Statics, short time dynamics and relaxation in polymers and viscous liquids

By performing Molecular Dynamics (MD) simulations it is possible to explain the validity of a theoretical model in a fully controlled environment. Their use became a relevant part of the normal activity of all scientific researching groups. The MD potentialities extend beyond the simply theoretical validation: thanks to the great precision and low-cost computational power archived presently, they can be applied to better interpret experimental observation too. The work here presented tries to highlight indeed both of these aspects in the context of glass-formers and polymers. During my PhD I worked on several projects all connected by one "lait motif": the interest for mechanical relaxation processes inside complex liquids. This huge theme in the matter physics borders with chemistry and material engineering due to the practical and also, why not, futuristic applications (e.g. pharmaceutical, dental and internal prosthesis, food preservation and cryogenic suspension of living beings, new functional materials with fine tuned optical and mechanical properties). The hidden heart, feeding all this research fields on the same landscape, is the Glass Transition (GT). The knowledge of the physics controlling the relaxation arrest experimented by liquids under hight density and low temperature regimes is still unraveled, but it continues to intrigue despite the decades of interest. The GT theme is approached here from the numerical point of view. To study this complex phenomenology, the chosen prototype of viscous liquid is the simple beads and springs model for polymeric chain liquids. Polymers represent indeed a central class in the GT research because of their "natural" disorder. For this reason a polymer liquid, rather than crystallize in a regular lattice, reaches an amorphous state, the glassy state. This thesis is structured into two parts: in the first two chapter, the numerical model of a polymeric liquid, its statics (Chpt.1) and its dynamics (Chpt.2) is presented; then this model is utilized in the context of GT speculations (Chpt.3). To be a little more precise in Chpts.1 and 2 the polymer model is analyzed in terms of Rouse modes which, carefully mixed, help to formulate predictions on bond relaxation functions. These are regularly observable in dielectric spectroscopy experiment. Of course, the Rouse picture represents a first approximation, nevertheless just to pose mind on this imperfections is sufficient to increase our knowledge on the model. Indeed, the effort spent was repaid with interesting results by comparing the theory and simulations data. In Chpt.3 the GT is faced moving from a series of relevant observations on a huge corpus of simulated state points. A strong correlation, between structural relaxation time and the Debye-Waller factor (DW), is proved to exist and to be described by a parabolic extension of the Hall-Wolynes law \cite{HallWolynes87}. The extreme robustness on numerical data, also on other MD simulations from literature, gave us the amazing possibility to successfully breakthrough into the ``real'' world. Indeed, both the observables have their experimental equivalents and can be found in literature for a not negligible number of liquids. What we propose represents the most "universal" law in this field both for the wide range of fragility (20 < m < 191) and for the time scales spanned ( 10E-12 sec < t < 10E2 sec).