Ph.D. thesis (pdf) - dirac

Chapter 3
What we learn from pressure
experiments
In this chapter we first introduce earlier results on density and pressure dependence
of the alpha relaxation (section 3.1 and 3.2) and next develope a framework in order
to better understand different types of correlations with fragility (section 3.3 and
3.4).
The steepness index is mostly used as a measure of fragility, but the results and
arguments, hold for other types of fragility criteria, e.g. the Olsen index just as
well.
3.1 Isochoric and isobaric fragility
The measures of fragility which we introduce in section 2.2 are in their original form
(implicitly) defined at constant atmospheric pressure because this is where most
experiments are performed. For instance the steepness index is actually
m P = ∂ log 10(τ)
∂ T τ /T
∣ (T = T τ ) (3.1.1)
P
where the derivative is to be evaluated at T τ . T τ is defined as being the temperature
at which the relaxation time reaches the value τ, e.g. τ = 100 s. The conventional
fragility is hence the atmospheric pressure isobaric fragility. However, the relaxation
time can also be measured as a function of temperature along other isobars. This
is illustrated in figure 3.1 where it can also be seen that the T τ (P) increases when
pressure increases. Isobaric fragility is well defined at any point on the isochronic
29