  Tiny grains such as PAHs have been thought to dramatically reduce the
coupling between gas and magnetic fields in weakly ionized gas such as in
protoplanetary disks (PPDs) because they provide tremendous surface area to
recombine free electrons. The presence of tiny grains in PPDs thus raises the
question of whether the magnetorotational instability (MRI) is able to drive
rapid accretion to be consistent with observations. Charged tiny grains have
similar conduction properties as ions, whose presence leads to qualitatively
new behaviors in the conductivity tensor, characterized by n_bar/n_e>1, where
n_e and n_bar denote the number densities of free electrons and all other
charged species respectively. In particular, Ohmic conductivity becomes
dominated by charged grains rather than electrons when n_bar/n_e exceeds about
10^3, and Hall and ambipolar diffusion (AD) coefficients are reduced by a
factor of (n_bar/n_e)^2 in the AD dominated regime relative to that in the
Ohmic regime. Applying the methodology of Bai (2011), we find that in PPDs,
when PAHs are sufficiently abundant (>1e-9 per H_2), there exists a transition
radius r_trans of about 10-20 AU, beyond which the MRI active layer extends to
the disk midplane. At r<r_trans, the optimistically predicted MRI-driven
accretion rate M_dot is one to two orders of magnitude smaller than that in the
grain-free case, which is too small compared with the observed rates, but is in
general no smaller than the predicted M_dot with solar-abundance 0.1 micron
grains. At r>r_trans, we find that remarkably, the predicted M_dot exceeds the
grain-free case due to a net reduction of AD by charged tiny grains, and
reaches a few times 1e-8M_Sun/yr. This is sufficient to account for the
observed M_dot in transitional disks. Larger grains (>0.1 micron) are too
massive to reach such high abundance as tiny grains and to facilitate the
accretion process.
