  Large scale Monte Carlo simulations of dense layers of grafted polymer chains
in good solvent conditions are used to explore the relaxation of a polymer
brush. Monomer displacements are analyzed for the directions parallel and
perpendicular to the grafting plane. Auto-correlation functions of individual
segments or chain sections are monitored as function of time. We demonstrate
that the terminal relaxation time $\tau$ of grafted layers well in the brush
regime grows exponentially with degree of polymerization $N$ of the chains,
$\tau\propto N^{3}\exp(N/N_{e})$, with $N_{e}$ the entanglement degree of
polymerization in the brush. One specific feature of entangled polymer brushes
is that the late time relaxation of the perpendicular component coincides for
all segments. We use this observation to extract the terminal relaxation time
of an entangled brush.
