Thursday, February 15, 2018

Physics in the kitchen: Jamming

Last weekend while making dinner, I came across a great example of emergent physics.  What you see here are a few hundred grams of vacuum-packed arborio rice:
The rice consists of a few thousand oblong grains whose only important interactions here are a mutual "hard core" repulsion.  A chemist would say they are "sterically hindered".  An average person would say that the grains can't overlap.  The vacuum packing means that the whole ensemble of grains is being squeezed by the pressure of the surrounding air, a pressure of around 101,000 N/m2 or 14.7 pounds per in2.  The result is readily seen in the right hand image:  The ensemble of rice forms a mechanically rigid rectangular block.  Take my word for it, it was hard as a rock. 

However, as soon as I cut a little hole in the plastic packaging and thus removed the external pressure on the rice, the ensemble of rice grains lost all of its rigidity and integrity, and was soft and deformable as a beanbag, as shown here. 

So, what is going on here?  How come this collection of little hard objects acts as a single mechanically integral block when squeezed under pressure?  How much pressure does it take to get this kind of emergent rigidity?  Does that pressure depend on the size and shape of the grains, and whether they are deformable? 

This onset of collective resistance to deformation is called jamming.  This situation is entirely classical, and yet the physics is very rich.  This problem is clearly one of classical statistical physics, since it is only well defined in the aggregate and quantum mechanics is unimportant.  At the same time, it's very challenging, because systems like this are inherently not in thermal equilibrium.  When jammed, the particles are mechanically hindered and therefore can't explore lots of possible configurations.   It is possible to map out a kind of phase diagram of how rigid or jammed a system is, as a function of free volume, mechanical load from the outside, and temperature (or average kinetic energy of the particles).   For good discussions of this, try here (pdf), or more technically here and here.   Control over jamming can be very useful, as in this kind of gripping manipulator (see here for video).  


Peter said...

On the well-known scientific principle that "once is never, twice is always", vacuum packed ground coffee behaves in the same way, but with grains that are much smaller and of different geometry.

Douglas Natelson said...

Peter, that's universality for ya :-) With coffee, I've noticed that it is possible to use a fingernail to deform the packed grounds, which I could not do with the rice, but that's probably because there is some critical yield stress (force per area) I exceeded that depends on the size and shape of the grains.

DanM said...

Well, I for one am gratified that your rice is Brown Rice.

Anonymous said...

You say that a jammed system is not in thermal equilibrium because it is not ergodic, meaning it is mechanically hindered into only exploring a fraction of all possible microstates.

However, I could say that a ferromagnet which spontaneously breaks symmetry so as to collectively orient itself in the +z direction is also "non-ergodic", in the sense that the order parameter does not explore any -z microstates. However, we generally don't claim such a system as being out of thermal equilibrium - we instead say that the system is ergodic in a given defined subregion of phase space, namely, that region which satisfies the constraints on the orientation of magnetization that arise from the spontaneous symmetry breaking. But such scenarios are most definitely labeled as being in thermal equilibrium.

Would it perhaps be fair to say that the distinction between a ferromagnet and a jammed state is that, in the former scenario, the constraints on the accessible phase space arise from an intrinsically thermodynamic property of the system (namely, that the spontaneously broken symmetry is the globally thermodynamically stable minimum free energy ground state), whereas in the jammed state, the constraint arises from the system being stuck in a 'metastable' local free energy minimum?

If so, is it really fair to call a jamming transition a 'phase transition', as it would not be a true thermodynamic equilibrium phase, but rather, a temporary metastable kinetically trapped state? Furthermore, I imagine that in such a scenario, as the size of your system scaled up to the approach the thermodynamic infinite limit, the stability of any such metastable, non-global-free-energy-minimizing states, would be suppressed more and more, until in the infinite limit, only the global thermodynamic minimum is stabilized? Granted, that thermodynamic minimum may not necessarily be globally ergodic - in addition to any of the obvious spontaneously broken symmetry states I mentioned previously, you could have things like phase separation, coexistence, pattern formation, etc... However, these too are also not necessarily viewed as indicators of thermal disequilibrium, but rather, as a consequence of the fact that the equilibrium free energy is minimized by the formation of surfaces/interfaces/etc...