This paper briefly summarizes two representative examples of investigation of fundamental polymer dynamics with dielectric and viscoelastic methods: 1) Entangled dynamics of flexible polymers: For type-A polymers having the electrical dipoles parallel along the chain backbone, the entanglement dynamics is differently reflected in the dielectric and viscoelastic relaxation functions. A simple relationship between these functions was deduced for the case of full dynamic tube dilation (full-DTD). This full-DTD relationship was found to hold experimentally for monodisperse linear chains, but not for branched (star and Cayley-tree) chains and linear/linear blends. A refined relationship, referred to as partial-DTD, was developed by taking into account the time necessary for constraint release equilibration. This partial-DTD relationship was found to valid for the linear, branched, and blend systems. 2) Effect of carbon dioxide (CO
2) on polymer dynamics: Pressurized CO
2 dissolves into polymers to exhibit a plasticizing effect. Dielectric tests revealed that the local dynamics of polymer chains was accelerated by pressurized CO
2 without changing relaxation mode distribution. This unusual plasticizing effect of pressurized CO
2 for the local dynamics was attributed to extraordinary fast diffusion of CO
2 compared to the segmental motion of the polymer chain. The concentration fluctuation of the polymers, being responsible for the relaxation mode broadening usually observed for plasticized polymer systems, is smeared by the fast CO
2 molecules in the time scale of segmental motion. In contrast, pressurized CO
2 behaves just as an ordinary solvent for the slow, global dynamics of polymer chains.
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