Gelation without Attraction

By Bulbul Chakraborty

Gels are one of the most puzzling of all solids. Originally coined as a short form of gelatin, gels can be jelly-like as in Jello, or quite hard as in silica gels. They appear in suspensions of particles at extremely low volume fractions, and yet they are rigid. The conventional wisdom is that gels are a consequence of arrested phase separation of the suspended particles from the fluid. A natural mechanism for the arrest is attraction between the particles, which leads to the formation of filamentous networks of particles weaving through the suspending fluid.

Attraction has been viewed as being essential to the formation of gels. However, a new study published in Physical Review Research led by Carl Merrigan from the Chakraborty group, shows that “active particles” can gel even in the absence of physical attraction. Active matter, composed of particles that convert ambient energy to directed motion, has emerged as an important model for the collective behavior of biological matter such as bacterial suspensions. Using a combination of theoretical analysis and numerical simulations, the collaboration between the groups of Chakraborty and Shokef (Tel Aviv University) showed that the directed motion acts like an effective attraction, leading to gelation of the active particles.

The figure below shows the structure of these gels. As the particles become more active, they jam into clusters of immobile particles (red) surrounded by fluid regions (blue), and often opening up voids. Intriguingly, these active particles, which repel each other also show a transition from a dense glassy solid to a gel as the speed of directed motion is increased. The remarkable similarity between the behavior of passive particles with attraction and active particles suggests that biological entities could form solid-like aggregates without any physical or chemical attraction, purely as a consequence of their dynamics.

Reasearch image from Gelation without Attraction post

Chakraborty lab provides new understanding on the physics of granular materials

By Kabir Ramola, Ph.D

In the late 1980’s Sir Sam Edwards proposed a framework for describing the large scale properties of granular materials, such as sand or salt. In this description, similar to the well-established framework of statistical mechanics, the global properties of a complex system are determined by an average over all possible microscopic configurations consistent with a given global property. This is usually attributable to the very fast dynamics of the constituent particles making up the system. The extension of such treatments to granular systems where particles are static or ‘jammed’ represents a fundamental challenge in this field. Even so, Edwards’ conjecture postulated that for given external parameters such as volume, all possible packings of a granular material are equally likely. Such a conjecture, like Boltzmann’s hypothesis in statistical mechanics, can then be used as a starting point to develop new physical theories for such materials based on statistical principles. Indeed, several frameworks have been developed assuming this conjecture to be true.

Figure 1 : Snapshot of the system studied and illustration of the associated energy landscape at different volume fractions.

A simple illustration of this conjecture would be, if one were to pour sand into a bowl, and not bias the preparation in any way, then all the trillion trillions of configurations allowed for the grains would be equally likely. Clearly such a conjecture is utterly infeasible to test experimentally.  In a recent paper that appeared in Nature Physics, we instead performed detailed numerical computations on a theoretical system of soft disks (in two dimensions) with hard internal cores. We focused on a system of 64 disks which already pushed the limits of current computational power. We found that if one fixes the density of a given system of disks, the probability of a packing occurring depends on the pressure, violating Edwards’ proposition. However, at a critical density, where particles just begin to touch or ‘jam’, this probability remarkably becomes independent of the pressure, and all configurations are indeed equally likely to occur. This jamming point is in fact very interesting in its own right since most granular materials are found at the threshold of being jammed and ‘unjammed’. To be fair to Edwards, the hypothesis was made for ‘hard’ grains in which particles are precisely at this threshold, and therefore our numerics seem to confirm the original statement. This is the first time that this statement has been out to a direct test and will no doubt lead to many interesting directions in the future.

Links to news sources describing this article:

doi: 10.1038/nphys4168
Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming.
Stefano Martiniani, K. Julian Schrenk, Kabir Ramola, Bulbul Chakraborty & Daan Frenkel.
Nature Physics
2017

 

“Granular Materials” video by NSF highlights research by Chakraborty group

From NSF Multimedia Gallery: “Granular materials — like sand, rice, or powdered pharmaceuticals — are everywhere, yet their behavior is poorly understood.  In some ways behaving like liquids, in other ways behaving like solids, such materials have unique properties and pose unique questions to answer.  From clogged coal hoppers to powdered-snow avalanches, scientists and engineers are gaining new perspective on the fundamental nature of grains.  In this video, see some of the latest research into the behavior of granular materials.”

Prof. Bulbul Chakraborty’s group website

Nature article

Shear-induced jamming

From breakfast cereals to sand on a beach, granular materials are all around us. Under different conditions, these materials can exhibit liquid-like behavior (flowing) as well as solid-like behavior. The transition between solid and liquid phases has been known as the jamming transition.

The basic concept of jamming is pretty intuitive. A simple example of what can induce jamming is the following: compacting loose sand inside a container increases its density. When the container is removed, the sand can form a self-supporting pile, hence becoming jammed. Jamming has been studied extensively in numerical simulations of systems composed of idealized grains without frictional forces.  These studies find a critical density at which jamming occurs. Since these idealized granular materials are non-cohesive (no attractive forces between them)  they can become solids only through externally imposed pressure, such as through compaction, and therefore a critical density makes sense.  Real granular materials, however, have friction, and how this affects jamming is not well understood.

