Abstract
A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.
Highlights
As noted long ago by Josiah Willard Gibbs [1], “Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension”
In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range
The premise that glass formation is a process of continuously breaking ergodicity with entropy loss does not merit serious consideration”
Summary
As noted long ago by Josiah Willard Gibbs [1], “Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension”. Considering first helium as a singular substance that can be cooled down to temperatures near to absolute zero remaining in a metastable equilibrium state, he demonstrated that the entropy difference, ∆s, of liquid and crystal tends to zero in this limit As he noted further, this must be the case in accordance with the third law of thermodynamics valid in its classical formulation for equilibrium states of the systems under consideration. A similar behavior as discussed by Simon for the vitrification of glass-forming melts had been observed later for crystals, for which disorder can be generated in different ways (e.g., point defects, impurities, dislocations, etc.) and can become frozen-in in cooling [36,37] Particular examples of this type of behavior have been treated by Linus Pauling in [38], but he was not at all the first to give a correct interpretation of the entropy of glasses or glass-like systems at low temperatures (cf [33]). A summary of results and further perspectives (Section 5) completes the paper
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