Synergy of entropy and intermolecular coupling in supercooling liquids

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Abstract
We show the Tg-scaled temperature dependence of the minimum number of molecules capable of undergoing a rearrangement, z*, in the Adam and Gibbs model of relaxation of glass-formers is strikingly similar to that of n and m=[d log τα/d(Tg/T)]. Here (1−n) and τα are, respectively, the exponent and the effective relaxation time in the Kohlrausch correlation function, exp[−(t/τα)1−n], of the primary α-relaxation, z* is obtained from the excess (configurational) entropy, Sc, of the Kauzmann paradox and Tg is the glass temperature. As functions of Tg/T, z*, n and m all assume their minimal values at high temperatures. On decreasing temperature they all increase monotonically with a more rapid change in the vicinity of some temperature TB above Tg. Moreover, from the data of a number of small molecule glass-formers in which the high temperature limit of Sc can be determined accurately, we find that at the glass temperature, Tg, z*(Tg) obtained from thermodynamic data correlates with the steepness index m=[d log τα/d(Tg/T)]T=Tg and the Kohlrausch exponents (1−n(Tg)). The similarity of the temperature dependencies of n, m, and z* makes plausible the explanation that the temperature dependences of the kinetic quantities, n and m, originate from that of z*, which is a pure thermodynamics quantity.