Ph.D. thesis (pdf) - dirac

6.4. Nonergodicity factor and fragility 113
2.4
2.2
Patm Q=2nm −1
2.4
2.2
Patm Q=2nm −1
300MPa Q=2nm −1
2
2
1/f(Q) Q=2nm −1
1.8
1.6
300MPa Q=2nm −1 b)
1/f(Q) Q=2nm −1
1.8
1.6
1.4
1.4
1.2
1.2
a)
1
0 50 100 150 200
T [K]
1
0 0.5 1 1.5
T/T g
Figure 6.20: The inverse nonergodicity factor of cumene as a function of temperature.
Figure a) shows an absolute temperature scale while figure b) shows temperature
normalized to the pressure dependent glass transition temperature. Lines are fits to
equation 6.4.1 , the slope of the lines in figure b) is equal to α.
implies that the moduli are constant, but when looking back at figure 6.11 we see
that also the sound speed of cumene increases below T g . From this we conclude that
there is a high frequency relaxation in the glassy cumene which brings down the
longitudinal modulus and the nonergodicity factor. There are no similar changes at
300 MPa, and it is why there is a crossover in the pressure dependence of f Q , seen
in figures 6.16 and 6.20 a).
The crossover in the pressure dependence has the consequence that while α determined
from low temperatures is pressure dependent then f Q (T g ) is almost pressure
independent. Moreover the weak change in f Q (T g ) is consistent with an anti correlation
between f Q (T g ) and m P .
For the mean square displacement which relates to the single particle dynamics
seen from the incoherent scattering we find that the pressure dependence can be
scaled out by scaling temperature with T g (section 7.3). For α it appears that the
situation is quite different. The pressure dependence seen in the 1/f(Q) versus
T/T g is largely (PIB3580) or solely (PIB680 and cumene) due to the scaling of the
temperature axis by T g as the isothermal pressure dependence of the nonergodicity
factor is weak (PIB3580) or non existing (PIB680 and cumene). IXS data taken
under pressure have earlier been performed on DBP by Mermet et al. [2002]. From
this experiment it is also reported that the nonergodicity factor does not change
as a function of pressure at constant temperature. The change in T g with pressure
therefore makes α of DBP increase with increasing pressure. DBP is an example of
a liquid with no significant pressure dependence of the isobaric fragility while the