On resolving the statistical and calorimetric entropies of glass and non-crystalline solids, and the residual entropy problem

In statistical terms, the configurational entropy, Sconf, of a structure of fixed configuration is zero, i.e., its Ω = 1 in the Boltzmann equation, Sconf = kB ln Ω. On that basis, a recent discussion has drawn two inferences: (a) Sconf is lost when a liquid vitrifies and thus a glass has no residual entropy, Sres, and (b) structural relaxation of a glass would first increase its Sconf with time from its zero value and then decrease Sconf to the equilibrium value, thus causing the slope of its free energy against time plot to abruptly decrease after a certain time period. Both conclusions conflict with the classical, textbook analysis of the calorimetric data, and with the experimental findings. To evaluate the merits of these conclusions, we use the difference between the free energy of glass (and of supercooled liquid) and its crystal phase. If the inferences based on the statistical view are valid, (i) this difference would show a gap between the glass and supercooled liquid in the Tg range, (ii) the slope of the plot of this difference against T would be much less at T < Tg than at T > Tg, and (iii) annealing would decrease this difference by a relatively large amount. After constructing such plots from the known Cp data, we propose that measurement of the vapor pressure, sublimation rate, solubility, chemical reaction rate, and emf of a cell made from glassy-metal electrodes may be useful for testing whether or not Sconf is lost on vitrification. The data available provide no support for the entropy-loss view.