physics – Softbites

2022-06-29

Trichoplax adhaerens: tropical sea-dweller, microscopic contortionist, and biomechanical marvel

Original paper: Motility-induced fracture reveals a ductile-to-brittle crossover in a simple animal’s epithelia

Content review: Heather Hamilton
Style review: Pierre Lehéricey

Figure 1: The dynamic range of *T. adhaerens* with size ranging from 100 microns to 10 millimeters. Snapshots taken from live imaging. Images courtesy of the original article.

Meet Trichoplax adhaerens, a microscopic marine animal from one of the oldest known branches of the evolutionary tree. It looks like a microscopic cell sandwich: two layers of epithelial cells (which make up the surfaces of our organs), with a layer of fibre cells in between. As depicted in Figure 1, T. adhaerens takes a wide variety of shapes from disks to loops to noodles and more. Oddly, T. adhaerens ruptures when it moves around, a self-induced fracture behavior that has recently captured the attention of physicists and engineers. Fracture is the technical term describing the process by which an object breaks into distinct pieces due to stress. These animals push their epithelial tissue to the breaking point, forming incredible and extreme shapes before separating altogether. This is a surprising behavior for epithelia, which usually prefer to maintain their integrity. By modeling how T. adhaerens rips itself apart when moving, we can improve our understanding of how soft materials and especially biological tissues behave on the verge of breaking.

Prakash, Bull, and Prakash conducted a two-pronged analysis of fracture in T. adhaerens: live imaging to record the fracturing in real time and computational modeling to simulate the response of the tissue when stretched too far. The drastic mechanical behavior in question also motivated the researchers to perform a more general inquiry into the competition between flow and fracture in materials that are dramatically deformed relatively quickly. Flow is like stretching out a piece of chewing gum, whereas fracture is like snapping the gum in two. The computational model proposed by the authors helped paint a clearer picture of what happens when T. adhaerens rips apart.

Figure 2: Model tissue is described as a collection of balls and springs. Balls represent cells, and springs represent the sticky adhesion between cells. Springs apply restorative forces to the cells, but can break if stretched too far. This model was used to study the ventral (bottom) epithelial layer, which consists of epithelial cells (green) and larger lipophil cells (red). Figure courtesy of the original article (Extended Data).

The computational model that the researchers used is based on a sticky ball and spring model, as shown in Figure 2, where each ball represents a cell and each spring represents the sticky junctions that cells use to adhere to one another. The springs break if the balls move too far away from each other, which represents cells being unstuck from their neighbors. Two cell types are represented in the model epithelial layer in Figure 2: epithelial cells, which are small and comprise the bulk of the tissue, and lipophil cells, which are larger and less common. Using this model for living tissue, the authors conducted computational simulations where the tissue was stretched to a breaking point. They found that there are three possible tissue behaviors that depend on the strength of the driving force applied to the simulated tissue. For weak forcing (low stress), the tissue behaved elastically and so responded in such a way that it could recover its original shape. For intermediate forcing (medium stress), the tissue underwent a “yielding transition” where the material transitioned from elastic response to plastic response. During plastic response, permanent distortions occurred in the material, and the material could not recover its original shape. In this case, the tissue is ductile and undergoes local changes, like cells interchanging with neighboring cells, to relax some of the pent-up stress. For stronger forcing (high stress), the tissue undergoes brittle fracture where the bonds between cells break with little opportunity for relaxation. The three behaviors in the model represent a transition from elastic to ductile to brittle responses. Using this model of tissue response to applied force, the authors mapped the conditions that lead to different tissue behaviors, as sketched in Figure 3.

Figure 3: Tissue phase diagram (elastic-ductile-brittle) generated by the tissue simulations. The elastic regime (i) implies that bonds do not break, and neighbors are not exchanged. Above the yield transition (blue line), cells undergo local relaxations and flow in the ductile yielding regime. To the left of the red line, cell bonds tend to break and form gaps between cells, demarcating the brittle fracture regime. Figure courtesy of the original article.

Guided by a better understanding of tissue mechanics thanks to the computer model, the authors experimentally measured the brittle and ductile responses in T. adhaerens. They found that both material responses can occur in our microscopic friend. The ability to access both regimes is important because the ductile response yields by flowing (helping form the longer shapes in T. adhaerens) whereas the fracture response accounts for asexual reproduction by splitting into two separate new individuals. The authors’ combined approach of experimental data that motivated the development of a computer model, which in turn guided further experimental inquiry, is an important modern scientific paradigm. Both approaches are incredibly important tools in the biological and soft matter sciences’ toolkit. Joint application of these tools lets us draw general conclusions from specific experiments as well as apply those general conclusions back to answer specific questions – like explaining how T. adhaerens achieves the diversity of shapes in Figure 1 and how this relates to its hardiness and evolutionary goal of reproduction. Further, the epithelial layer computational modeling technique generalizes this tissue mechanics study to help us describe fracture versus flow in any living tissue, including our own.

2020-02-202020-02-20

Researchers play with elastic bands to understand DNA and protein structures.

