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

Electrostatic Barrier against Dust Growth in Protoplanetary Disks. I. Classifying the Evolution of Size Distribution