  Context. In support of NASA's exploration program and the return to the Moon,
the polarimetric signature of dispersed individual Lunar regolith dust grains
is studied to enable the characterization of the dust exopsheric environment by
remote, in-situ, and standoff sensing. Aims. We explore the value of the
negative polarization branch (NPB) as a signature for characterizing individual
grains to determine if it can be used in the same way as for surfaces of
planets and atmosphereless bodies. Results. Calculations show that polarization
phase curves for spherical grains exhibit a sharp transition over a narrow
range of size parameter between two distinct regimes, one typical of Rayleigh
scattering and another dominated by a large NPB. The linear polarimetric
signature observed for aggregates is a composite of a) the polarization induced
by individual grains composing the aggregate and b) the polarization due to the
aggregate as a whole dust grain. The weight of each component varies depending
on the porosity of the aggregate. An NPB similar to the one observed for
atmosphereless astronomical bodies is present for different ranges of the size
parameter depending on the value of the porosity. It appears as a remnant of
the negative branch exhibited by the single spherical grains. The sharper,
narrow negative branch that is measured for some granular surfaces in the
laboratory or seen in astronomical observations is not observed here.
