  Using non-equilibrium Brownian dynamics computer simulations, we have
investigated the steady state statistics of a polymer chain under three
different shear environments: i) linear shear flow in the bulk (no walls), ii)
shear vorticity normal to the adsorbing wall, iii) shear gradient normal to the
adsorbing wall. The statistical distribution of the chain end-to-end distance
and its orientational angles are calculated within our monomer-resolved
computer simulations. Over a wide range of shear rates, this distribution can
be mapped onto a simple theoretical finite-extensible-nonlinear-elastic
dumbbell model with fitted anisotropic effective spring constants. The tails of
the angular distribution functions are consistent with scaling predictions
borrowed from the bulk dumbbell model. Finally, the frequency of the
characteristic periodic tumbling motion has been investigated by simulation as
well and was found to be sublinear with the shear rate for the three set-ups,
which extends earlier results done in experiments and simulations for free and
tethered polymer molecules without adsorption.
