Contributions to the entropy of a glass and liquid, and the dielectric relaxation time

An analysis of the heat capacity data of 21 materials shows that a glass loses 17%–80% of its entropy on cooling from its Tg to 0 K, and that the entropy difference between a glass and crystal phase at Tg, ΔS(Tg), is 1.2 to 4.9 times the entropy difference at 0 K. This is contrary to the premise that the vibrational entropy of a glass is the same as the entropy of its crystal phase, or that ΔS(Tg) is equal to Sconf(Tg), the configurational entropy at Tg. The excess entropy of a glass over the crystal phase is attributed to (i) the relatively lower frequency and greater anharmonicity of lattice vibrations which contribute to their vibrational entropy, (ii) the kinetically unfrozen modes corresponding to the tail of the distribution of the α-relaxation times, which contribute to the configurational entropy, and (iii) localized relaxations of molecular groups which also contribute to the configurational entropy. These contributions vanish or become negligible at 0 K. Therefore, ΔS(Tg) cannot be used in place of Sconf(Tg) in the Adam and Gibbs equation. The finding puts into question the basis for the recent inferences [J. Chem. Phys. 108, 9016 (1998)] on molecular dynamics of supercooled liquids. An upper bound Sconf may be estimated at Tg by extrapolation of the vibrational entropy of a glass and used in the Adam and Gibbs equation to estimate roughly Sconf of a supercooled liquid from the dielectric relaxation time data.