Ph.D. thesis (pdf) - dirac

14 Slow and fast dynamics
(linear) relaxation itself.
Simple Debye (exponential) relaxation is very rarely found in viscous liquids, hence
the relaxation is non-Debye. Instead the relaxation function is found to be broader
than a Debye relaxation. This can either be described as a superposition of Debye
processes or by one of the numerous phenomenological fitting functions which are
used in the area (see section 5.3 for details).
The most general question, concerning non-Debye relaxation in macroscopic quantities,
is whether it is due to an intrinsic non-Debye relaxation or whether the macroscopic
departure from Debye relaxation is due to heterogeneous dynamics. In a
homogeneous relaxation all the relaxation entities have relaxations identical to the
average relaxation. In a heterogeneous scenario every entity behaves differently, and
in this case it is possible that the individual relaxation is Debye. In this case the
non-Debye average relaxation stems from the fact that it is an average. [Richert,
2002]
In the last decade there has been extensive studies, using different experimental
techniques and simulations, of the heterogeneity of viscous liquids. The most common
conclusion is that the liquid is structurally homogeneous but that the dynamics
is heterogenous. This means that different parts of the liquid move in different ways
at a given time. [Richert, 2002]
A stronger deviation of the relaxation functions from an exponential dependence
on time (a more important “stretching”) has been found to correlate with larger
fragility Böhmer et al. [1993]. The reported correlation between the two is one of
the bases of the common belief that both fragility and stretching are signatures of
the cooperativity of the liquid dynamics. We discuss this correlation in chapter 5.
2.4 Energy landscape
The most detailed question we could ask regarding the dynamics of the liquid is of
course the following: Where are all the molecules as a function of time? That is,
we ask the time dependence of 3N coordinates (N being the number of particles).
But these 3N values are of course not accessible (except in computer simulations)
and moreover it is difficult, if not impossible, to interpret such an overwhelming
amount of information. It is, however, very common in glass physics to think and
argue in terms of the potential energy landscape. The energy landscape is a hypersurface
which describes the potential energy of the system as a function of the 3N
configurational coordinates. The dynamics of the liquid is viewed as an exploration