  We study the adsorption of semiflexible polymers such as polyelectrolytes or
DNA on planar and curved substrates, e.g., spheres or washboard substrates via
short-range potentials using extensive Monte-Carlo simulations, scaling
arguments, and analytical transfer matrix techniques. We show that the
adsorption threshold of stiff or semiflexible polymers on a planar substrate
can be controlled by polymer stiffness: adsorption requires the highest
potential strength if the persistence length of the polymer matches the range
of the adsorption potential. On curved substrates, i.e., an adsorbing sphere or
an adsorbing washboard surface, the adsorption can be additionally controlled
by the curvature of the surface structure. The additional bending energy in the
adsorbed state leads to an increase of the critical adsorption strength, which
depends on the curvature radii of the substrate structure. For an adsorbing
sphere, this gives rise to an optimal polymer stiffness for adsorption, i.e., a
local minimum in the critical potential strength for adsorption, which can be
controlled by curvature. For two- and three-dimensional washboard substrates,
we identify the range of persistence lengths and the mechanisms for an
effective control of the adsorption threshold by the substrate curvature.
