We present here a theoretical model to account for the stellar IMF as a result of
the composite behaviour of the gas and dust distribution functions. Each of these
has previously been modelled and the models tested against observations. The model
presented here implies a relation between the characteristic size of the dust grains
and the characteristic final mass of the stars formed within the clouds containing the
grains, folded with the relation between the mass of a gas cloud and the characteristic
mass of the stars formed within it. The physical effects of dust grain size are due to
equilibrium relations between the efficiency of grains in cooling the clouds, which is a
falling function of grain size, and the efficiency of grains in catalyzing the production
of molecular hydrogen, which is a rising function of grain size. We show that folding
in the effects of grain distribution can yield a reasonable quantitative account of the
IMF, while gas cloud mass function alone cannot do so.