The Kauzmann paradox interpreted via the theory of frustration- limited-domains

The entropy, Sliq(T), of many supercooled liquids decreases strongly and the structural relaxation time increases dramatically as the temperature T is lowered below the melting point, Tm. Below the glass transition temperature, Tg, the system relaxes too slowly for supercooled liquids to equilibrate in the experimental times; however, if the data above Tg are extrapolated to lower T, one finds that the extrapolated Sliq(T)→Sxtal(T) as T→TK, Sxtal(T) being the entropy of the crystal. This phenomenon is known as the “Kauzmann paradox.” If the extrapolation is extended below TK, it may be that the extrapolated Sliq(T)→0 as T→TKc>0; we call this apparent violation of the third law, the “Kauzmann catastrophe.” We discuss these phenomena, as well as the general problem of the entropy of supercooled liquids, in terms of the theory of frustration-limited domains. The apparent vanishing of [Sliq(T)−Sxtal(T)] and the apparent violation of the third law that results from extrapolation to T’s below Tg are consistent with extension of the scaling result predicted by the theory to inappropriately low T’s.