Ph.D. thesis (pdf) - dirac

34 What we learn from pressure experiments
different groups [Roland et al., 2005; Reiser et al., 2005; Floudas et al., 2006]. The
power law dependence is fulfilled to a good approximation for many systems, but
the range in density is often too small to distinguish from other functional forms
[Dreyfus et al., 2004]. For DBP which we study in this work (chapter 5), we find
significant deviations from the power-law form.
There are some differences in views regarding the physical interpretation of the
scaling law, particularly regarding the meaning of the exponent x Tarjus et al. [2004
a,b]; Roland and Casalini [2004]. In this work we do not deal with the explanation
of the scaling but rather consider its consequences when interpreting other results.
It is therefore important to stress that, despite the controversies, there is agreement
on the phenomenology, so far as to say that equation 3.2.1 gives a good description
of the density and temperature dependences of the relaxation time.
If the density dependent energy E ∞ (ρ) is determined from the high temperature
Arrhenius behavior, then it is given in absolute units - and it is associated with a
specific physical interpretation. However, most of the data leading to the scaling
is obtained in the low temperature non-Arrhenius regime, and the energy is only
obtained up to a multiplicative constant. We have therefore chosen the notation
e(ρ) rather than E ∞ (ρ).
Most of the data supporting the scaling-law is from dielectric measurements in the 0.1
Hz-MHz range. Another limitation of the result is that all the data are on molecular
liquids, Van der Waals bonded or hydrogen bonded or on polymers. Hence, strong
glasses and inorganic glasses in general have not been studied so far. Nevertheless,
the scaling law serves as a general description of the density and the temperature
dependences of the alpha relaxation time in molecular liquids and polymers in the
viscous regime where the super-Arrhenius behavior is seen. Note that if strong
glasses have a strictly Arrhenius behavior, then equations 3.2.1 and 3.2.2 trivially
apply with probably a weak or negligible dependence on density at least for moderate
pressures.
3.2.2 The consequences on fragility
It can be seen directly from equation 3.2.1 that X(ρ, T) = e(ρ)/T, evaluated at
T τ (ρ) has the same value at all densities (X τ = e(ρ)/T τ (ρ)) if T τ (ρ) is defined
as the temperature where the relaxation time has a given value (e.g. τ = 100s).
Exploiting this fact, it is easy to show [Tarjus et al., 2004 a; Alba-Simionesco and
Tarjus, 2006] that the scaling law has the consequence that the isochoric fragility
will be independent of density when evaluated at a T τ corresponding to a given