When can water be supercooled?

Question

Qualitatively, I understand that water can be supercooled when:

1. It is relatively pure.
2. It is in a container that is relatively smooth of defects.

The effect of both of these is to reduce nucleation points, which are needed to provide a place for the ice crystals to start growing.

Rate of cooling may also be a factor- this is less clear to me.

But.... surely water that is experimentally supercooled is not perfectly free of impurities, nor is its container smooth at the atomic level. So there must be some critical amount of nucleation sites available.

Is it possible to quantify somehow, whether in general or at least for a specific impurity, exactly what the critical amount is to prevent supercooling? Is it a critical density of these sites that matters, or just a critical total number, since each site has some probability of starting crystallization? Even better, is there some general energetic or thermodynamic inequality that describes what conditions are needed for successful supercooling?

Answer 1

Qualitatively, I understand that water can be supercooled when:

• It is relatively pure.
• It is in a container that is relatively smooth of defects.
• ...

Yes, but it's actually very complicated ...

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See here for a huge chart of ice types - this site seems to be down, with the last complete capture by Wayback on Oct. 9 2020); some later captures are incomplete, missing some of the images and links to other webpages.

 Phase Diagram

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Is it possible to quantify somehow, whether in general or at least for a specific impurity, exactly what the critical amount is to prevent supercooling? ... Even better, is there some general energetic or thermodynamic inequality that describes what conditions are needed for successful supercooling?

It is explained relatively simply at Wikipedia's Supercooling webpage; and at great length, but still relatively simply, at the "Amorphous Ice and Glassy Water" and "Explanation of the Phase Anomalies of Water (P1-P13)" webpages (so, 14 webpages, more than you likely wanted to know).

Conditions such as: cooling rate, impurities, pressure, container, shock waves, all have an effect on the results you obtain, sometimes a bit of luck is involved (something you don't account for, experimental error).

You can make syrup if you do it correctly.

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Wikipedia gives a simplified explanation of heterogeneous nucleation which in water usually occurs when a crystal of ice water is added to supercooled water.

Some experimental results were published in the Journal of Physics article "High-density amorphous ice: nucleation of nanosized low-density amorphous ice", the Journal of the American Chemical Society article "Heterogeneous Nucleation of Ice on Carbon Surfaces", and in the Proceedings of the National Academy of Sciences article "Observing the formation of ice and organic crystals in active sites".

Answer 2

Hopefully I can dig into these a bit more and flesh out the answer, but for now here are some relevant resources & quotes:

"Effect of solutes on the heterogeneous nucleation temperature of supercooled water: an experimental determination" Physical Chemistry Chemical Physics (2009):

Homogeneous nucleation
Homogeneous nucleation occurs only in water not influenced by surfaces and devoid of foreign particles or substances. Only the water molecules are involved in the freezing event and at some homogeneous nucleation temperature, $T_{hom}$, estimated to be $\approx -41^\circ$$C^5$ they form an ice-like nucleus, or cluster, large enough to then cause spontaneous freezing. The practicalities of the experimental determination of this temperature are difficult and usually involve an emulsion technique and an averaging of the measured $T_{hom}$ values in an attempt to smooth out the inherent stochastic nature of nucleation.$^6$

Heterogeneous nucleation
Ice nucleation can also occur at the surface of so called ‘‘ice nuclei’’ by heterogeneous nucleation.7 The nuclei can be dirt, large molecules, bacteria, or simply the container wall. In each case a specific nucleating surface allows scaling of the free energy barrier (in classical theory) and causes the freezing event to proceed. The study of heterogeneous nucleation is of much more practical importance than homogeneous nucleation because most nucleation events in nature are heterogeneous.

Effects of solutes on $T_{hom}$ and $T_{het}$

It is well established that for homogeneous nucleation in aqueous solutions the lowering of $T_{hom}$ is linearly related to solute concentration and is independent of the solute, at least for small molecules, i.e.

$\Delta T_{hom} = \lambda \Delta T_m$

$^{8,9}$ The multiplying factor $\lambda$ is generally cited as 2.0$^{10,11}$ although there is some debate, with values as low as 1.7 being quoted.$^{12}$ We are not aware of a molecular explanation of this factor. It has also been reported that high molecular weight solutes have a larger effect than smaller molecules and that l can reach values as high as five for large molecules.$^{13,14}$ It is clear that the effects of solute on the heterogeneous nucleation temperature, $T_{het}$, have wide-ranging consequences in areas as diverse as cloud formation,15 ice-cream and other foods16 and in freeze-tolerant organisms.17 As an example, if sugar is added to ice-cream prior to manufacture the freezing point is reduced by B1.86 1C per mole but the nucleation temperature is reduced by B3.7 1C, allowing for deeper supercooling and so causing more, but smaller, nuclei at the time of nucleation, and so smoother ice-cream. Accurate determination of $\lambda$ is of importance to all of these fields of study.

"Measurements of the concentration and composition of nuclei for cirrus formation" Proceedings of the National Academy of Sciences (2003):

measurements of the concentration and composition of tropospheric aerosol particles capable of initiating ice in cold (cirrus) clouds are reported

Answer 3

When pure water is cooled below freezing point,it may remain in a super cooled state.Super cooling is a state where liquids do not solidify even below their normal freezing point. This concept can applied in why water in cloud do not freeze.