  We study the motion of dust grains into the Intergalactic Medium (IGM) around
redshift z=3, to test the hypothesis that grains can efficiently pollute the
gas with metals through sputtering. We use the results available in the
literature for radiation-driven dust ejection from galaxies as initial
conditions, and follow the motion onward. Via this mechanism, grains are
ejected into the IGM with velocities >100 km/s; as they move supersonically,
grains can be efficiently eroded by non-thermal sputtering. However, Coulomb
and collisional drag forces effectively reduce the charged grain velocity.
Up-to-date sputtering yields for graphite and silicate (olivine) grains have
been derived using the code TRIM, for which we provide analytic fits. After
training our method on a homogeneous density case, we analyze the grain motion
and sputtering in the IGM density field as derived from a LambdaCDM
cosmological simulation at z = 3.27. We found that only large (a >~ 0.1-um)
grains can travel up to considerable distances (few times 100 kpc physical)
before being stopped. Resulting metallicities show a well defined trend with
overdensity delta. The maximum metallicities are reached for 10<delta<100
(corresponding to systems, in QSO absorption spectra, with 14.5 < log N_HI <
16). However the distribution of sputtered metals is very inhomogeneous, with
only a small fraction of the IGM volume polluted by dust sputtering (filling
factors of 18 per cent for Si and 6 per cent for C). For the adopted size
distribution, grains are never completely destroyed; nevertheless, the
extinction and gas photo-electric heating effects due to this population of
intergalactic grains are well below current detection limits.
