© 2015 The Royal Society of Chemistry. We report on the physical properties of lithium-ion conducting nanoparticle-polymer hybrid electrolytes created by dispersing bidisperse mixtures of polyethylene glycol (PEG)-functionalized silica nanoparticles in an aprotic liquid host. At high particle contents, we find that the ionic conductivity is a non-monotonic function of the fraction of larger particles xL in the mixtures, and that for the nearly symmetric case xL ≈ 0.5 (i.e. equal volume fraction of small and large particles), the room temperature ionic conductivity is nearly ten-times larger than in similar nanoparticle hybrid electrolytes comprised of the pure small (xL ≈ 0) or large (xL ≈ 1) particle components. Complementary trends are seen in the activation energy for ion migration and effective tortuosity of the electrolytes, which both exhibit minima near xL ≈ 0.5. Characterization of the electrolytes by dynamic rheology reveals that the maximum conductivity coincides with a distinct transition in soft glassy properties from a jammed to partially jammed and back to jammed state, as the fraction of large particles is increased from 0 to 1. This finding implies that the conductivity enhancement arises from purely entropic loss of correlation between nanoparticle centers arising from particle size dispersity. As a consequence of these physics, it is now possible to create hybrid electrolytes with MPa elastic moduli and mS cm-1 ionic conductivity levels at room temperature using common aprotic liquid media as the electrolyte solvent. Remarkably, we also find that even in highly flammable liquid media, the bidisperse nanoparticle hybrid electrolytes can be formulated to exhibit low or no flammability without compromising their favorable room temperature ionic conductivity and mechanical properties.