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The glass transition was first signaled by anomalous increases of the heat capacity, and its kinetic nature by the dependence of these anomalies on the thermal histories of the samples investigated (Chapter 10.11). Such effects are clearly apparent in early C_p measurements made on B₂O₃ (Figure 12a) where three different temperature intervals are distinguished [34]. Above about 270 °C, the liquid phase is in internal thermodynamic equilibrium because its heat capacity is uniquely defined by temperature (and pressure). In the 270–100 °C interval, internal equilibrium is lost as C_p is no longer defined by temperature only. The measurements made upon heating and cooling differ and C_p differences of up to 20% are found between samples initially cooled rapidly and slowly. Also noteworthy is the fact that the observed C_p hysteresis prevents a reversible thermodynamic pathway from being followed. It points instead to the creation of entropy through cycling in this interval and, therefore, demonstrates the irreversibility of the glass–liquid transformation.

Figure 12 Irreversibility of the glass transition: heat capacity hysteresis measured for boron oxide upon cooling and upon heating of a slowly (S) and rapidly (R) cooled glass [34]. (b) Enthalpy and C_p differences between glasses cooled at different rates q; Sup. liq.: enthalpy of the equilibrium supercooled liquid.

Below 100 °C, C_p depends again only on temperature. If integrated from 270 to 100 °C, however, the C_p and C_p /T differences between the rapidly and slowly cooled samples represent enthalpy and entropy differences, respectively. These are constant below 100 °C as the glass C_p does not depend sensitively on thermal history. They can be readily calculated for any two glasses, like a volume difference, if their fictive temperatures are known (Chapter 3.6). An important conclusion then follows: the existence of an entropy difference at 0 K between two samples implies that glasses have a residual entropy at 0 K: hence, glasses do not obey the third Law of thermodynamics because of the irreversible nature of the glass transition (cf. Chapters 3.6 and 10.11).

In more detail, the C_p hysteresis results from the observed contrast between a smooth decrease upon cooling and sharp increases upon heating followed by overshoots right at the end of the transition (Figure 12a). The former decrease simply points to the progressive loss of atomic mobility with decreasing temperatures. Upon heating, the situation is more complicated because relaxation resumes at the temperature at which it vanished on cooling, but its first effect is to lower the enthalpy of the glass to bring it closer to the equilibrium values of the supercooled liquid (Figure 12b). At higher temperatures, the enthalpy curve of the material has already crossed that of the supercooled liquid when relaxation becomes almost complete at the timescale of the experiment. The heat capacity then increases rapidly (Figure 12b) in a way that depends on thermal history. The rise is highest for samples initially cooled down at the slowest rates, whose enthalpy is initially the lowest, or for samples heated at the highest rates. If the heating and cooling rates are increased, the transition shifts to higher temperatures because the decrease of the experimental timescale must be matched by an analogous decrease of the relaxation time (Figure 12b).

Determination of a glass‐transition temperature is more complicated in calorimetry than in dilatometry because of the complex shapes of the observed C_p variations or even of the endothermic peaks recorded in thermal analysis. This temperature may, for instance, be taken as the inflection point of the C_p increase upon heating, but it can alternatively be defined in different ways so that is generally needed to specify which particular one has been selected [35].