Ph.D. thesis (pdf) - dirac

116 High Q collective modes
[Alba-Simionesco et al., 2004; Casalini and Roland, 2004], and the density dependence
of the relaxation time, which is contained in
d log e(ρ)
d log ρ .
m P
/m ρ
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
0 0.2 0.4 0.6 0.8
α
m P
/m ρ
2.2
2
1.8
1.6
1.4
1.2
1
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
f(T g
)
Figure 6.24: The ratio between isochoric and isobaric fragility as a function of f Q (T g )
and α. The legend is found in figure 6.21.
dlog e(ρ)
In figure 6.25 we show the f Q (T g ) value versus
d log ρ
. The amount of data is
limited and the uncertainty on this type of data is large, but it is striking that we
d log e(ρ)
d log ρ
. It is striking
can be determined from the dynamics of the non-viscous
obtain a new correlation. The smaller f Q (T g ) is the larger is
most of all because
d log e(ρ)
d log ρ
liquid at high temperatures [Alba-Simionesco et al., 2002]. We contemplate that
the correlation proposed between f Q (T g ) and m P is a reminiscent signature of a
dlog e(ρ)
correlation between f Q (T g ) and
d log ρ
. An excellent test case for this hypothesis
would be to measure f Q (T g ) on sorbitol which has a very high m P -value combined
d log e(ρ)
with an exceptionally low value of
d log ρ
[Roland et al., 2005].
It appears that the anti-correlation between
correlation between
d log e(ρ)
dlog ρ
dlog e(ρ)
d log ρ
and f Q (T g ) is better than the
and α. This is particularly true when considering the
pressure dependence of the quantities in the case of cumene;
d log e(ρ)
dlog ρ
does not depend
on pressure and the pressure dependence of f Q (T g ) is weak whereas α has a
significant pressure dependence. It is difficult to know if the pressure independence
dlog e(ρ)
of f Q (T g ) of cumene is a coincidence or if this could be general for systems with constant
dlog ρ . f Q(T g ) decreases with pressure both in the case of PIB and DBP, the
correlation suggested from figure 6.25 therefore implies that should increase
dlog e(ρ)
d log ρ
with pressure. In section 5.2.1 we show that DBP is in fact a system where
increases with pressure, and PIB could be a similar system (see appendix A).
d log e(ρ)
dlog ρ
A physical significance of the correlation is that the larger the vibrational compressibility
is relative to the total compressibility the more sensitive to density is the