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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 $latex L$ that is 10% longer than its original length $latex L_{0}$ $latex (L/L_{0} = 1.1)$ until it is twisted by $latex \Phi a \approx 1$, where $latex \Phi a$ is the degree of twist multiplied by the fiber’s width divided by its length. Above this value of $latex \Phi a$, the simulated fiber twists into the braided helix structure seen in Figure 2 (blue dots). Likewise, when $latex L/L_{0} = 1.2$, the fiber remains straight until it has a much higher twist, $latex \Phi a \approx 1.5$, 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 $latex L/L_{0}$, twisted by $latex \Phi$ normalized by the fiber dimensions $latex a$. 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.

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Huddling penguins make waves in the Antarctic winter

Original article: Coordinated Movements Prevent Jamming in an Emperor Penguin Huddle

Standing in the center of a crowded bus on your way to class, you might think: “why don’t these people just move? It’s hot and I can’t breathe!” Male penguins huddling to keep their eggs warm in the Antarctic winter have the opposite problem – no penguin wants to be at the cold edge of the huddle. A penguin in the huddle wants to stay in the warm center, since the outside temperature can reach -45 oC. However, penguins on the edge of the huddle are trying to push through the crowd to reach the center. Through the independent motion of each penguin, the huddle stays tight enough for the center to remain warm but loose enough to keep moving.

In today’s study, Zitterbart and colleagues investigate how huddling Emperor penguins can keep moving, as in this video.  They find that individuals take small, coordinated steps that reorganize the huddle on a time scale of hours.

Zitterbard and colleagues film a 2000-penguin colony (shown in Figure 1a) for 4 hours and track the positions of the penguins, with an x-coordinate corresponding to horizontal position on the camera image and  y-coordinate corresponding to the vertical position on the camera image. When huddling, the penguins all face in the same direction and are arranged roughly in a hexagonal grid. Every 30 to 60 seconds, the penguins take small steps, 5-10 cm long. Figure 1b shows the track of one penguin, with a point every 1.3 seconds. There are clusters of points where the penguin is standing still (with no significant change in position), and then a straight line when the penguin takes a step.

Since penguins at one spot in the huddle don’t know that another part of the huddle is moving, they don’t all step at once. Instead, there is a wave of moving penguins that moves through the huddle at a speed of 12 cm/s, like a sound wave traveling through a material. Figure 1c shows the tracks of several penguins at the same y-position and different x-positions in the huddle. Their horizontal motion is correlated – the penguin at the top track moves first, and then the motion propagates to the neighboring penguins as a wave. 

Figure 1. a. A photograph of huddling penguins with x- and y- coordinate axes. b. A track of a single penguin with points every 1.3 seconds. Clusters of points mean the penguin isn’t moving, and a straight line means the penguin took a step. c. Horizontal motion of several penguins. These penguins are at the same vertical position in the huddle but different horizontal positions. The slope represents the 12 cm/s motion of the wave of moving penguins.

An unusual aspect of this study is that the results section is short – the authors only report the traveling wave of penguins through the huddle. However, they then move to an explanation of penguin motion using very interesting  analogies to granular materials (such as sand or coffee beans). 

There are three effects of the small steps:

  1. They allow the penguins to reach the best density for warmth.
  2. They move the entire huddle forward, and merge small huddles into big ones.
  3. They reorganize the huddle, allowing penguins to leave the huddle at the front and join it at the back.

The combination of small penguin movements and organized huddling is similar to the way colloids [1] solidify when the particles in the colloid attract one another. Penguins huddle when they are “attracted” to each other by cold temperatures; colloids are attracted by electrostatic or intermolecular van der Waals forces. Thinking of a group of organisms as a fluid, such as smoothly flowing fish schools and turbulent bacteria, is a well known method for understanding their behavior. In contrast, the small steps in a dense group of penguins is reminiscent of a material going from a fluid to a solid state. The waves in the huddle are similar to waves in other groups of animals, like human crowds rushing to escape a room. Luckily, the penguin waves do not result in injury. (Usually.)

Through small, careful steps, penguins are able to create a solid cluster of warmth in the Antarctic winter. If we took a hint from the penguins and were more careful about our motion when on a crowded subway, maybe our commutes would be much more pleasant experiences. Of course, the huddling penguins are not bounded by the walls of a bus – how they would move if they didn’t have an open boundary is still a mystery!

[1] Mixtures of small particles dispersed throughout another substance, such as the fat suspended in a water solution to form milk.

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Baromorphs: Shape Shifting by Inflating

Original paper: Bio-inspired pneumatic shape-morphing elastomers

Conventional robots typically move by moving rigid pieces relative to one another — think of a robotic hand where rigid bars rotate at joints. In other words, conventional robots have a small number of “degrees of freedom” — the angle of bending of the joint of a robot hand would be one degree of freedom, for example.  Soft robots, on the other hand, have many degrees of freedom: they can bend and deform into lots of different configurations. Because of this, they often display continuum-like behaviour, similar to what is seen in the movement of natural organisms such as worms and octopuses. These robots offer great promise in many fields, from soft instruments for minimally invasive surgery to shape changing airfoils for increased flight control. One of the particularly difficult challenges in soft robotics is to design systems that are flat at rest but can rapidly transform to an arbitrary three dimensional shape when activated. Recently, Emmanuel Siéfert and co-workers developed baromorphs— thin, flexible sheets which can be air inflated (“pneumatically activated”) into a pre-programmed target shape.

