Reader Mihkel on EEStor Purity Announcement

Here's another interesting technical dissection of from todays blog comments...this time from Mihkel.  Again, I just want to pull out some of these technical comments and separate them from the discussion of zenn stock, etc.  My hope is other technical folks will add to the commentary and even, hopefully, add a little relief in terms of providing some plain english verbiage that average joes like me can follow. 

Mihkel said...

Word wraps removed (sorry for 2x post).

While considering solid state electrical energy storage device's (capacitor's) ability to store energy, maximal upper bound for volumetric energy density (energy per unit of volume) can be obtained knowing only operating device's dielectric's permittivity and (operating) electrical field strength. If we allow dielectric's material density (mass per unit of volume) to be known, we have one more energy storage characteristic: gravimetric energy density (energy per unit of volume).

So, formulae for both type of characteristics are:
volumetric: Uv = ε*E^2/2,
gravimetric: Ug = Uv/ρ = (ε*E^2/2)/ρ,
where
U - Energy density,
ε - actual permittivity of substance,,
E - Electric field,
ρ - material density.

ε and E can be calculated: E based on article and ε based on information known before. ρ can be obtained by encyclopedia lookup and making some assumptions. ε = εr*ε0 where εr (or k) is relative (to free space) permittivity of dielectric and ε0 permittivity of free space or the electric constant. Then take the voltage and divide it by the distance it was applied over (over dielectric's thickness) and you get E (E = U/l).

Now we can get computable formulae for a given dielectric considering source data available to us:
volumetric: Uv = εr*ε0*(U/l)^2/2,
gravimetric: Ug = Uv/ρ = (εr*ε0*(U/l)^2/2)/ρ.

I must emphasise we are considering only maximal bounds based on given numbers (not it's production feasibility) about dielectric. To ceramic capacitors, this bound depends only on dielectric's characteristics.

Let's get now source data. U = 350 V and l = 1 µm we take from the article. εr = ~18k has been stated before. For barium titanate, ρ = 6.02 g/cm^3 can be taken from Wikipedia, but we make a wild assumption here, that the actual material has the same density as barium titanate. ε0 can taken from any table of physical constants (ε0 = ~8.85 * 10^(-12) F/m).

Filling formulae with data and letting google's compute engine step into play, we have:
volumetric: Uv = ~2700 Wh/l
gravimetric: Ug = ~450 Wh/kg
(Verify:
Uv – http://www.google.com/search?hl=en&rlz=1G1GGLQ_ENXX252&q=18000*8.85*10^-12F%2Fm*(350V%2Fmicrometer)^2%2F2+to+Wh%2Fl&btnG=Search
Ug – http://www.google.com/search?hl=en&rlz=1G1GGLQ_ENXX252&q=(18000*8.85*10^-12F%2Fm*(350V%2Fmicrometer)^2%2F2)%2F(6.02g%2Fcm^3)+to+Wh%2Fkg&btnG=Search )
:

To put these numbers into perspective, consider enerergy density of current production lithium-ion energy storage: Uv = 270 Wh/l and Ug = 160 Wh/kg.

The key point to make such numbers available is EEStor's proprietary technology achieving dielectric material with outstanding properties, namely: Electrical field E = 350 V/µm (at production level) while maintaining permittivity εr (or k) = ~18k. At field 350 V/µm, one has to watch for two types of breakdowns: electrical and permittivity. 1st one occurs if dielectric (insulator) becomes conductor due to field's strength, 2nd one is the natural property (until EEStor proves wrong?) of high-k (high relative permittivity) dielectrics to loose their permittivity in high field strengths (orders of magnitude below 350 V/µm). I suspect the 1.1 kV/µm stated in the article is the lower one of the two.

This remains the point over which scientific community remains sceptical. EEStor seems to have resolved this problem some time ago and seems to deal with production issues.

To get some clue how these hypothetical maximum bounds relate to real world, one has to take into account that ceramic capacitors need also conductive plates sandwiched between dielectric layers. This makes Uv and Ug smaller, because you have to take plate material into account, which does not store energy. There are also packaging and structural materials, electronics, etc... They also use fields 350 V/µm instead of 1.1 kV/µm (as stated in the article) because of manufacturing process' mistakes and impurities in some points of dielectric material, which brings the electric field value for the two (possible) breakdowns down.

Imagine, if you can enhance the manufacturing process and rise operating electric field from 350 V/µm to somewhere higher? You get a nice boost in energy density, as it is quadratically (as seen from the formulae) proportional to electric field.