We present a study of the rheological and optical behaviour of
Kramers
bead–rod
chains in dilute solution using stochastic computer simulations. We consider
two
model linear flows, steady shear and uniaxial extensional flow, in which
we calculate
the non-Newtonian Brownian and viscous stress contribution of the polymers,
their
birefringence and a stress-optic coefficient. We have developed a computer
algorithm
to differentiate the Brownian from the viscous stress contributions which
also
avoids the order (δt)−1/2 noise associated
with
the Brownian forces. The strain or shear rate is made dimensionless with
a
molecular relaxation time determined by simulated
relaxation of the birefringence and stress after a strong flow is applied.
The characteristic long relaxation time obtained from the birefringence
and
stress are equivalent
and shown to scale with N2 where N is the
number
of beads in the chain.
For small shear or extension rates the viscous contribution to the effective
viscosity is constant and scales as N. We obtain an analytic
expression which explains the
scaling and magnitude of this viscous contribution. In uniaxial extensional
flow we
find an increase in the extensional viscosity with the dimensionless flow
strength
up to a plateau value. Moreover, the Brownian stress also reaches a plateau
and we
develop an analytic expression which shows that the Brownian stress in
an aligned
bead–rod chain scales as N3. Using scaling arguments
we
show that the Brownian stress dominates in steady uniaxial extensional
flow until
large Wi, Wi ≈ 0.06N2,
where Wi is the chain Weissenberg number. In shear flow the viscosity
decays as Wi−1/2 and the first normal stress
as
Wi−4/3 at moderate Wi. We demonstrate
that
these scalings can be understood through a quasi-steady balance of shear
forces with
Brownian forces. For small Wi (in shear and uniaxial extensional
flow)
and for long times (in stress relaxation) the stress-optic law is found
to be
valid. We show that the rheology of the bead–rod chain can be qualitatively
described by an equivalent FENE dumbbell for small Wi.