Coupling of Caged Molecule Dynamics to JG β-Relaxation: I

The paper (Sibik, J.; Elliott, S. R.; Zeitler, J. A. J. Phys. Chem. Lett. 2014, 5, 1968-1972) used terahertz time-domain spectroscopy (THz-TDS) to study the dynamics of the polyalcohols, glycerol, threitol, xylitol, and sorbitol, at temperatures from below to above the glass transition temperature Tg. On heating the glasses, they observed the dielectric losses, ε″(ν) at ν = 1 THz, increase monotonically with temperature and change dependence at two temperatures, first deep in the glassy state at TTHz = 0.65Tg and second at Tg. The effects at both temperatures are most prominent in sorbitol but become progressively weaker in the order of xylitol and threitol, and the sub-Tg change was not observed in glycerol. They suggested this feature originates from the high-frequency tail of the Johari-Goldstein (JG) β-relaxation, and the temperature region near 0.65Tg is the universal region for the secondary glass transition due to the JG β-relaxation. In this paper, we first use isothermal dielectric relaxation data at frequencies below 10(6) Hz to locate the "second glass transition" temperature Tβ at which the JG β-relaxation time τJG reaches 100 s. The value of Tβ is close to TTHz = 0.65Tg for sorbitol (0.63Tg) and xylitol (0.65Tg), but Tβ is 0.74Tg for threitol and 0.83Tg for glycerol. Notwithstanding, the larger values of Tβ of glycerol are consistent with the THz-TDS data. Next, we identify the dynamic process probed by THz-TDS as the caged molecule dynamics, showing up in susceptibility spectra as nearly constant loss (NCL). The caged molecule dynamics regime is terminated by the onset of the primitive relaxation of the coupling model, which is the precursor of the JG β-relaxation. From this relation, established is the connection of the magnitude and temperature dependence of the NCL and those of τJG. This connection explains the monotonic increase of NCL with temperature and change to a stronger dependence after crossing Tβ giving rise to the sub-Tg behavior of ε″(ν) observed in experiment. Beyond the polyalcohols, we present new dielectric relaxation measurements of flufenamic acid and recall dielectric, NMR, and calorimetric data of indomethacin. The data of these two pharmaceuticals enables us to determine the value of Tβ = 0.67Tg for flufenamic acid and Tβ = 0.58Tg or Tβ = 0.62Tg for indomethacin, which can be compared with experimental values of TTHz from THz-TDS measurements when they become available. We point out that the sub-Tg change of NCL at Tβ found by THz-TDS can be observed by other high frequency spectroscopy including neutron scattering, light scattering, Brillouin scattering, and inelastic X-ray scattering. An example from neutron scattering is cited. All the findings demonstrate the connection of all processes in the evolution of dynamics ending at the structural α-relaxation.