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 micr ...

materials, such as

granular material A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose gra ...

glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling ( quenching ...

es,

foam Foams are materials formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the ...

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

emulsion An emulsion is a mixture of two or more liquids that are normally 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 colloids. Altho ...

s, and other

complex fluid Complex fluids are mixtures that have a coexistence between two phases: solid–liquid (suspensions or solutions of macromolecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions). They exhibit unusua ...

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

phase transition In chemistry, thermodynamics, and other related fields, 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 states o ...

, with similarities to a glass transition 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, macros ...

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, 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 φ''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: :\phi_i = \frac Being dimensionless, its unit is ...

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 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, mathematicians, and many othe ...

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: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ...

, 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 elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackre ...

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 Deformation can refer to: * Deformation (engineering), changes in an object's shape or form due to the application of a force or forces. ** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies. * Defor ...

; the second (negative) term is due to internal relaxations needed to keep local mechanical equilibrium 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 jam Traffic congestion is a condition in transport that is characterized by slower speeds, longer trip times, and increased vehicular queueing. Traffic congestion on urban road networks has increased substantially since the 1950s. When traffic de ...

s, 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 A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...

that is being pumped through a tube. There under certain conditions the effective

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

may rapidly increase, dramatically increasing the

or fluids'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.

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 iRobot Corporation is an American technology company that designs and builds consumer robots. It was founded in 1990 by three members of MIT's Artificial Intelligence Lab, who designed robots for space exploration and military defense. The com ...

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 Ad ...

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, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

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