With an interest in exploring the limits of relative cation/anion mobilities in nonaqueous electrolyte solutions, we have measured the diffusivities of Li-and F-containing species in 0.5 M solutions of the new lithium salt, lithium bis͑perfluoropinacolato͒ borate, LiBPFPB, which contains a giant anion with 24 fluorine atoms. Using the pulsed field gradient spin echo method on the NMR resonances of 7 Li and 19 F in the temperature range 30-95°C we find, for the first time in nonaqueous salt-in-molecular solvent solutions, lithium diffusivities that are higher than those of the anion-containing species. Furthermore, solutions in propylene carbonate ͑PC͒ appear to be fully dissociated, since the conductivities calculated from the Nernst-Einstein equation exceed the measured conductivities by only 23% at ambient temperature and 41% at 95°C. These values are comparable with those observed for molten salts such as LiNO 3 , NaNO 3 , and aqueous LiCl solutions. Since such deviations are known to be due to interionic friction alone, transport numbers for Li ϩ may be calculated from the diffusivities without correction for neutral species. We obtain a value of 0.55 for PC solutions at 50°C. In the lower dielectric constant 1,2-dimethoxyethane solutions the ratio of calculated to measured conductivity is much higher. Here it would appear that ion association is still a problem and must be corrected for in calculating the transport number. For this case we obtain the value 0.53. We discuss means of increasing this value toward unity and show that this must involve abandoning simple salt solutions as electrolytes.The optimal functioning of a high-rate discharge battery demands the achievement of very specific characteristics for the electrolyte. Its performance depends not only on the ionic conductivity of the electrolyte but also on a high cationic transport number, t ϩ , since this condition minimizes the overpotentials due to the increase of concentration gradients in the vicinity of the electrodes and the depletion of electrolyte inside porous electrodes. 1 However, values of t ϩ for lithium ions commonly found in nonaqueous solutions fall below 0.5. 2,3 Furthermore, much of the transport of lithium is unfruitfully performed by neutral species according to the large deviations from the Nernst-Einstein equation that are usually found. Extensive ion-pairing has so far been the source of diffusivity-based transport numbers that fall near 0.5. 3 In an effort to obtain better electrolytes we have been attempting to design systems which combine high lithium mobilities with high lithium transport numbers and low ion-pairing.In this paper we give evidence of some progress in this direction, using a combination of self-diffusivity and conductivity studies on solutions containing a new lithium salt reported recently, 4 lithium bis͓1,2-tetrakis͑trifluoromethyl͒ ethylenediolato (2-)-O,OЈ͔ borate, LiB͓OC͑CF 3 ͒ 2 ͔ 4 , or more simply, lithium bis͑perfluoropinacolato͒ borate ͑LiBPFPB͒, which has a particularly large perfluorinated anio...