A series of hybrid organic/inorganic triblock copolymers of polystyrene-butadiene-polystyrene (SBS) grafted with polyhedral oligomeric silsesquioxane (POSS) molecules with different chemical constituents were synthesized by a hydrosilation method. Four POSS macromers, R'R7Si8O12, were designed to contain a single silane functional group, R', which was used to graft onto the dangling 1,2-butadienes in the polybutadiene soft block and seven identical organic groups, R. Small-angle X-ray scattering and theological techniques were used to study the effect of sterically similar, yet electronically different, organic R groups, cyclopentyl (Cp), cyclohexyl (Cy), cyclohexenyl (Cye), and phenyl (Ph), on the morphology of SBS triblock copolymer and the order-disorder transition behavior. It was observed that POSS with phenyl moiety, when grafted to the polybutadiene (PB) phase, appears to show favorable interaction with the polystyrene (PS) phase; effectively, the Ph-POSS is plasticizing the SBS due to an effect whereby the Ph-POSS is at least partially solvated by the PS phase. This causes a significant decrease in the overall lamellae d spacing and the order-disorder transition temperature, T-ODT, with increasing amounts of Ph-POSS attachment. As we change the POSS moiety to that of Cye, Cy, and Cp, the interaction between POSS-PS weakens, and the d spacing and TODT become less dependent on the amounts of POSS attachment. At the highest POSS loadings investigated (20 wt %), there is a change to a perforated layer morphology, resulting in an increase of TODT relative to the 10 wt % POSS-grafted copolymers for Cp, Cy, and Cye POSS moieties.