# Supercooling

Supercooling, also known as undercooling,[1] is the process of lowering the temperature of a liquid or a gas below its freezing point without it becoming a solid.

A liquid below its standard freezing point will crystallize in the presence of a seed crystal or nucleus around which a crystal structure can form creating a solid. However, lacking any such nuclei, the liquid phase can be maintained all the way down to the temperature at which crystal homogeneous nucleation occurs. Homogeneous nucleation can occur above the glass transition temperature, but if homogeneous nucleation has not occurred above that temperature an amorphous (non-crystalline) solid will form.

Water normally freezes at 273.15 K (0 °C or 32 °F) however it can also be "supercooled" at standard pressure down to its crystal homogeneous nucleation at almost 224.8 K (−48.3 °C/−55 °F).[2][3] The process of supercooling requires that water be pure and free of nucleation sites, which can be achieved by processes like reverse osmosis, but the cooling itself does not require any specialised technique. If water is cooled at a rate on the order of 106 K/s, the crystal nucleation can be avoided and water becomes a glass. Its glass transition temperature is much colder and harder to determine, but studies estimate it at about 165 K (−108 °C/−162.4 °F).[4] Glassy water can be heated up to approximately 150 K (−123 °C/−189.4 °F).[3] In the range of temperatures between 231 K (−42 °C/−43.6 °F) and 150 K (−123 °C/−189.4 °F) experiments find only crystal ice.

Droplets of supercooled water often exist in stratiform and cumulus clouds. Aircraft flying through these clouds seed an abrupt crystallization of these droplets, which can result in the formation of ice on the aircraft's wings or blockage of its instruments and probes, unless the aircraft are equipped with an appropriate de-icing system. Freezing rain is also caused by supercooled droplets.

The process opposite to supercooling, the melting of a solid above the freezing point, is much more difficult, and a solid will almost always melt at the same temperature for a given pressure. For this reason, it is the melting point which is usually identified, using melting point apparatus; even when the subject of a paper is "freezing-point determination", the actual methodology is "the principle of observing the disappearance rather than the formation of ice".[5] It is, however, possible, at a given pressure to superheat a liquid above its boiling point without it becoming gaseous.

Supercooling is often confused with freezing-point depression. Supercooling is the cooling of a liquid below its freezing point without it becoming solid. Freezing point depression is when a solution can be cooled below the freezing point of the corresponding pure liquid due to the presence of the solute; an example of this is the freezing point depression that occurs when sodium chloride is added to pure water.

## Constitutional supercooling

Constitutional supercooling – phase diagram, concentration, and temperature

Constitutional supercooling, which occurs during solidification, is due to compositional changes, and results in cooling a liquid below the freezing point ahead of the solid–liquid interface. When solidifying a liquid, the interface is often unstable, and the velocity of the solid–liquid interface must be small in order to avoid constitutional supercooling.

Supercooled zones are observed when the liquidus temperature gradient at the interface is larger than the temperature gradient.

$\left.\frac{\partial T_L}{\partial x}\right|_{x=0} > \frac{\partial T}{\partial x}$

or

$m \left.\frac{\partial C_L}{\partial x}\right|_{x=0} > \frac{\partial T}{\partial x}$

The slope of the liquidus phase boundary on the phase diagram is $m = \partial T_L / \partial C_L$

The concentration gradient is related to points, $C^{LS}$ and $C^{SL}$, on the phase diagram:

$\left.\frac{\partial C_L}{\partial x}\right|_{x=0} = - \frac{C^{LS} - C^{SL}}{D/v}$

For steady-state growth $C^{SL}=C_0$ and the partition function $k=\frac{C^{SL}}{C^{LS}}$ can be assumed to be constant. Therefore the minimum thermal gradient necessary to create a stable solid front is as expressed below.

$\frac{\partial T}{\partial x} < \frac{m C_0 (1-k) v}{kD}$

## In animals

The osmotic concentration of the body fluids of fish is lower than the osmotic concentration of sea water. Therefore the freezing point of fish can be above the temperature of sea water. The freezing point can be lowered by anti-freeze agents, but there are some fish (within the teleostei infraclass) whose freezing point is higher than the temperature of the surrounding sea water, and therefore the body fluids of these fish are supercooled. These fish must live well below the water surface, because they must not come into contact with ice nuclei (otherwise they would freeze immediately).[7]

## Applications

One commercial application of supercooling is in refrigeration. For example, there are freezers that cool drinks to a supercooled level[8] so that when they are opened, they form a slush. Another example is a product that can supercool the beverage in a conventional freezer.[9] The Coca-Cola Company also briefly marketed special vending machines containing Sprite in the UK, and Coke in Singapore, which stored the bottles in a supercooled state so that their content would turn to slush upon opening.[10]

## References

1. ^ Rathz, Tom. Undercooling. NASA. Archived from the original on 2010-01-12. Retrieved 2010-01-12.
2. ^ Moore, Emily; Valeria Molinero (24 November 2011). "structural transformation in supercooled water controls the crystallization rate of ice". Nature 479: 506–508. arXiv:1107.1622. Bibcode:2011Natur.479..506M. doi:10.1038/nature10586. Retrieved 24November2011.
3. ^ a b Debenedetti & Stanley 2003, p. 42
4. ^ Giovambattista et al. 2004, p. 047801-1.
5. ^ "A new method of freezing-point determination for small quantities", J. A. Ramsay, J. Exp. Biol..1949; 26
6. ^ http://chem.wzu.edu.cn/UploadFile/20094315104316.pdf#page=99 page from 99~100
7. ^ "Teleost fish have an osmotic concentration in their body fluids of about 300–400 mosm, and this corresponds to a freezing point of about −0.6 to −0.8 °C. Sea water in the polar regions often has a temperature of about −1.8 °C ... Do they have a lower freezing point than ordinary fish, or do they remain supercooled throughout life? The answer is that both possibilities seem to have been realized.", Knut Schmidt-Nielsen, Animal Physiology, Adaption and Environment (Cambridge University Press, 1975), p.279. "In summer, the surface fish in the Hebron Fjord, Labrador, have no freezing problem. The fish that live deeper, however, where the water is at −1.73 °C, have a freezing point in their body fluids of −1.0 °C and must remain supercooled (Scholander et al., 1957)." (Ibid., p. 280)
8. ^ http://www.chillchamber.hussmann.com
9. ^ http://www.slush-it.com
10. ^ Charlie Sorrel (2007-09-21). "Coca Cola Plans High Tech, Super Cool Sprite". Wired. Condé Nast. Retrieved 2013-12-05.