Some Comments on the Nature of Glasses Or a brief history of time and temperature in glass-forming liquids*

ABSTRACT I undertake a brief presentation of the early history of the development of our modern understanding of glass-forming liquids that provides a look at how the scientific and technological communities were viewing the state of the art and how the knowledge in the field developed. I discuss aspects of our understanding from how the Vogel–Fulcher–Tammann (VFT) equation became known to questions about the development of the concept of the “ideal” glass transition. The framework for this history leads us to ask whether some of the cautions that the pioneering researchers provided should have been taken more seriously by the community. I discuss, in particular, the view presented by Tammann and Hesse [Z. Anorg. Allg. Chem. 156, 245 (1926)] cautioning that the apparent singularity of the viscosity at a finite temperature was not physical and how the, now famous, VFT equation is accurate for interpolation rather than for extrapolation. The other point is the strong sense by much of the glass community that the so-called Kauzmann paradox [Chem. Rev. 43, 219 (1948)] is fundamental to glass-formation despite the comment by Kauzmann himself that the extrapolation of the entropy to negative values is “operationally meaningless.” I build on these ideas through a presentation of my own data and that of others that addresses the Tammann and Hesse comment through experiments that show that there is not a viscosity (or relaxation time) divergence near to the Kauzmann or VFT temperatures, and I show that the equilibrium entropy of a polymer that cannot crystallize shows no evidence of an ideal glass transition that is often invoked as a means of avoiding the Kauzmann paradox. In addition to providing some sense of the history of time (or a brief history of time and temperature in glass-forming liquids, with apologies to Stephen Hawking) and viscosity, I think that the data presented lead to the conclusion that much of our understanding of the problem of glass-formation is based on misleading interpretations of the original works as well as being inconsistent with the newer data that have been published over that past 25 yr or so. On an optimistic note, there are newer models that do not rely on the VFT divergence or the Kauzmann paradox to account for glass-formation in supercooled or equilibrium liquids. In addition, the experimental situation clearly leads to the possibility of deeper investigations into the “deep glassy state” through “finessing” the geological timescale issue of creating equilibrium glasses. Such investigations are ultimately important to understanding behavior of glassy materials, especially polymers, that are used deep in the glassy state, but still close enough to the glass temperature that models able to reliably predict their behavior require better representations of glass-formation to engineer their performance.