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Effects of interfaces and interphases in polydimethylsiloxane (PDMS) matrices with in situ synthesized titania (20 - 40 nm, in diameter) and silica nanoparticles (~5 nm), were studied employing dielectric and thermal techniques. The presence of the well dispersed inorganic particles and the hydrogen polymer - filler bonding result in a double effect on polymer mobility: suppression of crystallization and immobilization in a layer of a few nm around the particles. The effects were stronger in the case of titania nanoparticles, in consistency with stronger hydrogen bonding interactions, comparing to silica. Various contributions to the glass transition were recorded by both thermal and dielectric techniques, corresponding to bulk and modified polymer dynamics. The modified mobility originates from the restriction of polymer chains within the PDMS crystals and in an interafacial rigid amorphous PDMS layer around the nanoparticles. The thickness of the interfacial layer was estimated to 3-5 nm for titania and ~2 nm for silica. The mobile amorphous phase fraction giving rise to the glass transition was found to be nearly constant in the nanocomposites. The results were confirmed by employing various thermal (crystallization) treatments of the samples.