An experimental image of typical Shear Jammed state in a 2-D frictional granular material. The shear strain is applied in the horizontal direction. Red colored grains form the backbone of the system, which provides rigidity with respect to external shear

Newly published in Nature, are results of a collaboration between Prof. Bulbul Chakraborty’s group at Brandeis and Prof. Behringer’s group at Duke University, which show a new class of jammed states in frictional granular materials. This new class of “Shear-Jammed” states exhibits a richer phenomenology than previously seen. An initially unjammed or loose granular material can become jammed not just by increasing its density, but by applying shear strain on it while holding the density fixed. Shear-Jammed states are inherently anisotropic in their stress and grain-to-grain contact network (see photo above). The transition from an unjammed to shear-jammed state is clearly marked by a percolation of the strong force chains in all directions (see video below). The phenomenon of shear-jamming does not currently have a fundamental theoretical description. Ongoing work in Prof. Chakraborty’s group attempts to construct a theoretical framework for this non-equilibrium phase transition using a generalization of equilibrium statistical ensembles.

This video shows the evolution of the strong force cluster and transition from unjammed to fragile and eventually to SJ. The video shows experimental states created under pure shear. Green colored grains form the strong force cluster defined in the paper. Initially, the system is unjammed. As the fraction of force bearing grains increases with increasing strain, the strong force cluster percolates in the compressive (vertical) direction and we call the state fragile.  Eventually the system becomes percolated in all directions with sufficient number of force bearing grains. We call these states Shear Jammed.

see also:

Brandeis in Aspen II: Physics of granular materials

This post is a companion to Brandeis in Aspen I, and describes a workshop attended by Bulbul Chakraborty and Aparna Baskaran at the Aspen Center for Physics. The format of Aspen workshops is different from the usual academic workshop.  Each day has just one or two talks, which are primarily self-organized on a volunteer basis among the participants.  The format is designed to encourage  physicists working in a particular area to share research findings and enable cross-pollination of ideas in an informal and loosely structured setting.

The workshop attended by Chakraborty and Baskaran was entitled “Fluctuation and Response in granular materials”. Granular materials are ubiquitous in nature and industry. Examples range from sand and other geological materials, food and consumer products, and pebble beds in nuclear reactors. Understanding and controlling the properties of granular materials impacts such diverse processes as oil recovery, nuclear pebble bed reactors, printing and copying, and pharmaceutical processing. Granular media pose difficult and unique scientific challenges that distinguish them from atomic, nano-scale, and colloidal materials. Being intrinsically out of thermal equilibrium, assemblies of grains readily become trapped in metastable states, are extremely sensitive to preparation conditions, and can have strongly time-dependent properties.  Relaxing the constraints of thermal equilibrium, however, offers an advantage by opening up possibilities for creating novel static and dynamic phases that have distinctive functional properties.

At Aspen, the one-on-one and small sub group interactions among the participants covered a wide range of topics that are at the forefront of materials research, however, the program as a whole primarily focused on two questions. The first question was: What do we understand about jamming of granular materials? Jamming is what occurs in everyday life when we are trying to get coffee beans out of a hopper and they suddenly stop flowing. We fix this by tapping on the hopper. But this same phenomenon when it happens in giant grain silos causes them to collapse. So, one of the challenges is to be able to predict jamming events. The role of the physicist here is to design and carry out experiments in minimal model systems and develop theoretical frameworks that lead to predictive models of observed phenomena. Statistical Mechanics provides a powerful theoretical tool to address this question and our own Professor Chakraborty is one of the leading experts in the theory of jamming. The participants at the workshop had several robust discussions on the current understanding of this phenomenon and theoretical and experimental challenges that remain to be addressed.

The second question that the workshop focused on was : How does a dense granular material behave when sheared? Granular materials are called rheological fluids in that they exhibit shear-thinning and shear thickening behavior. In everyday life, we are all familiar with shear thinning. When we squeeze a tube of toothpaste, we are shearing it and it flows onto our brush. But once on the brush it stays put. This behavior is called shear thinning. Understanding rheology of granular materials is important for diverse applications ranging from pharmaceutical processes to being able to print well. The participants discussed in detail the physics of sheared granular materials and shared insight obtained from theory, simulations and experiments.

All participants departed the workshop invigorated by the robust exchange of ideas, ready to address the challenges presented by these complex materials.

Collective behaviors in active matter

Active matter is describes systems whose constituent elements consume energy and are thus out-of-equilibrium. Examples include flocks or herds of animals, collections of cells, and components of the cellular cytoskeleton. When these objects interact with each other, collective behavior can emerge that is unlike anything possible with an equilibrium system. The types of behaviors and the factors that control them however, remain incompletely understood. In a recent paper in Physical Review Letters, “Excitable patterns in active nematics“, Giomi and coworkers develop a continuum theoretical description motivated by recent experiments from the Dogic group at Brandeis in which microtubules (filamentous cytoskeletal molecules) and clusters of kinesin (a molecular motor) exhibit dramatic spatiotemporal fluctuations in density and alignment. Specifically, they consider a hydrodynamic description for density, flow, and nematic alignment. In contrast to previous theories of this type, the degree of nematic alignment is allowed to vary in space and time.  Remarkably, the theory predicts that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media and biological examples such as the cardiac cycle. At even higher activity the dynamics is chaotic and leads to large-scale swirling patterns which resemble those seen in recent experiments. An example of the flow pattern is shown below left, and the nematic order parameter, which describes the degree of alignment of the filaments, as shown for the same configuration below right. These predictions can be tested in future experiments on systems of microtubules and motor proteins.

The system behavior for an active nematic at high activity. (left) The velocity field (arrows) is superimposed on a plot of the concentration of active nematogens (green=large concentration, red=small concentration). (right) A plot of the nematic order parameter, S,  (blue=large S, brown=small S) is superimposed on a plot of the nematic director (arrows). The flow under high activity is characterized by large vortices that span lengths of the order of the system size and the director field is organized in grains.

 

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