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Is there an ideal glass transition ? Evidence from ultra-stable glasses
Abstract
One of the major questions related to the glass transition event is whether or not there exists an ideal glass transition temperature Tg,ideal [1,2]. Yet, because the laboratory observed glass transition Tg is some 40 to 100 K above the putative Tg,ideal it is virtually impossible to carry out direct measurements that even approach the true equilibrium state at this temperature. Therefore, it is important to develop methods to finesse the problem and to work in the so-called "unexplored" region of glassy behavior [3] where the non-equilibrium response can be interpreted as an upper bound to the dynamical behavior of the glass [4,5]. The framework for the study is that of the fictive temperature originally proposed by Tool [6] and that now serves as a solid framework for understanding the volume vs. temperature or enthalpy vs. temperature behaviors of glass-forming liquids as well as the evolution of the glassy properties during arbitrary thermal histories. In this framework, the fictive temperature TF of the glass defines a point of intersection of the glass-like behavior with that of the equilibrium liquid. When the temperature T of the material is below TF , the dynamics are faster than those of the material in the equilibrium state. When the material is above TF , the dynamics are slower, i.e., provide an upper bound to the equilibrium relaxation times at the given temperature. At T = TF the equilibrium response should, in principle, be obtained. Therefore, to test concepts such as the possibility that the relaxation times or viscosity diverge at a temperature above absolute zero (possibly at Tg,ideal ), as seen in multiple models of glass-forming liquids, the goal became to find or to create glasses with fictive temperatures as far as possible below the glass transition temperature Tg . Then, if one can work in the "window" between TF and Tg , the theoretical predictions or extrapolations from the known equilibrium behavior above Tg can be tested down to TF . We have succeeded in addressing this challenge by using a 20 million year old amber [4] that had a fictive temperature some 43.6 K below the conventionally measured Tg and were able to determine upper bounds to the relaxation times in the relevant temperature window. We subsequently were able to create an ultra-stable amorphous Teflon through a vapor deposition process that had TF some 55 K below the Tg of the same material and very close to the nominal Tg,ideal . In this case, and unlike the amber for which the dynamics could be measured by macroscopic rheological methods, there was an additional challenge. Here the vapor deposition process made only micro-gram quantities of material, at least in a reasonable time of multiple hours. Therefore the challenge was to make dynamic measurements on these ultra-small quantities of material. This we did by using the TTU bubble inflation method [7] of viscoelastic measurements to determine the creep response in the temperature range from just below TF to Tg and applying time-temperature superposition to estimate the temperature dependence of the relaxation times, again in the upper bound condition. Two important results came from these investigations. The first is that the temperature dependence of the dynamics was found to deviate significantly from the finite temperature divergence given by extrapolation of the equilibrium response obtained for temperatures greater than Tg , thus challenging the idea of an ideal glass transition, at least as seen in the temperature dependence of the dynamics. The second is that the data are good enough to permit the evaluation of more modern theories that do not predict diverging time scales at finite temperature. The comparison with several of these will be shown. It is also of interest that, in spite of the challenge to ideas of an ideal glass transition, the activation energies of these upper bound relaxation times are still extremely high, thus the "turn over" from super-Arrhenius to Arrhenius-like behavior does not resolve the conundrum of the high apparent activation energies of the relaxation processes in glass-forming liquids, one of the original motivating factors in the ongoing study of complex fluids [8-11].
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