Friday, August 14, 2015

Drought balls and emergent properties

There has been a lot of interest online recently about the "drought balls" that the state of California is using to limit unwanted photochemistry and evaporation in its reservoirs.  These are hollow balls each about 10 cm in diameter, made from a polymer mixed with carbon black.  When dumped by the zillions into reservoirs, don't just help conserve water:  They spontaneously become a teaching tool about condensed matter physics.

As you can see from the figure, the balls spontaneously assemble into "crystalline" domains.  The balls are spherically symmetric, and they experience a few interactions:  They are buoyant, so they float on the water surface; they are rigid objects, so they have what a physicist would call "hard-core, short-ranged repulsive interactions" and what a chemist would call "steric hindrance"; a regular person would say that you can't make two balls occupy the same place.  Because they float and distort the water surface, they also experience some amount of an effective attractive interaction.  They get agitated by the rippling of the water, but not too much.  Throw all those ingredients together, and amazing things happen:  The balls pack together in a very tight spatial arrangement.  The balls are spherically symmetric, and there's nothing about the surface of the water that picks out a particular direction.  Nonetheless, the balls "spontaneously break rotational symmetry in the plane" and pick out a directionality to their arrangement. There's nothing about the surface of the water that picks out a particular spatial scale or "origin", but the balls "spontaneously break continuous translational symmetry", picking out special evenly-spaced lattice sites.  Physicists would say they preserve discrete rotational and translational symmetries.  The balls in different regions of the surface were basically isolated to begin with, so they broke those symmetries differently, leading to a "polycrystalline" arrangement, with "grain boundaries".  As the water jostles the system, there is a competition between the tendency to order and the ability to rearrange, and the grains rearrange over time.  This arrangement of balls has rigidity and supports collective motions (basically the analog of sound) within the layer that are meaningless when talking about the individual balls.  We can even spot some density of "point defects", where a ball is missing, or an "extra" ball is sitting on top.

What this tells us is that there are certain universal, emergent properties of what we think of as solids that really do not depend on the underlying microscopic details.   This is a pretty deep idea - that there are collective organizing principles that give emergent universal behaviors, even from very simple and generic microscopic rules.  Knowing that the balls are made deep down from quarks and leptons does not tell you anything about these properties.

5 comments:

Don Monroe said...

Very nice example.

I assume you know that Bragg introduced "bubble rafts" as a kind of analog simulation model for crystals in 1947. Some decent movies on the web.
Don

Douglas Natelson said...

Hi Don - I almost mentioned bubble rafts. My dad had some book from his college days that had really cool pictures of bubble rafts showing grain boundaries and dislocations. I remember the pictures from when I was in middle school or so.

gilroy0 said...

Careful -- you'll end up sounding like Bob Lauglin. :)

jonah said...

Beautiful example!

jonah said...
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