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Is it possible that a material may become less dense as more pressure is applied, without a phase transition?

My initial layman thought is no because it seems to me that "density" is a form of "pressure" within a material (I know this to be true at least for gasses). However some materials do exhibit unintuitive properties, such as becoming less dense when solidifying. In the specific case of water, at some temperatures increasing the pressure on water will turn it into a solid. Other unintuitive material properties include water (yet again) becoming less dense as temperature decreases be below 4°, and fluids which lose viscosity under increased pressure. So maybe there is chemistry for a material that expands (becomes less dense) as pressure is applied.

To be clear, this question can be phrased as: Is there a material which expands as pressure is applied?

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    $\begingroup$ Dilatency observed in wet sand might be an example, however I personally do not have the expertise to explain this in detail. $\endgroup$
    – Ben Watson
    Oct 3, 2021 at 16:28
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    $\begingroup$ I could imagine a material which has this as a bulk property. If you squeeze one part, it rearranges - but that rearrangement catalyses/triggers a further rearrangement that then progresses through the unsqueezed part as well, giving it larger volume. $\endgroup$
    – Stilez
    Oct 4, 2021 at 7:25
  • $\begingroup$ You can construct metamaterials with negative linear compressibility. I have added an answer. $\endgroup$
    – AlphaLife
    Oct 4, 2021 at 15:36
  • $\begingroup$ You might also want to say whether this needs to be repeatable. $\endgroup$
    – Graham
    Oct 4, 2021 at 16:17
  • $\begingroup$ To clarify, what exactly do you mean by applying pressure? Do you mean pressure, as in, putting the material inside a fluid-filled piston and compressing it? Or do you mean pressure, as in, pressing/squeezing the material with bare hands? Both are valid; the first one is scientific usage, and the second one is used in spoken language. $\endgroup$
    – AlphaLife
    Oct 5, 2021 at 4:25

4 Answers 4

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Becoming less dense with pressure is an energy-producing quality; mass being conserved, volume must increase as pressure rises for density (mass/volume) to have that response. So, I'd say that fulminate of mercury does fit the description; it explodes when compressed. It does that once, and only once, of course, and one might not want to be present at such an event.

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  • $\begingroup$ Beat me to it!! $\endgroup$
    – Ben
    Oct 3, 2021 at 17:02
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    $\begingroup$ I would have thought explosive decomposition counted as a phase transition. $\endgroup$
    – timuzhti
    Oct 5, 2021 at 4:59
  • $\begingroup$ Related chemistry.stackexchange.com/questions/158428/… $\endgroup$
    – Alchimista
    Oct 5, 2021 at 9:22
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    $\begingroup$ are there videos of it ? So that we don't try it at home :) $\endgroup$ Oct 5, 2021 at 12:50
  • $\begingroup$ In fact, the units of pressure are units per volume. Pressure is equal to $\frac{\delta E}{\delta V}$. $\endgroup$ Oct 6, 2021 at 2:13
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It is impossible to have a homogeneous thermodynamically stable substance in which pressure increases along with the volume. If this happens, then the material can lower its energy by shrinking one half and expanding the other half (assuming constant entropy). This instability is exactly the reason, why the Van der Waals gas equation experiences liquid-gas phase separation.

Some materials, though, can exhibit drop in tension if they are stretched beyond a certain limit. This results in such effects as necking and beading (you can check a number of examples from the paper Necking, Beading, and Bulging in Soft Elastic Cylinder). I am not sure about a similar example for positive pressure, but I would not be surprised if such material exists. Some sponges, when one tries to squeeze them from the sides, instead of being deformed uniformly, they first squeeze at the surface, while the bulk remains largely undeformed. Such behavior is an indicator the instability resulting from the strain going down as the deformation increases.

