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New Polymer Could End Battery Fires, Quadruple Efficiency

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That's an exciting article, and I look forward to more rigorous testing, and reporting.

Good old PEG - it's good for what ails ya. Haven't come across PFPE before, however, to my recollection.
 
"spontaneous" here is used in its thermodynamic sense. it means that a phenomenon occurs by itself, or it is bound to happen.

also the author of the article misuses the word "trasnference rate". It is actually "transference number", as it is not a rate, but a fraction describing which mobile species in a solution is responsible for transferring most of the current. For example if you have 4 mobile ions in a solution, and only one of those is the desired mobile species (Li+ for example), it is not desirable for the other 3 mobile species to be too mobile. You would want the transference number of Li+ to approach unity (1.0 which means 100%).

The transference number however does not describe the "rate" at which the particular mobile species is moving. You can have a species A with a 0.2 transference number with much higher mobility than another species B with 0.9 transference number. The bottom line is how many Li+ can you move between electrodes per unit time. You can achieve high efficiencies with polymer gels/electrolytes but the rates of transport and conductivities of these electrolytes pale in comparison to liquid electrolytes. They are also expensive. This is why they are not used commercially, even though there is the safety argument in their favor.