Topology, Geometry, and Mechanics of Strongly Stretched and Twisted Filaments: Solenoids, Plectonemes, and Artificial Muscle Fibers

Much of how DNA and proteins function depends on their conformations. Diseases like Alzheimers’ and Parkinsons’ have been linked to misfolding of proteins, and unwinding DNA’s double-helix structure is crucial to the DNA self-copying process. Yet, it’s difficult to study an individual molecule’s mechanical properties. Manipulating objects at such a small scale requires tools like optical and magnetic tweezers that produce forces and torques on the order of pico-Newtons, which are hard to measure accurately. One way around these difficulties is by modeling a complicated molecule as an elastic fiber that deforms in predictable ways due to extension and rotation. However, there are still many things we don’t know about how even a simple elastic fiber behaves when it is stretched and twisted at the same time. Recently, Nicholas Charles and researchers from Harvard published a study that used simulations of elastic fibers to probe their response to stretching and rotation applied simultaneously. The results shed light on how DNA, proteins, and other fibrous materials respond to forces and get their intricate shapes.

Before continuing, I would recommend finding a rubber band. A deep understanding of this work can be gained by playing along with this article.

Long and thin elastic materials, (like DNA, protein, and rubber bands), are a lot like springs. You can stretch or compress them, storing energy in the material proportional to how much you change its length. However, compressing them too much may make the material bend sideways, or “buckle”. It might be more natural to think of this process with a stiff beam like in Figure 1, where a large compressive load can be applied before the beam buckles. But since your rubber band is soft and slender, it buckles almost immediately.

A stick is compressed and at a certain pressure, buckles. — **Figure 1.** A straight, untwisted stick is compressed and buckles. It’s stiffer and thicker than your rubber band, so it sustains a higher load before buckling. (https://enterfea.com/what-is-buckling-analysis/)

Likewise, twisting your rubber band in either direction will store energy in the band proportional to how much it’s twisted. And, like compression, twisting can also cause it to deform suddenly. Instead of buckling, the result is a double-helix-like braid that grows perpendicular to the fiber’s length, as shown in Figure 2. An important caveat is that the ends of the rubber band are allowed to come together. But what happens when the ends of the band are fixed?

An elastic fiber is twisted into a plectoneme. It looks like a double-helix. — **Figure 2.** An elastic fiber is held with little to no tension and twisted. A double-helix, braid-like structure is formed. (Mattia Gazzola, https://www.youtube.com/watch?v=5WRkBWXUCNs)

Fixing the ends of a rubber band forces it to stretch as it twists. When this happens, a different kind of deformation can occur that combines extending, twisting, and bending the fiber. By stretching and bending simultaneously, the band forms a solenoid that is oriented along the long-axis of the band, reminiscent of the coil of a spring. An example of the solenoid shape appears in Figure 3.

An elastic fiber is held under tension and twisted. A solenoid structure is produced. — **Figure 3.** An elastic fiber is held at high tension and twisted. A solenoid structure is formed. (Mattia Gazzola, https://www.youtube.com/watch?v=0LoIwE37aNo)

All of the phenomena described above can be seen by playing with rubber bands, yet a quantitative understanding of how these states form and how to transition between them has remained elusive. To tackle this problem, Charles and coworkers used a computer simulation to calculate the energy stored at each point along an elastic fiber when it is stretched and twisted. The simulated fiber was allowed to deform and search for its lowest energy configuration, a process critical to navigating the system’s instabilities and finding the state you would expect to find in nature.

Figure 4 summarizes some of the different conformations attained by a fiber that is first stretched, then twisted to different degrees. We can see how a fiber with the same tension and different degrees of twist can lead to any one of a wide range of conformations. For instance, a fiber remains straight (yellow dots) when it’s stretched to a length $L$ that is 10% longer than its original length $L_{0}$ $(L/L_{0} = 1.1)$ until it is twisted by $\Phi a \approx 1$ , where $\Phi a$ is the degree of twist multiplied by the fiber’s width divided by its length. Above this value of $\Phi a$ , the simulated fiber twists into the braided helix structure seen in Figure 2 (blue dots). Likewise, when $L/L_{0} = 1.2$ , the fiber remains straight until it has a much higher twist, $\Phi a \approx 1.5$ , where it forms a solenoid (red dots).

Phase diagram of fiber conformations as a function of twist and stretch. — **Figure 4.** Conformation of a simulated fiber under constant extension $L/L_{0}$ , twisted by $\Phi$ normalized by the fiber dimensions $a$ . Orange dots are straight, blue dots are double-helix braids, red dots are solenoids, and green dots are mixed states. Black and grey symbols are experimental results from a previous study.

**Figure 4.** Conformation of a simulated fiber under constant extension $L/L_{0}$ , twisted by $\Phi$ normalized by the fiber dimensions $a$ . Orange dots are straight, blue dots are double-helix braids, red dots are solenoids, and green dots are mixed states. Black and grey symbols are experimental results from a previous study.

Considering the vast understanding of the universe that physics has given us, it may be surprising that there is so much left to learn from the lowly rubber band. While it’s fun to play with, understanding the way fibers deform could help researchers understand all sorts of biological mysteries. For instance, your DNA is a unique code that contains all of the information needed to create any type of cell you have, but depending on where the cell is in your body, that same DNA only makes some specific cell types. The cell can do this by selectively replicating sections of its DNA while ignoring others. One way it does this is by hiding away certain regions of DNA through folding. Exploring the way simple elastic fibers deform could help explain the way DNA knows how to make the right cells, in the right places.