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  • $\begingroup$ What about Dilatency in, for example, wet sand. Think of walking on the beach; when you step the sand grains below your foot rearrange and increase in volume causing the patch to look dry as the water present no longer fills the volume. $\endgroup$
    – Ben Watson
    Oct 3, 2021 at 16:26
  • $\begingroup$ In your first sentence you seem to assume that the volume should increase as a collinear response to the compressing force. But there might be materials that expand to the sides more than they get compressed in perpendicular direction. This would then increase the volume without instability. $\endgroup$
    – Ruslan
    Oct 4, 2021 at 15:16
  • $\begingroup$ You are correct, a material can expand more to the sides than contract linearly when pressure is applied in one direction (increasing the total volume). It is not particularly counterintuitive though, and I assumed OP was interested in more unusual case, when the displacement is opposite to the direction of the force. $\endgroup$
    – Pavlo. B.
    Oct 4, 2021 at 15:35
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    $\begingroup$ @BenWatson The effect with the wet sand is caused by the shearing force that's applied to the sand, not by uniform pressure. $\endgroup$ Oct 4, 2021 at 20:37
  • $\begingroup$ Yes, such material would be unstable but I don't see impossibility. Apply sufficient force to nudge it out of the local minimum and have it reach the global minimum at higher volume than the start volume. Then change some parameters (maybe temperature) so the previous global minimum is gone and the previous local minimum is the global one. Once material gets in that minimum, slowly reset the temperature and you can repeat the procedure. $\endgroup$ Oct 6, 2021 at 9:05
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Is it possible that material may become less dense as more pressure is applied without a phase transition?

The answer to this is YES, it is possible, and this is an active area of research. You can have a material that becomes less dense when you compress it with your bare hands.

You can think of constructing metamaterials with this property (See this paper). This honeycomb-like material, for instance, gets less dense if you apply pressure in a specific direction. The material is hollow, and the sides of the hexagons are flexible.

Before applying pressure (smaller, denser)

enter image description here


After applying pressure (larger, less dense)

![enter image description here


Note that this is just a 2-D slice of the material, and if you can imagine a stack of such slices, you would have a real,3-D material.

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    $\begingroup$ Although of course the negative compressibility of that structure only applies for some distance. You might want to say "in a specific direction and for a specific maximum displacement". $\endgroup$
    – Graham
    Oct 4, 2021 at 16:14
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    $\begingroup$ I feel this unswer is misleading in the current form. First, linear compressibility is related to the change of linear dimensions with respect to the hydrostatic pressure, not just linear pressure, as the answer makes it seem. Second, materials with negative linear compressibility still have positive regular volume compressibility and their total volume still decreases if a hydrostatic pressure is applied (and thus density increases with pressure). $\endgroup$
    – Pavlo. B.
    Oct 4, 2021 at 16:40
  • $\begingroup$ @Pavlo.B. Thanks, there was indeed a mixup of terms. The main point of the answer still stands, though. $\endgroup$
    – AlphaLife
    Oct 4, 2021 at 17:25
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    $\begingroup$ I think this question poses some challenges even semantically. I think that the scale at one is looking might alter the answer. But even in this case, the material before and after the F is applied along one direction seems to me in two different phases. $\endgroup$
    – Alchimista
    Oct 4, 2021 at 19:32
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    $\begingroup$ That's not pressure, that's a shearing force. The force is applied only in a single direction, and not in the orthogonal direction. Pressure, however, is a scalar field that is independent of surface orientation, and it would force the structure to recolapse into its less voluminous form. $\endgroup$ Oct 4, 2021 at 20:42
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Density is mass/volume. The only way to become less dense without losing mass is to increase volume.

Therefore what you are asking for is

  • "is there a material which becomes larger as pressure is applied".
  • "is there a material which loses mass as pressure is applied".

This is not in-principle impossible.

  • For the first, high explosives (HE) with a pressure-sensitive switch would do it.
  • For the second, squeezing a sponge full of water might work.

In either case, these are not "simple" materials with "simple" interactions. The problem really is not that it can't be done, but that there are so many ways to do it, and they are all different.

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  • $\begingroup$ Thank you. Yes, my question is "is there a material which becomes larger as pressure is applied". I will clarify that in the OP. $\endgroup$
    – dotancohen
    Oct 4, 2021 at 6:15
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    $\begingroup$ @dotancohen you should add as you did early in the text "without phase transition". This will limit the possibilities (real or just thought). In my opinion it even warrant that the answer is no. $\endgroup$
    – Alchimista
    Oct 4, 2021 at 10:15

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