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This is more a physics/chemistry/nanotech question, but what's the theoretical best energy density you could get out of a chemical battery (or fuel cell), if you could arrange atoms in any manner you wanted? I'm thinking of the nanotech batteries described in Diamond Age. How does it compare to current technologies?

This is specifically about chemical batteries, which could be built atom-by-atom in the charged state, not nuclear, antimatter, CAM, or other more exotic technologies.

endolith
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    depending on how theoretical you want to be, an anti-mater battery would be the theoretical highest i believe as when it reacts with mater you get a perfect or near perfect conversion from mass to energy. – Mark Dec 02 '10 at 21:19
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    Do antimatter-matter reactions count as chemical reactions? – endolith Dec 02 '10 at 21:42
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    If you consider them physics, everything is physics - even chemistry. – sybreon Dec 03 '10 at 02:48
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    @sybreon: [Disciplines arranged by purity.](http://xkcd.com/435/) – Nick T Dec 05 '10 at 10:43
  • But my question's about chemical batteries. Nuclear batteries are not chemical batteries, and I don't think antimatter reactions count, either. – endolith Dec 05 '10 at 18:22
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    Although closed as a duplicate of this question, *[Is there a limit to the number of kilo-watt hours an AAA (or AA) battery can hold?](http://electronics.stackexchange.com/q/19115/3774)* has answers (like [this one](http://electronics.stackexchange.com/questions/19115/is-there-a-limit-to-the-number-of-kilo-watt-hours-an-aaa-or-aa-battery-can-hold/19125#19125) talking about energy density related to volume rather than weight, which these answers seem to concentrate on. – Mark Booth Sep 07 '11 at 18:29
  • Why aren't answers from a duplicate question merged with the original? – endolith Sep 07 '11 at 18:36
  • @endolith - On other stack exchange sites, questions tend not to be closed as duplicates *if* there have been significant answers already posted. Also, the other question is more specific in that it explicitly asks for answers based on volumetric energy density, whereas this question leaves it up to the answerer to assume volumetric or weight based 'density'. As such, I've been considering a vote to re-open. – Mark Booth Sep 07 '11 at 18:41
  • and I'm not sure whether to ask about nanotech supercapacitors here or in another question – endolith Jan 08 '15 at 17:54
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    As I understand it, the Vanadium-Boride-Air battery has a theoretical energy density on the order of 27kwh/liter, I forget what that worked out to in kwh/kg, but petrol's only ~10kwh/L. It's not rechargeable though as far as I know. 27kwh/L beats the pants off everything for maximum energy in the minimum space. Weight-wise though (kwh/kg), I think the winner is Lithium-Air. – Sam Jun 29 '17 at 00:15

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I don't know the actual answer to this question, but I know a least upper bound to the answer, and a means of figuring out the real answer.

Battery scientists have a metric called maximum theoretical specific energy; you can read about the definition in Advanced Batteries by Robert Huggins. Right now, the most energy dense batteries you can buy are lithium ion, which are in the 100-200 Wh/kg range. I don't know what the best battery is, but later in the book, Huggins shows calculations that indicate that Li/CuCl2 cells have an MTSE of 1166.4 Wh/kg. (5x the capacity of current batteries!)

We know that the highest MTSE is at least 1166.4 Wh/kg; you could use his method to calculate the same value for other chemistries, but the search space is pretty large.

I've also seen references on the internet to Li/O2 and Al/O2 batteries with MTSE of 2815 and 5200 Wh/kg, respectively. Not sure how credible those references are. Later references, like this 2008 article in the Journal of the Electrochemical Society, suggest that the MTSE for a Li/O2 cell is around 1400 Wh/kg.

pingswept
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    Seems like batteries that breathe air are sort of cheating the energy density calculation by using something outside the battery to help store energy (O2 in air) without counting it in the mass? They become more analogous to a car's engine than its fuel tank. – Matt B. Jul 07 '11 at 20:21
  • @MattB.: Yeah, it's kind of cheating, but kind of not. I'm glad it was mentioned as I hadn't thought of it. – endolith Aug 24 '11 at 17:42
  • "Of the various metal-air battery chemical couples (Table 1), the Li-air battery is the most attractive since the cell discharge reaction between Li and oxygen to yield Li2O, according to 4Li + O2 → 2Li2O, has an open-circuit voltage of 2.91 V and a theoretical specific energy of 5210 Wh/kg. In practice, oxygen is not stored in the battery, and the theoretical specific energy **excluding oxygen is 11140 Wh/kg** (40.1 MJ/kg). Compare this to the figure of 44 MJ/kg for gasoline (see petrol energy content)." http://en.wikipedia.org/wiki/Lithium_air_battery – endolith Aug 24 '11 at 17:48
  • The upper bond is achievable if you have a small cell but lots of fuel. – user3528438 Jun 29 '17 at 18:19
  • Also remember what the first fuel cell runs, the easiest and highest density fuel for fuel cell till this day. – user3528438 Jun 29 '17 at 18:20
  • The "this 2008 article" link is dead. Near as I can tell, at least the Internet Archive does not have a useful copy. – user Jul 13 '19 at 18:57
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If we want to broaden "battery" to mean some sort of device that generates electricity based on a chemical reaction (via magical means), the upper 100% efficient limit would be the chemical enthalpy of the reaction.

