Decrease in heat capacity and enthalpy of an aging glass - A conflict with standard procedure for determining enthalpy loss and fictive temperature

Effect of aging on thermodynamic properties of a glass is studied usually by measuring the apparent heat capacity, C-p, during heating at a fixed rate. In the standard procedure for this study, one identifies a temperature T in the C-p-T plot obtained by heating a glass at a fixed rate. When there is little indication of exothermic structural relaxation in these plots, T-x is taken as the temperature at which C-p of a glass begins to increase, but when there is a significant indication of exothermic structural relaxation on heating a fast-cool or quench-formed glass, T-x is taken as the temperature at which C-p begins to show a decrease. In the latter case, the fictive temperature, T-f, is higher than the glass formation temperature measured for a normal cooling rate. In all cases T-x is used as the low-temperature limit of the C(p)dT integral, and the integral is then used to determine both the decrease in enthalpy on aging and the T-f of a glass. Thermodynamics shows that at temperatures from 0 K to T-x, C-p of an aged and of slow-cool formed glass is less than the C-p of unaged, fast-cool and quench-formed glass, and the zero point enthalpy of the aged glass, like its residual entropy, is less than that of the unaged glass, i. e., there is no T-x. Therefore, the low temperature limit of the integrals should be 0 K. By an analysis of the available C-p data for four glasses we find that the standard procedure underestimates the enthalpy decrease on aging by 19-59 %, which means that the sum of the contributions from phonon, the anharmonic forces, and molecular relaxation to C-p of an aged glass at T below T-x is not equal to that of the unaged glass. After discussing the enthalpy decrease determined by using various calorimetric methods, we suggest a thermodynamically consistent analysis. A broad endothermic feature characteristic of the rigid glassy state may make C-p of an aged glass at some temperatures appear equal to C-p of an unaged glass, or higher.