So, one way or another, the response will be a kind of molecular envelope that involves at least two types of bonds: strong string- or leaf-shaped bonds that keep the entire molecule intact as it heats up, and weaker bonds that act as small magnets to wind the molecule as it cools. To work, the molecules must also have enough regularity for the roll-up to work properly, otherwise you`ll end up with a tangled mess that could take up even more space. Note the critical state in which the saturated liquid and saturated vapor pipes meet. The state variables for this single point are denoted as Pc, vc, and Tc. If a substance is above the critical temperature Tc, it cannot condense into liquid, regardless of pressure. This fusion of the liquid and vapour state above the critical temperature is a characteristic of all known substances. While a pure vapor state can exist at a pressure below Pc, at pressures above Pc, it is limited to being a vapor. States with pressures on pc are called “supercritical states”. And finally, is there an answer for simple inorganic compounds? I don`t know if anyone has ever optimized or looked for this, but probably someone did it somewhere.
In the periodic table, you could probably find the “best shrinkage element” directly from the existing tables. Sulfur would be an interesting candidate for its ability to form long filiform chains that (can!) swell when melted, and perhaps also phosphorus. For compounds, I would suspect that zeolites or related materials may have unusually high contraction rates in temperature ranges higher than those in the room, as their cage-like structures “settle” into more angular and bent configurations, but I also suspect that you would need to design zeolite to do so, because the goal is usually to make the cages bigger, not smaller. This is different from gases, as the binding force must already be present, at least enough to keep the material intact during cooling. So what you really need is a material that has strong and persistent bonds, but is also very, very extensible in some ways, so the heat causes the absorption of an excessive amount of volume by the same molecules. Finally, I can even give you a good starting point for the development of extremely cold contraction materials, at least in water: DNA. DNA has the strong bond needed to build waves, as well as a soft bond of exquisite precision to ensure proper folding and deployment of the necessary polygonal constructions. When a substance freezes, the average kinetic energy of the particles decreases.
This means that the particles move more slowly. Most substances also contract when they cool down to increase the organization of molecules (crystallization). Therefore, the particles of most substances will get closer as they freeze. A notable exception is water, which expands when it freezes (the same body of water that freezes into ice floats in liquid water due to an increase in volume). I see you asked what kind of material contracts the most when you cool it down. In this regard, almost nothing beats the ideal gas, the contraction of which at room temperature is about 0.1% per degree. If you want a material, look at a bunch of balloons mixed with drops of glue or something microscopic. A molecule like this could easily provide a fairly extreme contraction behavior per degree of behavior lost over its expected temperature range. As in @RonMaimon discussion of how to make molecules shine when 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 that some cage-like inorganic molecules (zeolites come to mind) would be capable of similar tricks. There is a very strange material (zirconium tungstate) that shrinks when heated from absolute zero to about 1000°C. You can form a material that contracts with heat as much as you want by making long polymers that easily prefer to be (energetically) straight.
All these chains prefer to become entangled randomly by entropy, so that at high temperatures, where the contribution of entropy is greater, the polymers contract into narrow spheres and shrink the network. Water is very strange, as it expands when it freezes – almost everything else contracts. Such a polymer should be a very long chain, like a hydrocarbon (but hydrocarbons are very rigid, you want something flexible). Then tie balls together using these polymers to form a grid. This is not quite the description of a rubber band. The universal reason why materials contract at higher temperatures is that they gain entropy by reducing their volume. (At some point, the rebound force exceeds the binding forces, and molecules or atoms escape from each other. At this point, the material melts, evaporates or decomposes and usually expands even more, with water being an exception.) The solid, liquid and gaseous (vapor) phases can be represented by regions on the surface. Note that there are areas on the surface that represent a single phase and areas that are combinations of two phases. A point on a line between a single-phase region and a two-phase region represents a “saturation state.” The line between the liquid and liquid vapor ranges is called the liquid saturation line, and each point in that line represents a saturated liquid state.
A point at the boundary between the vapor and liquid vapor ranges is called a saturated vapor state. Most materials contract during cooling. The notable exception to the rule are certain phase transitions and water. But the ice also contracts during cooling. Water only expands between $0^circtext{C}$ and $4^circtext{C}$ (including phase transition). This corresponds to the part of the next graph where the density increases with temperature (note removed zero). It seems that plastics contract the most when cooled. Ethylene acrylate (EWR), for example, has the highest coefficient among the solids in this table.
So, with all of this in place, here`s my best estimate of the type of molecule that would win “the fastest solid or liquid contraction in the cooled state” in a competition. Imagine a normal body, say a variant of the icosahedron with 20 triangular sides arranged in 12-sided dodecahedral symmetry. .
