Ph.D. thesis (pdf) - dirac

114 High Q collective modes
isobaric fragility of cumene decreases as a function of temperature. Yet it seems
that the increase of α with increasing pressure is quite general.
6.4.3 Comparing different systems
In this section we consider the proposed correlation(s) between nonergodicity factor
and isobaric fragility in terms of isochoric fragility and in terms of the effect of
density on the relaxation time (see section 3.3). We shall in all cases consider α and
f Q (T g ) in parallel.
In figure 6.22 we show the isobaric fragility α and f Q (T g ) respectively. We show
only data points which correspond to samples for which the isochoric fragility is also
known, the original correlation is indicated with a line. The first observation is that
the originally proposed correlation to m P fails when considering this limited set of
data. It has been suggested that the correlation might fail if Johari Goldstein beta
relaxations or other fast relaxations contribute to the intensity of the central peak
[Scopigno, 2007]. This could explain the outliers lying above the line in figure 6.22
while it could not explain the outlier below the line 4 .
5.5 oTP
5
4.5
4
3.5
3
2.5
2
salol
glycerol
DBP
PVAc
m−toluidine
pib
cumene
1.5
0 cumene 0.2 300.4Mpa
0.6 0.8
Figure 6.21: The legends for the symbols used in figures 6.22 to 6.25. The value
of alpha is not known for PVAc, and we have therefore calculated it from f Q (T g )
assuming equation 6.4.2. The value of f Q (T g ) is not published for salol and was
therefore calculated from α also assuming equation 6.4.2. These two values are
shown with small symbols in all the figures in order not to emphasize them.
4 DBP, which is an outlier in figure 6.22, is an example of a systems where the JG-relaxation
is rather prominent. However, it is worth noticing that it still has an intensity which is orders of
magnitudes lower than the alpha relaxation, meaning that its contribution to the nonergodicity
factor probably can be neglected. This is illustrated in the plots below with dielectric data of
Nielsen et al. [2006].
log 10
im(ε)
1
0
−1
T=174K
T=182K
−2
−2 0 2 4
log 10
Hz
im(ε)
2.5
2
1.5
1
0.5
T=174K
T=182K
0
−2 0 2 4
log 10
Hz