To develop a basic understanding of a new class of ionic liquids (ILs), "solvate" ILs, the transport properties of binary mixtures of lithium bis(trifluoromethanesulfonyl)amide (Li[TFSA]) and oligoethers (tetraglyme (G4), triglyme (G3), diglyme (G2), and monoglyme (G1)) or tetrahydrofuran (THF) were studied. The self-diffusion coefficient ratio of the solvents and Li+ ions (Dsol/DLi) was a good metric for evaluating the stability of the complex cations consisting of Li+ and the solvent(s). When the molar ratio of Li+ ions and solvent oxygen atoms ([O]/[Li+]) was adjusted to 4 or 5, Dsol/DLi always exceeded unity for THF and G1-based mixtures even at the high concentrations, indicating the presence of uncoordinating or highly exchangeable solvents. In contrast, long-lived complex cations were evidenced by a Dsol/DLi ~1 for the longer G3 and G4. The binary mixtures studied were categorized into two different classes of liquids: concentrated solutions and solvate ILs, based on Dsol/DLi. Mixtures with G2 exhibited intermediate behavior, and is likely the borderline dividing the two categories. The effect of chelation on the formation of solvate ILs also strongly correlated with electrolyte properties; the solvate ILs showed improved thermal and electrochemical stability. The ionicity (Λimp/ΛNMR) of [Li(glyme or THF)x][TFSA] exhibited a maximum at an [O]/[Li+] ratio of 4 or 5.