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I'm talking about very fine glass capillaries with a diameter under 1 mm. I've found that if I carry out melting point analysis, the material in the capillary doesn't crystallise again. I did wonder whether it was forming a glass, and I experimented using a larger volume of material and cutting/tilting the capillary. Definitely a liquid and definitely supercooled — it would often crystallise as I cut the capillary. If I put it in the fridge or freezer it would also give crystals.

I'm really struggling to understand this phenomenon — I've looked in textbooks and online, but I'm struggling to find anything, probably because capillary is a very common word.

I understand classical nucleation theory (I think), so I tried to relate that, but I'm struggling to see how the shape of a container would influence the clusters forming — surely even a very narrow capillary is huge to an atom! And as touched on in some of the answers, is it just nucleation that's slow to proceed, or crystal growth as well?

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  • $\begingroup$ In addition to the answers you got, it would be interesting to see if the resistance towards crystallisation is retained in general if you let the capillar in the bath. It is quite possible that removing it when the mp is established results in a relatively fast cooling even in air. The capillar is very small and whatever warm it cools down rapidly. Plus one for investigating a common fact. $\endgroup$
    – Alchimista
    Commented Aug 29, 2021 at 5:19
  • $\begingroup$ It is well known that imperfections on the surface of glass often act as nucleation centres (and sometimes when using larger vessels, chemists actively scratch the surface to promote nucleation). What is less-well known is that the process of creating small capillary tubes tends to create glass with very few surface defects. This is probably a significant factor. $\endgroup$
    – matt_black
    Commented Aug 30, 2021 at 11:02

3 Answers 3

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It has not (so much) to do with the shape of your container, rather than the accessible volume and thus, probability of events. To quote Meldrum and O'Shaughnessy:

"Nucleation in small volumes usually gives rise to a reduction in the nucleation rate, where this can be attributed to a number factors. i) The creation of small volumes is typically associated with the exclusion of impurities that promote nucleation in bulk solution [...]. Nucleation rates can therefore approach homogeneous rates, where it is of course impossible to eliminate all interfaces. This effect can be seen in finite volumes in the µL regime and below, provided the number of droplets vastly exceeds the number of impurities present."

(loc. cit., p. 3 of 64; emphasis added).

Of course, «the other» known (and unknown) parameters affecting crystallizations interfere here as they would do for a crystallization in a bulky beaker, too (e.g., concentration, temperature/temperature gradient, etc.). A recurrent difficulty for the crystallization of organic compounds from melt indeed is the tendency to yield supercooled liquids which spontaneously may solidify/crystallize. Benzoic acid is a cheap and experimentally easy example (mp $\pu{122 ^\circ{}C}$) for this sometimes showcased in demonstration lectures. Flexible alkyl chains tend to ease the formation of supercooled liquids and subsequently, glasses instead of crystals, too.

Note that conditions optimal for the creation of crystal seeds often are not optimal for crystal growth. Energetically speaking, it is an uphill battle for flexible molecules of the melt to orderly assemble in a crystal. Even if successful, small particles formed are (if normalized for their volume) of higher energy, than larger ones, too and heat of crystallization has to be dissipated which may inhibit crystallization, too. One experiment in physical chemistry is e.g. to follow the temperature when crystallizing water to ice: at one point, temperature actually rises briefly before crystallization continues. This reflects that a crystal seed needs to grow beyond a critical radius r before there is an overall gain in free energy:

enter image description here

(image credit, Meldrum et al.)

The caption of this diagram reads:

"Schematic of the free energy ($\Delta{}G$) of a growing crystal nucleus as function of the radius ($r$). The energy profile is a result of the favorable volume energy ($\Delta{}G_\mathrm{V}$) and the surface energy ($\Delta{}G_\mathrm{A}$). The maximum value ($\Delta{}G_\mathrm{C}$) is achieved at the critical radius ($r_\mathrm{crit}$)." (loc. cit., p. 9 of 64)

As the authors show, the critical nucleus size $r_\mathrm{C}$ can be described by

$$r_\mathrm{C} = \frac{2\gamma{}V_\mathrm{m}} {\Delta{}\mu{}} = \frac{2 \gamma{} V_\mathrm{V}} {kT \ln S}$$

dependent on the interfacial free energy ($\gamma{}$), the molecular volume ($V_\mathrm{m}$), the chemical potential of the molecule ($\mu{}$).

