ALPHA RELAXATION

1. Introduction

The α relaxation leads to a prominent peak in the dielectric-loss spectra of dipolar glass formers. It arises from the structural dynamics of the glass-forming particles (molecules, ions,...) whose continuous slowing down over many decades upon cooling leads to the glass transition. The α relaxation reveals two hallmark features of glassy dynamics namely non-exponentiality and non-Arrhenius behaviour. Both are investigated in our group. The latter denotes the non-canonical temperature dependence of the α-relaxation time, which characterises the typical dynamics of the particles constituting the glass. It can be easily determined from the measured loss spectra.

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.]

2. Examples

a) α-Relaxation time

Numerous formulae, based on various empirical or theoretical considerations, have been proposed to describe the temperature dependence of the α-relaxation time. Due to the broad frequency range accessible by our dielectric experiments, it can be determined from the highest temperatures, deep in the low-viscosity liquid regime, down to the structural arrest occurring at the glass temperature or even below [1-5]. Various examples have been collected in the following publication:

Those relaxation-time data cover a range of up to 16 decades (see examples below), enabling a critical test of the validity of model predictions.
For this purpose, the data are available for electronic download in the Supplemental Material of that paper.

Temperature-dependent α-relaxation times of four glass formers determined by broadband dielectric spectroscopy. The closed symbols denote results deduced from aging experiments. The lines are fits with the Vogel-Fulcher-Tammann formula. [from: P. Lunkenheimer, S. Kastner, M. Köhler, and A. Loidl, Temperature development of glassy α-relaxation dynamics determined by broadband dielectric spectroscopy, Phys. Rev. E 81, 051504 (2010).]

During these 100 years, dozens of alternatives to the VFT law were proposed, but, until now, none of them is as well-established as VFT. We used our broadband spectra to test two of these alternatives as published here:

b) Cooperativity

The typical non-Arrhenius behaviour of glassy dynamics is often ascribed to increasingly correlated motions of the glass-forming particles when approaching the glass transition upon cooling. The material is assumed to consist of regions, in which the particles move in a "cooperative" way and whose sizes increase when approaching the transition (see figure below), which should lead to an increase in the effective energy barriers. As discussed in the Nonlinear-Spectroscopy section, one way to check for cooperative motions is the investigation of the higher-order harmonic components of the dielectric susceptibility [7,9].

Schematic figure, indicating the growth of cooperativity at the transition from the liquid (right) to the glass (left).
Regions of cooperatively rearranging molecules are indicated by molecules of same color.

The relevance of cooperativity for the glass transition can also be investigated by measuring the particle dynamics of supercooled liquids that are confined in spaces of nanometer size, e.g., the pores of certain porous materials. As the size of the cooperatively rearranging regions is supposed to increase with decreasing temperature, below a certain temperature this size will exceed the pore diameter and the temperature dependence of the relaxation time changes. From such measurements, using, e.g., metal-organic frameworks (MOFs) as host materials [8,10], conclusions on the temperature dependence of the cooperativity length can be drawn as shown for glycerol in the figure below.

Temperature dependence of the cooperativity length Lcorr of glycerol as deduced from confinement and nonlinear measurements. The closed symbols show the results from confinement measurements performed using ZIF- and MFU-type MOFs as porous host materials [8,10]. The shaded areas indicate the excluded ranges for Lcorr inferred from the obtained limiting values. The plusses show the temperature-dependent correlation length from measurements of the 3rd harmonic susceptiblity [7], scaled to the value of 1.46 nm at 213 K that was obtained from the results on glycerol in ZIF-11 [10]. The dashed line indicates a fit of Lcorr(T) from the nonlinear measurements (plusses) with a critical law. The dash-dotted line indicates a possible temperature-independent Lcorr above TA ~ 288K. The arrows indicate the Vogel-Fulcher temperature, glass temperature and TA. [from: M. Uhl, J.K.H. Fischer, P. Sippel, H. Bunzen, P. Lunkenheimer, D. Volkmer, and A. Loidl, Glycerol confined in zeolitic imidazolate frameworks: The temperature-dependent cooperativity length scale of glassy freezing, J. Chem. Phys. 150, 024504 (2019).]

3. Some relevant publications from our group: