Ph.D. thesis (pdf) - dirac

6.4. Nonergodicity factor and fragility 115
m P
120
100
80
60
40
20
m P
120
110
100
90
80
70
60
50
40
30
0
0 0.2 0.4 0.6 0.8
α
20
0.6 0.7 0.8 0.9 1
f(T g
)
Figure 6.22: Isobaric fragility as a function of f Q (T g ) and α. The legend is found in
figure 6.21.
The next observation is that the correlation to m ρ is even poorer (figure 6.23). This
indicates that the correlation proposed between f(T g ) and m P is not related to the
effect of temperature on the alpha relaxation time. However, there does seem to be
a correlation to the ratio m P /m ρ (figure 6.24) implying a correlation between f(T g )
and the effect of density on the relaxation time.
m ρ
80
60
40
20
0
0 0.2 0.4 0.6 0.8
α
m ρ
90
80
70
60
50
40
30
20
0.55 0.6 0.65 0.7 0.75 0.8
f(T g
)
Figure 6.23: Isochoric fragility as a function of f Q (T g ) and α. The legend is found
in figure 6.21.
To examine the significance of this further we start by noting that the scaling law
(equation 3.2.1) leads to the following relation
(
m P /m ρ = 1 − dlog ρ
)
dlog e(ρ)
dlog T ∣ . (6.4.4)
P
dlog ρ
This expression clearly illustrates that the effect of density on the slowing down
upon isobaric cooling as measured by m P can itself be decomposed in two parts:
the temperature dependence of the density measured by dlog ρ
∣ (T = T g ) = −T g α P
P
dlog T