• rough substrate
• polymer
• layer
• glass transition
• confinement
• thin film
• universal scaling

If a liquid is cooled avoiding crystallization it shows an enormous slowing down of the molecular dynamics, becoming what is said a supercooled liquid. At a certain temperature Tg the dynamics timescales exceed the observation time and we obtain a liquid out of equilibrium, called glass. A glass has the mechanical response of a solid (very high viscosity), but still exhibits the microscopic disordered structure of a liquid.
Polymeric systems are especially useful to study supercooled liquid near the glass transition Tg. In fact, they present several different length scales, some related to the internal structure of the monomers, others to the entire chain. When cooled, the presence of different length scales leads to phenomena of geometric frustration, and the polymeric melt is not able to crystallise in an ordered phase, thus becoming a supercooled liquid.
Two important quantities that characterise the dynamics of a polymeric melt are the mean squared displacement (MSD) of the monomers and the structural relaxation time τα . The MSD is defined as the average displacement of the monomers from a certain time t0 to the time t0+t. Near the glass transition, the MSD shows a plateau region which is index of the cage dynamics, the rattling motion of the monomer in the cage of his neighbours. The structural relaxation time τα is the typical timescale in which the density fluctuation of the melt relax. It can be determined as the time at which the incoherent part of the intermediate scattering function drops below the value 1/e.
Larini et al found a universal scaling between the cage dynamics (of the order of the picosecond) and the structural relaxation of the liquid (up to 100 s at the transition temperature Tg ) in many experimental and simulative systems. They show that Log(τα) has a parabolic dependence on the inverse of the value of the MSD in the plateau region 1/<u^2>,
with parameters that are universal for the simulative model used for polymers, and depends on a single parameter for the experimental systems.
On the other hand, many researches have investigated the effects of the confinement on the dynamics of supercooled systems, caused by finite-size effects and interaction between the liquid and the interfaces (see, for instance, Bashnagel et al). In this thesis work, we investigate polymeric melts confined in thin film, that is, systems that are infinite in two dimensions but have a finite thickness (from few nm up to ∼ 100 nm) in the third. In particular, we focus on the simulation of supported films, where one of the surfaces is in contact with a substrate, while the other is free. These systems are of particular interest because they can be easily obtained experimentally.
This work is articulated in the following way.
• In chapter 1 the fundamental concepts about the glass transition and the physics of polymers are exposed. We see how the dimensional confinement affects the behaviour near the glass transition, and we define the physical properties of interest used in the thesis.
• In chapter 2 the Molecular Dynamics simulations of polymeric systems are described, and the coarse-grained model used is shown, with attention to the relation with real systems.
Chapters 3 and 4 contain the original part of the thesis.
• In chapter 3 a specific kind of confined system is analysed. We simulate polymeric melt confined in thin films supported on an atomic and attractive substrate, varying the temperature and the thickness of the film. We found that this system show a strong modulation of the linear
density in the confined direction: the monomers position themselves in well-defined layers parallel to the substrate. Then we measured <u^2> and τα for the single layers. These quantities show a strong variation with the distance from the substrate, i.e. with the layers in which they
are measured. Surprisingly, it seems that the universal scaling between cage dynamics and structural relaxation, despite being lost for the film as a whole, can be fully recovered if the measures are performed on the single layers.
• In chapter 4 the same analysis are performed on a smooth and structureless substrate, leading to completely different results. Some possible interpretation of these differences are proposed, and further investigations are suggested, varying the nature and strength of the confinement, in order to achieve a deeper understanding of the scaling in confined systems.