Ph.D. thesis (pdf) - dirac

90 Alpha Relaxation
keeping the relaxation time constant. If this finding is indeed general then it suggests
that the spectral shape of the alpha relaxation has the same intrinsic character as the
isochoric fragility, namely that it stays constant along an isochrone (chapter 3). The
isobaric fragility on the other hand will in general change when pressure changes.
Hence, the pressure dependence of the isobaric fragility and spectral shape is in
disagreement with the behavior expected from the correlation between the two.
This leads us to suggest that the stretching might/or better correlate to the isochoric
fragility than to the isobaric fragility.
200
150
m P
100
50
0
0.2 0.4 0.6 0.8 1
β KWW
Figure 5.17: Isobaric fragility as a function of the stretching parameter. Circles
represent polymers, diamonds represent molecular liquids. See the table in appendix
B for numerical values and references.
To test this hypothesis we have collected data from literature reporting isobaric
fragility and stretching of the relaxation at T g . We consider here the description
of the shape of the relaxation function in terms of the KWW stretching parameter
β KWW . This choice is made because it is convenient to use a description with only
one parameter for the shape and because β KWW is the most reported of the liquids
where m ρ is also available (see section 5.3.1).
The compilation of this data is shown in figures 5.17 and 5.18 where both the
isochoric (figure 5.18) and isobaric fragility at atmospheric pressure (figure 5.17)
are plotted against the stretching parameter. There is a great deal of scatter in
both figures. There is however an observable trend, the fragilities decrease with the
stretching. The relative effect on the slowing down of the relaxation is characterized
d log e(ρ)
by the term α P T g d log ρ
= m P /m ρ −1. In figure 5.19 we show the ratio m P /m ρ as
a function of β KWW . It is clear that no correlation is found between this ratio and
the stretching. This indicates that there is no relation between the effect of density
on the correlation time and the spectral shape (see chapter 3).
Based on the pressure dependence and the clear lack of correlation between stretching
and the relative effect of density (seen in figure 5.19) we suggest that a possible