Dynamical scaling laws in polymers near the glass transition

The mode-coupling theory for the dynamics of supercooled liquids predicts a universal behaviour for the relaxation properties of the beta -process. This is completely ruled by generic properties of underlying bifurcation singularities in the nonlinear equations of motion, which in the simplest case belong to the cuspoid family A k ; k>or=2. The theory gives various scaling scenarios involving one or more parameter sealing functions depending on the order k of the relevant singularity. These predictions are compared with dielectric measurements on the polymeric systems polyethylene terephthalate (PET), polyethylene oxybenzoate (PEOB) and polychlorotrifluoroethylene (PCTFE). Both amorphous and semicrystalline samples are considered, and in all cases the author finds quantitative agreement between theory and experimental results in the relevant frequency region.