Recent research has focused on solid polymer electrolytes (SPEs) as the best liquid electrolyte replacements. Poly(ethylene oxide) (PEO) is the most frequent one because of its fast segmental movements in the free volume which controls lithium-ion transport between electrodes. Therefore, PEO-based copolymer electrolytes that can be tailored for mechanical strength and ionic conductivity are often studied. The most popular material is PEO chains containing PMMA because PEO transports ions, and PMMA has good mechanical properties. Further investigations on PEO-based solid polymer electrolytes (SPEs) have shown that chain designs with more nonlinear branches prevent crystallinity and maintain fast segmental dynamics. For this purpose, we worked on PEO-grafted-PMMA copolymers in which the free volume probed by positron annihilation lifetime spectroscopy considerably affects the structure-ionic conductivity relationship. Finally, we investigated the free volume theory of ionic condcutivity using Yahsi-Ulutas-Tav (YUT) theory.