Evidence of Sub-T_K Fictive Temperatures Glasses: Vapor Deposited Amorphous Perfluoropolymer and a 50 Million-year-old Amber

A major premise in glass-formers is the concept of an ideal, thermodynamic glass transition taking place at the Kauzmann temperature T_K where the system entropy extrapolates to a zero value. This thermodynamically based T_K is associated with the Vogel, Fulcher, Tammann temperature T_VFT at which the dynamics extrapolate to divergence above zero Kelvin. At the same time, it is known that many non-crystallizable materials, especially polymers, form glasses. This suggests that the importance of the Kauzmann paradox to glass-formation may be problematic. Here we show results from two non-crystallizable ultra-stable glasses (evidenced by greatly reduced fictive temperatures) that give new insights into the conundrum of the Kauzmann paradox. In the first instance we use vapor deposition to make an ultra-stable amorphous perfluoropolymer (CYTOP^TM) that shows a fictive temperature T_F that is more than 60 K below the glass transition temperature T_g, and also approximately 11 K below T_VFT. The second instance uses length change dilatometry measurements on a 50 million-year-old amber from Fushun, China. In this case direct measurements of the fictive temperature show that the material is not only ultra-stable, but also that the T_F is as much as 196 K below the T_g, i.e., over 100 K below T_VFT.