| In this thesis work, three work problems address unifying features of surface and interfacial critical and growth phenomena. Emphasis is put into models that can be solved analytically but connections with numerical studies are also discussed.;The first, most extensive study examines several aspects of irreversible, mono-layer and multilayer particle deposition on regular surfaces. Experimental studies have shown that such processes are relevant in describing, for instance, the adhesion of proteins on solid substrates, the kinetics of polymer reactions and some stages of multilayer formation in packed-bed experiments with colloidal suspensions. For the latter, Monte Carlo simulations of unscreened models have suggested similarities with critical phenomena (universal exponents and no intrinsic length scales) recently understood as a purely dynamic effect.;In this thesis, multilayer studies established bounds for the validity of the mean-field models, at about 50% of the jamming coverage, and consideration of one-dimensional monolayer models yielded finite-size and boundary corrections, as small as ;The calculations were carried out within a rate-equation approach, neglecting fluctuations in the deposition rates and screening among layers.;The second topic treats, in the transfer matrix formalism, single polymer chains, in two and three dimensions, as directed self-avoiding walks undergoing conformational transitions near attractive surfaces.;The adsorption-desorption behavior of the chain is temperature driven except for penetrable surfaces, as described in this thesis. The average fraction of adsorbed monomers vanishes linearly at the transition but the set of critical exponents is sensitive to the type of grafting and the region of approach to the singularity. Recent efforts to incorporate other physical properties of the chain are also reviewed.;Finally, the third topic examines, at the level of capillary waves, the rounding of first-order phase transitions in finite-size systems with fluctuating longitudinal interfaces. Effective transfer matrix results indicate that, for cylindrical shapes, rounding involves unexpected scaling combinations with a form determined by the type of boundary conditions. Implications on the general features of the phase diagram and renormalization group portraits are advanced.;As a conclusion, a summary of the new findings in this thesis and a few remarks on possible extensions of the techniques used here, to more realistic models, are presented. |
