Istituto per i Processi Chimico Fisici

Supercooled liquids and glass transition.

Understanding the route followed by a supercooled liquid in becoming, by viscous slow-down, a glass well below the freezing point still represents one of the major challenges in condensed matter physics. In fact, in spite of countless and huge efforts on both the theoretical and experimental side, many significant questions on the very nature of the glassy state remain unanswered yet.

Even if there is a large consensus on the idea that the experimentally observed glass transition is simply the outcome of relaxation processes which, at low enough temperatures, become much slower than the experimental observation time, it is not clear whether such a slowdown of the dynamics of the system can be interpreted, following Kauzmann’s original discussion on this point, as an indication of an underlying, possibly continuous, phase transition, which would occur below the vitrication point Tg. In addition, it is not clear whether what appears, on the experimental time scale, as a kinetically arrested system, which is no longer at equilibrium, might eventually transform into a truly metastable state upon waiting a suffciently long time.  However, distinguishing broken ergodicity from metastability is not an easy task on the operational side and both experiments and numerical calculations give ambiguous indications on this point.

The Kautzmann observation was that, for infinitely slow cooling, the entropy of the supercooled liquid equates that of the stable solid at a given temperature, Tk. The extrapolation of this result to absolute zero would imply that the difference of entropy between the liquid and the solid becomes different from zero,  so violating the third principle of Thermodynamics. Kautzmann proposed that a phase transition from the liquid phase to a glassy state takes place at a temperature higher than Tk, so avoiding the thermodynamic paradox. In such a way Tk must be assumed as the thermodynamic glass transition temperature to which the experimental values, Tg, must tend, in the limit of infinite measure time.

Very recently, the Kauzmann argument revealed erroneous, because it implies the occurrence of an isothermal process which can produce the solid phase moving from the metastable liquid. This is thermodynamically impossible because such a process would imply the coexistence of liquid and solid at a temperature lower than their coexistence temperature. Escaping from metastability implies that latent heat must be released,  so that no external work is required and the process can take place spontaneously, hence adiabatically. The transition towards stable equilibrium takes place exothermically and the system worms up while solidifying. The comparison of the entropy of the liquid with the entropy of the solid at the same temperature becomes meaningless. When the liquid entropy is compared with the entropy of the equilibrated phase which is adiabatically accessible, it becomes clear that the process ever occurs at increasing entropy: no thermodynamic conflict is detected.

The stable phase towards which the metastable liquid evolves is (at not too much low supercooling temperatures)a mixture of liquid and solid, at their coexistence temperature. When the molar volume of the metastable phase is compared with that of the accessible stable phase a cross-over of the volume is observed. In the case of water, this cross-over takes place at a temperature very close to the accepted value for its homeogeneous nucleation temperature.

 This observation could be really not be just an accident. At the cross-over temperature, the required arrangement towards the stable configuration is only a local process which does not need to propagate in order to complete. In such conditions, any local fluctuation is not dissipated and the local transition, which results in a large local change of the temperature, immediately produces a further fluctuation in the adjacent volumes which can propagate shortly (on a time comparable with the time required for the local rearrangement of very few molecules) across the whole sample. This argument looks as a different way for saying that, at that temperature, any energetic barrier between metastable and stable equilibrium disappears, at least disregarding any contribution from interfaces.

Such an idea is strongly supported by experimental investigations of recalescence from supercooled water.

On these bases, it appears that most of the ideas which have led to the hypothesis of a thermodynamic transition, underlying the observed experimental glass transition, reveal to be ill founded. In particular, we have shown how distinguishing between supercooled liquids and equilibrated glasses can reduce to a mere semantic question. The apparent differences between them are only related with a cross-over temperature at which the experimental time scale becomes shorter than the configurational relaxation time of the system.

Once the main motivation for assuming an underlying thermodynamic transition beyond the experimentally observed glass transition has been ruled out, many questions remain unsolved as the consequence.  As an example, the assumption of a glass metastable phase would imply that a glass would be ergodic while the perspective which describes the system in terms of a kinetic arrest, over the observation time, would imply that it is intrinsically not ergodic. Unfortunately, both numerical calculations and experimental results give ambiguous indications, which should not be surprising in view of the accepted dependence of the data on the observation time scale. Moreover, other questions remain still open: a significant example concerns with the question if it is thermodynamically reasonable to hypothesize the existence of a liquid-liquid phase transition in the deeply supercooled region, with a liquid-liquid coexistence line which can possibly be prolonged well below the supposed homogeneous nucleation temperature, reaching the coexistence line between two distinct amorphous phases which have been experimentally observed.

This research is aimed to explore if there are surviving enough motivations suggesting that the glass obtained from a supercooled molecular liquid can be really described as a metastable phase, other than the metastable liquid. In particular, we are trying to explore the possibility of finding an aswer to many of the open questions within the framework of a simple out of equilibrium thermodynamic approach.

The research is carried on both with theoretical and experimental approaches (fast imaging techniques, Calorimetry, Raman and Brillouin Scattering).