Max specific energy (energy density by mass) in a capacitor

[timelessmidgen]

Hi folks, here's a thought/conceptual question I've been wondering about. What is the maximum theoretical specific energy (IE Joules/kg or equivalent) for energy stored in the electric field of a capacitor? I know the energy stored in a capacitor is given by U=C V^2/2, and the mass of the system will be the mass of the capacitor plates, plus relativistic mass due to the energy stored (mrel=U/c^2). Obviously at low energies the mass of the plates will dominate, but as we increase the voltage the overall energy efficiency will approach the ideal U/m=c^2. So what's the rub? Could we just take a set of parallel plates, ramp the potential difference up to ridiculously high values, and achieve specific energy values on par with stored antimatter? There must be some upper limit to the voltage before dielectric breakdown occurs, but what's the max theoretical value of this? Is it the "Schwinger limit" of 1.32e18 V/m if we're in a vacuum? (https://en.wikipedia.org/wiki/Schwinger_limit) If there's nothing else that comes into play to limit the specific energy, it doesn't seem all that difficult to achieve ridiculously high specific energy values.

As a numerical example, say I take two square aluminum plates (rho=2800 kg/m^3), each measuring 10m by 10m with a thickness of 0.01m, and a separation between them of d=0.1m, in a vacuum. The plate mass is then: mp=2*area*thickness*rho=5600 kg. The capacitance is: C=ε₀* area/d=8.85e-9 F. Given our plate separation, the max potential difference (if it's constrained only by the Schwinger limit) would be 1.32e17 V. Then the total energy stored would be: U=C V^2/2=7.71e25 J. The relativistic mass due to all that energy would be mrel=U/c^2=8.58e8 kg. The plate mass is a rounding error compared to the relativistic mass, and we find that U/(mrel+mp) is 8.98749e16 J/kg or 0.999993*c^2. Just a hairs breadth away from the maximum theoretical possible.

So what gives? Are there theoretical concerns I'm overlooking? If not, are there really difficult material concerns that would stop us from realizing this kind of performance?

Edit: A little more thought makes me realize at least one big problem. The parallel plates are going to have some pretty fierce force pulling them together. As soon as we introduce some support structure to keep the plates stationary it provides a conducting path which will have a breakdown voltage of ~plateseparation*delectric breakdown. So that brings the maximum possible voltage difference down from ~1e18 V/m for vacuum to ~2e9 V/m for diamond. Those nine orders of magnitude make a big difference! Replacing the maximum voltage in my example above with 2e9 V/m*0.1m yields a measly specific energy of 3.5e-13 *c^2.

 

[anorlunda]

A quick Google search found this https://www.electrochem.org/dl/ma/201/pdfs/0228.pdf which says 30 Wh/kg

 

[timelessmidgen]

A quick Google search found this https://www.electrochem.org/dl/ma/201/pdfs/0228.pdf which says 30 Wh/kg

Hmm, that is interesting, but I'm not sure it actually addresses my question. This appears to specifically discuss a battery/capacitor hybrid cell.

 

[anorlunda]

So, what does your own research on capacitor energy density say?

 

[timelessmidgen]

So, what does your own research on capacitor energy density say?

My apologies if I've given offense. Perhaps you can correct me if I've misunderstood the article, but it appears to address a very specific system of an electrochemical battery / capacitor system, and the limit they discuss is due largely to the mass of the electrolyte and electrodes - limits which would not apply to a simple capacitor.

I would still be curious to hear insight regarding absolute limits, or limiting effects that come into play in simple capacitors charged up to ridiculously high potential differences.

 

[anorlunda]

I'm not offended, but our role here at PF is to assist, not to do the research for you. We. Make students show their attempt at problems before offering assistance.

The following sounds relevant.

• Electrostatic double-layer capacitors use carbon electrodes or derivatives with much higher electrostatic double-layer capacitance than electrochemical pseudocapacitance, achieving separation of charge in a Helmholtz double layer at the interface between the surface of a conductive electrode and an electrolyte. The separation of charge is of the order of a few ångströms (0.3–0.8 nm), much smaller than in a conventional capacitor.