The researchers were inspired by what they saw in nature, where there are many examples of thin, sheet-like objects, such as flower petals, which grow into intricate curved shapes.  They do this by growing faster in some areas than others – this results in the petal curving in three dimensions. When biological growth is not an option, as in man made materials, the problem is difficult since thin, flexible sheets can only change shape by bending; they cannot stretch, as this is energetically unfavourable [1]. This places a strong restriction on the shapes that they can be morphed into. Researchers have previously approached this problem by swelling highly absorbent gels in a hot bath water; specifically, by controlling where the swelling occurs, they mimicked non-uniform growth seen in nature. Whilst promising, the time taken for the shape to change was limited by how quickly water can move from high to low concentrations—this is typically very slow—and, furthermore, the resulting structures were typically too soft to sustain their own weight. Pneumatically activated structures, on the other hand, depend only on the air flowing through them, and so can be made into a much wider variety of shapes.

Figure 1. (a) Mould used for producing baromorphs with radial air channels. (Scale bar: 1cm) (b) Inflating the baromorph (applying pressure to the channel walls) causes expansion in the transverse direction (indicated by blue arrows). (Figure adapted from original article).

The researchers produced pneumatically activated baromorphs by setting two identical thin, rubber pieces in 3D printed moulds containing cavities for air to flow (Figure 1a) and then sticking the two pieces together. The process leaves an embedded network of channels through which air can flow (Figure 1b). Inflating the channels applies pressure to the channel walls, inducing a stretch along the width of the channels but not along their length (blue arrows in Figure 1b). Depending on the arrangement of the tubes, inflation can create excess length in the structure which is incompatible with a flat shape, forcing the structure to buckle out of plane. This creation of excess length is analogous to the inhomogeneous growth that leads flower petals to curve.
The effect is demonstrated by Siéfert et al. with an initially flat, circular baromorph containing circular channels. For this geometry, the excess length, created by inflation, stretches  a channel of radius of radius $latex R_1$ to a radius $latex R_2>R_1$ (Figure 2a). This causes the baromorph to buckle out of plane and form a cone, whose apex, $latex \alpha$, satisfies $latex cos(\alpha)=R_1/R_2$ (Figure 2b). Moreover, by solving the equations of linear elasticity, the angle can be predicted as a function of the applied pressure.

Figure 2. (a) Schematic diagram of inflation of a baromorph with constant radius channels. Inflating this baromorph forces a circular channel with radius $latex R_1$ to stretch to radius $latex R_2$. Buckling into a cone shape relaxes this excess length. (b) The conical baromorph used as a demonstration by Siéfert et al. (Scale bar: 1cm)

Whilst inflating into a shape is not new, it has so far been limited to  movements which deform every part of the shape in the same way, e.g. bending, twisting, and expansion. And, since baromorphs are activated pneumatically, the time taken to transform from the two dimensional (flat) configuration to the three dimensional one is limited only by the air flow through the channels. In other words, they can change state very quickly; the researchers demonstrated this by oscillating a conical baromorph at a frequency of 2 Hz (see video). Further, the structures aren’t size limited; they can easily be made to support their own weight by simply increasing the inflation pressure. 

The key advantage of baromorphs over other pneumatically activated shape-morphers is their ability to take a wide variety of shapes obtained by simply tailoring the orientation and size of air channels in the network. For instance, baromorphs can be made into spherical caps, saddles, and helicoids (Figure 3a). This leads to the question: given a three dimensional target shape, how should the channel network be chosen? The team have derived a simulation which predicts which embedded channel structure should be chosen for a given target shape. The accuracy of this simulation is demonstrated by producing a baromorph that inflates into a face (Figure 3b).

Overall, baromorphs are an exciting prospect for future applications: they’re easy to produce; they can take virtually any pre-programmed shape [2]; and they can be inflated very quickly. The authors hope their work will allow other researchers to use shape-shifting materials in flow-optimization — tailoring the shape of air channels to maximise flow — as well as minimally invasive surgery.

Figure 3. (a) examples of inflated baromorph shapes: saddle, helicoid and spherical Cap. (b) Stepwise inflation of a face-shaped baromorph.

[1] The energy penalty associated with stretching an elastic membrane scales with its thickness, whilst the penalty associated with bending scales with its thickness cubed. As a result, sufficiently thin sheets experience a much larger penalty when stretching compared to bending.^

[2] Infinitely thin baromorphs can, in theory, take any shape. In practice, their finite thickness means they struggle to reproduce regions where the shape changes sharply, such as around the lips in Figure 3b.^

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PARNET 2019: Granular and Particulate Networks

A granular material, such as sand, coffee beans, or balls in ball pit, is a collection of particles that interact with each other and dissipate energy. These materials can act like solids, flow like liquids, or suddenly transition between the two phases – for example, in a landslide, the soil stops holding its shape and flows. The Granular and Particulate Networks Workshop, PARNET19, brought together the physicists, engineers, and mathematicians who study these materials in a series of lectures and discussions.

Figure 1. Examples of granular materials: a. sand, b. coffee beans and c. a ball pit. 

