Correlation between the secondary β-relaxation time atTgwith the Kohlrausch exponent of the primary α relaxation or the fragility of glass-forming materials

A strong correlation between the logarithm of the secondary \ensuremath{\beta}-relaxation time, ${\mathrm{log}}_{10}[{\ensuremath{\tau}}_{\ensuremath{\beta}}{(T}_{g})],$ and the Kohlrausch exponent, $(1\ensuremath{-}n),$ or the fragility index $m$ of the primary \ensuremath{\alpha}-relaxation correlation function $\mathrm{exp}[\ensuremath{-}(t/{\ensuremath{\tau}}_{\ensuremath{\alpha}}{)}^{1\ensuremath{-}n}],$ all at the glass transition temperature ${T}_{g},$ has been found in glass-forming materials in general. The \ensuremath{\beta} relaxations considered are restricted to a class that merges or tends to merge with the \ensuremath{\alpha} relaxations. For \ensuremath{\beta} relaxations in polymeric glass formers that involve side groups, the class is further restricted to those that entail some motions of the polymer backbone. The correlation found indicates the existence of a connection between the \ensuremath{\beta} and \ensuremath{\alpha} relaxations. A possible origin of this connection is rationalized by the conceptual basis of the coupling model.