  We study irreversible polymer adsorption from dilute solutions theoretically.
Universal features of the resultant non-equilibrium layers are predicted. Two
cases are considered, distinguished by the value of the local monomer-surface
sticking rate Q: chemisorption (very small Q) and physisorption (large Q).
Early stages of layer formation entail single chain adsorption. While single
chain physisorption times tau_ads are typically microsecs, for chemisorbing
chains of N units we find experimentally accessible times tau_ads = Q^{-1}
N^{3/5}, ranging from secs to hrs. We establish 3 chemisorption universality
classes, determined by a critical contact exponent: zipping, accelerated
zipping and homogeneous collapse. For dilute solutions, the mechanism is
accelerated zipping: zipping propagates outwards from the first attachment,
accelerated by occasional formation of large loops which nucleate further
zipping. This leads to a transient distribution omega(s) \sim s^{-7/5} of loop
lengths s up to a size s_max \approx (Q t)^{5/3} after time t. By tau_ads the
entire chain is adsorbed. The outcome of the single chain adsorption episode is
a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb
onto, late arriving chains form a diffuse outer layer. In a simple picture we
find for both chemisorption and physisorption a final loop distribution
Omega(s) \sim s^{-11/5} and density profile c(z) \sim z^{-4/3} whose forms are
the same as for equilibrium layers. In contrast to equilibrium layers, however,
the statistical properties of a given chain depend on its adsorption time; the
outer layer contains many classes of chain, each characterized by different
fraction of adsorbed monomers f. Consistent with strong physisorption
experiments, we find the f values follow a distribution P(f) \sim f^{-4/5}.