PARNET19 took place at the Max Planck Institute in Dresden, Germany on July 8-10, 2019. I attended to represent Softbites at the science communication panel and to present my research on fly larvae as an active granular material.

The focus of the workshop was exploring the networks formed by the forces in granular materials. When granular materials are stretched or squeezed, they form networks of high forces known as force chains. These networks can be visualized with photoelastic disks, as described by this previous Softbites post.  In a series of 30 minute to 1 hour long scientific talks at PARNET19, the experimentalists who study granular materials and mathematicians who study topological networks discussed how network math can be applied to the force chains found in granular materials. Unusually, talks were followed by 30-minute discussion sessions in which the previous speakers answered questions and posed some of their own.

Modeling granular materials is difficult because they are made up of many individual particles. Simulating the interactions of all of the particles takes a very long time, even with a powerful computer: imagine trying to predict the motion of each sand grain on a beach! The other traditional way to model a granular material is with a continuum model — considering the material as a smooth (continuous) mass, instead of keeping track of individual particles. This works for materials like fluids or solids because the individual molecules that make them up are so small that their individual interactions don’t need to be understood. However, the relevant particles in a granular material are much bigger, relative to the size of the material as a whole, than molecules, which makes the interactions between the particles important. In a granular material, the critical interactions between the particles can result in sudden transitions such as landslides.

The approach taken by the PARNET workshop was to model the part of granular materials that will cause the entire material to change if it moves — the force chains through the grains. The goal of the workshop was to apply existing mathematical theories used to model networks, such as the connection of roads on a map, to understanding the connections of force chains in granular materials. For example, understanding when a force chain in the rocks making up a cliff is likely to fail can inform workers near the cliff about impending danger and allow them to evacuate before a landslide occurs.

Figure 2. Connecting granular materials experiments, such as the force chains pictured in (a), with pure network math, such as the Konigsberg bridge problem pictured in (b), was the main theme of the workshop. This problem gets challenging if we consider real, 3D materials

The scientific communication panel I was part of discussed a variety of topics, such as publishing journal articles in high or low impact factor journals, making scientific journals open access, and writing for a broad audience. A result of the discussion, we made the Softbites style guide publicly available – everyone wanted to read how we write and edit our posts! 

Group photo

For me, the main takeaway of the workshop was that the network view of granular materials is a promising one to predict catastrophic events. Understanding what causes a force chain to break can explain why some arrangements of granular materials are stable for a long time while others come crashing down with no obvious warning. However, connecting the complex and chaotic real-life granular materials in 3D to the purely theoretical math behind topological networks will prove challenging. Mathematical models of networks can be very abstract, and these theories need to be connected to physics in the real world. As with any theory, it is important to verify predictions with real-life experiments, but the force chains inside granular materials are difficult to measure.

Overall, this was one of the best conferences I’ve attended as a graduate student. The format of longer discussion sessions was very effective, as it allowed more time for elaborating on each speaker’s points than the traditional 5 minute long Q&A sessions. The PARNET workshop was a useful introduction to a new (to me) way of thinking about granular materials, one which I am implementing in my own research. If complex systems, such as granular materials, can be modeled by a simple set of topological equations, they will be much easier to understand and predict in future studies.

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When you pull on a drop, how does it pull back?

Original paper: How drops start sliding over solid surfaces 

Physicists like to ignore things. In some cases, we may neglect gravity or assume that the temperature is zero degrees Kelvin — colder than any known substance in the universe. And friction is almost comically absent in most models, despite the fact that a world without it would be utterly uninhabitable (this is nicely illustrated in cartoon form here: https://xkcd.com/669/). 

Sometimes, these simplifications are justified. If you’ve ever seen your hair stand on end after taking off a sweater, you know gravity isn’t always the dominant force. And if you’ve ever slipped on ice or slid a puck across an air hockey table, you know that there are situations where friction doesn’t do much.

But there’s another reason we might leave out something like friction: it’s really complicated. Even today, friction between solid objects remains an active topic of research,

with all sorts of interesting topics arising: friction’s role in earthquakes, for example, or how it can encode a kind of memory.

All this talk of friction between solids led Nan Gao and collaborators to ask whether there might be a friction-like effect for liquid-solid interfaces. 

One of the characteristics of friction between two solid objects is that it decreases once the objects start sliding. You may have noticed this when pushing a heavy box: it’s hard to get the box moving, but once it budges it’s easier to continue pushing. This idea is shown in Figure 1 as a plot of force applied to an object versus the amount of time that force is applied. The force increases linearly before the object begins to move, then drops suddenly to a constant value after the object starts sliding. 

Figure 1. Force applied to an object with respect to the amount of time that force is applied for a typical solid object sitting on a solid surface. The force increases linearly before the object begins to move, then drops suddenly to a constant value after the object starts sliding. (Figure adapted from original article)

In this week’s article, Gao and colleagues devise a clever system for measuring the same type of force for a drop of liquid sitting on a solid surface. 

A drop sits on a platform that can be translated in one direction. Inserted in the top of the drop is a thin rod, called a capillary, which remains stationary even as the platform moves. Just as water will stick to your straw as you pull the straw out of your drink, the drop likes to be in contact with the capillary. So rather than simply moving along with the translating platform, the drop pulls on the capillary, causing it to bend. In turn, the capillary pulls back on the drop until the capillary exerts a force on the drop that overcomes the friction between the drop and the platform; the drop stops moving with the platform and remains stuck to the capillary.

