  A reasonably accurate representation of a polymer chain is provided by beads
connected with rods, or stiff, inextensible springs that mimic a single Kuhn
step. Due to high computational cost, coarse-grained bead-spring models are
used in typical applications, where each spring is supposed to replace several
Kuhn steps. Earlier investigations indicate that the BD simulation predictions
of the steady state in different flows, with these different levels of
discretization, are largely qualitatively similar. However, subtle quantitative
differences exist even for the steady states. In this study, we perform a
detailed analysis of the behavioral differences arising out of the varying
degrees of chain discretization, ranging from one to several hundred Kuhn
steps. We compare the transient and steady behavior of both configuration and
rheological properties for a single chain in uniaxial extension and steady
shear flow. Our analysis highlights differences, particularly in the stress and
viscosity values, obtained at intermediate and high flow rates, between the
bead-rod and bead-spring models. Such a thorough understanding helps to provide
an estimate of the best possible bead-spring representation for an underlying
polymer chain in a given application. Additionally, we also investigate the
limit of break-down of the spring laws i.e. the minimum number of Kuhn steps
that a spring can mimic faithfully.
