Polyhedral oligomeric silsesquioxane (POSS) had long been recognized as a critical building block for inorganic-organic hybrid materials with unique and desirable properties and performance. Through synthesis and characterization of polymer/POSS nanocomposites, direct insights into the significant effects of the polymer/POSS interactions on the resulting material properties are obtained. Random copolymers of a hydrogen-bond accepting monomer and a non-interacting monomer are synthesized and loaded with a model amine-functionalized hydrogen bond donating POSS molecule via solution casting, to create a material with well-controlled dynamical heterogeneity. The increase in the glass transition temperature (Tg) of these materials is found to strongly depend on the number of interacting groups in the system. Essentially, the effect of increasing the POSS loading is the same effect as increasing the number of interacting monomers in the copolymer. Likewise, POSS molecules with a variable number of amines were synthesized and loaded into a hydrogen bond accepting homopolymer. Similar to what was observed for the random copolymers, increasing the functionality of the nanofiller increased the Tg enhancement effect. To probe the purported effects of POSS molecules on entanglement dynamics, composites were prepared with a range of polymer molar masses. Across these materials, critical rheological timescales were observed which point to a relaxation process that occurs independently of the presence of entanglements, and scales exponentially with POSS loading. Attempts to probe this process with other experimental techniques such as dielectric relaxation spectroscopy were inconclusive due to competing experimental effects at similar frequencies. Overall, these results on highly controlled model materials reveal the role of specific nanofiller interactions on the properties of polymer composites.