  The behavior of a polyelectrolyte adsorbed on a charged surface of
high-dielectric constant is studied by both Monte-Carlo simulation and
analytical methods. It is found that in a low ionic strength medium, the
transition is first-order with the repulsive charged surface. The order
parameter which characterize the polyelectrolyte adsorption, the surface
monomer density, follows a linear relation with surface charge density. It
indicates the polyelectrolyte is always compressed on the substrate. No
conformation change exists before the de-sorption. Finally, a new scaling law
for the layer thickness is derived and verified by the simulation data.
