Ph.D. thesis (pdf) - dirac

3.4. Temperature dependences 39
measured in terms of the parameter R (see figure 2.7). The liquid is at (metastable)
equilibrium at T g and the quantity measured is thus a unique function of the state
point. The fragilities m P and m ρ as well as the ratio α P /α τ are likewise uniquely
defined at these state points. The comparison of the pressure dependence of a
property and the fragilities is therefore naturally done by monitoring the relevant
quantities along the glass transition line T g (P).
The situation is slightly more difficult when the considering a correlation between
fragility and a property in the glass, because the glassy properties under pressure
are path dependent [Chauty-Cailliaux, 2003]. We propose that the relevant path is
the one followed by compressing in the equilibrium liquid and subsequently forming
the glass by cooling. The glass formed in this way has a history equivalent to the
glass formed at atmospheric pressure and the structure in which it is frozen is that
corresponding to the equilibrium liquid at the same pressure. Secondly, one could
in principle distinguish isobaric and isochoric cooling in the glass itself. However,
the expansion coefficient in the glassy state is very small so that this difference can
probably be ignored at least insofar as the dynamics appear to be harmonic.
3.3.5 Temperature dependence of a correlation
In the above we have focused on the pressure dependence of fragility and we have
suggested that a correlation to fragility should be expected also to hold under pressure.
A related question is the relation between dependence on the relaxation time
(or equivalently on temperature) of the chosen property and of the fragility. Should
a property correlated to fragility at T g also be expected to have the same evolution
as the fragility when temperature is raised? And what is the relevant high
temperature-limit in the regime where the liquid follows the Arrhenius behavior?
These questions are hardly meaningful if the property correlated to fragility is a
glassy property. On the other hand they are relevant questions for a property in
the liquid which correlates to fragility. In deed T g is an arbitrary point and if a
correlation is reported at T g it should also be valid at other temperatures, at least
when the liquid stays viscous and equilibrated. Extrapolation of the correlation to
high temperatures and microscopic times may however be meaningless.
3.4 Temperature dependences
The fragility is sometimes suggested to correlate to the temperature dependence of
another property in the liquid. In other words this means that the temperature