As shown in Figure 2, the researchers tracked the position of a laser reflected off the capillary to measure how much the capillary bent. They were then able to back out the so-called “adhesion force,” which is an indicator of the force needed to make the drop move relative to the surface it’s sitting on. 

Figure 2. Cartoon of the setup used. The force due to friction between the drop and the platform, which points in the direction the platform is moving, is represented with a red arrow and labeled “F”. Here, the capillary’s bend is measured by detecting the reflection of a laser (shown in red) off of the capillary. The orange arrows show the length and width of the drop.

Gao and colleagues found that as the platform moves, the adhesion force increases more or less linearly before dropping back to a roughly constant value (see Figure 3). Sound familiar? Just compare with Figure 1 and you’ll see that this behavior strongly mimics friction between two solid surfaces.

Figure 3. Adhesion force of a drop of water on a moving surface of titanium dioxide as a function of time the surface has been moving. Measured values (from the bending of the capillary) are shown as blue circles and calculated values (from an equation for the adhesion force that depends on the shape of the drop) are shown as red squares. In both cases, the force increases roughly linearly for several seconds, reaching a maximum force of 100 uN before dropping to a constant force around 40 uN. (Figure adapted from original article)

This wasn’t just a lucky choice of liquids and solids — they found a similar effect for several fluids on surfaces ranging from titanium dioxide to silicone nanofilaments to goose feathers. The appearance of this effect in such a wide variety of systems suggests that this may be a general phenomenon.

Moreover, their measured values from the bend of the capillary match fairly well with values calculated independently using geometric parameters of their drops like the drop width, drop length, and angles the drop makes with the surface.

Even in systems as simple as a drop of water sitting on a surface, there is an incredible amount of physical richness, which means lots of science still to be explored. And it’s not just how drops stick — how drops land on a surface and how they evaporate both raise unexpectedly subtle and complex questions (see previous posts here and here). What area of drop-related research might physicists slide into next? 

For an even shorter summary of this article, see  https://phys.org/news/2017-11-droplet-friction-similar-solid.html

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Synthetic blood to power vascularized robots

New soft robots can flex their muscles with synthetic “robot blood” and multipurpose circulatory organs.

Original paper: Aubin, C. A. et al. Electrolytic vascular systems for energy-dense robots. Nature 571, 51–57 (2019)

The circulatory or vascular system of animals is a complex organ that performs multiple functions simultaneously. Take the human circulatory system for example: it transports oxygen and nutrients throughout the body, regulates temperature, helps in fighting diseases, etc. However, robots don’t usually function the same way. Despite the vast improvements in robot design, they still cannot do much multi-tasking. Part of the problem is that robots are typically built from rigid parts that only do one thing. A battery usually does not play any other role aside from providing energy, and moving parts are typically controlled by independent actuators.  These single-purpose components (such as batteries) are typically less efficient than their biologic counterparts, and add to the weight of the robots (limiting their performance, maneuverability, speed, and autonomy).

In order to create multi-functional robots, we can take inspiration from biology and build them out of multi-purpose components. A research team led by Robert F. Shepherd from Cornell University (NY, USA) has found a way around this problem by integrating a multifunctional circulatory system into untethered, autonomous soft robots. In a recent issue of Nature, they present an aquatic soft robot with a synthetic circulatory system which provides chemical energy. The synthetic blood has zinc and iodide ions that make it electrically conducting (like an electrolytic blood), and powers an artificial heart (a pump that circulates “blood” throughout the robot body). Rather than using traditionally rigid materials to build the robot, the circulatory system is encased in a soft, flexible body made out of stretchable silicone. The circulating “blood” can deform the flexible body of the robot when pumped through the vascularized fins, like electrolytic “robot blood” flexing a muscle, moving the fins of the fish and propelling the robot forward  (Figure 1, Video 1). By bringing materials and robot design closer to complex biological systems, their multifunctional synthetic vascular system can combine hydraulic force transmission, mechanical actuation, and energy storage (killing not two but three birds with one stone).

Figure 1. Lionfish-inspired robot powered by an electrolytic vascular system. a) Schematic shows synthetic blood in the tail fin (red) and in the dorsal and pectoral fins (yellow). b) The synthetic blood circulates through the robot body and actuates the tail fin by expanding and contracting the silicone parts at each side (adapted from Aubin et al.)

Although flow batteries are less energy dense than their lithium ion equivalents, their integration in soft robotic platforms has significant advantages: the electrolyte can fill up most of the volume of the robot and act as the hydraulic system (without the need of additional space), and the surface area of the flow batteries inside the soft robot can be maximized for an increased energy capacity (hence the large area of dorsal fins). With this approach, the autonomous robot can swim upstream for long operation times (up to 36 hours). 

Video 1. Autonomous lionfish-inspired robot swimming.

