liquid Crystals

visualization of partially relaxed nematic liquid crystal configuration with random placement of spherical colloids
Example image from visualization package open-ViewMin

When colloidal particles or nanoparticles are dispersed within nematic liquid crystals, the particles self-organize into complex arrangements guided by nematic topological defects, which are lines or points of quantized distortion. Our calculations show how the geometry and topology of the boundary conditions control the defect configurations, and thus the particle assemblies, in the bulk.

Self-assembled defect arrays in lamellar liquid crystals

In the smectic liquid crystal phase, molecules are ordered in layers of single particle thickness. The constraint of constant layer spacing results in a set of defect motifs, including focal conic domains. We model the material patterning that results from the self-assembly of these defects, and the effects on colloidal and nanoparticle inclusions.

nematic and smectic liquid crystal defect configurations

Spontaneous chirality in liquid crystal defects

simulated undulating disclinations in a square capillary

Liquid crystals often assemble into chiral structures because of molecluar chirality. However, a distinct class of phenomena arise when mirror symmetry is broken spontaneously; that is, the ground state is left-handed or right-handed with equal probability. We investigate the energetic frustrations that can cause this symmetry breaking, as well as consequences such as double-helical defect lines and multistability in the assembly of colloidal particles.

active matter Science cover Matter in living systems is inherently far from thermodynamic equilibrium; so too are many non-living systems. On scales from intracellular biofilaments and bacteria to flocks of birds, we find active matter that continually converts internal energy into motion. Even with simple rules for motion and interaction at the scale of the self-driven “units”, complex collective motions often emerge at the macroscale. The spontaneous self-organization follows rules familiar from equilibrium physics, but with internally driven motion producing dramatically different dynamics.

We study manifestations of liquid crystals physics, i.e. orientational order and topological defects, in active matter at the microscale. Such active liquid crystals behave as materials with spontaneous alignment at small scales but internally driven chaotic flows at larger scales. We use this perspective to develop understanding of growing bacterial colonies as well as collections of cytoskeletal filaments driven by motor proteins.

3D active nematics

schematic illustration of active nematic wedge-twist disclination loop

A suspension of microtubules (cytoskeletal biofilaments) and kinesin motor proteins exhibits complex active nematic dynamics. We found that, in three dimensions, these complex flows are characterized by topological defect lines of the type studied in 3D nematic liquid crystals. In particular, a network of extended defect lines coexists with a population of isolated closed-loop defects, which nucleate, self-annihilate, and undergo reconnections with other defects.

Active phases of self-propelled filaments

Simulated active flocking phase of microtubules (cytoskeletal filaments)
driven by kinesin motor proteins. Colors: orientation. [M. Athani]

Inspired by “gliding assay” experiments on microtubules and actin filaments, we study the myriad active phases that emerge from the interactions of many flexible filaments, propelled along their tangent directions by motor proteins. We identified a negative feedback loop in which motor proteins aggregate in, but destabilize, ordered “nematic lanes” of microtubules.

Growing bacterial colonies

simulated bacterial colony snapshot

Growing bacterial colonies can be active liquid crystals. Our agent-based simulations show that active mixing flows, while weak compared to the colony’s radial expansion, may help to mix a colony and slow the spontaneous segregation of mutations.

Population Genetics in Biological Range Expansions

When a species expands into new territory, genetic diversity is lost rapidly at the population front. Concepts from statistical physics and differential geometry shed light on how spatial structure—in the population and in the environment—can change evolutionary outcomes. Our recent work has shown how “topographic lensing” effects from bumpy terrain can affect genetic diversity and play a dramatic role in deciding which ancestral lineages dominate in the new territory. Current work is focused on how the environment’s spatial structure and the front propagation dynamics affect the coalescence of ancestral lineages in the reverse-time view. This affects, for example, our estimates of how long ago two organisms had a common ancestor.

Effects of surface topography on range expansions

Bumpy surfaces enhance the "survival of the luckiest" in expanding populations, compared to "survival of the fittest." Each bump acts as a lens for the population front passing through it.

Effects of heterogeneous nutrient distributions

lineages in a simulated range expansion over a plane with many nutrient hotspots
Surviving genetic lineages in an Eden model simulation
with randomly placed hotspots. [J. Gonzalez Nuñez]

Random variations in nutrient availability can control which genetic lineages dominate newly colonized territory, meaning that the environment's randomness prevails over the population's intrinsic randomness in neutral evolution.

Influence of active self-mixing on genetic diversity

simulated bacterial colony snapshot

Growing bacterial colonies can be active liquid crystals. Our agent-based simulations show that active mixing flows, while weak compared to the colony’s radial expansion, may help to mix a colony and slow the spontaneous segregation of mutations.

Tubular crystals

From carbon nanotubes to pineapple skins to microtubules in the cellular cytoskeleton, we find many examples of tubular crystals: repeating two-dimensional patterns wrapped into cylinders. Their mathematical description maps beautifully onto the study of phyllotaxis in botany.

Our work on tubular crystals as a soft-matter system is identifying relationships between defects in the crystal’s 2D pattern and the mechanical properties of the 3D tube. When defects move through the crystal, the tube morphs into bent and helical shapes that can be reconfigured by external stimuli—suggesting a novel route to responsive mechanical micromachines.

Shape multistability in flexible tubular crystals

tubular crystal helix

Elastic network simulations predict that mobile dislocations in free-standing tubular crystals stabilize distorted tube shapes with differing mechanical properties, and allow switching between metastable configurations.

Plastic deformation of tubular crystals by dislocation glide

tubular crystals

The chiral indices of a tubular crystal are altered stepwise by the motions of dislocation point-defects. Our elastic network simulations show that imposed forces and torques drive sequences of dislocation pair-unbindings, pushing the system through a discrete configuration space toward certain stable orientations of the crystal axes.

Crystallization kinetics on cylindrical surfaces


When colloidal particles assemble into 2D crystals on a cylindrical surface, a newly observed type of defect, the kinked line-slip, plays a key role in the crystallization kinetics.