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I know that water expands in the freezer, but I'm curious about which materials contract in response to cold temperatures --- and most importantly, which ones undergo the most drastic changes?

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I think your opening phrase may have been misinterpreted a bit. You don't care about water, right? That is, I think your question is about the extremes of the much more common response to cold, which is to contract, i.e.: "What material shrinks the most per unit drop in temperature?" –  Terry Bollinger May 11 '12 at 23:09
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4 Answers 4

up vote 5 down vote accepted

Most materials contract on cooling. The notable exception to the rule are some phase transitions and water. But even ice contracts on cooling. Water expands on cooling only between $0^\circ\text{C}$ and $4^\circ\text{C}$ (including phase transition). This corresponds to the part of the graph below, in which density rises with temperature (note suppressed zero).

resistivity of water

As regarding to what material contracts most, what are you looking for is the coefficient of linear thermal expansion $\alpha$

$$\frac{\text{d}L}{L} = \alpha \Delta T.$$

There is plentiful of various tables available on web, e.g.

http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html

It seems plastic materials contract most on cooling. Ethylene ethyl acrylate (EEA) for example has the largest one coefficient among the solids in this table.

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Cool figure, but it should come with a huge Note suppressed zero warning. The whole range is less than a 10% variation and the scale is less than 1% variation over the shown range. –  dmckee May 11 '12 at 18:30
    
@dmckee Yes, I like the figure too. Once I've searched for a decent figure for my lectures and it took me some time to find this one. I was surprised too about the actual details... –  Pygmalion May 11 '12 at 18:35
    
Interesting to note a typo(?) "4%C" in the explanation at the bottom of the image. –  Thunder Rabbit May 12 '12 at 0:57
    
Awesome -- thank you, Pygmalion –  kaneuniversal May 15 '12 at 20:29
    
@ThunderRabbit Looks fine to me, this is just another standard plot emphasizing the point where the temperature of water is 4% the speed of light. Nope, no typo there –  Jim Apr 16 at 22:00
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Water is very odd in that it expands when it freezes - almost everything else contracts.

I don't know what material has the largest volume change on freezing. But among liquids - organic solvents, with much weaker bonds between molecules than water, tend to have much larger expansivities.

There is a very odd material (zirconium tungstate) that shrinks as it is heated all the way from near absolute zero to 1000deg or so.

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Weird! Thanks, Martin –  kaneuniversal May 15 '12 at 20:30
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The cheap answer to your question is "a gas," probably most specifically helium since it stays a gas longer than anything else as it gets colder.

Your question boils down to how the ratio of two forces changes with temperature. First you have the separation forces that push molecules or atoms apart, and then you have the binding forces that pull the molecules or atoms back to together. Since colder temperatures remove energy, what usually happens during contraction is that the forces that drive separation shrink much faster than the forces that provide binding. Usually, it's the separation forces that take the greatest hit as temperatures decline, and for a very good reason: The single most important separation force in most substances is the bouncing and jostling provided by thermal agitation. Just as in paddle ball the elastically bound ball and paddle stay farther away from each other on average when quickly bounced, molecules and atoms on average stay farther away from each other when thermal agitation -- that is, high temperatures -- keeps them bouncing around.

(At some point the bouncing force exceeds the bonding forces, and the molecules or atoms escape from each other. At that point the material melts, evaporates, or decomposes, as well as usually expanding even further, water being an exception.)

So, in a contest to see which binding forces can most quickly get the upper hand over which separation forces, gases win hands-down because they cheat: Their bonding forces go from essentially nil to some finite value over the course of a very short temperature range. That short range covers when their average free kinetic energy finally drops below their inter-molecular bonding strength. Within that range, a gas that occupies a very large volume of space, even an interstellar-scale space, can start to compress itself very slowly (it takes time for such diffuse molecules to come together!) into tiny crystals or condensates that take up almost no volume. Now that's compression!

However, as I said earlier, however interesting that extreme case may be, it really is a bit of a cheat. You are really asking about what forms of condensed matter -- solids and/or liquids -- will compress down the most per unit of temperature as they chill.

That's different from gases, because the binding force must already be in place, at least enough to keep the material intact during cooling. So what you really need is a material whose bonds are strong and persistent, but which are also very, very stretchy in some way that allows heat to cause the same molecules to take up an excessive amount of volume.

