Mutual information, vibrational scaling, short-time dynamical heterogeneity and secondary relaxation in coarse-grained polymer systems

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.