2019-05-15

Mechanism of Contact between a Droplet and an Atomically Smooth Substrate

Floating droplets shed new light on the flow of fluid at interfaces

Original article: Mechanism of Contact between a Droplet and an Atomically Smooth Substrate

When an experiment doesn’t behave the way we expect, either our understanding of the relevant physics is flawed, or the phenomenon is more complicated than it appears. When a theoretical prediction is off by two orders of magnitude – like what was observed in this recent paper by Hua Yung Lo, Yuan Liu, and Lei Xu of the Chinese University of Hong Kong – something is seriously wrong.

If Lo and colleagues drop a liquid droplet onto a smooth, flat surface, it will take on an equilibrium shape which depends on the properties of the liquid and solid materials at the interface (eg. water on Teflon will form a nearly perfect spherical drop while water on stainless steel will spread out, forming a spherical cap). For low viscosity fluids, the equilibration process happens almost instantly… unless the surface is very flat and very smooth.

If the surface below a droplet is atomically smooth (not a single atom is out of place to roughen the surface), a thin layer of air will form between the droplet and the surface, keeping the droplet from making contact with the surface. Eventually the trapped air will escape, draining out like how a liquid would, allowing the droplet to collapse onto the surface. Traditional fluid dynamics simulations predict that the collapse would take between 10 – 100 seconds. In experiments, however, contact generally happens in less than one second. Lo and coworkers set about investigating this seeming contradiction by observing the flow that happens within the air and liquid at the boundary between a droplet and a smooth surface.

To study this problem, the researchers dropped small spherical oil droplets (1.7 mm diameter) onto a glass surface with a very thin coating of oil which could be tilted. They observed that droplets would compress and bounce as they floated on a pocket of air, before collapsing onto the surface. The contact area was imaged from the bottom and side simultaneously using two high-speed cameras. Side-on sequences are shown in Figure 1 with a slightly tilted surface (a) and a perfectly leveled surface (b). While both droplets collapsed onto the surface far quicker than predicted by simulations, the droplet on the leveled surface was observed to float just above the surface approximately 10 times longer than on the tilted surface before collapsing.

Figure 1. A time sequence of an oil droplet being dropped on an atomically smooth, oil coated, glass surface which is a) slightly tilted (0.3°) and b) leveled (0°). c). Schematic of the droplet and surface. A video of the process can be found here (Figure adapted from the original paper.)

The effect the tilted surface has on this phenomenon became more apparent when viewed from below. On the tilted surface, the droplet would “skid”, observed as a sliding of the droplet’s center from the red point to the blue point in the direction of the green arrow as shown in Figure 2 a) while the size and shape of the air pocket was measured using two-wavelength interferometry [1]. Tilting the surface caused an asymmetric air pocket to develop, with a thinner gap at the front of the droplet and a thicker gap at the back. When a droplet did not skid, it formed a symmetric air pocket like in Figure 2 b). A thinner gap (with difference of just half micrometer) lets the air drain out (and allows contact to be made) much faster than it would for a symmetric air pocket on a flat surface. However, even a flat surface drained 10-times faster than expected.

Figure 2. Images of the bottom of an oil droplet coming in contact with an oil-coated glass slide that is a) slightly tilted, showing a droplet skidding until it reaches full contact with the surface at 109 ms, and b) perfectly leveled, where the droplet still has not contacted the surface at 392 ms. Light and dark bands correspond to the change in thickness of the air pocket. A video of the process in a) and b) can be found here and here.

To understand the flow of air from under the droplet, the researchers modeled it as a low-viscosity fluid. When a low-viscosity fluid flows past a wall (like water through a tube), the friction at the walls may reduce the flow near the walls to something-close-to-zero. This is called a “no-slip boundary condition”. On the other hand, a “plug flow boundary condition” means there is significant slip and therefore flow along the walls. Each of these boundary conditions lead to characteristic velocity profiles like those presented in Figure 3 a). Typically, one would assume that air flowing through the air pocket near the oil interface would have a no-slip boundary condition while something like a sludge or gel would demonstrate plug flow. Yet, it is this assumption that ends up being incorrect.

The researchers measured the velocity of oil within the oil droplet and the surface coating using particle image velocimetry, a technique where small light-reflecting particles are mixed into a material and tracked down as they move along with the surrounding fluid. An image of the oil droplet seeded with the tracer particles is shown in Figure 3. In this way, the researchers were able to directly visualize flow of oil at the air-oil boundaries, finding a sort of “slip layer” along the walls corresponding to the layer of oil being dragged along by the air. This lets larger volumes of air drain from under the droplet, explaining the surprisingly short time it takes for droplets to collapse onto the surface.

Figure 3. a) The velocity profile of air under the droplet (Vr) is a combination of a no-slip (Vp), and slip (Vc) boundary conditions. b) Side-view image of an oil droplet. White dots are reflective particles with velocity shown as yellow arrows. c) Bottom-view of the same oil droplet where the colored streaks (red to purple) trace the flow of the oil on the surface. (Figure adapted from the original paper.)

