Ph.D. thesis (pdf) - dirac

8 Slow and fast dynamics
glass. The volume of the glass is also dependent on temperature, but its temperature
dependence is weaker than that of the liquid. This is so because the molecules in
the liquid rearrange upon cooling while the glass contracts only due to a decrease
in the distance between the molecules. The difference between the liquid and the
glass responses to temperature changes gives rise to an abrupt change in slope on a
T − V plot. A typical plot is shown in figure 2.1. The change in the temperature
dependence of the volume gives rise to a discontinuity in the expansivity when passing
T g . The heat capacity and other thermodynamical derivatives have equivalent
discontinuities at T g . If the glass is kept below T g the liquid approaches equilibrium,
though it happens slowly, and the volume and other properties are therefore time
dependent; the glass ages. This means that strictly speaking the thermodynamic
derivatives are not strictly well defined in the glass. It also leads to hysteresis in
the system. The hysteresis is seen in the re-heating curve which is also indicated in
figure 2.1.
The relaxation time increases very rapidly in the vicinity of T g ; this means that the
aging processes are very slow already a few degrees below T g . When considered at
times shorter than the relaxation time the glass behaves like a solid in all senses.
It is therefore possible to measure and assign meaningful “apparent” values to the
properties of the glass, including the thermodynamical derivatives (figure 2.1).
V or H
αP or cP
T g
Temperature
T g
Temperature
Figure 2.1: Illustration of the temperature dependence of volume, enthalpy and their
temperature derivatives when passing the glass transition.
The freezing in of the liquid at T g has the consequence that the structure of the
glass is that of the liquid when it fell out of equilibrium at T g . The glass is hence
a disordered solid, and it cannot be distinguished from a liquid from a structural
point of view.
A liquid has a T g that depends on the cooling rate (lower cooling rates give lower T g ).