Ph.D. thesis (pdf) - dirac

7.4. Lindemann criterion 131
DBP at atmospheric pressure and 500 MPa. The temperature scale in this figure
is scaled by the pressure dependent T g and the y-axis is scaled with a 2 ∝ ρ −2/3
evaluated at (T g (P), P). This scaling makes the entire temperature dependence
collapse on one curve (see figure 7.4 for the raw data). The scaling of the temperature
axis is by far the most important for this data collapse. The estimated increase
in density is less than 10% (see appendix A for equation of state). This gives a
decrease of a 2 by approximately 5%. This difference is almost indistinguishable in
figure 7.10 due to the scatter of the data. The same type of data collapse is found for
0.025
0.02
0.01 MPa
500 MPa
/ a 2
0.015
0.01
0.005
0
0 0.2 0.4 0.6 0.8 1 1.2
T / T g
Figure 7.10: The temperature dependence of the mean square displacement in DBP
at atmospheric pressure and 500 MPa. The temperature is scaled by the pressure
dependent T g and the y-axis is scaled with a 2 ∝ ρ −2/3 evaluated at (T g (P), P).
cumene (figure 7.11) within the rather large error-bars of the data on the measured
pressure (see section 7.1.1). A similar result has bean found earlier by Frick and
Alba-Simionesco [1999] on polybutadiene.
This scaling strongly supports the notion of a Lindemann criterion for the glass
transition. It is moreover striking to see that the whole temperature dependence
of the mean square displacement in the glass and in the liquid state collapses after
applying this scaling. This is particularly clearly seen in the case of glycerol, in
which case the deviation from linear temperature dependence sets in much above T g
(figure 7.12).