  We present a unified scaling theory for the dynamics of monomers for dilute
solutions of semiflexible polymers under good solvent conditions in the free
draining limit. Our theory encompasses the well-known regimes of mean square
displacements (MSDs) of stiff chains growing like t^{3/4} with time due to
bending motions, and the Rouse-like regime t^{2 \nu / (1+ 2\nu)} where \nu is
the Flory exponent describing the radius R of a swollen flexible coil. We
identify how the prefactors of these laws scale with the persistence length
l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD
of order l^2_p (at a time proportional to l^3_p). A second crossover (to
diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular
Dynamics simulations of a bead-spring model with a bond bending potential
(allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling
evidence for the theory, in D=2 dimensions where \nu=3/4. Our results should be
valuable for understanding the dynamics of DNA (and other semiflexible
biopolymers) adsorbed on substrates.
