  We examine the phase transition of polymer adsorption as well as the
underlying kinetics of polymer binding from dilute solutions on a structureless
solid surface. The emphasis is put on the properties of regular multiblock
copolymers, characterized by block size M and total length N as well as on
random copolymers with quenched composition p of sticky and neutral segments.
The macromolecules are modeled as coarse-grained bead-spring chains subject to
a short-ranged surface adhesive potential. Phase diagrams, showing the
variation of the critical threshold for single chain adsorption in terms of M
and p are derived from scaling considerations in agreement with results from
computer experiment.
  Using both scaling analysis and numerical data from solving a system of
coupled Master equations, we demonstrate that the phase behavior at
criticality, and the adsorption kinetics may be adequately predicted and
understood, in agreement with the results of extensive Monte Carlo simulations.
Derived analytic expressions for the mean fraction of adsorbed segments as well
as for Probability Distribution Functions of the various structural building
blocks (i.e., trains, loops, tails) at time t during the chain attachment
process are in good agreement with our numeric experiments and provide insight
into the mechanism of polymer adsorption.
