Sistemas de k-meros em rede

Abstract

The study of k-mers in lattice had as motivation investigate the isotropic-nematic phase transition present in liquid crystal systems. Liquid crystal molecules have a shape similar to discs or rods, wich align on one preferencial direction when changing temperature or density. On simulational study the molecule is represent as a k-mer (occupies k consecutive sites) in lattice. The vertical and horizontal are the only possible orientations. The interaction betwen two different k-mer is given by excluded volume interaction, that is, one k-mer can not cross with another. The phase of system is determined by the diference of k-mer on two directions. There are two phase transitions present in this model.The frist, on intermediate density, the system undergoes a phase transition from disordered phase to a nematic phase as the density is increased. The second transition ocor in high densitis returning to isotropic phase. Computational research of k-mers in lattice published often use traditional Monte Carlo method only. In these work, we use Monte Carlo and tomographic samples method to estimate the configuration number of k-mers in a complete density interval. The tomographic samples is an advantageous alternative method, once is not necessary run the simulations for specific values of densities. The numerical data obtained are compared to previous know results for dimers sistems and some theories that present the entropy for similar systems. In these last, it is possible observe regions where analitical results describe the entropy of the system better.