Primary and secondary relaxation time dispersions in fragile supercooled liquids

The relaxation time dispersions of the primary (α) and secondary (β) 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 α and β processes. Toward more fragile liquids, the width wα of the α peak at the glass transition temperature Tg 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 wβ of the β relaxation at Tg is somewhat lower for more fragile liquids and appears correlated with that of the primary relaxation. The extrapolated coincidence of the dispersions of the α and β processes occurs at the fragility "limit" of m=170, implying that wα ≤ wβ 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 wβ is seen to change steadily through the α-β -merging region, whereas wα displays a kink at the crossover temperature.