Study of some lattice models for polymers and fluids

• Ano de defesa: 2020
• Autor(a) principal: Rodrigues, Nathann Teixeira
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Viçosa; Física Aplicada
• Palavras-chave em Português: Transformações de fase (Física estatística); Fenômenos críticos; Física Estatística e Termodinâmica
• Link de acesso: https://locus.ufv.br//handle/123456789/31077

Lattice models have been widely employed in the modeling of a sort of real systems, being especially important in study phase transitions and critical phenomena. In polymers, lattice models have helped to unveil the universal nature present in these systems, allowing a deep understanding of important phenomena such as protein folding and adsorption. When applied in the study of fluid systems, lattice models have been used to explore several properties as, e.g., fluid interfaces, phase transitions and multiphase flown. Here we investigate lattice models for both polymers and fluids. We explore two-dimensional lattice models for a single linear polymer chain near to a surface, with the polymer modeled through the path lattice model of interacting self-avoiding trails (ISATs). By using efficient Monte Carlo methods, we have characterized the thermodynamic behavior of adsorbing ISAT on the square and triangular lattices. In the former case, we have analyzed the universal nature of the adsorption transition for different boundary and solvent conditions. We have confirmed the universality hypothesis for the ordinary adsorption but, on the special point, a non-universal behavior has been found. On the triangular lattice, we have tackled the challenging problem of building up the three-dimensional phase diagram of the model, which is featured by several phases separated by a number of surfaces of phase transition and multicritical lines. In the part of fluids, we have investigated lattice gas models of hard-particles that excluded up to their k nearest-neighbor (kNN) in the square and cubic lattices with semi-analytic solutions on Husimi Lattices (HLs). By solving the models 1NN and 2NN on L-level HL built with squares we have characterized the critical parameters and, by using the coherent anomaly method (CAM), we have obtained the critical exponent β and γ. For both models, we have found critical parameters in good agreement with the more accurate estimates from Monte Carlo simulations. The values of the exponentes, however, are far from the expected values. On the cubic lattice, we have studied the binary 0NN-1NN, 0NN-2NN and 1NN-2NN and the ternary 0NN-1NN-2NN mixtures. By solving these mixtures on a HL built with cubes we have found a very rich thermodynamic behavior, with the presence of four stable phases, two fluid, and two solids, being separated by continuous and discontinuous phase transitions. We also have found critical, tricritical and triple points and even a density thermodynamic anomaly. Keywords: Lattice models. Phase transitions. Critical phenomena. Self-avoiding trails. Lattice gas. Husimi lattice.