HIGH-FREQUENCY DYNAMICS

1. Introduction

When investigating glass-forming liquids up to high frequencies, the signatures of various further dynamic processes, in addition to the structural α relaxation, show up. At low temperatures, an excess-wing or a β relaxation is observed, usually occurring in the Hz-MHz frequency range (Fig. 1c). In measurements extending up to THz frequencies, however, an additional loss-peak shows up at very high frequencies, which can be identified as the boson peak, known from neutron- and light-scattering experiments (magenta peak in Fig. 1). Its microscopic origin is controversially discussed. Between the α and boson peak, a loss minimum is observed (orange area in Figs. 1b and c). It is rather shallow and cannot be ascribed to a simple superposition of the relaxational low-frequency processes (i.e., the α relaxation, excess wing, or β relaxation, depending on temperature and material) and the boson peak.

Fig. 1: Schematic view of the temperature dependence of relaxation processes of supercooled liquids as revealed in dielectric-loss spectra. Shown are three typical spectra: (a) At high temperatures, in the low-viscosity liquid. (b) In the supercooled-liquid regime, below the melting point Tm, but still well above the glass-transition temperature Tg. (c) Close to Tg, where the material becomes solid. Upon cooling, the α-relaxation peak shifts over many decades to lower frequencies, which is typical for a glass-forming material. With decreasing temperature, the signatures of various additional dynamic processes appear in the spectra. [from: P. Lunkenheimer and A. Loidl, Glassy dynamics: From millihertz to terahertz, in The scaling of relaxation processes, edited by F. Kremer and A. Loidl (Springer, Cham, 2018), p. 23.]

The existence of this additional fast contribution, its spectral shape and temperature development were predicted by the mode-coupling theory of the glass transition [W. Götze and L. Sjögren, Rep. Progr. Phys. 55, 241 (1992)]. Subsequently, the theoretical predictions were experimentally confirmed, mainly by light- and neutron-scattering experiments. However, this high-frequency range was only rarely covered by dielectric measurements. Utilizing advanced techniques, our group was able to acquire dielectric data in a considerably enlarged frequency range, extending well into the THz region. We found clear evidence for the expected fast process which should be universally present for all measurement techniques.

2. Example

Fast process in glass-forming glycerol and propylene carbonate

The figure below shows dielectric-loss spectra of two typical glassforming liquids at very high frequencies, covering the microwave, THz, and infrared range. The theoretically predicted shallow minimum between the α-relaxation peak (left; shifting out of the frequency window for the lower temperatures) and the boson peak (right; at about 2 THz) is clearly observed. The solid lines are fits with the simplest version of the mode-coupling theory. The insets demonstrate, that this minimum is too shallow to be explained by a simple superposition of the α and boson peak.

Fig. 2: Dielectric loss of glycerol (a) and propylene carbonate (b) at very high frequencies, in the microwave to infrared range. The solid lines are fits with the prediction of the mode-coupling theory. For the lowest temperatures, the increase towards the boson peak approaches power laws as indicated by the dashed lines. The insets demonstrate, for two temperatures each, that a simple superposition of the right flank of the α peak and the left flank of the boson peaks is not sufficient to explain the shallow minimum. [from: P. Lunkenheimer and A. Loidl, Glassy dynamics beyond the α-relaxation, in: Broadband Dielectric Spectroscopy, eds. F. Kremer and A. Schönhals (Springer, Berlin, 2003), p. 131.]

For further details, see:

3. Some relevant publications from our group: