I wonder what makes them a proper electrolyte, and what are the current working mechanism models (designed ways of Li ion transfer) for these electrolytes?
it might be a bit late to answer your question! But, just so you know:
One of the advantages of implementing solid state electrolytes in Li batteries is achieving high level of safety since the electrolyte is no longer volatile which reduces the risk of catching fire especially in high operating temperatures. However, due to the very low ionic conductivity of electroactive ions in solid state electrolytes, they have not been of much interest for energy storage applications.
Instead, ionic liquid electrolytes, which are basically ionic compounds with very low melting point due to their over sized cations and/or anions, have been studied as electrolytes in lithium air batteries. These ionic liquid electrolytes have very low vapor pressure and are often non-flammable! Besides, they're still liquid at room temperature (RTILs) and therefore the ionic conductivity of electroactive species in RTILs will be high enough for energy storage applications especially with the help of organic additives.
For more information read this article (I have added the link to the publisher as well):
Journal of Physical Chemistry C, 2014, 118 (47), 27183-27192