The Power Japan Plus battery is one of those not-so-great batteries, and here's why:
Lithium ion batteries work by shuttling ions between two "intercalation materials." The lithium rests in the crystal structure of a lithium oxide at discharge, then upon charging, shuttles that lithium from the lithium oxide, through the lithium salt electrolyte, and inserts it into the open spaces of a graphite anode, thereby storing energy. The "Ryden battery" is a similar lithium intercalation battery, except that the source of the lithium isn't a lithium oxide, it's the lithium salt electrolyte; there is no solid state source for lithium ions [1]. As such, the capacity of the battery is limited by how much lithium you have in the electrolyte, which is a function of volume and concentration. You don't want to have a large volume of electrolyte because that means it's a greater distance the lithium ion has to travel, increasing ionic resistance, and driving down cell efficiency. Therefore we have identified one limit to cell capacity.
Even if you manage to have an exceptionally high concentration of lithium (you can't, btw; it's stuck around 1M for safety considerations [2]), you're still limited by the specific capacity of graphite, which is the bottleneck in current lithium ion chemistries at around 100-150mAhr/g. Power Japan Plus gives us a diagram showing cell voltage as a function of capacity and the battery stops charging at 140mAhr/g; just what we'd expect. Here is another limit to cell capacity (granted a limit we come across all the time in lithium ion batteries).
Finally, all this talk about lithium intercalation into graphite wouldn't be possible unless we had a counter-reaction to balance the charges. The "Ryden battery" claims to use a negative ion intercalating into graphite as the cathode. There are a couple of ions that could do this but ones that comes to mind are halides like fluorine or bromine (I actually couldn't find much literature on the electrochemistry of negative ion intercalation compounds: a bit of a red flag actually). We have other evidence to think this might be the case: Power Japan Plus has a cell voltage of around 4.5V. Solid state electrochemistry is very different than aqueous chemistry, but it still follows similar trends; in order to get a cell voltage that large with lithium on one side, you need a very electronegative electrochemical couple. Fluorine or bromine will do it. In an aqueous system (which is impossible for materials compatibility reasons, but for this exercise let's go ahead and consider it), a LiF battery would have 5.8V, which is close to what the "Ryden battery" is. And fluorine is often featured in lithium ion battery electrolytes, adding support to our guess that the other couple is a halide. This goes against their idea that their all-cotton battery is earth friendly if it contains one of the most poisonous elements on the periodic table. I'm not faulting Power Japan Plus for their chemistry; I'm faulting them for their messaging. If they think cotton in a 3000C furnace (which is just carbon at that point) and fluorine are "earth friendly" then who am I to argue.
The long and short of this analysis is we have a battery that has the same fundamental limitations as lithium ion batteries (the graphite anode), with a cell architecture that has serious capacity limits, and questionable negative electrode chemistry.
I don't mean to be a killjoy, but energy storage is a serious problem that demands serious answers. This is not one of those serious answers; let's stop treating it that way.
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[1]: http://powerjapanplus.com/battery/equation.html
[2]: http://www.electrochem.org/dl/interface/sum/sum12/sum12_p045_049.pdf
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