  Adsorption of polymers to surfaces is crucial for understanding many
fundamental processes in nature. Recent experimental studies indicate that the
adsorption dynamics is dominated by non-equilibrium effects. We investigate the
adsorption of a single polymer of length $N$ to a planar solid surface in the
absence of hydrodynamic interactions. We find that for weak adsorption energies
the adsorption time scales $ \sim N^{(1+2\nu)/(1+\nu)}$, where $\nu$ is the
Flory exponent for the polymer. We argue that in this regime the single chain
adsorption is closely related to a field-driven polymer translocation through
narrow pores. Surprisingly, for high adsorption energies the adsorption time
becomes longer, as it scales $\sim N^{(1+\nu)}$, which is explained by strong
stretching of the unadsorbed part of the polymer close to the adsorbing
surface. These two dynamic regimes are separated by an energy scale that is
characterised by non-equilibrium contributions during the adsorption process.
