Primary and secondary relaxation time dispersions in fragile supercooled liquids

The relaxation time dispersions of the primary (alpha) and secondary (beta) dielectric relaxations are studied for molecular glass-forming liquids regarding their dependence on structural relaxation time [or lack thereof observed as time-temperature superposition (TTS)], their changes with fragility, and a possible correlation of the values for the alpha and beta processes. Toward more fragile liquids, the width w(alpha) of the alpha peak at the glass transition temperature T(g) is known to increase significantly. Additionally, we observe that TTS extends over a broader range of peak relaxation times in the case of higher fragility, with the approach to exponential (Debye) relaxation being delayed to faster dynamics. The width w(beta) of the beta relaxation at T(g) is somewhat lower for more fragile liquids and appears correlated with that of the primary relaxation. The extrapolated coincidence of the dispersions of the alpha and beta processes occurs at the fragility limit of m=170, implying that w(alpha)<= w(beta) for all molecular supercooled liquids. Materials of high fragility are also those with no clear low-frequency cutoff in the relaxation time distribution-i.e., their susceptibilities require Havriliak-Negami instead of Cole-Davidson fits. For sorbitol, the value of w(beta) is seen to change steadily through the alpha-beta-merging region, whereas w(alpha) displays a kink at the crossover temperature.