  We consider dynamics of an isolated polymer chain with a chemically active
end-bead on a 2D solid substrate containing immobile, randomly placed
chemically active sites (traps). For a particular situation when the end-bead
can be irreversibly trapped by any of these sites, which results in a complete
anchoring of the whole chain, we calculate the time evolution of the
probability $P_{ch}(t)$ that the initially non-anchored chain remains mobile
until time $t$. We find that for relatively short chains $P_{ch}(t)$ follows at
intermediate times a standard-form 2D Smoluchowski-type decay law $ln P_{ch}(t)
\sim - t/ln(t)$, which crosses over at very large times to the
fluctuation-induced dependence $ln P_{ch}(t) \sim - t^{1/2}$, associated with
fluctuations in the spatial distribution of traps. We show next that for long
chains the kinetic behavior is quite different; here the intermediate-time
decay is of the form $ln P_{ch}(t) \sim - t^{1/2}$, which is the
Smoluchowski-type law associated with subdiffusive motion of the end-bead,
while the long-time fluctuation-induced decay is described by the dependence
$ln P_{ch}(t) \sim - t^{1/4}$, stemming out of the interplay between
fluctuations in traps distribution and internal relaxations of the chain.
