• soft matter
• supercooled liquid
• glass transition
• molecular dynamics
• simulation
• scaling
• dynamical heterogeneity
• information theory

Understanding the extraordinary viscous slow-down that accompanies glass
formation is one of the major open challenges in condensed matter physics.
On approaching the glass transition from the high fluidity regime, a particle
spends increasing time within the cage formed by the first neighbors where it
rattles with amplitude <u^2>. Its average escape time, i.e. the structural relaxation
time, increases from a few picoseconds in the low-viscosity regime
up to thousands of seconds at the glass transition. The transition from a liquid
to a glass is accompanied by the progressive appearance of dynamical
heterogeneity: it is observed the growth of transient spatial fluctuations in the local dynamical behavior. Experimentally, dynamical heterogeneity manifests itself in the relaxation spectra, measured through mechanical or dielectric
probes, showing a very broad range of relaxation times and a strongly
non-exponential behavior. This suggests the existence of wide distributions
of relaxation rates. Despite the huge difference in time scales between the
rattling motion and the relaxation, several studies addressed the fast rattling
process within the cage to understand the slow relaxation dynamics. Within
this context, several correlations between the amplitude of the rattling motion
and the structural relaxation time have been found in a large variety of
systems.
This correlation is summarized in the form of a universal master curve.
An analytical derivation for this relation, in the framework of the Hall-Wolynes model, relies on the wide distribution of relaxation time, which is a manifestation of the dynamical heterogeneity.
This Thesis work has two main purposes, both central in the field of
research of the glass transition physics by means of coarse-grained molecular
dynamics simulations: i) achieving a deeper understanding of the connection
between fast dynamics and slow relaxation ii) gaining further insight on the
role of the dynamical heterogeneity in such a connection.
Chapters 1 and 2 are the introductory ones. The first one gives a quick
presentation of the general context of this research. The second chapter is dedicated to a brief introduction to Information Theory, as in some of the
works presented in this thesis, Mutual Information is employed as a more
refined and sensitive measure of correlation.
Chapter 3 and 4 are dedicated to the study of displacement-displacement
correlation in a simple molecular liquid by means of mutual information. The
research is motivated by, and as a follow-up to, previous studies based on
displacements correlation function in the light of novel investigation carried
out on atomic liquids by employing mutual information. Chapter 3 focuses
on the mutual information correlation length. A comparison with both the
results obtained in atomic liquids and the ones resulting from simple correlation
function is carried out to determine whether mutual information could
improve the analysis of correlated motion. Chapter 4 extends the previous
investigation with a closer look at dynamical heterogeneity. Two particle
fractions, with different mobilities and relaxations, are identified on the basis
of mutual information related properties. The two fraction scalings, in the
form of the aforementioned universal relation between relaxation and rattling
amplitude, are investigated. The spatial and structural properties of these
two fractions are studied as well.
In Chapter 5 and 6 a slightly more complex system is taken into consideration:
a liquid of 25-mers with bending potential and a nearly fixed
bond length shorter than the zero of the Lennard-Jones interaction. Such
peculiar features give rise to the emergence of a faster secondary relaxation
process. Chapter 5 investigates whether the presence of a secondary relaxation
could interfere with the universal correlation between vibrational
dynamics and primary relaxation. An analysis of the performance of
secondary relaxation probe functions, including mutual information, is also
carried out. Chapter 6 focuses on the role of the secondary relaxation on the
system dynamical heterogeneity as sensed by the non-Gaussian parameter.
A microscopical explanation of the phenomenon, as well as its impact on
other standard observables, is also given.