One way or another, the answer thus is going to be some kind of molecular wrap-up that involves at least two kinds of bonds: strong string-like or sheet-like bonds that keep the overall molecule intact when it heats up, and weaker bonds that act like little magnets to help roll the molecule up when it cools down. To work, the molecules will also need to exhibit enough regularity for the roll-up to work smoothly, else you will just wind up with a tangled mess that might take up even more room.

So, with all of that in place, here's my best guess at the kind of molecule that would win in a "fastest solid or liquid contraction when chilled" contest. Imagine a regular solid, say a variant of icosahedron with 20 triangular sides arranged in 12-sided dodecahedral symmetry. The surfaces are both "hinged" (they have easily rotated bonds) and "sticky" (they bond weakly to each other) so that the most stable form is also the most compact. As it heats up, however, it expands, almost balloon-like, into a more fully "inflated" form in which only the strong bonds keep it from flying apart.

(I should note that other roughly similar ideas are possible. My favorite visually is the idea of a 12-side jack-in-the-box in which 12 lids all spring outward when a certain temperature is reached, but stay connected by strongly bonded "springs." The molecules need roughly spherical shapes, however, since otherwise they may simply roll up in other ways, e.g. jelly-rolls could easily just turn into flat crystals.)

A molecule like this could easily provide rather extreme contraction-per-degree-lost behavior over its designed range of temperatures. As in @RonMaimon's discussion of how to make molecules shink as they get hotter (an even more interesting problem!), the best candidates for maximum expansion with heat (shrinking with cold) would be richly complex organic molecules. However, I'm pretty sure some cage-like inorganic molecules (zeolites come to mind) would be capable of similar tricks.

If you allow water molecules or other solvent molecules to wander in and out of the cages, all of these contractions and expansions can be made even more extreme, since the water molecules could fill in what would otherwise be a strongly size-limiting vacuum inside of each expanded molecule. With water allowed you get into the range of temperature-dependent gels. With gels, a teaspoon of material can easily "gel up" liters of water, and if you can keep the gel temperature dependent, it will then shrink back down to miniscule size whenever the pool of water gets cold enough for a long enough period of time. (I do not know for sure if such gels exist, I should note.)

Finally, I can even give you a good starting point for designing extreme cold-contracting materials, at least within water: DNA. DNA has the necessary strong bonding to build shafts, plus exquisitely precise soft bonding to ensure proper folding and unfolding of the needed polygon-like constructs.

And finally, is there an answer for simple inorganic compounds? I don't know if anyone has ever optimized or searched for that, but likely someone has somewhere. Within the periodic table you could likely find the "best shrink element" directly from existing tables. Sulfur would be an interesting candidate for its ability to form long stringy chains that (may!) puff up on melting, and possibly phosphorus also. For compounds I'd guess that zeolites or related materials at higher-than-room-temperature ranges may exhibit unusually high contraction rates as their cage-like structures "settle in" to more angular, folded configurations, but I also suspect you'd have to design the zeolite to do just that, since usually the goal is to make the cages larger, not smaller.

And with those guesses, alas, it's time to punt: There are design principles and even specific cases possible, but for the current "right now" champ, I have no answer!

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Thanks for the extensive detail, Terry :) –  kaneuniversal May 15 '12 at 20:31
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EDIT: I misread the question

I see you asked what kind of material contracts the most when you cool it. In this regard, hardly anything beats the ideal gas, whose contraction is about .1% per degree at room temperature. If you want a material, consider a bunch of balloons mushed together with drops of glue, or something microscopic equivalent.

Materials that shrink when heated

One can make up a material which contracts as much as you like with heat, by making long polymers which slightly prefer (energetically) be straight. All such chains prefer to be tangled randomly by entropy, so at high temperature, where the entropy contribution is more important, the polymers contract into tight balls, shrinking the lattice.

Such a polymer should be a very long chain, like a hydrocarbon (but hydrocarbons are very stiff, you want something which is flexible). Then you attach spheres to each other using these polymers to make a lattice. This is not quite the description of a rubber band. The universal reason materials contract at higher temperature is that they gain entropy from reducing their volume.

For a realizable material of this sort, rubber is pretty good, but you could make longer chains in more regular arrangements, with supporting materials in the interstitials making it straight. There is no limit to the engineering potential.

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Thanks for the visual, Ron -- that's useful. –  kaneuniversal May 15 '12 at 20:31
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