  Rigid macromolecules or polymer chains with persistence length on the order
of the contour length (or greater) have traditionally been modelled as rods or
very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely
extensible about a non-zero natural length with tunable harmonic stiffness, is
one such model which has previously been shown to reproduce bead-rod behaviour
in the absence of hydrodynamic interactions. The force law for the
FENE-Fraenkel spring reduces to the Hookean or FENE spring force law for
appropriately chosen values of the spring parameters. It is consequently
possible to explore the crossover region between the limits of bead-spring and
bead-rod behaviour by varying the parameters suitably. In this study, using a
semi-implicit predictor-corrector Brownian dynamics algorithm, the
FENE-Fraenkel spring is shown to imitate a rod with hydrodynamic interactions
when spring stiffness, extensibility and simulation timestep are chosen
carefully. By relaxing the spring stiffness and extensibility, the
FENE-Fraenkel spring can also reproduce spring-like behaviour, such as a
crossover from $-1/3$ to $-2/3$ power-law scaling in the viscosity with shear
rate, and a change from positive to negative second normal stress difference.
Furthermore, comparisons with experimental data on the viscosity and linear
dichroism of high aspect ratio, rigid macromolecules shows that the
extensibility and stiffness of the FENE-Fraenkel spring allows for equal or
improved accuracy in modelling inflexible molecules compared to rodlike models.
