We have simulated encounters between planetary systems and single stars in
various clustered environments. This allows us to estimate the fraction of
systems liberated, the velocity distribution of the liberated planets, and
the separation and eccentricity distributions of the surviving bound system
s. Our results indicate that, for an initial distribution of orbits that is
flat in log space and extends out to 50 au, 50 per cent of the available p
lanets can be liberated in a globular cluster, 25 per cent in an open clust
er, and less than 10 per cent in a young cluster. These fractions are reduc
ed to 25, 12 and 2 per cent if the initial population extends only to 20 au
. Furthermore, these free-floating planets can be retained for longer than
a crossing time only in a massive globular cluster. It is therefore difficu
lt to see how planets, which by definition form in a disc around a young st
ar, could be subsequently liberated to form a significant population of fre
e-floating substellar objects in a cluster.