The proposed bio-inspired approach reduces the gap between biological complex systems and synthetic, traditionally bulky robotic platforms. According to the authors, “this concept can be generalized to other machines and robots”, which opens a wide design space for multifunctional soft machines, from materials design to actuation and control. Such improvements in energy storage and performance could advance the development of soft robots for search-and-rescue operations, marine exploration, inspection of underwater pipelines, and coral reef health monitoring (all applications where autonomy and safety are critical). Although still in its infancy, “robot blood” could one day power, actuate, and control untethered soft robots that can safely and autonomously interact with humans in delicate environments. And just like in science fiction, robots with synthetic organs and circulatory systems could one day live among us.

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Soft engines: Leidenfrost effect in elastic solids

Original article: Coupling the Leidenfrost effect and elastic deformations to power sustained bouncing

Have you ever wondered why a water droplet rolls around on a hot pan instead of evaporating instantly? The part of the droplet touching the pan does indeed evaporate. The resulting vapor forms a thin insulating layer that enables the drop to hover over the pan for seconds, even minutes. This is known as the Leidenfrost effect. Because they also produce vapor when heated, sublimable solids (solids that skip over the liquid phase and directly produce vapor) also exhibit the Leidenfrost effect. This effect has been studied extensively for both liquids and sublimable solids.

In their letter in Nature (2017), Waitukaitis et al. studied the Leidenfrost effect for the first time in soft elastic solids. They used hydrogels, polymer networks that can absorb water. Because they can contain up to 99% water by volume, hydrogels are deformable and bendy. Contact lenses, for example, are hydrogels. The large water content provides vapor, making hydrogels ideal soft candidates for the Leidenfrost effect.

Figure 1. Bounce height vs. number of bounces (nb) for a gel (A) dropped on the cold plate, (B) dropped from h>h0 on the hot plate, and (C) dropped from h<h0 on a hot plate. The gel on the cold plate successively bounced to lower heights before coming to rest, but on the hot plate it achieved the same steady bounce height (h0) irrespective of the initial dropping height (Figure adapted from original article).

In their experiment, the researchers dropped a hydrogel sphere ~1.5 cm in diameter on a hot plate and recorded its activity. As seen in Figure 1B, the sphere eventually bounced at a constant height h0~3.5 cm around 1000 times. The sphere finally came to a stop when it cracked due to heat and water loss. A sphere dropped from a lower height also eventually bounced at the height h0 (see Figure 1C). This was surprising when compared to the behavior of an identical gel bouncing on a cold plate. As seen in Figure 1A, the gel on the cold plate successively bounced at lower heights and eventually stopped, just like a tennis ball would. Existence of a constant bounce height on a hot plate suggested that the hydrogel gained kinetic energy during its collisions with the hot surface.

Figure 2. Red: Experimental data for energy gained on a hot plate vs. initial drop height. Blue: Experimental data for energy lost on a cold plate vs. initial drop height. The two lines cross at ~3.5 cm, the constant bounce height (Figure adapted from original article).

The authors repeated this experiment for different initial drop heights to obtain the kinetic energy gained as a function of the drop height (see Figure 2). Comparing the kinetic energy gained on the hot plate to the energy lost on the cold plate, the researchers found that there was a sweet spot where the energy lost and gained cancel each other out. This sweet spot was exactly at h0! Thus, once the gel reached the bounce height h0, it kept bouncing at the same height until it lost its elasticity due to cracking. 

Figure 3. Red: Model prediction for energy gained on a hot plate vs. initial drop height.
Blue: Energy lost on a cold plate vs. initial drop height due to inelastic collision. The prediction as well as the crossover point show good agreement with the experimental data. (Figure adapted from original article).

To understand the mechanism of bouncing, the researchers looked at the impact at a high resolution. During impact, a gap opened up between the hydrogel and the plate, and the thickness of this gap oscillated between 0 and 100 ?m several times. The authors proposed the following physical process to explain the kinetic energy gain of the hydrogel. When the gel touches the hot plate, a small amount of water evaporates. The vapor deforms the gel bottom and gets trapped in a pocket between the gel and the plate. As the pressure builds up inside the pocket, the vapor eventually escapes. The gel bottom then elastically recoils towards the plate. This gap oscillation repeats itself several times. According to the authors, work is done on the hydrogel during each such oscillation. The gel therefore gains a small amount of energy from the hot plate, effectively acting as a tiny engine. The authors also numerically modeled the gel as a vertical chain of masses connected with springs between them and considered the forces acting on each mass. Despite being much simpler than the real system, the model’s predictions showed good agreement with the experimental results (see Figure 3).

In conclusion, the researchers studied the Leidenfrost effect in elastic hydrogels. Even though the experimental details were similar for the regular (liquids and sublimable solids) and the elastic (hydrogels) Leidenfrost effects, the mechanisms for the two phenomena are different. In the regular Leidenfrost effect, there is no transfer of energy between the hot plate and a liquid drop. However, for a soft hydrogel, the elastic oscillations of the gel bottom convert some of the heat energy from the plate into the elastic (and in turn kinetic) energy of the gel, enabling it to bounce at a steady height. According to the authors, the gel is “effectively a soft engine that harvests energy from the hot surface,” with water vapor acting as a fuel. This research may have exciting implications for robotics. Most conventional robots are made of hard materials, but it is desirable to have soft and bendy robots for performing human-like functions. This work with elastic hydrogels that can be energized with heat could lead to self-actuating soft robots. 

