Ph.D. thesis (pdf) - dirac

22 Slow and fast dynamics
and suggest that it is related to the intensity of the central peak [Buchenau and
Wischnewski, 2004]. The central peak is a measure of the density fluctuation that
are frozen in when the alpha relaxation is arrested at the glass transition. Hence,
this view on the correlation points to a relation between the amplitude of the alpha
relaxation at T g and the temperature dependence of the alpha relaxation.
2.7.2 Mean squared displacement
The mean squared displacement is classically proportional to temperature in the
harmonic approximation, where the shear and bulk moduli are constant. This linear
behavior is often followed in the glass, but the temperature dependence of the short
time mean squared displacement becomes stronger at temperatures above T g (see
figure 2.6). Moreover, the temperature dependence of the mean square displacement
above T g has been found to be stronger the more fragile the system is [Ngai, 2004].
In this situation it is therefore the high frequency (and not the glassy) dynamics
of the equilibrium liquid that is related to fragility. Some of the interpretations of
the finding are however very close to some of the notions suggested to understand
the above result concerning the nonergodicity factor: namely, that the shape of the
minima in the energy landscape are related to the energy barriers. In this view
it is assumed that the vibrations stay essentially harmonic above T g but that the
curvature of the potential around the minima visited by the system changes as a
function of temperature once the alpha relaxation becomes active. The change of
curvature is expected to also change the barrier height and thereby the temperature
dependence of the alpha relaxation time itself [Dyre and Olsen, 2004].
Another interpretation of the change in the temperature dependence of the mean
square displacement is that it is related to the setting in of fast relaxational processes
[Buchenau and Zorn, 1992; Ngai, 2000]. These processes are thought to serve as
precursors of the alpha relaxation, with the alpha relaxation being faster the larger
the amplitude of these relaxations.
There is in both views a subtle suggestion of a two way causality. A larger amplitude
of the mean square displacement gives rise to a faster alpha relaxation, and the alpha
relaxation itself changes the liquid structure and thereby changes the properties
which govern the mean square displacement.