Rapid elimination of small dust grains in molecular clouds

We argue that impact velocities between dust grains with sizes of less than similar to 0.1 mu m in molecular cloud cores are dominated by drift arising from ambipolar diffusion. This effect is due to the size dependence of the dust coupling to the magnetic field and the neutral gas. Assuming perfect sticking in collisions up to approximate to 50 m s(-1), we show that this effect causes rapid depletion of small grains, consistent with starlight extinction and IR and microwave emission measurements, both in the core center (n similar to 10(6) cm(-3)) and envelope (n similar to 10(4) cm(-3)). The upper end of the size distribution does not change significantly if only velocities arising from this effect are considered. We consider the impact of an evolved grain-size distribution on the gas temperature, and argue that if the depletion of small dust grains occurs as expected from our model, then the cosmic ray ionization rate must be well below 10(-16) s(-1) at a number density of 10(5) cm(-3).