Despite its apparent simplicity, Lo et al. revealed a fundamental misunderstanding in the way scientists thought about how fluids flow near an interface. Accounting for the effect of slip, the researchers unified both theory and observation and explain why liquid droplets will make contact with a perfectly smooth surface so much faster than originally expected.

[1] a technique that uses light interference to quantify changes in thickness as light and dark bands; narrow bands correspond to rapidly changing thicknesses, much like the lines on a topographic map show changes in elevation. ^

2019-01-032019-01-03

What is soft matter?

Look inside a glass of milk. Still, smooth, and white. Now put a drop of that milk under a microscope. See? It’s not so smooth anymore. Fat globules and proteins dance around in random paths surrounded by water. Their dance—a type of movement called Brownian motion—is caused by collisions with water molecules that move around due to the thermal energy. This mixture of dancing particles in water is called a colloid.

Colloids are one of the classic topics in soft matter, a field of physics that covers a broad range of systems including polymers, emulsions, droplets, biomaterials, liquid crystals, gels, foams, and granular materials. And while I can keep adding items to this list, I can’t give you a precise definition for soft matter. I’ve never seen a completely satisfying definition, and I’m not going to even attempt to provide that here. But I can give you a taste of some of the definitions, and I hope you’ll come away with the feeling that you sort of know what soft matter is.

The phrase “soft matter” brings to mind pillows and marshmallows. These things fall under physicist Tom Lubensky’s definition (given in a 1997 paper) of soft materials as “materials that will not hurt your hand if you hit them.” And while many materials in soft matter are too squishy to hurt you, some of them might—cross-linked polymers can be pretty hard. And what about colloids? Slapping milk won’t hurt, but it also seems strange to call milk soft.

To understand what the “soft” refers to in “soft matter”, we first have to know where the name came from. The French term “matière molle” was coined in Orsay around 1970 by physicist Madeleine Veyssié, who worked in the research group of one of the founding fathers of soft matter, Pierre-Gilles de Gennes. The phrase apparently started as a private joke within the de Gennes group (don’t ask me what it meant), and the English translation of “soft matter” was popularized by de Gennes in a lecture he gave after winning the Nobel prize in 1991. De Gennes wrote that soft matter systems have “large response functions”, meaning that they undergo a large (don’t ask me how large) change in response to some outside force. So it seems we’re meant to take “soft” to mean something closer to “sensitive”, not necessarily soft in a tactile sense.

Now we can think about why colloids are soft from a different perspective. Remember that milk droplet under the microscope? The fats and proteins move around in the droplet due to thermal energy in the water; they are “sensitive” to the forces caused by thermal energy.

But even this “large response functions” idea doesn’t describe everything in soft matter. Some topics often considered a part of the field are concerned with general mathematical concepts instead of particular materials or systems. Take, for example, particle packing—the way particles arrange themselves to fit into confined spaces. Studying how particles can be arranged to pack on a curved surface is a mathematical problem and isn’t directly related to large response functions. However, since classic soft matter systems such as colloids are made up of particles you might want to pack, it makes sense to include packing as part of the field.

For every definition you give for soft matter, you can find a system that doesn’t quite fit. In an APS news article from 2015, Jesse Silverberg described soft matter as “…an amalgamation of methods and concepts” from “physics, chemistry, engineering, biology, materials, and mathematics departments. The problems that soft matter…examines are the interdisciplinary offspring that emerge from these otherwise distinct fields.” So maybe it’s not that important to have a rigid definition for soft matter; maybe its indefinability should be part of its definition. Soft matter is a field where the lines between traditional scientific disciplines are becoming ever more blurred—or, rather, soft.

Image credits: Marangoni bursting from the Lutetium Project video and Keiser et al. PRL 2017. 2017 APS/DFD Milton van Dyke Award Winners.

2018-10-102018-10-09

Spider silk: Sticky when wet

Original paper: Hygroscopic Compounds in Spider Aggregate Glue Remove Interfacial Water to Maintain Adhesion in Humid Conditions

If you were Spider-Man, how would you catch your criminals? You could tangle them up in different types of threads, but to really keep them from escaping you would probably want your web to be sticky (not to mention the utility of sticky silk for swinging between buildings). Like Spider-Man, the furrow spider spins a web with sticky capture silk to trap its prey. This silk gets its stickiness from a layer of glue that coats the thread. What makes this capture silk really interesting is that, unlike commercial glues, these spider glues don’t fail when wet.

The tendency for water to interfere with glues should come as no surprise. For example, sticky bandages become unstuck when they’re wet, whether it’s because of swimming, taking a shower, or going for a run on a humid day. This interference occurs on the microscopic scale, where water prevents the components of a glue from forming adhesive chemical bonds. Even just high humidity provides enough water vapor in the air for it to condense on nearby surfaces and interfere with adhesion. One would naturally expect this very general and simple mechanism to cause problems for spiders that lay traps near water, as our furrow spider does. As you may have guessed, our furrow spider is a bit more clever than that: their glues are highly effective regardless of the water content of the air, and this humidity-resilience has caught the attention of Saranshu Singla and colleagues at the University of Akron, Ohio.

spider-516653_960_720 — Figure 1. A spider unperturbed by the water droplets formed on its sticky web.

