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Cooperativity and the freezing of molecular motion at the glass transition


Since centuries, glass blowers make use of the gradual increase of viscosity when a liquid transforms into a glass under cooling. However, in all classes of glass-forming matter the corresponding slowing down of the motion of the structural units (atoms, molecules, ions, polymer segments, etc.) proceeds significantly stronger than predicted by the naively expected Arrhenius law. Increasingly correlated motions of molecules are sometimes invoked to explain this drastic slowing down of molecular motion at the glass transition. This is a highly debated notion and until now it was unclear how this so-called cooperativity is related to the typical glassy dynamics showing up, e.g., in the temperature-dependent viscosity or the relaxation times quantifying the molecular mobility.

relaxation process
Figure 1: Third-order harmonic component of the dielectric susceptibility of glycerol. Spectra are shown for various temperatures, measured at a field of 565 kV/cm. The inset shows the number of correlated molecules Ncorr as determined from the measured nonlinear susceptibility. The line is a guide to the eye. [Th. Bauer et al., Phys. Rev. Lett. 111, 225702 (2013)]

 

In order to help solving this long-standing problem, we have collected detailed spectra of the third-order dielectric susceptibility of four materials belonging to different classes of glass formers (see Fig. 1 for an example). To measure this rarely investigated quantity, extremely high voltages of up to 2000 V have to be applied to very thin samples, an experimentally challenging task. The third-order susceptibility was recently shown to provide direct experimental access to the number of cooperatively moving molecules in glass-forming materials [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005)].

For all investigated materials, we found a surprisingly simple relation of this number and of the energy barriers impeding molecular motion, which can be determined from the temperature-dependent relaxation times deduced by conventional dielectric spectroscopy (Fig. 2). Our results show that it is an increase of these energy barriers, which we find to be directly proportional to the increasing number of correlated molecules, that causes the non-canonical slowing down of molecular motion at the glass transition. This finally explains the unconventional glassy freezing of molecular motion, which universally occurs in such different materials as conventional silicate glasses, polymers, alcohols, ionic liquids, metallic glasses, or even various kinds of biomaterials.

relaxation times

Figure 2: Correlation of activation energy with number of correlated molecules. The lines show the temperature-dependent activation enthalpies (right scale), determined from the temperature-dependent relaxation times shown in the inset. The symbols represent the number of correlated molecules Ncorr, determined from the measured nonlinear susceptibilities (left scale). The Ncorr data points were multiplied by separate factors for each material, leading to a good match with the enthalpy curves. This provides strong evidence that the increase of Ncorr is responsible for the increase of the activation enthalpies at low temperatures. [Th. Bauer et al., Phys. Rev. Lett. 111, 225702 (2013)]

 

To learn more, see:

Cooperativity and the freezing of molecular motion at the glass transition
Th. Bauer, P. Lunkenheimer, and A. Loidl
Phys. Rev. Lett. 111, 225702 (2013)

This work was also selected for a "Viewpoint" in Physics, see:
Clearing Up the Mysteries of Glassy Dynamics
G. Biroli and J.-P. Bouchaud
Physics 6, 128 (2013)