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 r esearch into glass transition. This paper is generally considered as the tu rning point from rare free volume to small configurational entropy as the r eason for slow molecular mobility in glass formers. The render, however, is confronted with a dilemma. The slowing down is conceptually linked with in creasing cooperativity, but in fact we find only a formula for a link of mo bility 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 f or two post Adam-Gibbs variants - the first via the configurational entropy and the second via a fluctuation approach - with the temperature dependenc e of cooperativities determined by means of heat-capacity spectroscopy (BCS ) data far polystyrene, polyisobutylene, and a random copolymer (SBR 1500). The data yield a strong increase of cooperativity with lower temperature a nd, taking previous HCS data into account, indicate a cooperativity onset a bout 100 K above the Vogel temperature for these polymers. An acceptable fi t 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 cofigurational entropy approach and the fluctuation approach to glass transition are discussed.