THE KAUZMANN PARADOX INTERPRETED VIA THE THEORY OF FRUSTRATION-LIMITED-DOMAINS

The entropy, S-liq(T), Of many supercooled liquids decreases strongly and the structural relaxation time increases dramatically as the tempe rature T is lowered below the melting point, T-m. Below the glass tran sition temperature, T-g, the system relaxes too slowly for supercooled liquids to equilibrate in the experimental times; however, if the dat a above T-g are extrapolated to lower T, one finds that the extrapolat ed S-liq(T)-->S-xtal(T) as T-->T-K, S-xtal(T) being the entropy of the crystal. This phenomenon is known as the ''Kauzmann paradox.'' If the extrapolation is extended below T-K, it may be that the extrapolated S-liq(T)-->0 as T-->T-Kc>0; we call this apparent violation of the thi rd law, the ''Kauzmann catastrophe.'' We discuss these phenomena, as w ell as the general problem of the entropy of supercooled liquids, in t erms of the theory of frustration-limited domains. The apparent vanish ing of [S-liq(T)- S-xtal(T)] and the apparent violation of the third l aw that results from extrapolation to rs below T-g are consistent with extension of the scaling result predicted by the theory to inappropri ately low Ts. (C) 1998 American institute of Physics. [S0021-9606(98)5 0437-0].