The furrow spider glue being studied by Singla and co-workers is essentially a cocktail of 3 main components: specialized “glycoproteins” that act as the primary adhesive molecule, a group of smaller low molecular mass compounds (LMMCs), and water. The LMMCs group covers a wide range of chemicals (both organic and inorganic), but the main distinguishing feature of this group is that they are hygroscopic, which means they are water absorbing. The exact recipe of this glue is specific to each spider species, and previous research has shown that individual species’ glues stick best in the climate that spiders evolved in—rather than humidity causing them problems, tropical spider webs are in fact most effective in humid conditions.

To understand how spiders achieve this, the researchers used a combination of spectroscopy [1] techniques to observe the arrangement of molecules during adhesion. They took a densely packed layer of web threads collected from the furrow spider and stuck them to one side of a sapphire prism, an ideal surface for its smoothness and transparency to the light rays used for spectroscopy (See Figure 1 for experimental schematic). They then measured the chemical bonds at the point of contact between the glue droplets and the sticking surface over a range of humidity conditions. These measurements allowed them to figure out what happens when these sticky glues get coated in water.

41467_2018_4263_Fig1_HTML — Figure 2. Experimental setup schematic from the manuscript. The white scale bar in c is 0.1 mm. Here “flagelliform” refers to the silk material prior to the glue layer being added, and “BOAS” refers to the classic beads-on-a-string structure that droplets form on threads. SFG stands for “sum frequency generation” spectroscopy, the noninvasive technique used in this research for analyzing the molecular arrangement at the sticking interface between the glue droplets and the sapphire surface.

Singla and her colleagues find that there is very little liquid water at the sticking interface, despite water being one of the three main glue elements. They concluded that the hygroscopic LMMCs are drawing water away from the droplet surface and storing it near the center. The LMMCs make it possible for the sticky glycoproteins to fulfill their role: in high humidity the glue droplet first absorbs nearby water, and then draws that water away from the droplet surface, preventing it from interfering with the sticky molecules’ adhesive chemical bonds. The researchers also conclude that the glue’s efficiency at drawing water to the center of the droplet is controlled by the local humidity and the ratio of the three components. Tweaking this ratio would then make the glue better adapted to different humidities. This suggests that the addition of hygroscopic compounds provides a simple method to tune adhesives to suit specific environments.

This continues to be an exciting time for materials science as scientists unlock the secrets of nature, but perhaps more importantly, Peter Parker can now rest easy with the knowledge that Humidity-Man will be a highly ineffective foe.

1. Broadly, spectroscopy is a study of the interaction between matter and light. There are many different types of spectroscopy, as there are many different ways that light and matter interact, but typically, a beam of light covering a range of the electromagnetic spectrum (hence the “spectro” prefix) is shone onto a substance, and then regathered by a light detector. The brightness of the detected light at each wavelength can then be used to carefully analyze the properties of the substance. Here, the researchers combined infrared spectroscopy and SFG, a non-invasive technique that is specifically tailored to probe molecular arrangements at interfaces, and so is perfectly suited for probing interfacial adhesion.

2018-09-07

From errant to coherent motion

Original paper

Emergence of macroscopic directed motion in populations of motile colloids. By Bricard A., Caussin J-B, Desreumaux N., Dauchot O. & Bartolo D.

Have you ever seen those wide shapes moving in the sky at dawn, made of thousands of starlings, or the swarms of fish swimming in the ocean (see Figure 1)? The ability to organize and move in groups without a leader is called collective motion and has been observed at various spatial scales in the living world, from birds to locusts, cells, and bacteria. Even humans can perform collective motion in some situations, as it has been modeled in crowd movements (for example Mosh pits). Physicists have gazed at this phenomenon over the last couple of decades trying to answer questions such as: How can different organisms exhibit the same behavior? What common features do all these organisms have that allow them to move in such a synchronized way?

The key to the emergence of collective motion is interactions, the ability of individuals to modify their behavior to coordinate their movements with those of their neighbors. The details of these interactions are difficult to model and control in many living or man-made systems, or may even still be unknown. Yet, in today’s paper, Antoine Bricard and colleagues showed how collective motion can arise solely from known physical interactions.

birds_fishes — Figure 1. Examples of collective motion in nature. (a) a flock of starlings (image adapted from howitworksdaily.com), (b) a swarm of fish (image adapted from scielo.br).

One of the first scientists who tackled these questions was Tamas Vicsek in the 90’s. He showed how collective motion can emerge from simple rules using a computer simulation. Although numerous theoretical and numerical studies followed, only few experiments were done. The biggest difficulty in studying collective motion experimentally is gaining control and reproducibility over a living system. Raising thousands of birds in a lab might not be the most convenient way of study, and even simpler biological systems, like bacteria, have problems of their own. Luckily, if you don’t want to deal with a biological system, you can build an artificial one. This is what Antoine Bricard and collaborators did, at Ecole Normale Supérieure de Lyon. To study collective motion, they built an artificial system made of millions of tiny, plastic beads (5 µm diameter) that were able to move freely, interact with their neighbors, and even self-organize as a group.

