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I was surprised to learn that freeze distillation has the same inefficiencies as vapor distillation: Namely, that it is impossible to get two miscible fluids to fully separate in one "pass" of subjecting the mix to a temperature between the melting point of its constituents.

I can understand why this is the case in vapor distillation, because vaporization of a liquid still occurs below its boiling point.

But AFAIK the same is not generally true of freezing: assuming it has a nucleus, a single liquid will either crystallize completely at a given temperature or it won't at all.

My guess is that the inefficiency of freeze distilling has something to do with the chemistry of miscible fluids: I.e., whatever phenomenon allows them to mix also drags molecules of the lower-melting chemical out of the mix above its melting point when the higher-melting chemical crystallizes. If so then the efficiency of freeze distilling should have some relationship to a measurable quantity (like a miscibility coefficient?). What theories and models of miscible fluids are applicable to the question of efficiency of freeze distillation?

(If there is no attraction between the two fluid chemicals then presumably "single-pass freeze distillation" could be perfect. It would probably require agitation to help the more volatile of the two stay out of the crystals forming from the first chemical to freeze. For example, agitation during freezing is how ice is formed without visible bubbles from dissolved gasses. But if "there is no attraction" then presumably the fluid chemicals are not miscible, right?)

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  • $\begingroup$ The whole thing gets weirder when you toss in the fact that recrystallization from solution is a common technique to purify a chemical... $\endgroup$ – MaxW Nov 18 '15 at 4:02
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Solids have solubility, just as liquids do. This is easily seen in metal alloys, where different amounts of different compounds can cause different crystal structure, low-level phase separation, and large-scale phase separation (if the solid solution is not stable). The changing of these nanostructures of the material can even occur with a material fully in the solid state, such as tempering of steel.

This relates to your question in that liquids freezing will behave very similarly with respect to phase composition as vapors condensing. The composition of the solid will be proportional to the composition of the liquid and affected by differing freezing points, just like you would expect from a liquid-vapor Txy diagram.

There are some differences, however. Molecules in solids can, as I said above, move around within the solid. However, this diffusion is substantially slower in solids than in liquids, and in non-metal solids, slow enough to be largely insignificant within the process of freezing. This means that the freezing process will create regions of differing composition within the solid. Further and related to this phenomena, the speed of freezing will impact the concentration of the solid, as faster freezing will push it even further from equilibrium.

The slow diffusion in solids also means that once trapped in the crystal structure, compounds with higher freezing points will not as easily exit the solid as they might from a liquid. This means that melting can behave very differently from vaporization, and solids might become a slush in the process of melting.

An explanation as to why this all occurs could go as follows: solubility is a factor of the strength of the interaction between different types of molecules. Those interactions must be stronger than interactions within the individual types to avoid phase separation. The process of freezing tends to not fundamentally shift the strength of these interactions. It is possible for materials partially soluble in liquid to be mostly insoluble in solid, but pairs of miscible liquids have such intense cross-compound interactions that freezing typically can only impact concentration of the separate phases.

The really important chemistry in this case takes place at the phase boundary between the solid and liquid, which behaves almost identically to that between a liquid and a gas. Molecules with weaker interactions with the solid phase (weaker interactions with other molecules in that phase) will tend to leave the solid phase more often - but there is an equilibrium where molecules will enter their less-favored phase. Essentially, everything you would have learned about liquids and vapors applies here, except diffusion is too slow to allow good mixing within the more condensed phase.

Of course, there are, in specific cases, more complicated explanations. One is of interstitial compounds, where a second compound might occupy spaces within a solid. While this happens to a degree in all solids, interstitials that are small enough to fit fully in a crystal structure without deforming it might exhibit unusual solid solution behavior, such as a compound with a lower freezing point showing a greater affinity for solid phase than the other compound.

To answer the title question, yes, separation depends on solubility. Unlike vapor distillation, though, it can also depend on temperature difference (thus speed) and mixing.

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  • $\begingroup$ If I understand this correctly: Then in all cases the most efficient freeze distillation (i.e., maximum separation) will occur at the slowest rate of freezing combined with maximum agitation? And factors that determine how much of the lower-freezing chemical get stuck in the solid include: Interstitial compounds, and the strength of solution forces? So pairs of miscible liquids that would most efficiently separate are those with the weakest interactions (which are measured/characterized how?), and where higher-freeze-point molecule forms the tightest crystals (minimizing interstitial voids)? $\endgroup$ – feetwet Aug 12 '15 at 21:26
  • $\begingroup$ @feetwet Pretty much. Those do to an extent impact vapor distillation, too, though. That's part of why distillation columns maximize surface area. Miscible are miscible because they have strong interactions, which is why it's harder to separate those compounds (via any kind of distillation). My post doesn't fully address interstitials (and I do not feel qualified to fully discuss them), just that voids can cause unusual behavior in general. Like slow diffusion, the existence of voids is one of the ways solids differ from liquids/vapors. $\endgroup$ – user7652 Aug 12 '15 at 21:29
  • $\begingroup$ Got it; thanks! Are you aware of general methods other than distillation that are commonly used to separate miscible fluids? $\endgroup$ – feetwet Aug 12 '15 at 21:49
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    $\begingroup$ @feetwet I suggest you look here: en.wikipedia.org/wiki/Separation_process . With regards to liquids, the best options are usually centerfugation (which can separate basically any compounds) and absorption/adsorption. In a lab context, liquid-liquid extraction (introducing a non-miscible liquid) could allow some separation, as could chromatography. Reactions could also be used to enhance separation by producing a separate, more easily separated compound. $\endgroup$ – user7652 Aug 12 '15 at 21:58

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