Kauzmann paradox
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In thermodynamics, the Kauzmann paradox is the apparent result that it is possible to obtain a supercooled liquid with an entropy lower than that of its corresponding crystal. This is viewed as a paradox, since the disordered liquid must have a higher entropy than the ordered crystal.
As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the heat capacity of the supercooled liquid below its glass transition temperature, it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the Kauzmann temperature.
If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, this would have severe consequences. The Kauzmann paradox has been the subject of much debate and many publications since it was first put forward by Walter Kauzmann in 1948. It is named after its creator.
One resolution of the Kauzmann paradox is to say that there must be a phase change before the entropy of the liquid drops. In this scenario, the transition temperature is known as the calorimetric ideal glass transition temperature T0c. In this view, the glass transition is not merely a kinetic effect, i.e. merely the result of fast cooling of a melt, but there is an underlying thermodynamic basis for glass formation [1]. The glass transition temperature Tg → T0c as dT⁄dt → 0.
There are at least three other possible resolutions to the Kauzmann paradox. It could be that the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly drops to a smaller value. It could also be that a first order phase transition to another liquid state occurs before the Kauzmann temperature with the heat capacity of this new state being less than that obtained by extrapolation from higher temperature. Finally, Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached.
[edit] Further reading
- W. Kauzmann, The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures; Chemical Reviews 43 (2), 1948.[1]
[edit] References
- ^ Baeurle, S.A., Hotta, A., Gusev, A.A. (2006). "On the glassy state of multiphase and pure polymer materials". Polymer 47: 6243–6253. doi:.
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