Equações de Langevin para modelos de deposição e corrosão - Silveira, Flávio A. da (2012)
In this work, we studied thin-film growth through lattice-gas models. Discrete models, in which particles interact through simple rules, are capable of generating non-trivial behaviour at large scales of lenght and time and may, by an apropriate choice of these rules, describe properties of the surface of materials. As recently as 20 years ago, a microscopic theory which takes into account the markov character of the interaction rules, has made possible, through a master equation formulation, to associate analytical equations to the processes defined by discrete models. According to this theory, a perturbative expansion of the master equation associated to the rules of the model connects it to a Langevin-type equation, generically called growth equation. The applicaton of this theory specifically to discrete models for the growth of thin-films is analyzed in detail, and subjects such as the choice of the expansion parameter and the nature of the stability of the solutions are addressed. Among the many properties we can obtain through both numerical realizations of discrete models and growth equations, there exist some scaling exponents which charaterize the modeled surface dynamics. We analized four discrete models in which the surface evolves by the deposition of particles and, for all of them, we have made measurements of these exponents through numerical simulations. These exponents may be compared to results from the continuous theory for these models, but, in order to take into account the singular character of certain approximations involved in the limiting process, we developed a scaling theory. This theory allows us to determine the universality class of the studied models by both analytical and numerical methods. We extended this analysis to a model of dissolution of solids with the solidon- solid (SOS) restriction, which disallows the formation of holes and pores on the surface. We then have deepened our study on models for corrosion, by forsaking the SOS restriction, the purpose of which was to bring understanding on how height fluctuations evolve in a model where the surface develops on a grain structure. We observe, in this non-SOS metal dissolution model, how the detachment of clusters formed by more than on particle from the electrode can approximate deviations from the Faraday law by the mecanism known as chunk effect.