Cutting/tilting the capillary just disturbed the (metastable) equilibrium reached and possibly introduced new sites where crystallization may start. (As if you scratch the inner of a beaker with a glass rod when recrystallizing a product from hot solution.) This being said, crystallization in capillaries often is a necessity if (e.g., biochem) materials of interest are scarce or/and do not form large crystals:

enter image description here

(image credit, access on ResearchGate)

especially if the crystals may be obtained by counter-diffusion of reagents.

Reference

Meldrum, F. C. and O'Shaughnessy, C. Crystallization in Confinement. Adv. Mater 2020, 32, 201068; doi 10.1002/adma.202001068 (an open access publication).

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    $\begingroup$ Thank you, that's helpful. Would you be able to expand a little bit more on the accessible volume/probability point please? I think that's where I'm getting stuck. $\endgroup$ Commented Aug 28, 2021 at 11:56
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    $\begingroup$ I wonder if surface tension may play any role in triggering of the phase change. $\endgroup$
    – Poutnik
    Commented Aug 28, 2021 at 12:00
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    $\begingroup$ @BeginTheBeguine In first place, it boils down to the reduction of nucleation. The answer now includes this aspect. $\endgroup$
    – Buttonwood
    Commented Aug 28, 2021 at 13:45
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    $\begingroup$ @Poutnik The now added literature reference (open access) targets crystallization in confinement (well, not the one of 2020/21) and surface interactions e.g., of the crystal and the solution equally are mentioned there. $\endgroup$
    – Buttonwood
    Commented Aug 28, 2021 at 14:02
  • $\begingroup$ Thank you, and thank you for the reference I will read that now. One last question (and I might edit the main question to add this), does that mean that if I added a nucleating agent it should then freeze at about the right temperature inside the capillary? $\endgroup$ Commented Aug 28, 2021 at 14:15
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I'm no expert, but I think it likely IS related to both the shape and dimension. If I understand how the capillary tube method (I referred to 2.2.15. MELTING POINT - OPEN CAPILLARY METHOD in https://file.wuxuwang.com/yaopinbz/EP8.0_1_00025.pdf , Ph. Eur. 8.0, 20215 (01/2008). , cited as described in their FAQ: https://faq.edqm.eu/pages/viewpage.action?pageId=1377105, I quote: "The official abbreviation is ‘Ph. Eur.’ and not ‘EP’ (which is registered for the European Parliament). A good example of a reference would be: Ph. Eur. 6.0, 1742 (01/2008).") of determining melting point works in the first place, it is essentially by seeing when it is liquid enough to move up the capillary. To do the reverse means one will need to be able to overcome the capillary action forces per se. At least that is my intuitive (and so quite possibly wrong) interpretation, i.e. we have found where something comes apart by slowly adding energy while under a tension of sorts, now we still have that tension, but want to put it back together per se. I found a paper that goes into more depth:

The temperature at which the crystal is thermodynamically stable is also a func- tion of the capillary diameter. As the diameter decreases, the freezing point of water is lowered, which is called the capil- lary freezing point depression. The relation between the freezing point depression and the curvature of the interface is described by the Kelvin equation [1]. The original Kelvin equation was a liquid-vapor version that quantifies the devia- tion in equilibrium vapor pressure above a curved surface from that which would exist above a plane surface at the same temperature. It was later extended to solid-liquid phases and became well known as the ‘‘Gibbs-Thomson’’ relation in solidification that defines the local displacement of equilibrium temperature on a curved solid-liquid interface [2,3]. According to this relation, the freezing point depres- sion due to curvature is

(1) Equation that doesn't copy paste easily unfortunately

where Kappa is the mean curvature of the interface (m^-1 ), v_S is the specific volume of the solid phase (m 3 /kg), L is the latent heat of fusion (J/kg), sigma_LS is the interfacial excess energy per unit area of ice-water interface (J/m^2 ), and T_C and T_E are the freezing point and the normal equilibrium temperature of the ice-water interface (i.e., 273.15 K), re- spectively.

The paper is available here: https://www.researchgate.net/publication/7525813_Measurement_of_freezing_point_depression_of_water_in_glass_capillaries_and_the_associated_ice_front_shape/link/00b7d52bd2dd8da068000000/download

APA Style Citation: Liu, Z., Muldrew, K., Wan, R. G., & Elliott, J. A. (2003). Measurement of freezing point depression of water in glass capillaries and the associated ice front shape. Physical review. E, Statistical, nonlinear, and soft matter physics, 67(6 Pt 1), 061602. https://doi.org/10.1103/PhysRevE.67.061602

