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,
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
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.
Tuesday, July 29, 2008
Word wraps removed (sorry for 2x post).
They have revealed a few tasty tidbits.
1) pure aluminum oxide (AlO3) coating of the pure 1 micron powdered composition-modified barium titanate (CMBT) allow "the **potential** to reach its target working voltage. " The 2 "sentences after that indicate that purity is needed for resistance to breakdown (catastrophic leakage).
2) the AlO3 coating and the closely-sized 1 micron CMBT "assists" in "meeting the energy storage stabilization over the temperature range"
3) the plastic PET matrix is key to physically turning the particles in a strong electric field to get the best polarization. Polarizing BT in a strong electric field while the material is still hot during manufacturing is standard practice, much the same way magnets are created by using a magnetic field while the metal is very hot. "Polarization along with other proprietary processing steps provides the **potential** of a polarization saturation voltage required by EEStor." The plastic matrix is unique and this may be the explanation I have been looking for. I believe i had guessed here before that better polarization was the reason for the PET.
to better explain polarization: the CMBT crystals work best when oriented in a certain way. That orientation is forced up the crystal by a very strong electric field as the last stage in manufacturing. However, it's not completely effective when the crystal are "bumping" against each other. This causes some "domains" (localized volumes) of the BT to be better oriented than others. However, using the plastic PET keeps the particles seperate so that they can achieve perfect polarization if the plastic is melted during the manufacturing polarization, with each 1 micron particle having a homogeneous single domain. The plastic also allows the domains to expand/contract more during use which allows more energy to be stored so that energy saturation is not reached. Being perfectly aligned also helps for greater expansion/contraction.
The press release states very clearly that either they DO NOT have any prototypes ... or ... DO NOT KNOW if they can achieve production of a high energy capacitor described in the patents by their use of the word "potential" in the following sentence:
"Polarization along with other proprietary processing steps provides the potential of a polarization saturation voltage required by EEStor."
"polarization saturation voltage required" means "energy storage" (high permittivity saturation) as the crystal is polarized during use and not to be confused with the polarization step during manufacturing which is the meaning of "polarization" in the first part of the sentence.
1,100 V/micron applies only to the AlO3 and not to the BT which is 350 V/micron. And "breakdown voltage" does not mean energy storage or maintaining high permittivity.
EEStor Announces Certification of Additional Key Production Milestones and Enhancement of Chemical Purity
Here is the press release.
Another link to the story.
Here's the link to the PRNewswire release.
Also, many people are trying to figure out what the significance of this press release is for interested parties. Among the other signficances discovered in this press release, let's not forget that it did already cause a moderate earthquake in Los Angeles, home to all those future electric vehicles.