Jamming is the physical process by which the viscosity of some

mesoscopic Mesoscopic physics is a subdiscipline of condensed matter physics that deals with materials of an intermediate size. These materials range in size between the nanoscale for a quantity of atoms (such as a molecule) and of materials measuring mic ...

materials, such as

granular material A granular material is a conglomeration of discrete solid, macroscopic scale, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when granulation, grains collide). T ...

glass Glass is an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...

es,

foam Foams are two-phase materials science, material systems where a gas is dispersed in a second, non-gaseous material, specifically, in which gas cells are enclosed by a distinct liquid or solid material. Note, this source focuses only on liquid ...

polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...

emulsion An emulsion is a mixture of two or more liquids that are normally Miscibility, immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloi ...

s, and other

complex fluid Complex fluids are mixtures that have a coexistence between two Phase (matter) , phases: solid–liquid (Suspension (chemistry) , suspensions or solutions of macromolecules such as polymers), solid–gas (Granular material, granular), liquid–gas ...

s, increases with increasing particle density. The jamming transition has been proposed as a new type of

phase transition In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...

, with similarities to a

glass transition The glass–liquid transition, or glass transition, is the gradual and Reversible reaction, reversible transition in amorphous solid, amorphous materials (or in amorphous regions within Crystallinity, semicrystalline materials) from a hard and rel ...

but very different from the formation of

crystalline solid A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...

s. While a glass transition occurs when the liquid state is cooled, the jamming transition happens when the density, or the packing fraction of the particles, is increased. This crowding of the constituent particles prevents them from flowing under an applied stress and from exploring

phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...

, thus making the aggregate material behave as a solid. The system may be able to unjam if

volume fraction In chemistry and fluid mechanics, the volume fraction \varphi_i is defined as the volume of a constituent ''V'i'' divided by the volume of all constituents of the mixture ''V'' prior to mixing: :\varphi_i = \frac . Being dimensionless quantit ...

is decreased, or external stresses are applied such that they exceed the yield stress. This transition is interesting because it is

nonlinear In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...

with respect to volume fraction. The jamming phase diagram relates the jamming transition to inverse density, stress and temperature. The density at which systems jam is determined by many factors, including the shape of their components, the deformability of the particles, frictional interparticle forces, and the degree of

dispersity In chemistry, the dispersity is a measure of the heterogeneity of sizes of molecules or particles in a mixture. A collection of objects is called uniform if the objects have the same size, shape, or mass. A sample of objects that have an inconsi ...

of the system. The overall shape of the jamming manifold may depend on the particular system. For example, a particularly interesting feature of the jamming transition is the difference between attractive and repulsive particle systems. Whether the jamming surface diverges for high enough densities or low temperatures is uncertain. Simulations of jammed systems study particle configurations leading to jamming in both static systems and systems under shear. Under

shear stress Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...

, the average cluster size may diverge after a finite amount of strain, leading to a jammed state. A particle configuration may exist in a jammed state with a stress required to "break" the force chains causing the jam. The simplest realization of a static jammed system is a random

sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...

of frictionless soft spheres that are jammed together upon applying an external hydrostatic pressure to the packing. Right at the jamming transition, the applied pressure is zero and the

shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the Elasticity (physics), elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear s ...

is also zero, which coincides with the loss of rigidity and the unjamming of the system. Also, at the jamming point the system is isostatic. Above the jamming point, the applied pressure causes an increase of

by squeezing the soft spheres closer together, and thus creates additional contacts between neighboring spheres. This leads to an increase of the average number of contacts

z

. As shown in numerical simulations by Corey O'Hern and collaborators, the

increases with increasing

z

following the law:

G \sim (z-2d)

, where is the dimension of space. A first-principles microscopic theory of elasticity developed by Alessio Zaccone and E. Scossa-Romano quantitatively explains this law in terms of two contributions: the first term is a bonding-type contribution, thus proportional to

z

, and related to particle displacements which exactly follow the applied shear deformation; the second (negative) term is due to internal relaxations needed to keep local

mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is ze ...

in a strained disordered environment, and thus proportional to the total number of degrees of freedom, hence the dependence on space dimension . This model is relevant for compressed emulsions, where the friction between particles is negligible. Another example of static jammed system is a sand pile, which is jammed under the force of gravity and no energy is being dissipated. Systems which are consuming energy are also sometimes described as being jammed. An example is traffic jams, where due to jamming the average velocity of cars on a road may drop sharply. Here the cars on a road may be thought of like a

or a non-Newtonian fluid that is being pumped through a tube. There under certain conditions the effective

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

may rapidly increase, dramatically increasing the

fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...

s's resistance to flowing and so causing the velocity to drop or even come to a complete stop. In this analogy the cars are like the grains in a

and if they are dense enough (i.e., closely enough spaced along the road) then interactions between the cars (as they must avoid each other to avoid crashing) cause jamming. A simple model of this behavior is the Nagel-Schreckenberg model. The notion of jamming can also be considered from a biophysical perspective to characterize the arrest of cellular motion. Cell motility is of importance in many biological processes including tissue morphogenesis, wound healing, and cancer invasion. Characterizing the mechanisms that result in these "jamming" and "unjamming" phenomena can yield a more nuanced view of tissue development and aid in identifying new targets for disease therapies. Identifying properties defining these cellular phase changes has been a topic of recent interest. Cell density-based jamming is analogous to particle jamming in physical science, as the viscosity of a group of cells, like a group of particles, will increase as cell density increases. Other key parameters uniquely discussed for cell jamming include cell shape, cell-cell contact, and cell motion, studied in both embryonic organization and asthma. These factors are closely related to each other. In one attempt to illustrate the mechanisms of cell jamming, Lawson-Keister et. al. use three factors: a) density, b) geometric incompatibility, and c) fluctuations. Efforts of experimentally quantifying cellular viscoelastic phases include in-vivo injection of force-sensing

ferrofluid Ferrofluid is a dark liquid that is attracted to the poles of a magnet. It is a colloidal liquid made of nanoscale ferromagnetic or ferrimagnetic particles suspended inside a carrier fluid (usually an organic solvent or water). Each magnetic ...

, micropipette aspiration, and 3D digital image correlation of cellular displacement.

References

External links

* (YouTube link) A video of th
robotic grippers based on granular jamming
designed by th
Creative Machines Lab
at Cornell University shows the principle applied to a robotic arm. * (YouTube link) A video of th
jamming-skin robot
designed by iRobot and funded under the

DARPA The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adva ...

Chemical Robots program, shows the principle applied to robot locomotion. * * * * *{{cite journal , last=Campàs , first=Alessandro Mongera , author1-link = Alessandro Mongera , author2=Payam Rowghanian , date=20 September 2018 , title=A fluid-to-solid jamming transition underlies vertebrate body axis elongation , journal=

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

, volume=561 , issue=7723 , pages=401–405 , doi=10.1038/s41586-018-0479-2 , pmid=30185907 , pmc=6148385 , bibcode=2018Natur.561..401M Phase transitions