Ph.D. thesis (pdf) - dirac

Chapter 9
Summarizing discussion
When a liquid is cooled along an isobar the density increases and the temperature
decreases. These two effects both contribute to the slowing down of the dynamics
and the isobaric fragility is a combined measure of the two effects.
It has been found empirically over the last five years that the isochoric fragility, which
gives a measure of the effect of temperature alone, is independent of density for a
large group of different systems, while the isobaric fragility changes when evaluated
at higher density. This change in isobaric fragility with pressure is therefore related
to the change in the effect of density on the relaxation time.
The effect of density on the change of relaxation time upon cooling along an isobar
is governed by two things. First the thermal expansivity α P , or α P T = d log ρ
d log T , which
measures how much density changes as a function of temperature, and secondly a
term that measures how sensitive the relaxation time is to changes in density. The
thermal expansivity decreases when pressure is increased. Thus the volume does not
change very much as a function of temperature along high pressure isobars and a
high pressure isobaric experiment is consequently closer to being isochoric. Or put
in other words, the relative effect of density on the viscous slowing down is smaller
at high pressure because density itself changes less as a function of temperature at
high pressure. It is due to this effect that isobaric fragility most commonly decreases
with increasing pressure. The change in fragility with increasing pressure is therefore
due to a change in the thermodynamics rather than to a pressure induced change in
the response to temperature changes. The pure effect of temperature as measured
by the isochoric fragility is found to be independent of density, and in this sense to
be intrinsic to the liquid. 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
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