Ph.D. thesis (pdf) - dirac

112 High Q collective modes
pressure and 300MPa. Note first of all that the f Q (T) = 1/(1 + aT) behavior is
followed all the way up to T g in this case, meaning that equation 6.4.2 is valid.
0.6
100
0.5
80
α, Q=2nm −1
0.4
0.3
0.2
m P
60
40
0.1
20
a)
0
2.5 3 3.5 4 4.5 5 5.5 6
log 10
Mw
b)
0
0 0.2 0.4 0.6
α IXS
Figure 6.19: The parameter α (see text) as a function of molecular weight. Q =
2 nm −1 , ambient pressure.
It is clearly seen the slopes on figure 6.18 that α is larger for the larger molecular
weight. We have also determined α for the PIB1100 and the PIB500k samples (figure
6.19 a) and find a monotonous molecular weight dependence which levels off around
Mw=10.000 g/mol much like the sound speed in the liquid (figure 6.6) and other
dynamical properties. We do not have the fragility of the samples at intermediate
molecular weight, but the low molecular weight sample has considerably higher
fragility than the high molecular PIB (see appendix A). The molecular weight
dependence of α is thus opposite to what one expected from the correlation between
α and fragility. This is illustrated in figure 6.19 b).
From figure 6.18 we can also anticipate the pressure dependence of α; for the PIB3580
sample it is seen that α increases significantly when the pressure is increased from
atmospheric pressure to 300 MPa. The tendency is the same for the PIB680 sample
although the effect is much weaker (almost within the error-bars). We will return
to this result after considering the situation for cumene.
The temperature dependence of the inverse nonergodicity factor of cumene at atmospheric
pressure and 300MPa is shown in figure 6.20. The data is shown both on an
absolute temperature scale and as a function of T/T g . The value of α increases when
pressure is increased from atmospheric pressure to 300MPa. The isobaric fragility
on the other hand decreases (see appendix A). The pressure dependence is hence
not consistent with a correlation between α and m P .
It is striking in figure 6.20 that there are deviations from the harmonic f Q (T) =
1/(1 + aT)-behavior below T g at atmospheric pressure. The harmonic behavior