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We report on dielectric susceptibility measurements for the glass-forming systems toluene and 1-propanol, both of which exhibit slow secondary relaxation (Johari β-process). We present a complete lineshape analysis for both α-and β-process covering the real and imaginary parts. The observation of secondary relaxation in the rigid molecule toluene shows that this process is not of intramolecular origin. The β-process is well resolved in the supercooled liquid and in the glass. Above Tg a strong temperature dependence of the relaxation strength ∆ε β is observed. For the activation energy E β of many glass-forming systems we find the relation E β ∝ Tg.

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