[EmpyreanCookie]

Background: I'm looking for a substance which stores energy most efficiently when oversaturated. In technical terms: a substance whose graph in a diagram of temperature (x-axis) vs the soluble amount in water has the steepest average (in the interval of 0–100 °C) slope possible.

Question: I'm wondering whether you can divide substances up into groups depending on the behavior their graph shows in described diagram.

Example of a temperature vs solubility diagram:
https://en.wikipedia.org/wiki/Solubility#/media/File:SolubilityVsTemperature.png

Thanks in advance

[AWK]

This diagram has nothing with storing energy ot oversaturation.
The best known substances that easily form oversaturated solutions arre sodium thiosulfate and sodium acetate

[EmpyreanCookie]

So what does the stored energy depend on?

Thanks for your reply.

[AWK]

Some compounds during dissolution in water increase temperature of solution (eg. NaOH), the others decrease temperature of solution (eg Na₂S₂O₃ or NH₄Cl).

Why? How this can be connected with oversaturation and energy storage in solution?

[EmpyreanCookie]

The temperature in the graph refers to the temperature of the solvent, which is adjusted manually using a stove or a bunsen burner. For most substances, the amount which the water is able to dissolve increases as the water's temperature increases. When the solvent cools down again, the dissolved substance stays dissolved in the solvent. As soon as a seed crystal is introduced into the fluid, the excess substance forms a crystal around the seed crystal and gives off heat simultaneously.

My question is whether one is able to distinguish different groups of substances (possibly depending on their molecular composition or other factors) depending on their thermal behavior when oversaturated.

[AWK]

Start reading from:
Crystallization of molecular systems from solution: phase diagrams, supersaturation and other basic concepts
Gérard Coquerela 
Chem. Soc. Rev., 2014,43, 2286-2300
DOI: 10.1039/C3CS60359H

[Arkcon]

My question is whether one is able to distinguish different groups of substances (possibly depending on their molecular composition or other factors) depending on their thermal behavior when oversaturated.

Briefly no.  Going into more detail, you can with advanced knowledge of chemistry, but we can't teach you PhD level chemistry one posting at a time.  This is the sort of thing advanced theoretical chemists do.

You have a fine example from your chart:  Na₂HAsO₄ had the most solubility change over temperature.  Maybe there's better ones, but you'll find that faster in a reference book than in a mountain of theoretical calculations.

The big problem that I have is that I think your premise is flawed in two ways.  You keep mentioning supersaturation.  There's no guarantee that any substance will allow that.  Again, advanced crystal theory will tell you when and why, but I just know of a couple of examples as trivia, the phenomena isn't ubiquitous.  If as soon as the temperature drops, you get the thermal energy back gradually, you can't use that to do work.

Furthermore, you're convinced that you will get all the thermal energy back (I'm guessing you know to expect inefficiency losses.)  This is not absolutely true.  If the entropy of the crystal forming or dissolving is lower, you can waste some thermal energy that way.  There's the example of things with a negative heat of solution:  they dissolve better when they're warmed, yet they cool the solution as they dissolve. This effect may be less for some reagent or another, but its still a way to lose thermal energy, while keeping overall energy the same.

Now, phase change, that's a transition that's as straightforward as can be.  But we do that all the time.  We use melting ice to keep things cool in shipment, or steam to drive turbines.  But I'm getting the feeling you simply find that dull.  Still, I don't know if you can get the heat back from a solution.

[Enthalpy]

Could there be a matter of wording here? Oversaturated, supersaturation...

If the solid sinks to the bottom of the container, that's just as good for energy storage - or possibly even better for the efficiency of heat recovery.

Just a matter of good mixing when injecting or recovering heat.

To choose a solvent and solute, I'd go straight to experimental data, as my intuition tells that even if a theory exists, it must rely on experiment to provide the real figures. Or is there some magic there?

I like the general idea. It could be nearly as efficient as fusion/solidification, but keeps a conveniently flowing medium, and may also be safer.