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.
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.
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:
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:
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
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.
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
