Ph.D. thesis (pdf) - dirac

3.5. Summary 41
assumption that the empirical scaling law (equation 3.2.1) holds, it moreover follows
that the temperature and density dependence of G should be described in terms of
an equivalent scaling law. This is most easily seen by inserting equation 3.4.1 in
equation 3.2.2 (where Φ ′ below is proportional to Φ) :
( ) T
G(ρ, T) = e(ρ)Φ ′ e(ρ)
(3.4.4)
where e(ρ) is the same as in (equation 3.2.1). See also [Alba-Simionesco and Tarjus,
2006] for similar ideas.
3.5 Summary
Fragility involves a variation with temperature that a priori depends on the thermodynamic
path chosen, namely constant pressure (isobaric) versus constant density
(isochoric) conditions. On the other hand, many quantities that have been correlated
to fragility only depend on the thermodynamic state at which they are considered.
It has been found empirically that the isochoric fragility is intrinsic in the sense that
it is independent of pressure when evaluated along an isochrone. Based on these
observation we conclude that a property which is related to the “pure” effect of
temperature on the relaxation time, should correlate to the isochoric fragility (when
comparing systems), and that it should possess the same type of intrinsic character;
that is, they should be constant along an isochrone for a given system. Properties
related to a combined effect of temperature and density are on the other hand expected
to correlate with isobaric fragility and to have a pressure dependence that
corresponds to its pressure dependence - that is most often decrease with increasing
pressure. The ideas put forward in this chapter are a central part of the work and
serve as a reference point for a large part of the analysis in the proceeding chapters.