Effects of discretization on viscosity in the necklace model

The consequences of discretization on the resulting viscosity for the necklace model are analyzed to find out the mechanisms by which this model leads to results different from what could be anticipated. In order to accomplish this, various models of increasing complexity are proposed. First, the effects of the jump distance and temporal discretizations are studied. Then, the lack of proportionality between the length and the mass of the chains and the fact that chains do not perform a random walk are analyzed. Knowing of these influences on the viscosity, we finally address the effect of length fluctuations. It is shown that fluctuations can have unexpected effects that lead to larger or smaller values of viscosity. The simplicity of the studied models allows us to quantify the effects of discretization and fluctuations, effects that can be present in other models of similar or larger complexity.