Effect of grain size on differential desorption of volatile species and on non-ideal MHD diffusivity

We developed a chemical network for modelling the chemistry and non-ideal magnetohydrodynamic (MHD) effects from the collapsing densemolecular clouds to protostellar discs. First, we reformulated the cosmic-ray desorption rate by considering the variations of desorption rate over the grain size distribution. We find that the differential desorption of volatile species is amplified by the grains larger than 0.1 mu m, because larger grains are heated to a lower temperature by cosmic-rays and hence more sensitive to the variations in binding energies. As a result, atomic nitrogen, N, is similar to two orders of magnitude more abundant than CO; N2H+ also becomes a few times more abundant than HCO+ due to the increased gas-phase N-2. However, the changes in ionization fraction due to freeze-out and desorption only have minor effects on the non-ideal MHD diffusivities. Our chemical network confirms that the very small grains (below a few 100 angstrom) weakens the efficiency of both ambipolar diffusion and Hall effect. In collapsing dense cores, a maximum ambipolar diffusion is achieved when truncating the Mathis-Rumpl-Nordsieck size distribution at 0.1 mu m, and for a maximum Hall effect, the truncation occurs at 0.04 mu m. We conclude that the grain size distribution is crucial to the differential depletion between CO-and N-2-related molecules as well as to the non-ideal MHD diffusivities in dense cores.