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It is usually more difficult to account for the kinetics of a reaction than for its thermodynamics. Relaxation in glass‐forming systems does not depart from this rule. Whereas a single‐order parameter such as the fictive temperature may be appropriate for characterizing the volume or enthalpy of a glass, relaxation kinetics requires models much too complex to be discussed here (see Chapter 3.7). One can nonetheless have a first look at the mechanisms involved in relaxation by examining whether their kinetics varies or not with the particular property considered.

As done for viscosity, the kinetics of volume equilibration can, for instance, be measured by isothermal dilatometry experiments. If samples with the same thermal history are studied, comparisons between the relaxation kinetics of different properties can be made in terms of normalized variables

(8)

where Y_t, Y_∞, and Y₀ are the property Y at time t, initial time, and equilibrium, respectively. To within experimental errors, experiments on E glass, for example, show in this way the same kinetics for viscosity and volume (Figure 14).

Figure 14 Kinetics of equilibration for the viscosity and volume of E glass. Differences between the ascending branches mainly due to the uncertainties on the Y₀ values caused by unrecorded relaxation during the initial thermal equilibration of the sample.

Source: Data from [28].

More general conclusions are readily derived from comparison between different glass‐transition temperatures even though these are not necessarily defined in the same way in different kinds of measurements. What is important is that they be defined consistently and refer to samples with the same thermal histories. For volume and enthalpy, the latter condition is fulfilled in dilatometry experiments and differential thermal analyses performed simultaneously, whose results can also be compared with standard glass‐transition temperatures (Figure 15). The close 1 : 1 correspondences found in this way for the three temperatures of silicates, calcium aluminosilicates, titanosilicates, and borosilicates over a 400 K interval thus confirm the equivalence of the relaxation kinetics for differing properties [28]. In other words, one must conclude that the same configurational changes are involved in enthalpy, volume, or viscosity relaxation at least in oxide systems, which illustrates their overall cooperative nature.

Figure 15 Equivalence of the relaxation kinetics for the enthalpy, volume, and viscosity illustrated by 1 : 1 correlations between the relevant glass‐transition temperatures determined by differential thermal analysis (DTA), dilatometry (dil), and viscometry (vis, i.e. standard T_g). BNC: sodium borosilicate; WG: window glass; E: E glass; Ab: NaAlSi₃O₈; Di: CaMgSi₂O₆; N:Na₂O; S: SiO₂; T: TiO₂; Ca.xx.yy: xx mol % SiO₂, yy % Al₂O₃^.

Source: Data from [28].