To put these inert beads in motion, researchers used a phenomenon called Quincke electro-rotation. The idea is to convert electrostatic energy into mechanical rotation. Here, the rotation is triggered by an electric field, $E_0$ , applied to insulating beads, which are immersed in a conductive liquid. Under this field, small fluctuations in the charge distribution tilt the orientation of the bead. Then, the small rotational perturbation is amplified, resulting in a constant rotation and the bead rolling on the bottom of a pool. The researchers refer to these activated beads as “rollers”. All rollers move at the same speed, directly controlled by $E_0$ , yet they don’t move in the same direction but rather randomly. As you can see in Figure 2, the beads move individually in different directions and there is no general directed motion. So how can this disordered system switch to an ordered motion?

Figure quincke — Figure 2. (a) The propulsion mechanism of a bead under an electric field, *$E_0$* , inducing an electric polarization, P. When P is tilted, the bead starts to rotate and moves forward at a constant speed, v. (b) A superposition of 10 images taken at successive timesteps showing the trajectories of 4 rollers activated by the Quincke electro-rotation. (Image adapted from the Antoine Bricard and coworkers’ paper.)

Figure 2. (a) The propulsion mechanism of a bead under an electric field, *$E_0$* , inducing an electric polarization, P. When P is tilted, the bead starts to rotate and moves forward at a constant speed, v. (b) A superposition of 10 images taken at successive timesteps showing the trajectories of 4 rollers activated by the Quincke electro-rotation. (Image adapted from the Antoine Bricard and coworkers’ paper.)

Using Quincke electro-rotation, the exact interactions between the rollers were described by the research team mathematically. Firstly, the beads interact through electrostatics, like two magnets, via an interaction that depends on how far they are from each other. Secondly, the beads interact through hydrodynamics, because when a bead moves in a liquid a flow is generated around it. This generates a pull similar to a swimmer who is feeling the flow produced by another swimmer nearby. What’s more, the theory shows that the combination of these two physical interactions tends to align a group of rollers. When two beads are close enough to each other, they slightly change their course to roll in the same orientation and they all eventually move in the same direction.

To study rollers for millions of particle lengths, the researchers chose to put them in a racetrack-shaped area (Figure 3 a). The rollers spontaneously organized, and a large band made of millions of rollers moved around the track. Of course, rollers had to be close enough in order for interactions to be effective. Figures 3 b-d show how the rollers changed behavior as they get more densely packed. In Figure 3 b, the rollers look like they are wandering in random directions because they are too far from each other to interact, while in Figure 3 d high-density rollers move in the same direction. And as more rollers are added in the same area, the interactions between rollers become more effective. This transition from a disordered state to an ordered state is called a phase transition. In most familiar cases, for example, water-to-ice, phase transitions are driven by temperature. Here density is the control parameter, meaning the research team measured what is the minimum density required for a collective motion to emerge. And being able to couple this observation with a theoretical description of the interactions, the key ingredient underpinning of the system, is what got them further than anyone else at the time.

Figure 3. (a) The racetrack band (watch the movie here) made of millions of self-organized rollers circulating around the area. (b-d) Screenshots of rollers at different densities; (b) at low density, (c) at the front of the band, and (d) at high density of rollers (watch the close view here). (Image adapted from the Antoine Bricard and coworkers’ paper.)

Collective motion seems natural in many living organisms but is still poorly understood by scientists. This paper highlights the importance of interactions between individuals in a group during the process of collective motion. Even though this study is specific and does not account for the mechanisms at work in most biological systems, it was a great achievement toward understanding this phenomenon. Comparing these results with the studies of biologists, ethologists, and mathematicians make me wonder: if a scientist working in his/her lab is like a random walker, then, what beautiful picture will emerge from the work of thousands of scientists interacting with each other to understand collective motion?

2018-06-062018-06-05

Are squid the key to invisibility?

Original paper: Adaptive infrared-reflecting systems inspired by cephalopods

While many today would associate a “cloak of invisibility” with Harry Potter, the idea of a magical item that renders the wearer invisible is not a new one. In Ancient Greek, Hades was gifted a cap of invisibility in order to overthrow the Titans, whereas, in Japanese folklore, Momotar? loots a straw-cloak of invisibility from an ogre, a story which is strangely similar to the English fairytale Jack the Giant-Slayer. Looking to the future in Star Trek, Gene Roddenberry imagined a terrible foe known as the Klingons, a war-driven race that could appear at any moment from behind their cloaking devices – indeed, any modern military would bite your arm off to get hold of this kind of device. Clearly, invisibility is a concept that has captured minds across many cultures, genres, and eras, so it should be no wonder that scientists are working on making it a reality.

As is often the case in materials science, a good starting point for inspiration is to look to biology, after all, life has had billions of years of competition-driven evolution to craft its tools. To that end, Gorodetsky and his team at of the University of California, Irvine, have been attempting to replicate the master of disguise: the cephalopod. From this class of mollusk, squid and octopuses in particular excel at adaptively altering the color, texture, and patterning of their skin to camouflage against a wide variety of oceanic backdrops (see Figure 1). They accomplish this primarily by stretching and contracting pigment-containing skin cells. More importantly to this research, some species of squid have additional skin cells called ‘iridocytes’, which are structured reflective cells that resemble a microscopic comb or folded pleats. These folds reflect light at specific wavelengths that correspond to the fold size. By actively stretching and contracting these cells on-demand, the squid effectively becomes a self-modifying bioelectronic display.