You may also look at the related phenomenon of capillary condensation, e.g. https://www.nature.com/articles/s41586-020-2978-1 , (Yang, Q., Sun, P.Z., Fumagalli, L. et al. Capillary condensation under atomic-scale confinement. Nature 588, 250–253 (2020). https://doi.org/10.1038/s41586-020-2978-1) governed by the same Kelvin equation. https://www.dora.lib4ri.ch/empa/islandora/object/empa%3A7600/datastream/PDF/Nowak-2008-Thermodynamic_and_kinetic_supercooling_of-%28published_version%29.pdf (APA: Nowak, D., Heuberger, M., Zäch, M., & Christenson, H. K. (2008). Thermodynamic and kinetic supercooling of liquid in a wedge pore. The Journal of chemical physics, 129(15), 154509. https://doi.org/10.1063/1.2996293) is potentially also a useful read though I think the math is different for the wedge pores they examine vs. the more classical capillary you're working with.

I wouldn't discount the probabilistic approach given in other answers, but I think there may be more at play here. Wikipedia article on the Kelvin equation, mostly as it relates to condensation: https://en.wikipedia.org/wiki/Kelvin_equation In that context they state: "It is unlikely, however, that new phases often arise by this fluctuation mechanism and the resultant spontaneous nucleation. Calculations show that the chance, e−ΔS/k, is usually too small. It is more likely that tiny dust particles act as nuclei in supersaturated vapours or solutions. In the cloud chamber, it is the clusters of ions caused by a passing high-energy particle that acts as nucleation centers. Actually, vapours seem to be much less finicky than solutions about the sort of nuclei required. This is because a liquid will condense on almost any surface, but crystallization requires the presence of crystal faces of the proper kind."

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  • $\begingroup$ It is preferable to include human readable citations to also prevent any fallout from possible link degradation. See for more details: chemistry.meta.stackexchange.com/q/2944/4945 $\endgroup$ Commented Aug 28, 2021 at 22:19
  • $\begingroup$ This seems the more to the point answer. Tough the other are also valid as general to crystallisation. $\endgroup$
    – Alchimista
    Commented Aug 29, 2021 at 5:15
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Here is a simple explanation, which is valid for elementary chemistry classes.

When a liquid or a solution is cooled under its melting point, it must solidify. But it sometimes happens that the crystallization is delayed. Everything looks as if no particular molecule (or atom) feels decided to start the first crystal and show how and where the other ones must be alined. Usually the first crystal appears on an impurity (dust), or any irregularity in the flask. And an irregularity may be created by scratching the flask or by a cosmic ray crossing the liquid. Cosmic rays are able to remove an electron in an atomic target, which is immediately recombined. But this creates an irregularity for a while. We are continuously crossed by cosmic rays at a rate of about $1$ ray per cm2 of skin and per second. We are used to it. But if the sample is small enough, there are no cosmic rays crossing the liquid during the first seconds. The liquid stays liquid even though the temperature gets lower than the melting point. The crystallization starts with delay. Some substances (sodium acetate, sodium thiosulfate) display this strange property more easily than others.

But this explains why crystallization starts with delay in a tiny glass capillary. The probability of being touched by a cosmic ray is rather small.

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  • $\begingroup$ If the explanation by cosmic rays did work, we wouldn't be able to have bottles of supercooled water for such long times as to be able to pour it (and watch its freezing on hitting the dish). $\endgroup$
    – Ruslan
    Commented Aug 28, 2021 at 22:22
  • $\begingroup$ It is easy to get supercooled liquid water down to -$5$°C in small test tubes, if they are dipped in a mixture salt + ice, whose temperature can be $-20$°C. It usually lasts about half a minute. And suddenly when the first ice crystal appears, the temperature suddenly goes up to $0$°C, and stays there as long as some liquid water is visible $\endgroup$
    – Maurice
    Commented Aug 29, 2021 at 13:21
  • $\begingroup$ In my opinion the cosmic rays factor is overemphasised at least respect to the fact that a capillar cool down fast (due to size shape mass), to the role of surface tension (see ttbek answer) and the reduction of nucleation rate (answer by Button) which of course seems dictated by the all the reason mentioned in this thread, including the cosmic rays one that you propose. It is also interesting, to be clear. $\endgroup$
    – Alchimista
    Commented Aug 30, 2021 at 10:25
  • $\begingroup$ @Alchinmista. You are right. But in my experience of high school chemistry teacher, I have observed that the explanation with cosmic rays is immediately understood by students, faster than the mechanism with nucleation or surface tension. $\endgroup$
    – Maurice
    Commented Aug 30, 2021 at 16:00

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