(641d) Deep Glass State Properties: Evidence That Glass Formation Is a Liquid-State Property Unrelated to the Kauzmann Paradox and Crystal Entropy

One of the major challenges in working with glassy materials in the deep glassy state, i.e., > 30 K below the glass transition temperature T_g is that the times required to achieve equilibrium become geologically or even astronomically long. Thus, it becomes important to find ways to create or discover ultra-stable glasses. We have found both methods provide the ability to establish a deep glassy state region that is ultra-stable in that the fictive temperature T_F is further below the T_g than seems possible within the framework of models of an ideal glass that relate the Kauzmann temperature T_K to the ideal glass transition temperature T₂ or T_VFT. Here we remark that T₂ is the temperature where the configurational entropy goes to zero according to the Gibbs-DiMarzio model of the glass transition and T_VFT is the temperature of relaxation time or viscosity divergence of the dynamics as determined from the Vogel, Fulcher, Tammann equation. We have succeeded in the endeavor of finding extremely stable glasses through the use of vapor deposition of amorphous perfluorinated co-polymers or by studying ancient ambers, some of which show extreme stability. In the present work we show evidence from vapor deposition (using vacuum pyrolysis deposition [VPD]) of an amorphous Cytop fluoropolymer and that has an extreme stability based on having a value of T_F which is over 10 K below the value of T_VFT. Such a finding challenges the idea of the Kauzmann temperature representing the minimum in the energy landscape at an ideal glass transition. In addition, we discovered a a 50 million year old amber from Fushun China that has a value of T_F some 193 K below the T_g as determined by length-change dilatometry measurements. hence well below the expected T_VFT (or T_K) based on the fact that amber is a polymeric material and one would anticipate that the VFT temperature would be only 30 to
70 K below the T_g. Similar to the findings of the VPD perfluoropolymer, this challenges the importance of the Kauzmann temperature as a driver of glass formation. In addition, for the Fushun amber, we carried out additional experiments in which the viscoelastic response was determined for a range of glassy states that were obtained by partial devitrification steps. Three important findings were obtained. First, in the regime where T>T_F, the upper bound relaxation times were always shorter than expected from a VFT type of extrapolation of the data, consistent with prior work on a 20 million year old amber and on a VPD amorphous Teflon. Second, we were able to perform experiments in the condition where T=T_F, i.e., where the dynamics should be equal to those obtained in equilibrium at the specific value of T,T_F. In this case
the relaxation times not only did not diverge, but unlike prior work in which the temperature range was smaller, we were able to also show that the relaxation times follow an exponential dependence on the temperature rather than a possible activated or Arrhenius-type behavior as an exponential in reciprocal temperature. This novel finding is not consistent with any current theory of glasses or super-cooled liquids. Third, because we were able to work so far below the glass transition temperature we accessed relaxation times as long as yotta seconds (10²⁴ s) which would correspond to a viscosity of over 10³³ Pa-s (1,000 quetta Pa-s) upon assuming a simple Maxwell model and glasy modulus of approximately 1 GPa. Clearly, these data show that there remains much to be learned of the extremely deep glassy state. One important point is that understanding such behavior is related to our ability to formulate appropriate equilibrium models of glasses, thus forming the basis of non-equilibrium theories that are needed for
lifetime predictions in applications of glasses, for which the conditions of formation invariably lead to materials that are out of equilibrium.