Can Diamond or Buckytube Materials Contain Electron Degenerate Matter?

[pervect]

Robert Forward once suggested that diamond was strong enough to contain electron degenerate matter (white dwarf star material).

I'd like to get some basic insight into the physics. It's half for a story purpose, and half personal curiosity. Some questions I have are:

1) What sort of pressures would be required to contain electron degenerate matter. Could diamond or buckytube based materials theoretically have the strength required?

1a) I get the stress in a thin-walled pressure vessel is pressure*r/2t , which is equal to (3/2)* pressure * (volume enclosed) / (volume of vessel). Thick walled vessels are more complicated, I don't have much insight as to the peak stress for those,.

2) What sort of densities would be achievable?

3) Within a few orders of magnitude (hopefuly 1-2, but as accurate as one can get simply), how much energy/kg is required to do the compression? I suppose I'm envisioning adiabatic compression, but if there's some other reasonable model, I'd be interested in that too. Would the energy required be affected much by the original source material or phase (solid, liquid, gas, hydrogen, water, iron, for instance)? Would the source material affect the answer to 2 (achievable density)?

3a) How hot would the compressed material get?

5) Is there any known or semi-plausible method for creating this much pressure?

6) Would fusion conditions potentially occur spontaneously under these sorts of conditions if hydrogen were used? If deuterium was used? (This might give some insight into 5 as well.)

 

[Vanadium 50]

Robert Forward once suggested that diamond was strong enough to contain electron degenerate matter (white dwarf star material).

He was wrong, except in the trivial sense that one could build a diamond shell around a white dwarf. True, but one could also build a whipped-cream shell.

The yield strength of diamond is actually not very high - otherwise they could not be cut. Diamonds are hard, but not strong. Anyway, simple dimensional analysis shows this won't work: most uniform solid materials have Young's moduli of around 100 GPa, and yield strengths of 100 MPa. So they can be squeezed to about 99.9% of their size and held there by some kind of shell or vise. I'll spot you an order of magnitude for selecting optimal materials, and that gets us to 99%. We need to get to 0.1%.

 

[pervect]

He was wrong, except in the trivial sense that one could build a diamond shell around a white dwarf. True, but one could also build a whipped-cream shell.

The yield strength of diamond is actually not very high - otherwise they could not be cut. Diamonds are hard, but not strong. Anyway, simple dimensional analysis shows this won't work: most uniform solid materials have Young's moduli of around 100 GPa, and yield strengths of 100 MPa. So they can be squeezed to about 99.9% of their size and held there by some kind of shell or vise. I'll spot you an order of magnitude for selecting optimal materials, and that gets us to 99%. We need to get to 0.1%.

Bucky tubes have a young's moduls of 1-5 Tpa (according to wiki) , and elongate 16% before the break (according to wiki).

If the curve remains inear, that's 16% for the nanotube, and the object with the lower modulus should stretch 10x more.

It's probably not linear, but I don't think a super-simple analysis can rule out the idea. Unless I made some silly error. Or wiki did.

http://en.wikipedia.org/w/index.php?title=Carbon_nanotube&oldid=536886212

 

[Vanadium 50]

A large Young's modulus doesn't help you, as that makes it worse. You need a large yield strength.

 

[pervect]

A large Young's modulus doesn't help you, as that makes it worse. You need a large yield strength.

The yield strength would be the 15-53 Gpa in the wiki article, right? 16% elonation at 1 Tpa or so?

You can also gain some factor by having a thick shell -perhaps not quite as large as the volume ratio I mentioned.

Even if bucky tubes won't do the job, I'd like a better handle on the pressure volume relation than the Young's modulus linear slope, if ayone knows.

[add]
(also: would we really want the Young's modulus, or the bulk modulus? Even for the iear approximation. I think we'd want deltaV-V, not delta-L/L)

 

[Vanadium 50]

You can't increase the yield strength by adding more material. (Think about two identical concentric shells. Once the inner shell yields, so will the outer one)

If you were off by a factor of 2, maybe there would be some way to fiddle with this and make it work. And it would make a difference whether we are talking linear or volumetric moduli. But you are many orders of magnitude off.

 

[pervect]

You can't increase the yield strength by adding more material. (Think about two identical concentric shells. Once the inner shell yields, so will the outer one)

If you were off by a factor of 2, maybe there would be some way to fiddle with this and make it work. And it would make a difference whether we are talking linear or volumetric moduli. But you are many orders of magnitude off.

I've been thinking about this, and I think I have a convincing (to me) and simple argument that shows that one can contain a more or less arbitrary pressure with whatever material is available (including wet tissue paper :-)). Though the material would have to be chemically inert to whatever it was supposed to contain, etc. I'm just addressing the mechanical aspects.

Lets say you design a shell that can handle say 300 bar pressure differential between the inside and outside.

You pressurize that shell to 300 bar, and put in another shell inside it. You can pressurize the interior shell to 600 bar. (300 more than the outer pressure).

As you keep nesting shells, you can increase the pressure indefinitely. 3 stacked shells support 900 bar, etc etc etc.

One rather unwiedly realization would add pumps inside the shells. Each pump would support the desired pressure differential between the shells as you added or removed material.

Mechanically, there isn't any upper limit to what pressure you can contain that I can see. You just need a lot of low strength material.