  Collisional growth of submicron-sized dust grains into macroscopic aggregates
is the first step of planet formation in protoplanetary disks. These grains are
expected to carry nonzero negative charges in the weakly ionized disks, but its
effect on their collisional growth has not been fully understood so far. In
this paper, we investigate how the charging affects the evolution of the dust
size distribution properly taking into account the charging mechanism in a
weakly ionized gas as well as porosity evolution through low-energy collisions.
To clarify the role of the size distribution, we divide our analysis into two
steps. First, we analyze the collisional growth of charged aggregates assuming
a monodisperse (i.e., narrow) size distribution. We show that the monodisperse
growth stalls due to the electrostatic repulsion when a certain condition is
met, as is already expected in the previous work. Second, we numerically
simulate dust coagulation using Smoluchowski's method to see how the outcome
changes when the size distribution is allowed to freely evolve. We find that,
under certain conditions, the dust undergoes bimodal growth where only a
limited number of aggregates continue to grow carrying the major part of the
dust mass in the system. This occurs because remaining small aggregates
efficiently sweep up free electrons to prevent the larger aggregates from being
strongly charged. We obtain a set of simple criteria that allows us to predict
how the size distribution evolves for a given condition. In Paper II
(arXiv:1009.3101), we apply these criteria to dust growth in protoplanetary
disks.
