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Glass transition

Hard knock for thermodynamics

Nature volume 405, pages 521–523 (2000)Cite this article

A thermodynamic phase transition must involve abrupt changes in certain thermodynamic properties, such as volume. According to the thermodynamic viewpoint, the experimentally observable glass transition is a kinetically controlled manifestation of an underlying thermodynamic transition. This explanation originates with the famous work of Kauzmann3. He observed that the entropy (structural disorder) of a supercooled liquid would fall below that of the corresponding crystal structure — which is expected to have the lowest entropy — if cooled below what is referred to as the Kauzmann temperature, creating an ‘entropy crisis’. The crisis is averted in practice by the intervention of the glass transition. In contrast, the kinetic viewpoint explains the observed structural changes as the consequence of a dynamic transition in the relaxation of the supercooled liquid, which is not accompanied by abrupt changes in thermodynamic properties.

To understand the glass transition, investigators (including Santen and Krauth) have studied idealized models in which the atoms, represented by spheres or disks, interact through hard-core repulsions only4. Because the interaction potential is either zero or infinite, such systems are athermal — that is, the thermodynamic and kinetic properties are (after a trivial rescaling) independent of temperature. One might well question whether such a simplified model can shed any light on the nature of the glass transition in real materials. Interestingly, identical hard spheres are known to undergo a transition from a disordered, liquid-like state to an ordered, crystal-like state at a high enough density5. Thus, increasing the density in hard-sphere systems plays the same role as decreasing the temperature in thermal systems. Indeed, by increasing the density of hard-sphere systems quickly enough, crystallization can be avoided (albeit only for short periods of time6), in analogy with the ‘supercooled’ branch of the thermal system in Fig. 1.

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Figure 1: Two cooling paths by which a liquid may solidify.

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  1. Department of Chemistry and the Princeton Materials Institute, Princeton University, Princeton , 08544, New Jersey, USA

    Salvatore Torquato

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  1. Salvatore Torquato
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Correspondence to Salvatore Torquato.

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Torquato, S. Hard knock for thermodynamics. Nature 405, 521–523 (2000). https://doi.org/10.1038/35014711

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