Calculations for a theoretical "sugar+air" battery:

  • Standard enthalpy of combustion of glucose: −2805 kJ/mol (I think this is a shortcut beyond decomposition into standard elements?)
  • 2805 kJ/mol / 180 g/mol = 4328 W·h/kg

Not sure what the most chemically dense compound is, but you could just plug it into that.

Nuclear powered cells could be even more magical, E=mc²:

  • 1 kg × c² = 2.5 × 10**13 W·h
Nick T
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  • These other chemistries would have to be magical because they don't directly push electrons through metal? – endolith Dec 02 '10 at 19:35
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    Mostly because they aren't electrochemical cells, so the energy to electricity conversion would have to happen some other way (e.g. power plants or [plant plants](http://nexus404.com/Blog/2010/04/16/stanford-university-succesfully-generates-electricity-from-plants-stanford-scientists-harness-energy-in-algae-photosynthesis/).) – Nick T Dec 02 '10 at 20:10
  • Sugar + Air? Why not, say, C4 + air? – Kevin Vermeer Jan 23 '11 at 19:40
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    C4 (or TNT anyway) is less energy-dense than sugar. http://en.wikipedia.org/wiki/Energy_density – Matt B. Jul 07 '11 at 20:25
  • or carbon-air, with less hydrogen involved. Use diamond as your carbon? Pure C12 diamond, for low weight? :) – wbeaty Jun 29 '17 at 01:20
  • @wbeaty Seariously? Why less hydrogen makes it higher energy? Hydrogen is the highest energy fuel and the hydrogen fuel cell was the first cell invented hundreds of years ago, and widely available now, too. – user3528438 Jun 29 '17 at 18:25
  • @user3528438 just calculate. Diamond gives 4.4X more energy than sugar if compared by volume, or 2x more energy if by weight. Or, compare anthracite coal to carbohydrate in https://en.wikipedia.org/wiki/Energy_density. But why? Perhaps because carbohydrate had already emitted energy to form H-O bonds and C-O bonds in the molecule, while straight C or H has not. Stupid photosynthesis making sugars, when it should store energy by making graphite or compressed hydrogen! – wbeaty Jun 30 '17 at 06:49
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    @endolith Visualize metals as being single giant molecules. Then we see that battery plates are "molecules" which make available at the macro-scale all the electron-transfers usually hidden inside single reacting molecules. So, any solid, if conductive, could act as a giant molecule or battery plate. Fractal diamond foam might be good, but make it from conductive doped diamond! – wbeaty Jun 30 '17 at 07:08
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Current state of the art lithium/sulfur batteries are about 350 Wh/kg. And therefore not unobtainium like many of the listed chemistries.

Here's some detailed info: https://en.wikipedia.org/wiki/Lithium-sulfur_battery

Glenn
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Nano silicon anode lithium ion battery has a theoretical upper limit of 12000 watt hours a kilogram. I don't know volumetric density. The issue is silicon swelling which causes cracking. As of 2023 they are working on using sulfur to add some flexibility so the swelling doesn't cause cracking. That's the best I've got.

Vladimir Silver
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fuel cells will have higher theretical energy densitites than batteries, but lower power densities. on the other hand, capacitors will have higher power densities but lower energy densities.

Consider these theoretical values

energy density= voltage x capacity

power density= voltage x current

capacity= Faraday const x #electrons transferred (ex: 1 for Li-ion batteries) x 1/MW

current depends on the capacity and the rate of discharge. For example at a C/2 rate, you will discharge fully in 2 hours, so if the total capacity is 100 mAh/g, then the current will be 50 mA for 1g. Lets say we have a 2V battery, then the Power will be 100 mW for 1g. (also the energy density of this battery would be 200 mWh/g)

voltage = E0cathode - E0anode, E0= - delta G (as in Free Gibbs Energy) / (#charges x Faraday const)

in the most prevalent case where you have reduction of a metal ion at the anode (Li-ion included) E0anode is the reduction potential of the metal, see here: http://en.wikipedia.org/wiki/Standard_electrode_potential_%28data_page%29

for example: Li+ +  e− is in equilibrium with Li(s) E0=−3.0401 V

guywithaquestion
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