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The Future of Shape-Memory Polymers: Just Add Water and Glycerol

Original paper: Magnetically Addressable Shape-Memory and Stiffening in a Composite Elastomer

Video 1. Heat-shrink tubing demonstration.

Have you ever used heat-shrink tubing at home to seal an exposed wire? As shown in Video 1, you would place the tubing around your wire, apply heat, and voilà! The tubing shrinks and tightly wraps itself onto the exposed wire, and you don’t have to worry about an electric shock anymore. This type of material that changes its shape upon increased temperature is called a shape-memory polymer. Since its commercial development in 1962, scientists have found this type of material so useful that its popularity rose, especially in the biomedical and aerospace fields. However, it comes with a few drawbacks: applying the desired temperature uniformly can be tricky and the shape change induced by the heat can be quite slow. In addition, changing the temperature isn’t ideal for biological applications where the environment surrounding the material is sensitive to heat, such as in tissues and living cells. In today’s post, I’ll introduce you to a different type of shape-memory material that “remembers” its temporary shape when subjected to a magnetic field, instead of heat.

Video 2. Demonstration of the material developed by the authors.

Paolo Testa and coworkers from the Paul Scherrer Institute and ETH Zurich developed a shape-memory polymer composite that can preserve a new shape when a magnetic field is present. As you can see in Video 2, the initially flexible material sitting on the center stage is manually twisted with a tweezer and held by force. When the magnetic ring is raised around the stage and held up so that the material can “feel” the magnetic field, the material “freezes” in its twisted shape, even when the tweezer is removed. After a certain time, the magnetic ring is removed and the material regains its original shape within one second, dramatically faster than the time it took for a heat-shrink tubing in Video 1 to change its shape. The material—at least a part of it—that looks like black rubber is a flexible polymer that is the main ingredient of the Silly Putty, called poly(dimethylsiloxane) (PDMS). However, PDMS is normally transparent in color, and PDMS itself isn’t a shape-memory polymer. So what makes it black and capable of holding the twist when the magnetic field is present?

The answer is in iron particles. However, iron particles alone cannot perform well enough. Shape-memory materials that were previously developed had iron particles directly embedded in the polymer but didn’t have such a high sensitivity to magnetic fields. What makes the material in this paper so unique is the liquid surrounding the particles. The iron particles are dispersed in a water and glycerol mixture, making the fluid six times more viscous and stiff when subjected to the magnetic field. This type of fluid, called a magneto-rheological fluid, is then injected into the PDMS polymer, making the material sensitive to the presence of a magnetic field.

3D visualization of the material and 2D slices of that visualization with and without magnetic field
Figure 1. (a) 3D visualization of the PDMS injected with magneto-rheological fluid. (b)(c) 2D slices of a droplet surrounded by PDMS with the magnetic field (b) off and (c) on. (Adapted from the original paper.)

Figure 1 shows the 3D structure of the developed material, as well as a 2D schematic of a magneto-rheological fluid droplet with and without the magnetic field. When the fluid is injected into the polymer, the polymer encases the fluid and a composite is formed, which is shown in Figure 1a. In the absence of the magnetic field, shown in Figure 1b, the iron particles are dispersed and mobile inside the fluid droplet. However, when the magnetic field is turned on, shown in Figure 1c, the particles reorganize and align along the direction of the magnetic field, and, in turn, the droplet stiffens. The alignment of the iron particles and the resulting stiffening of the fluid, induced by the presence of a magnetic field, are the reasons why the polymer composite can hold its new shape (as in Video 2). When the magnetic field is removed, the particles regain their mobility and the fluid droplets soften, which lets the polymer return to its original shape.

On the left, a graph of stiffness as a function of the fluid volume fraction. In the middle, a graph of connectivity as a function of the fluid volume fraction. On the right, two 3D construction of material's internal structure, one representing 10% fluid and the other representing 40% fluid.
Figure 2. (a) The volume fraction (ratio) of magneto-rheological fluid over PDMS (?) versus the material stiffness. The blue and red lines indicate the magnetic field being on and off, respectively. (b) The volume fraction (ratio) of magneto-rheological fluid over PDMS (?) versus the connectivity between the fluid droplets. (c) 3D reconstructions of the material’s internal structure when the fluid occupies 10% (top) and 40% (bottom) of the total volume. PDMS and the fluid are represented in grey and red, respectively. (Adapted from the original paper.)

By controlling the ratio between the magneto-rheological fluid and PDMS (?), the authors tried to understand the relationship between the stiffness and structure of the material and the said ratio. When the percentage of the fluid increases, as shown in Figure 2a, the overall stiffness of the material measured in the presence of the magnetic field increases as well. This increase is enhanced when fluid occupies more than 20% in volume, as highlighted in yellow in Figure 2a. Compared to a factor of two increase going from 10% to 20%, the stiffness increases by a factor of 13 going from 10% to 30%.

By measuring the connectivity [1] between the fluid droplets using an X-ray scan [2], the authors discovered that the stiffness increase is related to the network connection between the fluid droplets when the magnetic field is applied (Figure 2b). This network connection is visualized in Figure 2c; the fluid, shown in red, is isolated when the fluid composes only 10%. However, when increased to 40%, the dispersed fluid pockets become connected to one another, enhancing the stiffness of the overall material under the magnetic field.

