Application of the Adam-Gibbs equation to the non-equilibrium glassy state

The Tool-Narayanaswamy-Moynihan (TNM) equation for the temperature (T) and fictive temperature (T-f) dependence of the relaxation time in glassy mater ials is compared with the usual nonlinear form of the Adam-Gibbs (AG) equat ion. It is shown that the relationship derived between the Narayanaswamy pa rameter x and the temperature T-2 at which the configurational entropy redu ces to zero, namely x approximate to 1 - T-2/T-f, leads to unrealistic valu es of T-2 for many polymer glasses. This problem is resolved by expressing the configurational entropy as a function of both T and T-f, with a partiti oning parameter x(s) (0 less than or equal to x(s) less than or equal to 1) controlling their respective contributions. Comparing TNM with this new no nlinear AG expression incorporating S-c(T,T-f) leads to an explicit relatio nship between x and x, involving T, T-2, and T-f, from which a number of pr edictions may be made. (1) For T approximate to T-f, i.e., for relaxations close to equilibrium, the quantity 1 - T-2/T-f is identified as the minimum possible value for x, implying that T-2 greater than or equal to T-f(1 - x ), by an amount depending on the value of x(s). This resolves the apparentl y anomalous values of T-2. (2) For relaxations further from equilibrium, th e TNM equation with constant x becomes increasingly inappropriate. (3) With increasing annealing temperature and increasing annealing time, the analys is predicts increasing values of x, as has often been reported in the liter ature. The origin of the dependence of S-c on T and T-f is considered from the theory of Gibbs and DiMarzio, and it is argued that typical values of x observed experimentally may be associated with the freezing-in of only a c ertain fraction of either flexed bonds and/or vacant lattice sites (holes) at the glass transition. Thus, it is possible to identify x(s), and indirec tly x, with the relative contributions of physically meaningful parameters, such as intermolecular and intramolecular bond energies, to the freezing-i n process.