8. Glass transition and entropy: Kauzmann's paradox
After melting, the entropy of a liquid is higher than that of the crystal. Since the C
p
(C
p
= T ∂S / ∂T) of a liquid is higher than that of the crystal, the entropy S of the liquid decreases faster than that of the crystal. For brittle liquids, the entropy difference between liquid and crystal decreases by around a factor of 3 between T
m
and T
g
. For most glass formers, especially molecular compounds, extrapolation below T
g
of the entropy evolution S (T), measured at higher temperatures, leads to a virtual crossover with the crystal entropy at a positive temperature T
K
(Kauzmann temperature
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Glass transition and entropy: Kauzmann's paradox