Temperature dependence of glass-transition cooperativity from heat-capacity spectroscopy: Two post-Adam-Gibbs variants

The Adam-Gibbs paper [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)], one of the most cited works in physics, has a continuing influence on research into glass transition. This paper is generally considered as the turning point from rare free volume to small configurational entropy as the reason for slow molecular mobility in glass formers. The reader, however, is confronted with a dilemma. The slowing down is conceptually linked with increasing cooperativity, but in fact we find only a formula for a link of mobility with configurational entropy. Neither the size of cooperativity nor its temperature dependence can be calculated from Adam-Gibbs formulas. The present paper compares predicted temperature dependences of cooperativity for two post Adam-Gibbs variants --- the first via the configurational entropy and the second via a fluctuation approach --- with the temperature dependence of cooperativities determined by means of heat-capacity spectroscopy (HCS) data for polystyrene, polyisobutylene, and a random copolymer (SBR 1500). The data yield a strong increase of cooperativity with lower temperature and, taking previous HCS data into account, indicate a cooperativity onset about 100 K above the Vogel temperature for these polymers. An acceptable fit of the cooperativity data can formally be reached by both post Adam-Gibbs variants only upon the condition that this onset is included. The problem of a final decision between both variants and the conceptional differences between the configurational entropy approach and the fluctuation approach to glass transition are discussed.