Ph.D. thesis (pdf) - dirac

A.1. Cumene 195
the value found from the density measure at atmospheric pressure. The density is
calculated at T > 240 K from the density at room temperature and the expansion
coefficient. This gives essentially linear temperature dependence at all pressures
and this temperature dependence is finally extrapolated to low temperature. As a
consistency check we verify that ρ x g/T g = const holds on the T g line at all pressures.
1.15
1.1
1 GPa
1.05
ρ [g/ml]
1
0.95
0.9
0.85
300 MPa
0.1 MPa
0.8
0.75
100 150 200 250 300 350 400
T [K]
Figure A.2: Illustration of the determination of the density of cumene as a function
of pressure and temperature. Stars are measured densities from Bridgman [1949].
Black fill line is the density from Barlow et al. [1966]. Colored full lines are calculated
from the estimated pressure dependent expansion coefficient (see the text for details).
Crosses are densities found on the T g -line by assuming that the density scaling holds
yielding ρ x /T = constant.
3
13
3
13
−1
9
−1
9
log 10
τ max
[s]
−5
5
log 10
η [Poise]
log 10
τ max
[s]
−5
5
log 10
η [Poise]
−9
1
−9
1
a)
−13
−3
3 4 5 6 7 8
1000/T [K −1 ]
b)
−13
−3
0.4 0.5 0.6 0.7 0.8 0.9 1
T g
(P)/T
Figure A.3: The relaxation time (•) at 300 MPa and viscosity () at atmospheric
pressure of cumene as a function of temperature under isobaric conditions. The full
lines illustrate the position of T g (P) and m P (P). Figure a shows the data on an
absolute temperature scale (1000/T) and figure b) shows the data versus T g /T.
Based on the density data we can calculate xα P T g at all pressures. Assuming that
the scaling shown in figure A.1 holds we calculate the pressure dependent isobaric
fragility using m P = m ρ (1 + xα P T g ). We find that the isobaric fragility decreases
with pressure and that it is 20% lower at 300 MPa giving a fragility of m P (P =
300MPa) = 72.
The relatively low T g = 127 K of cumene makes it difficult to measure with our di-