Effects of discretization on viscosity in the necklace model

TL;DR

This paper investigates how discretization choices and chain fluctuations affect viscosity predictions in the necklace model, revealing mechanisms that cause deviations from expected results and quantifying these effects.

Contribution

It introduces a series of progressively complex models to analyze the impact of discretization and fluctuations on viscosity in the necklace model.

Findings

Discretization of jump distance and time affects viscosity results.

Lack of proportionality between chain length and mass influences viscosity.

Chain length fluctuations can unexpectedly increase or decrease viscosity.

Abstract

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.