Structural dependence of fast relaxation in glass-forming substances and correlation with the stretch exponent of the slow structural α-relaxation

The fast relaxation in glass-forming substances is often identified with the β-relaxation of the idealized mode coupling theory (MCT), which involves a critical temperature, Tc, higher than the glass transition temperature, Tg. However, several recent experimental works indicate that the fast relaxation may not be so simply described. These findings include the breakdown of the predictions of the idealized MCT below Tc in 0.4Ca(NO3)2–0.6KNO3 (CKN) and ortho-terphenyl (OTP), the existence of the fast relaxation also in crystalline OTP, and the flat dielectric susceptibility minimum (i.e., nearly frequency independent or constant loss) observed in CKN and propylene carbonate at temperatures below Tc. These experimental facts indicate that the fast relaxation observed below Tc is outside the predictions of the idealized MCT and a recent two-component schematic model of MCT, which includes hopping. It is unlikely that this non-MCT fast relaxation existing below Tc will abruptly vanish at temperatures above Tc. The need for an alternative model of the fast relaxation not only below but also above Tc is thus clear. We analyzed susceptibility spectra of many glass-formers with the assumption that the susceptibility minimum is caused by a temperature dependent near constant loss. Good fits to the susceptibility spectra were obtained and in the process the near constant loss was determined as a function of temperature. When compared in a plot against Tg-scaled temperature, the near constant losses of different glass-formers exhibited a pattern that correlates with the stretch exponent, βα(Tg), of the Kohlrausch–Williams–Watts (KWW) function which describes the time dependence of the structural α-relaxation at Tg. The correlation suggests that the fast relaxation and the slow structural α-relaxation are both determined by the same factor, which we attribute to the anharmonic intermolecular potential of interactions between the molecules. The fast relaxation is suggested to be the relaxation of a vibration by anharmonicity. The vibration is likely the one that attempts to relax the structure of the glass-former.