Ph.D. thesis (pdf) - dirac

78 Alpha Relaxation
for the 1 s isochrone in [Paluch et al., 2003 a]. Along this 100 s isochrone we calculate
α τ and determine
d log e(ρ)
dlog ρ
from
d log e(ρ)
d log ρ
= 1/(T g |α τ |). From this we determine
ln(e(ρ)) (up to an additive constant) by integrating dln(e(ρ))
ln ρ
d(ln(ρ)), and ln(e(ρ))
is finally converted by e(ρ) = exp(ln(e(ρ))). This gives e(ρ) with an arbitrary
multiplicative constant. The quality of the data collapse is independent of this
constant, as it only depends on the density dependence of e(ρ) not on its absolute
value. In figure 5.7 we show the data as a function of e(ρ)/T, using the e(ρ) found
from this construction. The constructed e(ρ) has an apparent “power-law” exponent
x(ρ) = dloge(ρ)/dlogρ that increases from 1.5 to 3.5 with density in the range
considered. It is seen that this makes the higher density data fall reasonably well
on the master curve and that gives an even better collapse in the low density region
than with the scaling with a simple power law.
As a last note regarding the e(ρ)/T-scaling in figure 5.7, we want to stress that we
cannot test the scaling (Eq. 3.2.1) in the density range above 1.25 g/cm 3 where
there is only one set of data. Indeed, with a unique set of data in a given range of
density it is always possible to construct e(ρ) in this range to make the data overlap
with data taken in other density ranges.
We have determined the ratio between the isochoric fragility and the isobaric fragility
at atmospheric pressure by calculating α τ along the isochrone of 100 s and inserting it
in equation 3.1.5. This leads to m P /m ρ ≈ 1.2, when m P is the atmospheric-pressure
fragility. In figure 5.8 we show the isobaric data taken at atmospheric pressure and
at 230 MPa scaled by their respective T g (P). No significant pressure dependence of
the isobaric fragility is observed when going from atmospheric pressure to 230 MPa,
which is consistent with the result of Sekula et al. [2004]. The pressure independence
of m P is connected to the relatively low value of m P /m ρ = 1.2, (typical values
are 1.2-2 [Alba-Simionesco et al., 2002]); m ρ is pressure independent and the ratio
m P /m ρ cannot be lower than one (see Eq. 3.1.5), so that m P can at most decrease
by 20% from its atmospheric-pressure value. Moreover, the increase in dln(e(ρ))
ln ρ
with
density will tend to cancel the decrease in α P T g , which is usually responsible for the
decrease in fragility with increasing pressure.
5.2.2 m-Toluidine
The glass transition temperature at atmospheric pressure is T g = 187 K and the
isobaric fragility based on dielectric spectra is reported to be m P = 82±3 [Mandanici
et al., 2005; Alba-Simionesco et al., 1999]. (There has been some controversy on the
dielectric relaxation in m-toluidine at atmospheric pressure, see [Carpentier et al.,