SquidCamouflage (1) — Figure 1: Squid before (left) and after (right) deploying camouflage. Images reproduced from
a video by H. Steenfeldt under the YouTube Creative Commons Attribution license.

Following this technique of stretch-induced camouflage, the authors devise a technique for replicating some squid-like properties in an artificial material. The procedure consists of using electron-beam evaporation[1] to deposit an aluminum layer onto a stretched polymer film held under strain. When they release the strain, the metallically coated material shrinks and buckles to form microscopic wrinkles that are analogous to the structures in squid iridocyte cells. The polymer film of choice is an excellent proton conductor, so when mounted to electrodes, it can be stretched back to the flat state simply by applying a voltage.

When stretched, the aluminum coated film will reflect infrared light like a perfect mirror, whereas when wrinkled, the incoming light is reflected diffusively in multiple directions, like sunlight hitting the moon. To see this effect, the scientists shine infrared light – a heat source – at the material and position an infrared camera at a specific angle so that when flat, it reflects all the incoming radiation toward the camera and appears hot; when relaxed and wrinkled, much less of the light is scattered towards the camera, making the material appears to take on the thermal properties of the background and disappear from view.

Perhaps as a head-nod to their biological inspiration, the team then recreate this material in the likeness of a squid and watch as its infrared silhouette disappears from the camera’s view (Figure 2).

InfraInvisibleSquidShape_Fixed (1) — Figure 2: The flexible squid-shaped material, viewed under an infrared camera. When relaxed (left), very little infrared is reflected towards the camera, and it appears cold. When stretched (right), it reflects most incoming infrared light towards the camera and appears hot. Image edited from Fig. 5 in the manuscript.

The authors conclude that this ready-for-manufacturing material will have immediate applications in heat-regulating technology, and while it is currently limited to the infrared part of the spectrum, they also note that there is no reason why this technique couldn’t be adapted to the optical range.

Squid haven’t solved our desires for a cloak of invisibility just yet, but these mysterious creatures may hold more secrets than we realize. We would be wise to keep an eye on them … if we can.

[1] Electron beam evaporation is the technique of bombarding a solid metal with energetic electrons, causing it to evaporate. This metal vapor then cools and condenses uniformly on all nearby surfaces, forming a uniform metallic coating.

2018-05-232018-05-21

Elastogranularity and how soil may shape the roots of plants

Original paper: Elastogranular Mechanics: Buckling, Jamming, and Structure Formation

How an elastic beam deforms under load has been a question for as long as there have been engineers to ask it. In some cases, the force on a beam is approximated as a single point. For example, if a diving board is large enough, a diver at the end can be treated as a point mass on the beam. Another common approximation is to consider the force to be a continuous pressure along its length. Treating wind that bends a tree branch as a continuous pressure along the branch’s length is much simpler than adding up the force from every molecule of air on the branch. However, consider the case of a root growing into a granular material like soil. As the root burrows through the soil it will bend due to varying point-like forces along its length. The result is a branching and twisting root system that tries to grow along the path of least resistance. An example of the diversity in plant root morphologies is shown in Figure 1 and gives a sense of how complicated and interesting the physics behind this growth can be.

Figure 1. An example of the complex and diverse morphology of several types of plants which all live in the same ecosystem [1]

With this in mind, David J. Schunter Jr. et al. from the Holmes group at Boston University have developed a beautiful experiment to study what they call “elastogranular” phenomena. In their experiment, an elastic beam is inserted into a box which is filled at a particular density with uniform beads. An image of a typical experiment is shown in Figure 2. Once the beam reaches the end of the box it will not be able to penetrate any further, and trying to push more of the beam into the box will cause a compression along the beam’s length. This resembles a classic experiment where a beam is compressed in the same manner, but in the absence of beads. Compressing the beam against the end of the box becomes increasingly difficult until eventually the beam “pops” into one large buckle. In this simpler case, the beam was free to buckle with no restrictions. Introducing beads to the system reinforces the beam non-uniformly and constrains the shapes it can take on when it buckles. This complicates the buckling event and leads to interesting new behaviors.

Screenshot 2018-05-11 at 6.13.31 PM.png — *Figure 2*. An elastic beam is inserted into a box of length $L_{0}$ and width $2W_{0}$ filled with beads at an initial packing fraction of $\phi_{0} = 0.89$ . After a length of beam is inserted equal to $L_{0}$ , inserting additional length $\Delta$ results in buckling. In this experiment the beam takes on two buckles with wavelength $\lambda$ , and amplitudes of $A_{0}$ and $A_{1}$ respectively.

*Figure 2*. An elastic beam is inserted into a box of length $L_{0}$ and width $2W_{0}$ filled with beads at an initial packing fraction of $\phi_{0} = 0.89$ . After a length of beam is inserted equal to $L_{0}$ , inserting additional length $\Delta$ results in buckling. In this experiment the beam takes on two buckles with wavelength $\lambda$ , and amplitudes of $A_{0}$ and $A_{1}$ respectively.