As mentioned above, the addition of the fluid was the key to the material’s drastic functional improvement. Since the fluid provides freedom for the iron particles to move around and align under the magnetic field, the stiffening process becomes more dramatic compared to having the particles alone inside the polymer. Also, the fluid acts as a buffer, lessening any damages caused to the polymer by the motion of the hard particles. The authors hope that their research will open up an even wider range of applications using this shape-memory polymer, such as a magnetic-controlled micromachine that can deliver drugs to targeted areas inside our body. Unlike the temperature-controlled shape-memory material introduced in the beginning, the stiffening of this new magnetically controlled shape-memory material is reversible. This might offer a greater potential for new applications which might require several cycles of deformation. Maybe in the near future, we’ll use items made out of magnetically controlled shape-memory polymers in our daily lives.

[1] The connectivity is defined as the volume of the biggest droplet over the total volume of the magneto-rheological fluid in the polymer composite.^

[2] The authors used X-ray tomography, a method where a 3D image is constructed using 2D X-ray images.^

 

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Small structures, Big facilities

Science Village Scandinavia

I am writing this as I embark on a journey from Copenhagen to Chicago for a 24-hour experiment. Luckily, I am going to be in the city longer than I will be flying, but only just. Traveling over 4,000 miles may seem like a long way to go for an experiment, and it is. I perform small-angle scattering experiments for a living though, and sometimes this is just what needs to be done. My previous post on Softbites was all about the fundamentals of X-ray and neutron scattering, but I didn’t give an indication of what an experiment is actually like. This post focuses on the practicalities. What are the experimental facilities like? What do you have to do to access them?

The first X-ray and neutron sources (developed by Röntgen and Chadwick, both of whom duly received Nobel Prizes for their discoveries) could fit on a desktop; examples are shown in Figure 1. Unfortunately, these historical apparatuses produce insufficient X-ray or neutron intensity for the kind of experiments that actually make use of the radiation. To enable these experiments, large-scale facilities have been built across the world, which produce much higher fluxes. For example, a next generation X-ray source will be 1015 times more brilliant than one of these historical X-ray tubes, and a new neutron source will have a flux 1018 times greater than that produced by Chadwick. The greater intensity of X-rays and neutrons generated at these large-scale facilities not only makes measurements possible but enables smaller and smaller samples to be analyzed at higher and higher throughputs.

Early apparatuses to produce X-rays and neutrons.
Figure 1. Early apparatuses to produce X-rays and neutrons. (Left) Crookes tube with concave cathode, the early way to produce X-rays. (Image from the Science Museum Group Collection, copyright The Board of Trustees of the Science Museum) (Right) James Chadwick’s Neutron Chamber device. (Image from the Department of Physics, The Cavendish Laboratory, University of Cambridge)

Intense and well-defined X-ray beams are primarily produced by the acceleration of electrons in machines called synchrotrons, which emit X-rays when magnets are used to bend electrons as they travel around the ring. Neutron beams are produced either by a nuclear reactor or at a spallation source, which emit neutrons from a metal target that has been bombarded by high energy protons. None of these are on the scale of a typical laboratory though, and instead, they require large-scale facilities.

These large-scale facilities are definitely required for some small-angle scattering experiments. The larger a particle is, the smaller an angle that it will scatter at. Small-angle scattering measurements do indeed measure very small angles (less than 1°). This means that large distances between samples and detectors are required to measure scattering at these very small angles. There are instruments with 40 meter vacuum tanks and even 100 meter vacuum tanks. Examples of some long instruments are shown in Figure 2. This means that the size of the structures you are studying (ångströms, nanometers or micrometers) is very out of proportion with the size of the facilities you use (multiple meters).

ng instruments for neutron and X-ray scattering.
Figure 2. Long instruments for neutron and X-ray scattering. (Top) The new 40m long detector tank of the small angle neutron scattering (SANS) instrument D11, at the Institut Laue–Langevin. (Image from Peter Lindner) (Bottom) Inside view of the 34 m detector tube at ID02 at the ESRF. The detector that measures scattered X-rays travels along the tube. (Image from T. Narayanan)

The ability of some instruments to access very long length scales from scattering at very small angles is the exact reason for my journey to the Advanced Photon Source (APS) near Chicago. For this experiment, I am interested in studying nanoparticles with diameters of several hundred nanometers but with interactions between particles that span distances much longer than this. To study interactions at the scale of micrometers, we need to measure scattering at the APS’s ultra-small-angle X-ray scattering instrument.

As you might guess given my long journey from Copenhagen to Chicago, there are a limited number of these instruments in the world. Even if there is a facility nearby, only a small number of samples can normally be measured rapidly, and even that might require waiting weeks or months. It is not possible to easily do test measurements at facilities, like you can with laboratory-based equipment. There are two ways to access time on these instruments, which as it is “time” on instruments using “beams” of X-rays or neutrons, is literally called “beamtime”.

Commercial access is more rapid, but it is costly (on the order of tens of thousands of dollars a day). Academic access costs less, and tends to be funded by the facility or a national fund, but you have to compete to get access this way. To gain beamtime via the academic route, I had to design and propose an experiment and have it accepted by a panel. Competing for and booking time at large-scale facilities is common in other fields, like astrophysics or particle physics. However, it is not typically necessary for soft matter experiments.

