Ph.D. thesis (pdf) - dirac

10 Slow and fast dynamics
energy in equation 2.1.1 to be temperature dependent. In most cases, it also appears
that this activation energy is density (or pressure) dependent. Such an activation
energy can formally be defined from the equation:
or a similar expression for the viscosity.
( ) E(ρ, T)
τ α (ρ, T) = τ 0 exp , (2.1.2)
T
Within the last ten years there has been a lot of progress in mapping out the temperature
and pressure (or T and density) dependences of the alpha relaxation time
particularly in terms of the temperature and density dependences of E(ρ, T). This
approach is central to the present work. However, before presenting the findings in
this field we shall take a step back and introduce some of the other central concepts
and findings in the field. These latter are originally based on studies performed at
constant atmospheric pressure.
In chapter 3 we return to the temperature and density dependence of the dynamics
and at this point we will commence the central aim of the present thesis, namely
to revisit (discuss and test) results obtained at atmospheric pressure by combining
them with our knowledge of the influence of pressure on the dynamics of glasses and
glass-forming liquids.
2.2 Fragility
The glass transition is, as described above the passage from a thermodynamic
(metastable) equilibrium state to a non-equilibrium state. This transition is a natural
consequence of the fact that the relaxation time of the system surpasses the
timescale on which we are able to perform observations. In our opinion the main
question is therefore not to understand the glass transition itself, but rather to
understand why the relaxation time increases so dramatically when the liquid is
cooled.
While the viscous slowing down is universal, there are still large variations to be
found when comparing the temperature dependences seen in different liquids. The
classification and description of systems according to this difference play a major
role in the attempt to understand the universal features of the slowing down.
The concept of “fragility” [Angell, 1991] has become a standard scheme for characterizing
the temperature dependence of the relaxation time (or viscosity) of a
liquid. Fragility is a measure of how much this temperature dependence deviates