In the experiment performed by the Holmes group, a beam is compressed against the end of the box until the beam buckles. If the packing fraction $\phi_{0}$ (the fraction of space within the box that is covered in beads) is low, it buckles much like one would expect in the absence of beads—one large buckle, as in Figure 3i. If $\phi_{0}$ is higher at the beginning of the experiment, like in Figures 3ii and 3iii, the buckling behavior becomes more complicated. The beam will form one large buckle as before, and as the buckle grows it will take up more area on one side of the box. This forces the beads to reorganize themselves, and the beads on the compressed side of the box become very tightly packed. At this point, they are in a hexagonal arrangement, and they are said to have crystallized [2]. As the beads in one side crystalize, that side becomes stiffer and suppresses further growth of the amplitude of the first buckle, $A_{0}$ . In order to accommodate the extra length being inserted, $\Delta$ , an additional buckle forms. The difference in buckling behavior for three values of $\phi_{0}$ are shown in Figure 3. [3]

**Figure 3.** Shape profiles of the inserted rod for various packing fractions ( $\phi_{0}$ ) for the same normalized inserted length $\Delta/L_{0}$ . i) At low $\phi_{0}$ the beam forms one large buckle. ii) As $\phi_{0}$ increases, the amplitude of the single buckle is suppressed, leading to a second buckle forming on the other side. iii) At even higher $\phi_{0}$ , the buckles rotate and grow toward each other.

**Figure 3.** Shape profiles of the inserted rod for various packing fractions ( $\phi_{0}$ ) for the same normalized inserted length $\Delta/L_{0}$ . i) At low $\phi_{0}$ the beam forms one large buckle. ii) As $\phi_{0}$ increases, the amplitude of the single buckle is suppressed, leading to a second buckle forming on the other side. iii) At even higher $\phi_{0}$ , the buckles rotate and grow toward each other.

Figures 3 shows that not only are the number and amplitude of buckles significantly affected by the beads that surround the beam, but the orientations of the buckles are changed as well. When the experiment begins at a high $\phi_{0}$ , the beam finds both sides of the box to be stiff and hard to penetrate. The initial buckle does not grow very much before the second buckle forms, and at high enough $\phi_{0}$ both buckles occur nearly simultaneously, forming a twin buckle. Figure 4 shows two systems with different $\phi_{0}$ forming twin buckles. In the top sequence where $\phi_{0}$ is lower, the buckles maintain a constant distance between each other as they grow since there are plenty of uncrystallized areas (light blue circles) ahead of the buckles into which they can grow. The lower sequence shows that, at higher $\phi_{0}$ , the majority of uncrystallized beads are found in the wake of a buckle so the buckles instead grow into these regions, as demonstrated by the red lines.

*Figure 5*. Twin buckles increase in amplitude as $\Delta$ increases (left to right) growing into less-dense, uncrystallized regions (light blue circles). For lower $\phi_{0}$ (top sequence), uncrystallized beads in front of the buckles can be pushed aside, crystallizing beads away from the buckles (dark blue and yellow circles). At higher $\phi_{0}$ (lower sequence), the uncrystallized sections occur behind the buckles, causing the two buckles to grow closer together which is shown by the red lines.

*Figure 5*. Twin buckles increase in amplitude as $\Delta$ increases (left to right) growing into less-dense, uncrystallized regions (light blue circles). For lower $\phi_{0}$ (top sequence), uncrystallized beads in front of the buckles can be pushed aside, crystallizing beads away from the buckles (dark blue and yellow circles). At higher $\phi_{0}$ (lower sequence), the uncrystallized sections occur behind the buckles, causing the two buckles to grow closer together which is shown by the red lines.

This system bears a striking resemblance to that of plant roots growing into the soil and could be useful in understanding how environmental pressures cause plant root systems to evolve. For example, cacti need to absorb as much water as they can from their environment. One way of accomplishing this is to increase the surface area of the root system by growing wide and close to the surface, rather than deep, in order to collect water from a larger area. By developing thin roots that buckle before they can deeply penetrate the soil, many cacti are able to produce the shallow, wide-reaching roots system they need to find water.

David J. Schunter Jr. and coworkers have shown that combining two well-understood problems—buckling of a beam and reorganization of beads—can lead to unique and interesting bending dynamics. By confining a beam to a box of beads, the buckling of the beam becomes strongly influenced by the packing fraction and reorientation of the beads. This particular system shows a strong resemblance to plant root growth, but also be informative for synthetic applications involving the insertion of flexible filaments into deformable materials.

[1] Michigan Natural Shore Partnership, http://www.mishorelinepartnership.org/plants-for-inland-lakes.html

[2] When spheres crystallize in two dimensions, the hexagonal lattice is the closest possible packing with an area fraction of $\phi = 0.9069$ . Interestingly, Figure 3iii shows a packing fraction of 0.91, which is higher than this maximum value. This is because the beads are able to pop out of the plane at very high compressions, which can lead to a calculated packing fraction larger than that of the hexagonal lattice. For more information on hexagonal packing, see Wikipedia.

[3] For more information about the specifics of how the deformation of the beam is quantified, a summary of the analysis is available here.