After being granted access by the panel for some beamtime on my desired instrument, the planning begins. The first thing to do is to schedule a time for the measurement with a local scientist at the facility. This might be during a weekend or a holiday, and I may have to be there overnight. I then need to update my radiation safety and awareness trainings and tests, which enables me to enter the facility, and book my travel. Finally, I prepare the samples, which I send to the facility a few weeks before my experiment. Once I arrive at the facility and familiarize myself with operating the instrument, I will finally perform my measurements. If all goes well, I will come home with a mountain of data to analyze. This time I am looking at nanoparticles, but depending on the materials I bring, I may reveal the structure of a protein or the size and shape of a micelle or the interactions between components in a complex mixture. There are a lot of possibilities in studying soft matter and biology. However, even if I haven’t found all the answers,  I should hopefully have enough preliminary data to write my next proposal. This may sound like a lot of work, but given the capabilities available on the instruments at large-scale facilities, we can really push the limits of what is achievable in soft material characterization. There are over 100 neutron and X-ray facilities around the world, and one may be near you. If not, you too may get to travel thousands of miles for a brief window of beamtime.

The featured image at the top is an impression of Science Village Scandinavia, which is designed to surround the new MAX IV X-ray synchrotron and ESS neutron source being constructed in Lund, Sweden. (Image from COBE.)

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The dance of swarming flies

Original article: Emergent dynamics of laboratory insect swarms

Imagine yourself as a small fly called a midge (shown in Figure 1a). You used to live in a lake as a small larva with no concerns in life except swimming, eating, and growing. One day, you hid underwater and formed a cocoon around your body as it developed wings, legs, and antennae. A few days later, you swam to the surface and burst out of your cocoon as an adult fly — a male. As a new adult male, you find the clock ticking – you have only a few days to find a mate before you die.

Attracting a female is difficult for a tiny midge – how is she going to see you flying around? Fortunately, you can team up with hundreds of other male midges. Together, you fly above the lake in a stationary swarm that looks like a large cloud. Females can find this swarm and fly into it for their choice of mate. 

In today’s study, Douglas Kelley and Nicholas Ouellette investigate how the motion of midges in a swarm helps the swarm stick together.

Figure 1. (a) A midge is a tiny fly that forms mating swarms above lakes (image from Wikipedia). (b) Midges tracked in a swarm in the laboratory, with different midges in different colors (Figure adapted from original article)

The researchers set up midge swarms in the laboratory and film them with three infrared cameras. They track all of the individual midges in the swarm and calculate their trajectories. Tracking dozens of small midges is not easy! First, they use the 2D images from the three cameras to locate the flies in 3D for each frame. Then, they use a technique originally developed for studying turbulent fluid flows to generate the trajectories over time. This technique uses the history of each midge to estimate where it is likely to be next and looks for midges in that area at the next time step. The resulting trajectories are shown in Figure 1b.  The positions, velocities, and accelerations of the midges give clues about how the swarm moves.

First, Kelley and Ouellette discuss the position of the midges. They plot the logarithm of the probability ($latex log_{10} P$) of finding a midge in a point in the swarm in three dimensions in Figure 2. Bright red represents a high probability of finding a midge, and blue represents a very low probability. Midge swarms are nearly symmetric, but larger swarms (of 100 individuals or more) are slightly taller than they are wide. This is unlike bird flocks, which are nearly two-dimensional.

Figure 2. Probability of finding a midge at x, y, and z coordinates in the swarm. Bright red colors indicate high likelihood of finding a midge, and blue represents a very low chance of finding a midge in that position. (Figure adapted from original article)

The researchers then investigate the velocities of the midges. Since the swarm is stationary, the average velocity of all the midges in the swarm is nearly zero. It turns out that the standard deviation, or the variation, of the velocities of the individual midges is more useful for understanding the motion inside the swarm. Midges fly twice as fast horizontally as vertically, just like birds in a flock. However, unlike flocks of birds, the midge swarms  are not polarized — a midge does not tend to fly in the same direction as its neighbors. Finally, Kelley and Ouellette investigate the acceleration of the midges in the swarm. The midges are equally likely to turn in any direction, unlike birds or fish. Relative to their body size, larger animals have more inertia than smaller ones, and must exert a lot more effort to turn, accelerate, and decelerate. Thus, they tend to keep moving in the direction they are currently moving. Midges, on the other hand, can turn and easily move in any direction. Kelley and Ouellette find the average acceleration of the midges in the swarm in the x-direction as a function of the midge’s x-position, $latex \langle a_x|x \rangle$, in Figure 3.  The midges tend to accelerate towards the center of the swarm, keeping the entire swarm together despite the midges’ constant motion. [1]

Figure 3. Acceleration of the midges in the x-direction as a function of the x-position for several midge swarms.  Each line represents a different swarm. When a midge is at the right edge of the swarm, it accelerates to the left (and vice versa).  (Figure adapted from original article)

In this study, Kelley and Ouellette quantify a new type of swarming behavior. Unlike most other animal aggregations like bird flocks and fish schools, midge swarms stay in one place, helping female midges find the love of their very short lives.

[1]  Surprisingly, when Kelley and Ouellette investigated the mean square displacement of the midges, they found that the midges act as if they are trapped in a box with walls.