The addition of polyhedral oligomeric silsesquioxane‐styrene copolymers, co(POSS#‐sty), to entangled polystyrene (PS) reduced (1) the glass‐transition temperature, Tg,blend, (2) the rubbery modulus, and (3) the melt viscosity. POSS#‐sty copolymers with # = 15, 25, and 45 wt% POSS were blended with PS. The blends were miscible and Tg,blend decreased with POSS#‐sty content. Strikingly, POSS#‐sty copolymers also reduced the melt viscosity, up to an order of magnitude reduction. The reductions of Tg,blend and melt viscosity were driven by the type of POSS#‐sty copolymer, POSS45‐sty producing the largest decrease of Tg,blend. Linear viscoelasticity and the time–temperature superposition (TTS) principle (using Tref = Tg + 50 K to ensure iso‐frictional conditions) revealed that POSS#‐sty induced up to an order of magnitude reduction of the rubbery modulus Ge. The increase of free volume fg promoted by POSS#‐sty induced the reduction of Tg,blend and Ge, as revealed by TTS analysis. The increase of free volume promoted by POSS#‐sty induced chain intercalation (TEM showed that POSS domains were smaller than the molecular mesh) and these are key factors for the chain disentanglement with the consequent rubbery modulus and melt viscosity reductions. The use of low‐molecular weight polystyrene alone will not produce increase of free volume and tube dilation. POLYM. ENG. SCI., 59:2377–2386, 2019. © 2019 Society of Plastics Engineers